1 Department of Modern Mechanics, Universityof Science and Technology of China, Hefei 230027, China2 Institute of Systems Engineering, China Academy of Engineering Physics, Sichuan, Mianyang 621999, China3 The State Key Lab of Explosion Science and Technology,Beijing Institute of Technology, Beijing 100081, China4 Advanced Research Institute for Multidisciplinary Science,Beijing Institute of Technology, Beijing 100081, China
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2019 中国力学学会 This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Made by high-density metals, long-rod penetrators have excellent performances on penetration and perforation when launched at hypervelocities around 1.5$\sim $3.0km/s. Due to their important background in the military application, long-rod penetration at hypervelocity has become an active research focus. The present paper reviews research advance up-to-date on long-rod penetration at hypervelocity. Firstly, basic concepts, research methods, and theoretical models are introduced. Secondly, highlighted issues which are focused in past studies and their applications, including rod and target materials, nose shape, $L/D$ effect and segmented rods, ceramic targets and interface defeat, as well as non-ideal long-rod penetration, etc. Finally, some future research proposals are suggested.
JIAOWenjun, CHENXiaowei. Review on long-rod penetration at hypervelocity[J]. Advances in Mechanics, 2019, 49(1): 201904-201904 https://doi.org/10.6052/1000-0992-17-021
自20世纪七八十年代起, 长杆高速侵彻领域开展了大量实验.西德恩斯特马赫研究所 (Ernst Mach Institute, EMI)的Hohler和Stilp(1977)开展的$L / D =10$钨合金长杆弹侵彻半无限厚装甲钢靶的实验成为后来检验理论模型和数值模拟的标准.Silsby(1984)进行了更大长径比 $(L/ D = 32)$和更大尺寸的实验.Hohler和Stilp(1987)总结了已发表的实验数据,讨论了侵彻深度、弹坑半径等与撞击速度、弹靶材料以及长径比的关系.其中提出的长径比效应后来成为长杆侵彻一个相当重要的特征效应.美国陆军弹道研究实验室 (Ballistic Research Laboratory,BRL)的Sorensen等(1991)总结了钨合金连续和分段长杆侵彻轧制均质钢(Rolled Homogeneous Armor, RHA)的全尺寸与半尺寸实验.美国西南研究院 (Southwest Research Institute, SwRI)的Anderson等(1992a)编辑了侵彻数据库,对此前开展的终点弹道实验数据进行了较全面的搜集整理.
In the last decade, the dynamic response of ceramicmaterials and the penetration/perforation of targets of ceramics,ceramic/metal, ceramic/composite and layered ceramics is an activeresearch area. It has applications, especially, in the military field. Relatively little work in thisarea is conducted in China. The present paper introduces therecent advances in this area.Theexperimental techniques, penetration/perforation mechanisms and theoreticalmodels are reviewed. The cavity expansion model in ceramics penetration andthe effect of failure wave are specially addressed. Some research proposalsare made at the end of the paper.
(Chen XW, Chen YZ.2006.
Review on the penetration/perforation of ceramics targets
In the last decade, the dynamic response of ceramicmaterials and the penetration/perforation of targets of ceramics,ceramic/metal, ceramic/composite and layered ceramics is an activeresearch area. It has applications, especially, in the military field. Relatively little work in thisarea is conducted in China. The present paper introduces therecent advances in this area.Theexperimental techniques, penetration/perforation mechanisms and theoreticalmodels are reviewed. The cavity expansion model in ceramics penetration andthe effect of failure wave are specially addressed. Some research proposalsare made at the end of the paper.
The processes of penetrating the semi-infinite rolled homogeneous armor (RHA) targets with four kinds of nose shapes of long-rod projectiles were studied by numerical simulation method, the effects of nose shapes on penetration were inspected emphatically. The results show that the depth of penetration (DOP) depends on pronouncedly the iailure mechanism of the rod material, the variation of the nose shapes of long-rod projectiles results in slight difference of the penetration depths at the same condition for high strength material, but the nose profile of long-rod has a certain influence on the breakup of targets, especially on the cross-section of crater in the early stage.
(Cheng XW, Wang FZ, Li SK, WangL.2007.
Numerical simulation on the penetrations of long-rod projectiles with different nose shapes
The processes of penetrating the semi-infinite rolled homogeneous armor (RHA) targets with four kinds of nose shapes of long-rod projectiles were studied by numerical simulation method, the effects of nose shapes on penetration were inspected emphatically. The results show that the depth of penetration (DOP) depends on pronouncedly the iailure mechanism of the rod material, the variation of the nose shapes of long-rod projectiles results in slight difference of the penetration depths at the same condition for high strength material, but the nose profile of long-rod has a certain influence on the breakup of targets, especially on the cross-section of crater in the early stage.
以侵彻深度（depth of penetration，DOP）实验为基础，利用LSDYNA软件进行数值模拟，对钨合金长杆弹侵彻45钢鉴证靶和约束AD95陶瓷复合靶进行了对比研究。通过数值模拟与实验结合的方法，得到了AD95陶瓷的JH2模型（Johnson—Holmquist ceramic material model）参数；深入分析了钨合金长杆弹侵彻约束AD95陶瓷复合靶侵彻响应过程。
(JiangD, Li YC, Yu SJ, Deng SC.2010.
Penetation of confined AD95 ceramic composite targets by tungsten long rods
以侵彻深度（depth of penetration，DOP）实验为基础，利用LSDYNA软件进行数值模拟，对钨合金长杆弹侵彻45钢鉴证靶和约束AD95陶瓷复合靶进行了对比研究。通过数值模拟与实验结合的方法，得到了AD95陶瓷的JH2模型（Johnson—Holmquist ceramic material model）参数；深入分析了钨合金长杆弹侵彻约束AD95陶瓷复合靶侵彻响应过程。
The numerical simulation of the penetration of a spherical-nosed 4340 Steel Long Rod into Semi-infinite 6061-T6511 Aluminum Targets is performed with ALE method and Steinberg constitutive model using the ANSYS/LS-DYNA finite element code. It transpires that the state of the steel long rod penetrator changes with increasing impact velocity: first it penetrates the aluminum alloy targets as a rigid body, then as a deformable body without mass loss and finally as an erosive body at higher impact velocities, which is in agreement with the experimental observations made by Forrestal et al. It also transpires that for a deforming non-erosive penetrator the head of the penetrator becomes bigger only in the initial phase and followed by the subsequent thickening of the shank during which the velocity of the penetrator tail decreases rapidly whilst the penetration velocity remains relatively steady; that the stresses in the penetration direction at the two ends of the transition zone between the deformed region and undeformed region are close to Hugoinot Elastic Limit and its initial yield stress, respectively.
(LanB, Wen HM.2009.
A numerical simulation of the penetration of a spherical-nosed 4340 steel long-rod into semi-infinite 6061-T6511 aluminum targets
The numerical simulation of the penetration of a spherical-nosed 4340 Steel Long Rod into Semi-infinite 6061-T6511 Aluminum Targets is performed with ALE method and Steinberg constitutive model using the ANSYS/LS-DYNA finite element code. It transpires that the state of the steel long rod penetrator changes with increasing impact velocity: first it penetrates the aluminum alloy targets as a rigid body, then as a deformable body without mass loss and finally as an erosive body at higher impact velocities, which is in agreement with the experimental observations made by Forrestal et al. It also transpires that for a deforming non-erosive penetrator the head of the penetrator becomes bigger only in the initial phase and followed by the subsequent thickening of the shank during which the velocity of the penetrator tail decreases rapidly whilst the penetration velocity remains relatively steady; that the stresses in the penetration direction at the two ends of the transition zone between the deformed region and undeformed region are close to Hugoinot Elastic Limit and its initial yield stress, respectively.
(Li JC, Chen XW.2011a. Theoratical analysis on the interface defeat of a conical-nosed projectile penetration. Chinese Journal of Theoretical and Applied Mechanics, 43: 63-70).
For their excellent mechanical, physical and chemic performance, metallic glasses and their composite materials is becoming as an active research focus now. Especially, metallic glass matrix composite may be employed as the material of kinetic enrgy penetrator for its intense shear banding sensitivity. The present paper introduces the research advance up-to-date on the compressive shear characteristics and self-sharpening behavior of metallic glasses and their composite materials during the high-speed impact. The related experimental research, theoretical analysis and FEM simulations are reviewed, and also some future research proposals are made.
(Li JC, Chen XW.2011c. Compressive-shear behavior and self-sharpening of bulk metallic glass and their composite materials. Advances in Mechanics, 41: 480-518).
For their excellent mechanical, physical and chemic performance, metallic glasses and their composite materials is becoming as an active research focus now. Especially, metallic glass matrix composite may be employed as the material of kinetic enrgy penetrator for its intense shear banding sensitivity. The present paper introduces the research advance up-to-date on the compressive shear characteristics and self-sharpening behavior of metallic glasses and their composite materials during the high-speed impact. The related experimental research, theoretical analysis and FEM simulations are reviewed, and also some future research proposals are made.
ceramics are often used as protective materials against impact damage because of their desir-able properties such as low density, high hardness and compressive strength. Ceramic targets are fragment?ed and comminuted locally by the extreme compressive stress wave occurring at the penetrator-target inter?face when a penetrator impacts the ceramic targets at high velocity. As the penetrator proceeds, a commin?uted zone is finally produced near the tip of the penetrator. The paper considers the influence of this region and derives the target strength term Rt in an A-T model based on the spherically symmetric cavity expan?sion theory. The depth of penetration is calculated using the A-T model when long tungsten rods impact targets at 1.5?4.5km/s. Results of this model are compared with experimental data.
(Wei XY, Yu MH.2002.
Analysis of tungsten rods on penetrating ceramic targets at high velocity
ceramics are often used as protective materials against impact damage because of their desir-able properties such as low density, high hardness and compressive strength. Ceramic targets are fragment?ed and comminuted locally by the extreme compressive stress wave occurring at the penetrator-target inter?face when a penetrator impacts the ceramic targets at high velocity. As the penetrator proceeds, a commin?uted zone is finally produced near the tip of the penetrator. The paper considers the influence of this region and derives the target strength term Rt in an A-T model based on the spherically symmetric cavity expan?sion theory. The depth of penetration is calculated using the A-T model when long tungsten rods impact targets at 1.5?4.5km/s. Results of this model are compared with experimental data.
With Tate penetration theory and cavity expansion theory, the kinematic parameters of the long rod penetration and the ceramics differential efficiency factor DEF are expressed as functions of the materials properties. In this way the experimental index of the ballistic performance of armor ceramics is theoretically expressed and the key ceramic properties which have the most significant influences on ballistic performance are mathematically formulated. Calculation shows that this theoretical method can give a good ballistic performance estimate for ceramics against long-rod penetration.
(Zhang LS, Huang FL.2005.
Theoretical characterization of ballistic performance of armor ceramics
. Transactions of Beijing Institute of Technology, 25: 651-654).
With Tate penetration theory and cavity expansion theory, the kinematic parameters of the long rod penetration and the ceramics differential efficiency factor DEF are expressed as functions of the materials properties. In this way the experimental index of the ballistic performance of armor ceramics is theoretically expressed and the key ceramic properties which have the most significant influences on ballistic performance are mathematically formulated. Calculation shows that this theoretical method can give a good ballistic performance estimate for ceramics against long-rod penetration.
[27]
Alekseevskii VP.1966.
Penetration of a rod into a target at high velocity. Combustion, Explosion,
The penetration of metal rods into semi-infinite metal targets has been investigated experimentally at velocities up to 0.3 cm/ sec. The rods were composed of Au, Pb, Cu, Sn, Al, and Mg; the targets were aluminum. Results are compared with predictions from the hydrodynamic theory of jet penetration. Basic assumptions of the hydrodynamic theory were used to determine an effective yield strength of the target-rod combination. Experimental results indicate that the effective yield strength is relatively independent of the strength of the rod. The hydrodynamic theory of penetration was determined to be generally acceptable except where the density of the jet is much greater than that of the target.A gold jet reveals a new effect of secondary penetration which results in penetration greater than that predicted by theory.
[29]
Aly SY, Li QM.2008.
Numerical investigation of penetration performance of non-ideal segmented-rod projectiles
. Transactions of Tianjin University, 14: 391-395.
The design of a segmented-rod projectile is often simplified into an ideal one in theoretical analysis for the convenience of modeling of its performance. But the actual performance of non-ideal segmented-rod projectiles over the impact velocity range in practical applications was rarely explored. AUTODYN numerical code is used to investigate the influence of the component design upon the penetration performance of non-ideal segmented-rod projectiles over a wide range of impact velocities, which can be used to guide the optimal design of weaponry segmented-rod projectiles.
[30]
Anderson Jr. CE.1987.
An overview of the theory of hydrocodes
. International Journal of Impact Engineering, 5: 33-59.
Hydrocodes are large computer programs that can be used to simulate numerically highly dynamic events, particularly those which include shocks. Lagrangian and Eulerian descriptions are reviewed, and advantages and disadvantages are summarized. The question of how to best represent the continuum equations on a finite computer is answered by summarizing the topics of accuracy and stability. The concept of artificial viscosity is introduced to permit the continuum code to deal with the discontinuities of shocks. Finally, a review of the treatment of materials, i.e., equation of state and constitutive response, including failure, is presented.
[31]
Anderson Jr CE.2003.
From fire to ballistics: A historical retrospective
. International Journal of Impact Engineering, 29: 13-67.
This article is the acceptance keynote presentation after receiving the Distinguished Scientist Award from the Hypervelocity Impact Society at HVIS 2000, held in Galveston, TX, November 2000. As dictated by precedence, the article highlights some of the significant events and activities in my career. My technical activities and contributions can be divided into nominally three areas: 1) fire/thermal loading; 2) warhead mechanics; and 3) penetration/armor mechanics. A commonality of the areas is that they all deal with characterizing and understanding the response of materials or structures to intense loads. A summary of my research activities and significant findings are presented. Additionally, a brief history of the formation of the Hypervelocity Impact Society is presented. (C) 2003 Elsevier Ltd. All rights reserved.
[32]
Anderson Jr. CE.2017.
Analytical models for penetration mechanics: A review
. International Journal of Impact Engineering, 108: 3-26.
A review of analytical penetration models has been conducted and summarized. Models include the Poncelet equation, hydrodynamic theory, modified hydrodynamic theory, Recht-Ipson, Tate-Alekseevskii, cavity expansion, Ravid-Bodner, Walker-Anderson, and similitude modeling. These models describe, depending upon assumptions, rigid-body penetration, eroding penetration, steady-state and transient penetration, and perforation. Model assumptions are highlighted, and examples are provided of model predictions against experimental data. The manuscript has 30 figures, many of which compare model results to experimental data; 59 reference citations are included.
[33]
Anderson Jr. CE, BehnerT, Orphal DL, Nicholls AE, Holmquist TJ, WickertM.2008.
Long-rod penetration into intact and pre-damaged SiC ceramic
. Southwest Research Institute, San Antonio, TX, USA.
The penetration behavior of tungsten-alloy long-rod penetrators into glass targets is investigated and contrasted at two impact velocities, 1.25 km/s and 1.70 km/s. Penetration depths and residual rod lengths were measured by means of a 600-kV flash X-ray system at different times during penetration. The wavecode CTH was used to simulate numerically the experiments using a Drucker–Prager constitutive model, where the constitutive constants were determined from independent characterization experiments. The numerical results are compared to the experimental data and good agreement is shown.
[36]
Anderson Jr. CE, HohlerV, Walker JD, Stilp AJ.1999a.
The influence of projectile hardness on ballistic performance
. International Journal of Impact Engineering, 22: 619-632.
Parametric studies were conducted using a recent computational glass model [1] to assess its ability to replicate the rate and extent of damage resulting from ballistic impact of borosilicate glass. Penetration and the position of the failure front were determined as a function of time in experiments using long and short rods at two impact velocities, nominally 1000 m/s and 2100 m/s. Simulations were conducted of the experiments and the results compared to the experiments. Parametric studies examined the effects of very slight changes in the initial impact velocity, time-dependent failure, the inclusion of the third deviatoric stress invariant (J3), mesh resolution, and changes in the strength of intact glass. Results are compared and contrasted, and conclusions drawn on the effect of model parameters in simulating results of impact experiments in different velocity regimes.
[38]
Anderson Jr. CE, Morris BL.1992.
The ballistic performance of confined Al$_{2}$O$_{3}$ ceramic tiles
. International Journal of Impact Engineering, 12: 167-187.
The penetration of aluminum oxide tiles inserted into a 4340-steel block that also serves as a emi-infinite steel substrate is investigated for two length-to-diameter projectiles at a nominal impact velocity of 1.5 km/s. The experimental observable is the depth of penetration of the projectile into the backup steel. These data are compared with the total penetration into semi-infinite steel. The data are analysed and displayed as normalized depth of penetration as a function of areal density and tile thickness. Data from Woolsey et al. ( Fifth Annual TACOM Armor Coordinating Conference , Monterey, CA, 1989) are in good agreement with data from this study, and are used to extend the range of tile thicknesses. A methodology, assuming quasi-steady-state penetration, provides an estimate of the penetration resistance R 1 of the ceramic tile; R 1 is then used to estimate the erosion rate and length of projectile eroded as it penetrates the ceramic. A second approach that does not rely as heavily on the assumption of steady-state penetration is also developed and applied to the data to estimate the length of projectile eroded. It is found that the various measures of ceramic performance, for a well-confined target, are relatively constant as tile thickness is varied.
A penetration mechanics database has been compiled that contains experimental results from a variety of researchers of different nationalities (German, French, English, Canadian, and American), during different decades (the 1960's to the 1990's), and with different purposes or objectives (space debris impact, armor design and evaluation, penetrator design and evaluation, and theoretical verification). The data fall naturally into three subgroupings: (1) penetration into semi-infinite targets; (2) perforation of finite-thickness targets; and (3) penetration from multiple impact (segmented rods). Data collection was primarily limited to experiments conducted against generic type targets, and emphasis was placed on data that would be more relevant to heavy armor issues. This diverse collection of data for metallic targets has been tabulated; data tables include the initial impact conditions, the projectile and target geometries and materials, and the measured response. Information on the materials, e.g., hardness of yield strength, along with impact information such as yaw has been tabulated if available. Graphical displays of the data have been used to summarize the data, and cross-plotting that combines data from different sources has also been provided.
[40]
Anderson Jr. CE, Littlefield DL, Walker JD.1993.
Long-rod penetration, target resistance, and hypervelocity impact
. International Journal of Impact Engineering, 14: 1-12.
ABSTRACT The terminal phase, or Phase 3, of penetration is investigated using numerical simulations. Results of the first set of simulations, for zero-strength tungsten-alloy projectiles into armor steel at velocity of 1.5, 3.0, and 6.0 km/s are reported here. For these simulations, the mechanisms for Phase 3 penetration are limited to the transient deceleration of the eroding projectile and "afterflow," the extension of penetration after the projectile has fully eroded. It is found that for projectile L/D less than or equal to similar to2, there is effectively no steady-state penetration (Phase 2) and penetration is dominated by Phase 3. For projectiles of L/D greater than or equal to 3, steady-state penetration is achieved. For L/D greater than or equal to 3, the deceleration of both the nose and tail of the projectile are essentially independent of LID. For LID greater than or equal to 3, the target penetration associated with Phase 3 is found to increase with impact velocity approximately as P-3/D proportional to V (1.0). "After-flow" as a separate, identifiable mechanism could not be discerned in the results. We therefore question whether the phenomenon of "after-flow," as usually defined, exists; rather, projectile deceleration and crater depth growth are intimately coupled.
[42]
Anderson Jr. CE, Orphal DL.2008.
An examination of deviations from hydrodynamic penetration theory
. International Journal of Impact Engineering, 35: 1386-1392.
The hydrodynamic theory of penetration (HTP) was first developed in the U.S. during WWII, and independently and essentially simultaneously in England. Since then the theory has proved very useful in understanding and predicting results of many penetration experiments. The assumptions and limitations of HTP were well stated in the initial paper. The most obvious limitation is that, strictly speaking, HTP only applies to hydrodynamic materials, i.e., both the projectile and the target have no strength. But for nearly all cases of interest, penetration does depend on material strengths, even at quite high velocities. Consequently, effects of projectile and target strength on penetration physics have been studied by many researchers, and modified versions of HTP have been proposed. While material strength is an important reason for deviations from HTP, it is not the only one. Other assumptions underlying HTP are steady-state behavior and incompressibility. In this paper we present new numerical simulation results that examine and quantify deviations from HTP due to compressibility for several material combinations of interest as a function of impact velocity. For these calculations all the materials are modeled as having zero strength. This is done in order to separate effects of compressibility from effects due to material strength. Some discussion of transient effects is also provided.
[43]
Anderson Jr. CE, Orphal DL, BehnerT, HohlerV, Templeton DW.2006.
Re-examination of the evidence for a failure wave in SiC penetration experiments
. International Journal of Impact Engineering, 33: 24-34.
Previous work suggested the possibility that the effects of a failure wave, evidenced through a change in the slope of the penetration velocity vs. impact velocity ( u– v p) curve resulting from an increase in target penetration resistance, could be observed in penetration experiments of SiC. However, the previous work had to combine two different sets of experimental data, one using long tungsten rods and the other copper shaped-charge jets. A new set of experiments was conducted to address the uncertainties associated with combining the two disparate data sets. Analysis of the new experiments showed no evidence of a distinct change in the slope of the u– v p response of SiC, up to an impact velocity of 6.2 km/s. We re-examine the original data and analysis in light of the new experiments to understand the origins of the original misinterpretation.
[44]
Anderson Jr. CE, Orphal DL, BehnerT, Templeton DW.2009.
Failure and penetration response of borosilicate glass during short-rod impact
. International Journal of Impact Engineering, 36: 789-798.
In Anderson Jr CE, Orphal DL, Behner T, Templeton, DW [Failure and penetration response of borosilicate glass during short-rod impact. Int J Impact Eng 2009, doi:10.1016/ j.ijimpeng.2008.12.002.] it was demonstrated that the failure front (FF) produced by the penetration of a borosilicate glass target by a gold rod ceased to propagate a short time after the rod was fully eroded. This strongly suggests that progression of the FF is not described by a wave equation. Here it is shown that propagation of the FF is reinitiated if a second co-axial rod, spaced a distance from the first, impacts the glass at the bottom of the penetration channel. The experiments were performed in reverse ballistic mode with two short rods spaced apart. In some experiments both rods were gold; in other experiments, one rod was copper and the other gold. FF propagation was measured using high-speed photography; rod penetration was measured using multiple, independent flash X-rays. Much of the observed phenomenology can be modeled assuming that the rod, either first or second, “communicates” with the FF at a speed corresponding to the bulk sound speed of the undamaged glass.
[45]
Anderson Jr. CE, Orphal DL, Franzen RR, Walker JD.1999b.
On the hydrodynamic approximation for long-rod penetration
. International Journal of Impact Engineering, 22: 23-43.
Steady-state hydrodynamic theory, or variations thereof, has been applied to long-rod penetration since the 1940s. It is generally believed that projectile strength is of little consequence at high velocities, and that hydrodynamic theory is applicable to long-rod penetration when penetration pressures are much greater than the target flow stress. Substantiating this belief is the observation that at approximately 2.5 km/s, for tungsten alloy projectiles into armor steel, normalized penetration (P/L) nominally saturates to the classical hydrodynamic limit of the square root of the ratio of the projectile to target densities. Experimental data herein, however, show penetration velocities and instantaneous penetration efficiencies fall below that expected from hydrodynamic theory, even at impact velocities as high as 4.0 km/s. Numerical simulations, using appropriate strength values, are in excellent agreement with the experimental data. Parametric studies demonstrate that both projectile and target strength have a measurable effect even at such high impact velocities.
[46]
Anderson Jr. CE, Riegel IiiJ J P.2015.
A penetration model for metallic targets based on experimental data
. International Journal of Impact Engineering, 80: 24-35.
61Semi-infinite penetration data are used to predict finite-thickness target effects.61A procedure is developed to estimate ballistic limit velocity and/or ballistic limit thickness.61Similitude analysis extends the database to other materials.61Residual projectile velocity and length are estimated for overmatched targets.61Algorithms are provided to adjust for projectile aspect ratio and size effects.
[47]
Anderson Jr. CE, Royal-Timmons SA.1997.
Ballistic performance of confined 99.5%-Al$_{2}$O$_{3}$ ceramic tiles
. International Journal of Impact Engineering, 19: 703-713.
The one-dimensional modified Bernoulli theory of Tate [ J. Mech. Phys. Solids 15 , 287 399 (1967)] is often used to examine long-rod penetration into semi-infinite targets. The theory is summarized and the origins of the target resistance term examined. Numerical simulations were performed of a tungsten-alloy, long-rod projectile into a semi-infinite hardened steel target at three impact velocities sufficiently high to result in projectile erosion. The constitutive responses of the target and projectile were varied parametrically to assess the effects of strain hardening, strain-rate hardening, and thermal softening on penetration response. The results of one of the numerical simulations were selected to compare and contrast in detail with the predictions of the Tate model.
[49]
Anderson Jr. CE, Walker JD.2005.
An analytical model for dwell and interface defeat
. International Journal of Impact Engineering, 31: 1119-1132.
An analytical model that captures the essential mechanics of dwell and interface defeat—the phenomenon where an impacting projectile flows radially outward (erodes) along the surface of the target (usually ceramic) with no significant penetration—is presented. During dwell, the projectile loses kinetic energy due to mass loss and deceleration. It is shown that model predictions are in very good agreement with experimental data.
[50]
Anderson Jr. CE, Walker JD, Bless SJ, PartomY.1996.
On the L/D effect for long-rod penetrators
. International Journal of Impact Engineering, 18: 247-264.
A common measure of penetration efficiency is given by the depth of penetration P into a semi-infinite target normalized by the original length of the projectile L. It has been known for over 30 years that P/L depends upon the aspect ratio LID for projectiles with relatively small aspect ratios, e.g. 1 ≤ L/D ≤ 10. This influence of L/D on penetration is referred to as the LID effect. Although observed, the LID effect for large aspect ratio rods is not as well documented. Further, published penetration equations have not included the LID effect for high aspect ratio rods. We have compiled a large quantity of experimental data that permits the quantification of the L/D effect for projectiles with aspect ratios of 10 ≤ L/D ≤ 30. Numerical simulations reproduce the observed experimental behavior ; thus, no new physics is required to explain the phenomenon. The numerical simulations allow investigation of the fundamental mechanics leading to a decrease in penetration efficiency with increasing aspect ratio.
[51]
Anderson Jr. CE, Walker JD, Bless SJ, Sharron TR.1995.
On the velocity dependence of the $L/D$ effect for long-rod penetrators
. International Journal of Impact Engineering, 17: 13-24.
At ordnance velocities (1.0 – 1.9 km/s), there is a pronounced decrease in penetration efficiency, as measured by P / L , when projectiles of larger L / D are used. The influence of L / D on penetration is referred to as the L / D effect d. We numerically examine the L / D effect at higher velocities, from 2.0 km/s to 4.5 km/s. It is found that as the velocity increases, there is a change in mechanism for the L / D effect. At ordnance velocities the L / D effect is mostly due to the decay in penetration velocity during the “steady-state” region of penetration. At higher velocities, the steady-state region of penetration shows no L / D dependence, and the L / D effect is due primarily to the penetration of the residual (non-eroding) rod at the end of the penetration event. This change in mechanism is related to the change in slope of the penetration-versus-impact velocity “S-shaped” curve for eroding projectiles.
[52]
Anderson Jr. CE, Walker JD, Hauver GE.1992b.
Target resistance for long-rod penetration into semi-infinite targets
An important parameter in the one-dimensional modified-Bernoulli penetration theory of Tate is the target resistance R t . In the model, it is assumed that R t remains constant during the total penetration event. In this paper, a parametric study using the Tate model is used to show that the total depth of penetration is sensitive to the value of R 1 , Time-resolved depth-of-penetration experiments and numerical simulations are used to examine R t as a function of penetration depth for long-rod tungsten-alloy projectiles impacting semi-infinite targets of S-7 steel and a titanium alloy. It is found in these studies that R t changes considerably during penetration and that the values which are used in predicting penetration performance must be considered to be an average value over the entire penetration profile.
[53]
AnderssonO, LundbergP, RenströmR.2007.
Influence of confinement on the transition velocity of silicon carbide//Proceedings of the 23rd international symposium on ballistics,
The phenomenon of dwell during projectile impact on ceramics has been an active area of research for several decades. Dwell in confined ceramics has received much attention, particularly the role of cover plates and their influence over the dwell to penetration transition. Dwell during long rod impact on unconfined ceramics has received relatively less attention. The present work will compare and contrast the results of two series of long rod impacts on hot pressed silicon carbide targets. One series utilized gold wire rods. The other series utilized rods fabricated from tungsten carbide with 10% cobalt matrix. A novel ten-flash X-ray system captured spatially resolved images of the penetration events. The experimental results are compared with simulations and predictions from the Alekseevskii-Tate equation to explore the role of shock pressure, the effects of the strength of the rod material in dwell to penetration transition behavior, and the behavior of defects within silicon carbide.
[55]
BehnerT, Anderson Jr. CE, Holmquist TJ, WickertM, Templeton DW.2008.
Interface defeat for unconfined SiC ceramics//Proceedings of the 24th international symposium on ballistics,
To determine the behavior of silicon carbide (SiC) against long rod impact a detailed study with experiments in the velocity range from 0.8 to 3 km/s at normal impact conditions was performed in recent years. Interest ranged from penetration performance of intact and pre-damaged SiC to interface defeat capability of SiC. Together with impact data in the hypervelocity regime this paper provides a comprehensive overview of the penetration dynamics of SiC over a wide velocity range and during different phases of the penetration process.
[57]
BehnerT, Anderson Jr. CE, Orphal DL, HohlerV, MollM, Templeton DW.2008.
Penetration and failure of lead and borosilicate glass against rod impact
. International Journal of Impact Engineering, 35: 447-456.
This paper presents the experimental design and results for gold rod impact on DEDF (5.19 g/cm 3) and Borofloat (2.2 g/cm 3) glass by visualizing simultaneously failure propagation in the glass with a high-speed camera and rod penetration with flash radiography. At a given impact velocity, the velocity of the failure front is significantly higher during early penetration than during steady-state penetration of the rod. For equal pressures but different stress states, the failure front velocities determined from Taylor tests or planar-impact tests are greater than those observed during steady-state rod penetration. The ratio of average failure front velocity to rod penetration velocity decreases with increasing impact velocity ( v p) in the range of v p=0.4 2.8 km/s. As a consequence, the distance between the rod tip and the failure front is reduced with increasing v p. The Tate term R T increases with impact velocity.
[58]
BehnerT, HeineA, WickertM.2013.
Protective properties of finite-extension ceramic targets against steel and copper projectiles//Proceedings of the 27th International Symposium on Ballistics, Freiburg, Germany
Impact experiments with a tungsten heavy alloy long rod projectile against silicon carbide tiles were performed to study the transition from dwell to penetration and to compare against earlier investigations which focused either on small scale semi-infinite set-ups or on finite thickness set-ups with confinement. A depth-of-penetration configuration consisting of a ceramic tile and an extended steel backing was used to assess the impact response of the unconfined finite-thickness ceramic. The ceramic tile was either bare or had a cover plate attached to the front. The cover plate thickness has been varied and gives best results for a thickness of about half the projectile diameter used in the experiments. For the bare ceramic, a long dwell phase can be maintained up to impact velocities of around 900 /s. For the buffered ceramic, partial dwell can be achieved up to around 1700 /s. The results corroborate those of earlier investigations mentioned above. More importantly, the present results show that it is possible to substantially erode a heavy alloy long-rod penetrator at the surface of a finite thickness ceramic element without lateral confinement in direct impact experiments even at high impact velocities.
[60]
BehnerT, Orphal DL, HohlerV, Anderson Jr. CE, Mason RL, Templeton DW.2006.
Hypervelocity penetration of gold rods into SiC-N for impact velocities from 2.0 to 6.2km/s
. International Journal of Impact Engineering, 33: 68-79.
This paper presents the experimental design and results of an advanced set of reverse ballistic experiments with long gold rods, impacting SiC-N ceramics at impact velocities from 2.0 to 6.2 km/s. Important issues for these experiments were the high accuracy and position requirements necessary to detect a possible failure wave or failure kinetics in SiC-ceramics as might be evidenced by a change in the slope of the penetration velocity–impact velocity curve. New and sophisticated evaluation methods were developed for this purpose and produced very reliable results. Analyses of the experimental results show clearly that there is no change in the slope of the penetration velocity–impact velocity curve, contrary to that inferred from previous data and analysis.
The terminal ballistic behavior of ductile tungsten alloy long-rod penetrators is examined as impact yaw is increased from values of approximately zero to those which cause penetration performance to significantly decrease. The impact signatures remaining in the target crater from high yaw impacts are examined and used to identify the physical mechanisms which cause penetrator performance to degrade. A threshold limit of penetrator yaw beyond which penetration performance decreases is derived. An empirically based model which quantifies the decrease in penetration due to yaw once this threshold limit is exceeded is presented for impacts with normal incidence semi-infinite RHA targets. The results from a computational effort using the HULL code to simulate high yaw impacts are presented and compared with the empirical penetration degradation model.
[64]
Bless SJ, Barber JP, Bertke RS, Swift HF.1978.
Penetration mechanics of yawed rods
. International Journal of Engineering Science, 16: 829-834.
The penetration of rod projectiles is a function of impact yaw. Armor steel targets were struck at 0° obliquity by long steel rods at ~2.15 km/s and various angles of yaw. Crater dimensions varied systematically with yaw angle. Trenching behavior was observed for yaw angles exceeding about 30°. Analysis indicates that the rods collapsed into the targets with no significant rotation, and that penetration chiefly depends on the parameters D and D sin θ (where D is rod diameter and θ is yaw angle).
[65]
Bless SJ, RosenbergZ, YoonB.1987.
Hypervelocity penetration of ceramics
. International Journal of Impact Engineering, 5: 165-171.
The penetration resistance of alumina was found to decrease with velocity for armor-piercing bullets. However, it was relatively independent of velocity for rods and fragment-simulating projectiles. These results are explained in terms of compressive yielding caused by high velocity pointed projectiles.
[66]
Bukharev YI, Zhukov VI.1995.
Model of the penetration of a metal barrier by a rod projectile with an angle of attack. Combustion, Explosion,
A relatively simple dynamic model is proposed for calculating parameters characterizing the penetration of a barrier by a rod projectile with an angle of attack. Together with the factors examined in the case of axisymmetric penetration within the framework of the well-known Alekseevskii-Tate scheme, the model considers the action of transverse forces and rotation of the rod. Calculations of the penetration of steel barriers by tungsten projectiles with a relative length of 12.8–17.4 at collision velocities of 1800–2100 m/sec along a normal to the surface showed good agreement with experimental data for angles of attack from 0 to 68°.
[67]
Burkins MS, Paige JI, Hansen JS.1996.
A ballistic evaluation of Ti-6Al-4v vs
. long rod penetrators. Army Research Laboratory Report ARL-TR-1146.
The penetration of semi-infinite steel and spaced-plate armors by continuous and segmented rods has been analyzed and measured by direct ballistic tests, hydrocode calculations, and hydrodynamic models at velocities from 2 to 4 km/s. An empirical equation of rod penetration in semi-infinite steel was formulated from hydrodynamic models of rod impact. Penetrations predicted by the equation agreed well with measured values. Increasing the spacing between segments from one to two diameters increased the penetration significantly ( 20%). Structures to support and align the segments can either increase or decrease the penetration, depending on their design. The relative penetrations of continuous and segmented rods depend on the parameters selected for the comparison: the segmented rod having greater penetration for equal mass and diameter and vice versa for equal mass and length. Tests of segmented rods penetrating spaced-plate armor showed that the armor is defeated by the front segment (or segments) punching a hole in the front plate (or plates) that allows the remaining segmented rod through intact to attack the main armor.
[69]
Chen XW, Li QM.2002.
Deep penetration of a non-deformable projectile with different geometrical characteristics
. International Journal of Impact Engineering, 27: 619-637.
A general non-dimensional formula based on the dynamic cavity-expansion model is proposed to predict penetration depth into several mediums subjected to a normal impact of a non-deformable projectile. The proposed formula depends on two dimensionless numbers and shows good agreement with penetration tests on metal, concrete and soil for a range of nose shapes and impact velocities. The validity of the formula requires that the penetration depth is larger than the projectile diameter and the projectile nose length while projectile remains rigid without noticeable deformation and damage.
[70]
Chen XW, Li QM.2004.
Transition from Nondeformable Projectile Penetration to Semihydrodynamic Penetration
The present paper defines a third dimensionless parameter, i.e., the damping function , besides the impact function and geometry function of projectile introduced previously, in the penetration/perforation dynamics of a rigid projectile. It only depends on the interaction of projectile and target materials and is independent of projectile geometry. A general penetration resistance, which contains the terms of viscous effect and dummy mass of projectile induced by the deceleration effect, is adopted in the formulation. Dimensionless formula of depth of penetration (DOP) is conducted with only three parameters , and for general convex shapes of various rigid projectiles. Different geometry parameters are also presented for some common shapes of projectiles. With accounting for viscous effect and dummy mass of a projectile, the normal perforations of thick metallic plates struck by sharp-nosed rigid projectiles are further studied and only , and as well as the dimensionless target thickness dominate in perforation. The influence of damping function on penetration/perforation has been discussed in detail. Theoretical predictions of penetration and perforation in the present manuscript show good agreement with the individual published test data of different projectiles and impact velocities as well as different targets.
[72]
Chen XW, Wei LM, Li JC.2015.
Experimental research on the long rod penetration of tungsten-fiber/Zr-based metallic glass matrix composite into Q235 steel target
. International Journal of Impact Engineering, 79: 102-116.
61Penetration tests of WF/Zr-MG composite and WHA long rods are conducted.61Failure modes of WF/Zr-MG composite and WHA are identified systemically.61The “self-sharpening” behavior of composite rod and its mechanism are investigated.61Impact velocity range which is favorable for the “self-sharpening” is suggested.61Comparative analysis between the composite rod and the WHA rod is conducted.
[73]
ChocronS, Anderson Jr. CE, Walker JD, RavidM.2003.
A unified model for long-rod penetration in multiple metallic plates
. International Journal of Impact Engineering, 28: 391-411.
The Walker–Anderson and Ravid–Bodner analytical models for penetration of projectiles in metallic plates are well known in the ballistics community. The Walker–Anderson model uses the centerline momentum balance in the projectile and target to calculate the penetration history into a semi-infinite medium, while the Ravid–Bodner model uses the upper bound theorem of plasticity theory modified to include dynamic effects. The Ravid–Bodner model also includes a rich selection of failure modes suitable for finite-thick metallic targets. In this paper a blended model is presented: momentum balance is used to calculate the semi-infinite portion penetration (before the back of the target plate begins to flow), and the Ravid–Bodner failure modes are used to determine projectile perforation. In addition, the model has been extended to handle multiple plate impact. Numerical simulations show that after target failure the projectile still continues to erode for some microseconds. This time has been estimated and incorporated into the model. Examples are presented for long-rod projectiles against thick and spaced-plate targets backed by a witness pack that is separated from the main target element(s) by an air gap. Agreement with results from numerical simulations is quite good.
[74]
Christman DR, Gehring JW.1966.
Analysis of High-Velocity Projectile Penetration Mechanics
A series of experiments was performed to evaluate the performance of projectiles impacting targets at velocities two to three times larger than conventional ordnance velocities. The results were positive, where low L/D ratio projectiles exceeded the theoretical hydrodynamic limit of penetration for the given projectile-target combination. High L/D ratio projectiles did not appreciably exceed the limit. A second set of experiments was devised to test the hypothesis that a segmented projectile, - consisting of a series of low L/D projectiles, assembled in a long rod configuration, - could penetrate deeper into the target than a monolithic projectile of equivalent mass. The results were again positive, with a gain of about 10% shown in some cases. The balance of the experiments was devoted to developing a set of design rules and to exploring variations in the configuration and materials.
[76]
Deshpande VS, Evans AG.2008.
Inelastic deformation and energy dissipation in ceramics: A mechanism-based constitutive model
. Journal of the Mechanics and Physics of Solids, 56: 3077-3100.
A mechanism-based constitutive model is presented for the inelastic deformation and fracture of ceramics. The model comprises four essential features: (i) micro-crack extension rates based on stress-intensity calculations and a crack growth law, (ii) the effect of the crack density on the stiffness, inclusive of crack closure, (iii) plasticity at high confining pressures, and (iv) initial flaws that scale with the grain size. Predictions of stress/strain responses for a range of stress states demonstrate that the model captures the transition from deformation by micro-cracking at low triaxiality to plastic slip at high triaxialities. Moreover, natural outcomes of the model include dilation (or bulking) upon micro-cracking, as well as the increase in the shear strength of the damaged ceramic with increasing triaxiality. Cavity expansion calculations are used to extract some key physics relevant to penetration. Three domains have been identified: (i) quasi-static, where the ceramic fails due to the outward propagation of a compression damage front, (ii) intermediate velocity, where an outward propagating compression damage front is accompanied by an inward propagating tensile (or spallation) front caused by the reflection of the elastic wave from the outer surface and (iii) high velocity, wherein plastic deformation initiates at the inner surface of the shell followed by spalling within a tensile damage front when the elastic wave reflects from the outer surface. Consistent with experimental observations, the cavity pressure is sensitive to the grain size under quasi-static conditions but relatively insensitive under dynamic loadings.
[77]
Eichelberger RJ.1956.
Experimental test of the theory of penetration by metallic jets
Experimental measurements of jet velocity and of penetration velocity as functions of depth of penetration are described for lined cavity charges fired into several types of target material and under a variety of experimental conditions. The results show that the hydrodynamic theory of penetration of Pugh and of Hill, Mott, and Pack describes very accurately the early stages of the penetration process. Strength of the target becomes an appreciable factor in the later stages, however. A simple modification of the theory is described which appears to account adequately for these strength effects. Some alterations in ideas concerning the mechanism of penetration by the jet after fracture are also described.
The mechanism of crater formation due to hypervelocity impact is described, using a variety of experimental observations and theory as a basis. The currently accepted empirical correlations are also presented. The evidence is considered in the light of the problem of meteoroid impacts upon space vehicles, and such generalized predictions as are possible at the present state of the art are erived. (Author)
We conducted depth of penetration experiments with ogive-nose projectiles concrete targets with unconfined compressive strengths of nominally 14 MPa (2 ksi), 35 MPa (5 ksi), and 97 MPa (14 ksi). From our data and the data presented by Canfield and Clator [ J. A. Canfield and I. G. Clator , Development of a scaling law and techniques to investigate penetration in concrete . NWL Report No. 2057, U.S. Naval Weapons Laboratory, Dahlgren, VA (1966) ] [1], we developed an empirical equation for penetration depth of ogive-nose projectiles penetrating concrete targets at normal impact. Our penetration equation contains a single, dimensionless empirical constant that depends only on the unconfined compressive strength of the target. We determine the empirical constant from penetration depth versus striking velocity data with six sets of penetration data for striking velocities between 250 and 800 m/s. Predictions are in good agreement with all six data sets.
[80]
Forrestal MJ, Frew DJ, Hanchak SJ, Brar NS.1996.
Penetration of grout and concrete targets with ogive-nose steel projectiles
. International Journal of Impact Engineering, 18: 465-476.
We conducted depth of penetration experiments into grout and concrete targets with ogive-nose steel projectiles. Powder guns launched 0.064 kg, 12.9 mm diameter projectiles into grout targets with unconfined compressive strengths of 13.5 M Pa (2.0 ksi) and 21.6 MPa (3.1 ksi). For the concrete targets, powder guns launched projectiles with length-to-diameter ratios of 10; a 0.48 kg, 20.3 mm diameter rod, and a 1.60 kg, 30.5 mm diameter rod. Concrete targets had unconfined compressive strength of 62.8 M Pa (9.1 ksi) for the 0.48 kg rods and unconfined compressive strength of 51.0 MPa (7.4 ksi) for the 1.60 kg rods. For these experiments, penetration depth increased as striking velocity increased until nose erosion became excessive. Thus, we determined experimentally the striking velocities corresponding to maximum penetration depths. Predictions from a previously published model are in good agreement with data until nose erosion becomes excessive.
[81]
Forrestal MJ, J. PiekutowskiA.2000.
Penetration experiments with 6061-T6511 aluminum targets and spherical-nose steel projectiles at striking velocities between 0.5 and 3.0km/s
. International Journal of Impact Engineering, 24: 57-67.
We conducted depth of penetration experiments with 7.11-mm-diameter, 74.7-mm-long, spherical-nose, 4340 steel projectiles launched into 250-mm-diameter, 6061-T6511 aluminum targets. A powder gun and two-stage, light-gas guns launched the 0.023 kg projectiles at striking velocities between 0.5 and 3.0 km/s. Post-test radiographs of the targets showed three response regions as striking velocities increased: (1) the projectiles had slight bulges near the nose and some shank bending, (2) the projectiles had large bulges and kinked shanks, and (3) the projectiles eroded and lost mass. For the first response region, penetration depth increased as striking velocity increased. However, when the second region was reached, there was a dramatic reduction in penetration depth. For the third response region penetration depth increased with increasing striking velocity. To show the effect of projectile strength, we compared depth-of-penetration as a function of striking velocity for spherical-nose rods with average Rockwell hardnesses of 36.6, 39.5, and 46.2. To show the effect of nose shape, we compared penetration data for the spherical-nose projectiles with previously published data for ogive-nose projectiles.
[82]
Forrestal MJ, Longcope DB.1990.
Target strength of ceramic materials for high-velocity penetration
We derived equations for the target‐strength term used in the modified hydrodynamic model that describes long rod penetration into ceramic targets. Since ceramics have tensile strengths that are usually an order of magnitude lower than their compressive strength, this model allows for tensile cracking. In addition, our model includes the effect of pressure‐dependent shear strength.
[83]
Forrestal MJ, Piekutowski AJ, Luk VK.1988.
Long-rod penetration into simulated geological targets at an impact velocity of 3.0km/s. Military Technology Weaponry &
Abstract Experimental data for ceramic armor materials from two test methods, small-scale reverse ballistic tests and depth-of-penetration (DOP) tests, are reviewed and compared. Results from reverse ballistic tests can be used to estimate the length of rod erosion in the ceramic tiles of DOP tests. The outcome of a given DOP test can then be predicted by using recently published data bases on RHA penetration to determine the residual penetration into the steel back-up of the DOP test. Results of this methodology, compared to experimental DOP-test results, agree reasonably well for aluminum nitride and silicon carbide, even though scale sizes, impact velocities and experimental procedures varied considerably between investigators. The methodology was then applied to single-valued performance criteria for ceramic armor materials, for example, mass efficiency. This analysis demonstrates that in certain cases, test parameters, like the ratio of penetrator length to ceramic tile thickness, affect test results considerably more than differences between ceramic types. Thus, DOP tests must be properly designed and interpreted in order to assess correctly the ballistic performance of ceramics.
[85]
Franzen RR, Walker JD, Orphal DL, Anderson Jr CE.1994.
An upper limit for the penetration performance of segmented rods with segment-$L/D \leq 1$
. International Journal of Impact Engineering, 15: 661-668.
ABSTRACT This study investigates the question of whether the penetration performance of a segmented rod penetrator with segment-L/D 81 1 can exceed that of a uniform density continuous rod of equal mass, length (including spaces), diameter and velocity (“comparison rod”). The answer, based on experimental, computational and analytical data published to-date, is negative. The well-known fact that segmented rods penetrate better than their so-called “parent rods” (rods of equal mass, diameter and velocity and a length equal to the sum of segment lengths only), together with findings presented here, limits the penetration performance of segmented rods to Pparent rod < Psegmented rod < Pcomparison rod· The limitations of the data base used here may limit the generality of the findings: in particular, the database is fairly small, only unyawed, normal impacts at velocities of 2 km/s and higher are included, and, with few exceptions, only tungsten segments and steel targets were studied.
[86]
Galanov BA, Kartuzov VV, Ivanov SM.2008.
New analytical model of expansion of spherical cavity in brittle material based on the concepts of mechanics of compressible porous and powder materials
. International Journal of Impact Engineering, 35: 1522-1528.
In this paper, the concepts of mechanics of porous and powder media are applied for development of new analytical model of expansion of spherical cavity in brittle materials. The model is based on the approach that recognizes the existence of three regions with different rheology: region of comminuted and compacted material; region of pore formation formed by radial cracks; elastically deformed region. Strain-stress state in each region is determined and analyzed. Cavity expansion pressure is determined. Energy losses on elastic deformation, fracture and compaction of material are calculated and compared for a number of ceramic materials. It is shown that the contribution of compaction and fracture in total energy losses is considerable. The presented model avoids the use of rheological characteristics that are difficult to determine and uses instead the porosity of the material.[All rights reserved Elsevier].
[87]
Gold VM, Vradis GC, Pearson JC.1996.
Concrete penetration by eroding projectiles: Experiments and analysis
Sufficient technical information is presented to provide a reasonable assessment of the character, approach and results obtained for the various studies. If more detailed information concerning analytical or experimental procedures are required, the reader should consult the original references which are fully listed.
[89]
Grabarek CL.1971.
Penetration of Armor by Steel and High Density Penetrators (U)
Analytical equations are presented herein to predict the penetration of semi-infinite metallic targets struck normally by long rods at high velocities for Y p < S where Y p is the rod strength and S is the static target resistance. The equations are derived based on energy balance method. It is assumed that the kinetic energy loss of a long rod is related to the energy dissipated by the plastic deformations in the target, the energy consumed by the long-rod penetrator itself and the energy carried by the eroded rod debris. Secondary penetration is also examined in the present paper due to the fact that the eroded rod debris forms a tube which can penetrate the target further if the density of the rod is greater than that of the target and the impact velocity is high enough. The present analytical equation is found to be in good agreement with the experimental data for a wide range of impact velocities.
[92]
HerrmannW, Wilbeck JS.1987.
Review of hypervelocity penetration theories
. International Journal of Impact Engineering, 5: 307-322.
A review is given of the emperical and approximate theoretical expressions which have been developed to describe various aspects of impact at hypervelocities where the projectile and some of the target materials undergo massive plastic deformation, breakup, melting or vaporization. Various stages of the penetration process are identified on the basis of experimental evidence. Empirical fits to experimental data, or, at velocities above the experimental range, to results of finite difference calculations of the penetration event, are reviewed. In some cases simple theories, usually requiring the evaluation of some undetermined parameters from experimental or numerical data, have been developed. These are described, with emphasis on those which have found use in the design of offensive or defensive systems.
[93]
Hetherington JG, Lemieux PF.1994.
The effect of obliquity on the ballistic performance of two component composite armours
. International Journal of Impact Engineering, 15: 131-137.
ABSTRACT This paper examines the performance of composite armours when subjected to oblique impact. Experimental results are presented from a programme of trials on ceramic-aluminium targets using 7.62 mm ball ammunition. The results show that an inclined ceramic composite armour plate will perform better, on a thickness basis, than one arranged perpendicular to the line of impact. However, the degree of improvement thus obtained is much less than for steel armours. Moreover, it is shown that minimum weight protection to a vulnerable area, using ceramic composite armours, is achieved when the armour is perpendicular to the threat. The degree of thickness reduction which is obtained by angling ceramic composite armours is much less than for steel armours. A theoretical model of oblique impact is presented and shown to correlate well with the experimental results.
[94]
Hirt CW, Amsden AA, Cook JL.1974.
An arbitrary Lagrangian-Eulerian computing method for all flow speeds
Beside a short remark on the “hydrodynamic theory of rod projectiles”, the paper deals with the terminal ballistic behaviour of cylindrical projectiles against semi-infinite targets. Experimental data of EMI, completed by results of some other authors, are presented. Crater parameters like depth, diameter and volume and their dependence on projectile velocity (up to 5000 m/s), projectile and target material properties, as well as L/D-ratios (1–32), will be discussed. Mainly the projectile materials steel and tungsten sinter-alloys are considered. Target materials are mild steel and high strength steel, an Al-alloy and a tungsten sinter-alloy. The results show that the influence of material density on the crater dimensions is considerably greater than the influence of strength. The L/D ratio determines the velocity dependence of crater depth, diameter and volume. At high velocities in the hydrodynamic regime, the crater depth of short cylinders (L/D 65 1) is approximately proportional to v p 2/3 (V p=projectile velocity). With increasing L/D-ratio, the slope of the penetration curves decreases and converges for rods (L/D 62 1) versus a saturation, i. e. becomes nearly independent on v p. A consequence of this saturation is the existence of a so-called “tangent velocity”, above which an optimal increase of efficiency is only realized by increasing the projectile mass and not the velocity. Furthermore, ballistic limits of real targets like single plates and symmetric double plates meteorite bumper shield) are taken into account. The expected better performance of “segmented rods” is also discussed.
[99]
HohlerV, Stilp AJ, Walker JD, Anderson CE.1993.
Penetration of long rods into steel and glass targets: Experiments and computations
The penetration of tungsten sinter-alloy rods having length-to-diameter ratios of L/D= 10 and 12.5 into alumina targets was investigated in the velocity range v p = 1.25 to 3km/s. The depth of penetration (DOP) test and the time resolved oberservation using a 600 kV flash X-ray system were applied to assess the protection efficiency of the ceramics. From DOP tests, the residual penetration into a steel backing yields the differential efficiency factor DEF and the mass efficiency factor MEF. DEF increases with v p ; MEF decreases. On the other hand, DEF decreases as ceramic thickness increases; MEF increases and converges to DEF for residual penetration zero. From the time resolved measurements, position and length reduction of the rod during penetration in the ceramics were obtained. The process can be described by Tate's fluid jet model in good approximation. The target resistance parameter R, defined in the modified Bernoulli equation, characterizes the ceramic performance. The average R values are 5.4, 6.1 and 4.8 GPa at impact velocities v p = 1.7, 2.5 and 3km/s, respectively, i.e. there is no strong dependence of R on v p .
[101]
HohlerV, StilpA.2002.
Penetration performance of segmented rods at different spacing-comparison with homogeneous rods at 2.5-3.5km/s
. Journal of Neuroscience the Official Journal of the Society for Neuroscience, 22: 2541-2549.
An experimental programme is presented which investigated the performance of oblique, ceramic/metal, bilayer composite armours. The ceramics, alumina and silicon carbide, were backed by either Rolled Homogeneous Armour steel (RHA) or 7000 series aluminium. Using a model scale tungsten penetrator at two velocities (representing current and future ordnance threats) the effect of configuration on ballistic limit or depth of penetration (DOP) areal densities was determined. Areal densities of the DOP targets decreased with increasing ceramic thickness, achieving a minimum at zero residual penetration in the backing. The bilayer targets, loaded at the ballistic limit needed a larger areal density to defeat the penetrator. This areal density also decreased with ceramic thickness but showed a minimum with respect to ceramic thickness, as a result of reduced support by the thinner metallic backing. At 1450ms 1 the most efficient system was found to be a SiC/Al, which demonstrated a 25% weight saving over the monolithic aluminium reference target. The Al-alloy backing performs better than RHA, and SiC better than Al 2O 3.
[103]
Holmquist TJ, Anderson CE, BehnerT, Orphal DL.2010.
This work presents computed results for the responses of ceramic targets, with and without prestress, subjected to projectile impact. Also presented is a computational technique to include prestress. Ceramic materials have been considered for armor applications for many years because of their high strength and low density. Many researchers have demonstrated that providing confinement enhances the ballistic performance of ceramic targets. More recently, prestressing the ceramic is being considered as an additional enhancement technique. This work investigates the effect of prestressing the ceramic for both thin and thick target configurations subjected to projectile impact. In all cases the targets with ceramic prestress provided enhanced ballistic performance. The computed results indicate that prestressed ceramic reduces and/or delays failure, resulting in improved ceramic performance and ballistic efficiency.
[105]
Holmquist TJ, Johnson GR.2005.
Modeling prestressed ceramic and its effect on ballistic performance
. International Journal of Impact Engineering, 31: 113-127.
This article presents computed results for the responses of ceramic targets, with and without prestress, subjected to projectile impact. Also presented is a computational technique to include prestress. Thin and thick ceramic target configurations are used to understand the effect prestressing has on ballistic performance. For both targets two prestress levels (small and large), and two prestress states (radial and hydrostatic) are investigated. The small prestress is similar in magnitude to values obtained experimentally and the large prestress is approximately the maximum prestress the confinement can produce (determined computationally). The targets are subjected to projectile impact and the resulting ballistic responses are evaluated. In all cases prestressing the ceramic enhanced the ballistic performance, although the effect of the different prestress conditions on the ballistic response was not always obvious.
[106]
Holmquist TJ, Johnson GR.2011.
A Computational Constitutive Model for Glass Subjected to Large Strains, High Strain Rates and High Pressures
This article presents a computational constitutive model for glass subjected to large strains, high strain rates and high pressures. The model has similarities to a previously developed model for brittle materials by Johnson, Holmquist and Beissel (JHB model), but there are significant differences. This new glass model provides a material strength that is dependent on the location and/or condition of the material. Provisions are made for the strength to be dependent on whether it is in the interior, on the surface (different surface finishes can be accommodated), adjacent to failed material, or if it is failed. The intact and failed strengths are also dependent on the pressure and the strain rate. Thermal softening, damage softening, time-dependent softening, and the effect of the third invariant are also included. The shear modulus can be constant or variable. The pressure-volume relationship includes permanent densification and bulking. Damage is accumulated based on plastic strain, pressure and strain rate. Simple (single-element) examples are presented to illustrate the capabilities of the model. Computed results for more complex ballistic impact configurations are also presented and compared to experimental data. [DOI: 10.1115/1.4004326]
[107]
Holmquist TJ, Johnson GR, Cook WH.1993.
A computational constitutive model for concrete subjected to large strains, high strain rates and high pressures//Proceedings of 14th international symposium on Ballistics, Quebec, Canada
For concrete target penetration and/or perforation simulation, the Holmquistu2013Johnsonu2013Cook (HJC) material model is widely used as concrete material model. However, the strain rate expression of the model has failed to explain the sudden increase in concrete strength at high strain rates. The pressure-volume relationship of the HJC model is complex and requires a large number of material constants. In this study, a modified Holmquistu2013Johnsonu2013Cook (HJC) model is proposed for concrete material under high velocity impact. The modification involves simplification and improvement of the strain rate expression and pressure-volume relationship. Material parameters identification procedure for the MHJC model is also elaborated. The numerical simulations using the proposed model show a good agreement with experimental observations, especially, on the residual velocities, penetration depths and failure patterns of the target plates. These validate the applicability of the MHJC model for high velocity projectile impac...
[109]
Jiao WJ, Chen XW.2018.
Approximate solutions of the Alekseevskii--Tate model of long-rod penetration
The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, penetration velocity, rod length, and penetration depth were obtained implicitly as a function of time and solved numerically By employing a linear approximation to the logarithmic relative rod length, we obtain two sets of explicit approximate algebraic solutions based on the implicit theoretica solution deduced from primitive equations. It is very convenient in the theoretical prediction of the Alekseevskii–Tate model to apply these simple algebraic solutions. In particular, approximate solution 1 shows good agreement with the theoretical(exact) solution, and the first-order perturbation solution obtained by Walters et al.(Int. J. Impac Eng. 33:837–846, 2006) can be deemed as a special form of approximate solution 1 in high-speed penetration. Meanwhile, with constant tail velocity and penetration velocity approximate solution 2 has very simple expressions, which is applicable for the qualitative analysis of long-rod penetration. Differences among these two approximate solutions and the theoretical(exact) solution and their respective scopes of application have been discussed, and the inferences with clear physical basis have been drawn. In addition, these two solutions and the first-order perturbation solution are applied to two cases with different initial impact velocity and different penetrator/target combinations to compare with the theoretical(exact) solution. Approximate solution 1 is much closer to the theoretical solution of the Alekseevskii–Tate model than the first-order perturbation solution in both cases, whilst approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration.
[110]
Johnson GR, Cook WH.1983.
A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures//Proceedings of the 7th International Symposium on Ballistics:
An improved computational constitutive model for brittle materials is presented. It is applicable for brittle materials subjected to large strains, high strain rates and high pressures, and is well锕晆ited for computations in both Lagrangian and Eulerian codes. The equivalent strength is dependent on the intact strength, fractured strength, strain rate, pressure, and damage. The pressure includes the effect of bulking, which is introduced through the transfer of internal energy from decreased shear and deviator stresses to potential internal energy associated with increased hydrostatic pressure. Examples are presented to illustrate the model.
[112]
Johnson GR, Holmquist TJ, Beissel SR.2003.
Response of aluminum nitride (including a phase change) to large strains, high strain rates, and high pressures
This article contains a description of a computational constitutive model for brittle materials subjected to large strains, high strain rates, and high pressures. The focus of this model is to determine the response of aluminum nitride under high velocity impact conditions that produce large strains, high strain rates, and high pressures. The strength is expressed as a function of the pressure, strain rate, and accumulated damage; and it allows for strength of both intact and failed material. The pressure is primarily expressed as a function of the volumetric strain, but it also includes the effect of bulking for the failed material. For materials without a phase change this model is an extension of the previous Johnson olmquist models for brittle materials. The primary new feature of this model is the capability to include a phase change, and this is required for aluminum nitride. Computations are performed to illustrate the capabilities of the model, to compare computed results to experimental results,...
[113]
Johnson GR, Stryk RA.2003.
Conversion of 3D distorted elements into meshless particles during dynamic deformation
. International Journal of Impact Engineering, 28: 947-966.
This paper presents a description of an algorithm to automatically convert 3D distorted elements into meshless particles during dynamic deformation. It also includes an improved (invariant) particle algorithm that allows for a more accurate treatment of boundaries and interfaces. These new 3D algorithms have been incorporated into an explicit Lagrangian code that includes both elements and particles. They provide for increased capability and accuracy for Lagrangian computations involving severe distortions. Several 3D examples are included to demonstrate the new technique.
[114]
Johnson GR, Stryk RA, Beissel SR, Holmquist TJ.2002.
An algorithm to automatically convert distorted finite elements into meshless particles during dynamic deformation
. International Journal of Impact Engineering, 27: 997-1013.
This paper presents an explicit 2D Lagrangian algorithm to automatically convert distorted elements into meshless particles during dynamic deformation. It also provides the contact and sliding algorithms to link the particles to the finite elements. For this approach the initial grid is composed entirely of finite elements and the response is computed with finite elements until portions of the grid become highly strained. When finite elements on the boundaries reach a user-specified plastic strain they are converted to particles and linked to the adjacent finite element grid. This approach allows for the use of accurate and efficient finite elements in the lower distortion regions, and for the use of meshless particles in the higher distortion regions. Example computations are presented to demonstrate the accuracy and utility of this approach.
[115]
Kong XZ, FangQ, Li QM, WuH, Crawford JE.2017a.
Modified K & C model for cratering and scabbing of concrete slabs under projectile impact
. International Journal of Impact Engineering, 108: 217-228.
The HJC material model, which has been widely used for numerical predictions of projectile penetration, is modified for the improved numerical simulations of the cratering and scabbing phenomenon in concrete slabs subjected to projectile impact. Four modifications, i.e. the modified yield surface, introduction of the tensile damage, introduction of Lode-angle dependency and modified strain-rate effect, are presented. The modified HJC model is implemented into the finite element code LS-DYNA through user defined material model. The improved performances due to the modifications are firstly demonstrated by single finite element numerical tests. And then several sets of projectile perforation experiments, in which the projectile mass, impact velocity and concrete slab thickness vary, are simulated by the modified HJC model, where corresponding predictions of the original HJC model are also presented to demonstrate the improved simulation of the cratering and scabbing phenomenon. Sensitivity analysis of three independent parameters that govern the tensile dynamic behavior of the modified model shows that the fracture strain and dynamic increase factor for tension are crucial for the correct modeling of the scabbing phenomenon, and the dynamic increase factor for tension as well as the ratio of the current meridian to the compressive meridian are important for the simulation of the cratering phenomenon.
Abstract This paper presents an improved model for the critical impact yaw (or simply the critical yaw) in long-rod penetration with considering the deceleration and rotation of the rod and the crater shape of the target. Two critical yaws, θc1 and θc2, under normal impact were identified, below which there is no contact between the rod and crater sidewall (for θc1) and between the rod and the crater entrance (for θc2) during the entire penetration process. Contact functions and iterative algorithms were proposed in order to obtain these two critical yaws numerically. The influences of four dominant nondimensional numbers (i.e., the ratio of the target resistance to the rod strength λ, Johnson's damage number of the rod ζ, square root of the target-projectile density ratio μ, and the diameter-length ratio of the rod ψ) on two critical yaws were studied for three typical rod-target systems (tungsten alloy rods penetrating steel targets, steel rods penetrating aluminum alloy targets, and steel rods penetrating steel targets). The relationship between two critical yaw angles was also discussed. A new empirical formula for the critical yaw θc2 was proposed based on the parametric study results and dominant nondimensional numbers, which extends the valid application range of the existing empirical formula.
[118]
Kong XZ, WuH, FangQ, PengY.2017b.
Rigid and eroding projectile penetration into concrete targets based on an extended dynamic cavity expansion model
. International Journal of Impact Engineering, 100: 13-22.
A hyperbolic yield criterion and Murnaghan equation of state were introduced to describe the plastic behavior of concrete material under projectile penetration, and an extended dynamic cavity expansion model was proposed. Then, a unified one-dimensional resistance of concrete target to projectile penetration was formulated, in which the projectile nose shape influences were taken into account by three non-dimensional coefficients. Furthermore, combined with the Newton's second law and Alekseevskii-Tate equations, both rigid and eroding projectile penetration models into concrete targets were established. By comparing with the existing tests data as well as prediction results of previous model based on the linear yield criterion and equation of state, the proposed models were verified. Besides, a series of practical parameters of hyperbolic yield criterion and Murnaghan EOS for the extended dynamic cavity expansion model were given and verified.
[119]
Kong XZ, WuH, FangQ, ZhangW, Xiao YK.2017
c. Projectile penetration into mortar targets with a broad range of striking velocities: Test and analyses
. International Journal of Impact Engineering, 106: 18-29.
Eighteen shots of flat nosed cylindrical 45# steel projectiles penetrating into mortar targets with cubic compressive strength of 50 MPa are conducted, where the striking velocities are ranged from 510 m/s to 1850 m/s. By examining the damages of targets, linear dependences of the cratering diameter and depth on the initial striking velocity, as well as the cratering volume on the initial kinetic energy of projectile are found. Three penetration regimes, i.e., rigid projectile penetration, deforming projectile penetration without eroding and eroding projectile penetration are observed successively with the increase of striking velocity. Furthermore, the experimental depths of penetration are compared with the predictions of our recently established rigid and eroding penetration models based on an extended dynamic cavity expansion model (Kong et al. 2017). The rigid projectile penetration model is further validated, and the eroding projectile penetration model is further justified, improved and validated by considering the succeeding rigid penetration stage. Finally, the analytical expressions for the upper limit velocity of rigid projectile penetration and the lower limit velocity of eroding projectile penetration are given and validated, respectively.
[120]
Lambert JP.1978.
A residual velocity predictive model for long rod penetrators
The modified hydrodynamic theory of long rod penetration into semi-infinite targets was established independently by Alek-seevskii and Tate over forty years ago and since then many investigators contributed much to the development of the high speed penetration mechanics.However,in all the models proposed so far,the target resistance Rt is not well defined and usually determined by adjusting it until the predicted depth of penetration comes to an agreement with experimental data.In this paper,assumptions are first made about particle velocity and pressure profiles together with response regions in the target and then an extension is made to the modified hydrodynamic theory of long rod penetration into semi-infinite targets,in which Rt has explicit form and is dependent on penetration velocity as well as thermo-mechanical properties of target material.The present model is compared with long rod penetration tests for different material combinations.It transpires that the present model predictions are in good agreement with the experimental data and numerical simulations in terms of penetration depth although many assumptions and simplifications are introduced into the paper.
[122]
LeeM.2000.
An engineering impact model for yawed projectiles
. International Journal of Impact Engineering, 24: 797-807.
When a long-rod projectile penetrates a thick target with an angle of attack, interfering of the projectile with the sidewall of a crater is the mechanism for the degraded penetration performance. By using an engineering model, significant parameters and how they vary over a wide velocity range can be quickly obtained. A transient discreet impact model is developed to predict not only the crater profile but final depth generated by the penetration of a yawed long rod. The yawed long rod is described as a series of continuous finite disk elements which enables us to keep revising the time-dependent crater profile. To consider the interaction with the crater sidewall, effective diameters for each element are used, and the revised crater profile is calculated based on these effective diameters. Three possibilities of the degree of degradation in penetration for the elements that interact with crater sidewall are discussed. The model reduces, in the case of the impact with no yaw, to the Alekseevskii ate's solution. Theoretical predictions are compared with the corresponding experimental data.
[123]
LeeM.2003.
Hypervelocity impact into oblique ceramic/metal composite systems
. International Journal of Impact Engineering, 29: 417-424.
A numerical study for the analysis of oblique ceramic/metal composite armour systems against L/D = 20 projectiles has been performed. The ballistic performance of the add-on lightweight armours was examined by determiningthe effect of areal density of the system on ballistic limit or depth of penetration (DOP). To do this, a series of three-dimensional numerical simulations has been conduced. The impact velocities considered are 2.2 and 2.6 km/s. The oblique angle of the plate is 60 degrees. Simulation results for ballistic limits appear to match fairly well with the test values. Although the previous data for the penetration of 7.62 AP projectile into relatively thin alumina/aluminium composite targets revealed an optimum value of the front plate to back plate thickness ratio in the region of 1.5, the current data for the impact of long rod into relatively thick composite targets are scattering. This is because the distinguishing features of thin composite armour systems against 7.62 AP and 40.7g steel projectiles are crack propagation, ceramic conoid formation and failure of backing plate, while these effects are less significant in thick targets, especially at high impact velocities.
[124]
LeeM, Bless SJ.1998.
Cavity models for solid and hollow projectiles
. International Journal of Impact Engineering, 21: 881-894.
ABSTRACT Two analytical models for the crater size generated by long-rod and thick-walled tube projectiles are presented. The first is based on energy; in a steady-state penetration, the kinetic energy loss of a projectile is related to the total energy deposited in the target. This simple approach provides an upper bound for the crater size. The second approach is based on the observation that two mechanisms are involved in cavity growth due to long projectiles: flow of projectile erosion products, which exerts radial stress on the target and opens a cavity, and radial momentum of the target as it flows around the projectile nose (cavitation). This analysis includes the centrifugal force exerted by the projectile, radial momentum of the target, and the strength of the target. Thus, it can estimate the extent of cavity growth due to projectile mushrooming, which cannot be predicted by other analyses. This model is shown to be in good agreement with experimental data.
[125]
LeeM, BlessS.1996.
Cavity dynamics for long rod penetration
. The Univercity of Texas at Austin Institute for Advanced Technology.
Ricochet of a tungsten heavy alloy long-rod projectile from oblique steel plates with a finite thickness was investigated numerically using a full three-dimensional explicit finite element method. Three distinctive regimes resulting from oblique impact depending on the obliquity, namely simple ricochet, critical ricochet and target perforation, were investigated in detail. Critical ricochet angles were calculated for various impact velocities and strengths of the target plates. It was predicted that critical ricochet angle increases with decreasing impact velocities and that higher ricochet angles were expected if higher strength target materials are employed. Numerical predictions were compared with existing two-dimensional analytical models. Experiments were also carried out and the results supported the predictions of the numerical analysis.
[127]
Li JC, Chen XW.2017.
Theoretical analysis of projectile-target interface defeat and transition to penetration by long rods due to oblique impacts of ceramic targets
. International Journal of Impact Engineering, 106: 53-63.
612-D and 3-D models of composite rod are established based on its innerstructure.61A modified constitutive model is employed to describe the metallic glass matrix.61The mechanism of “self-sharpening” for the composite rod is analyzed in detail.61The effects of various factors on the “self-sharpening” behavior are discussed.
[129]
Li JC, Chen XW, NingF.2014.
Comparative analysis on the interface defeat between the cylindrical and conical-nosed long rods
. International Journal of Protective Structures, 5: 21-46.
61Three deformation modes of the long rod and the ceramic target are summarized.61The critical impact velocity range for the transition is further identified.61Critical transition time is analyzed and an analytical expression is formulated.61The analytical formula is convenient for the engineering application.
[131]
Li JZ, Zhang LS, Huang FL.2017.
Experiments and simulations of tungsten alloy rods penetrating into alumina ceramic/603 armor steel composite targets
. International Journal of Impact Engineering, 101: 1-8.
The experiments and numerical simulations of tungsten alloy rods penetrating into alumina ceramic/603 armor steel composite target were conducted. Both the experiments and numerical simulations produced measurements of residual penetration depths in the steel back plates. The numerical simulations also showed damage distribution during the penetrating process. This study concludes that the residual penetration depth decreases linearly with increasing ceramic thickness. Therefore, both the mass efficiency factor and the differential efficiency factor increase with increasing ceramic thickness. The ceramic was seriously comminuted at the impact site and split into very small fragments whose sizes depend on the distance from the impact site. The ceramic targets without lateral constraint were more severely pulverized due to the tensile stress reflected from the lateral boundary.
[132]
Li QM, Chen XW.2003.
Dimensionless formulae for penetration depth of concrete target impacted by a non-deformable projectile
. International Journal of Impact Engineering, 28: 93-116.
Based on the dimensional analysis of concrete penetration by a non-deformable projectile and an analytical penetration model, two dimensionless numbers, i.e., the impact function I and the geometry function of projectile N are defined and used in a dimensionless formula to predict the penetration depth. It is shown that experimental data on shallow, medium and deep penetrations in a broad range of concrete strength, impact velocity and projectile geometry can be uniquely represented by these two dimensionless numbers. It is also shown that the formula based on these two dimensionless numbers is comparable to the unit-dependent empirical formulae on penetration depth.
[133]
Littlefield DL, Anderson Jr CE, PartomY, Bless SJ.1997.
The penetration of steel targets finite in radial extent
. International Journal of Impact Engineering, 19: 49-62.
An experimental, analytical, and computational effort was undertaken to examine the effect of confinement on penetration in armor-like steel targets. For the experiments, LD 10, tungsten-alloy projectiles were fired at 1.5 km/s into 4340 steel cylindrical rounds of various diameters. Penetration efficiencies, as measured by the depth of penetration normalized by the original projectile length (PL), were determined and the results plotted as a function of normalized target diameter DD, where Dis the target diameter and D is the projectile diameter. As DD changed from 20 to 5, PL increased by 28%, although PL was approximately independent of DD for DD ? 15. An analytical model using a modified cavity expansion theory was developed to estimate the resistance to penetration for targets of finite lateral extent. The analytical model shows decreasing target resistance as DD decreases below approximately 30; in particular, target resistance decreases rapidly forDD < 20. Numerical simulations were performed and the computational predictions are in excellent agreement with the experimental results; simulations were used to extend DD between 3 and 78. Plastic strain contours are plotted to assess the extent of plastic flow within the target; the results of the simulations demonstrate thatPL begins to increase when the extent of plastic flow in the target reaches the radial boundary.
[134]
Liu JC, Pi AG, Huang FL.2015.
Penetration performance of double-ogive-nose projectiles
. International Journal of Impact Engineering, 84: 13-23.
61A double-ogive-nose penetration body scheme with a low penetration resistance is proposed.61The influence of the nose shape coefficient N65 on the penetration resistance and DOP is discussed.61The feasibility of the proposed method is validated through theoretical, experimental, and simulation results.
[135]
LiuY, MaA, Huang FL.2009.
Numerical simulations of oblique-angle penetration by deformable projectiles into concrete targets
. International Journal of Impact Engineering, 36: 438-446.
Numerical simulations of oblique-angle penetration by deformable projectiles into concrete targets are performed in this paper by using the three-dimensional finite element code LS-DYNA, into which a combined dynamic constitutive model which can simultaneously describe both the compressive and tensile damage of concrete is implemented. As a consequence, the ballistic trajectories and the depths of penetration under different oblique angles (from 10 to the ricochet angle) are obtained. Moreover, the damage distribution of concrete after oblique penetration is procured, which can really reflect the tensile and compressive damage of concrete. The numerical results for the depths of penetration are compared with experimental data obtained by previous authors and show good agreement.
[136]
Lu ZC, Wen HM.2018.
On the penetration of high strength steel rods into semi-infinite aluminium alloy targets
. International Journal of Impact Engineering, 111: 1-10.
One observation from interface defeat experiments with thick ceramic targets is that confinement and prestress becomes less important if the test scale is reduced. A small unconfined target can show similar transition velocity as a large and heavily confined target. A possible explanation for this behavior is that the transition velocity depends on the formation and growth of macro cracks. Since the crack resistance increases with decreasing length scale, the extension of a crack in a small-scale target will need a stronger stress field, viz., a higher impact velocity, in order to propagate. An analytical model for the relation between projectile load, corresponding stress field, and the propagation of a cone-shaped crack under a state of interface defeat has been formulated. It is based on the assumption that the transition from interface defeat to penetration is controlled by the growth of the cone crack to a critical length. The model is compared to experimentally determined transition velocities for ceramic targets in different sizes, representing a linear scale factor of ten. The model shows that the projectile pressure at transition is proportional to one over the square root of the length scale. The experiments with small targets follow this relation as long as the projectile pressure at transition exceeds the bound of tensile failure of the ceramic. For larger targets, the transition will become independent of length scale and only depend on the tensile strength of the ceramic material. Both the experiments and the model indicate that scaling of interface defeat needs to be done with caution and that experimental data from one length scale needs to be examined carefully before extrapolating to another.
[138]
LundbergP, LundbergB.2005.
Transition between interface defeat and penetration for tungsten projectiles and four silicon carbide materials
. International Journal of Impact Engineering, 31: 781-792.
Armour systems capable of defeating an incoming projectile on the surface of a ceramic have been reported by several authors. This capability, called interface defeat, signifies that the projectile material is forced to flow radially outwards on the surface of the ceramic without penetrating significantly. In order to investigate the conditions for interface defeat, two models for the interaction of a metallic projectile and a ceramic target were established. With the aid of them, upper and lower bounds for the transition impact velocity between interface defeat and normal penetration were estimated for a given combination of metallic projectile and ceramic target. These approximate bounds were found to be consistent with transition velocities determined experimentally for two projectile materials (tungsten and molybdenum) and five target materials (two types of silicon carbide, boron carbide, titanium diboride and a polycrystalline diamond composite).
[140]
LundbergP, RenströmR, LundbergB.2006.
Impact of conical tungsten projectiles on flat silicon carbide targets: Transition from interface defeat to penetration
. International Journal of Impact Engineering, 32: 1842-1856.
Normal impact of conical tungsten projectiles on flat silicon carbide targets was studied experimentally and numerically for half apex angles 5 and 5 15 , respectively, and comparisons were made with cylindrical projectiles. A 30 mm powder gun and two 150 kV and four 450 kV X-ray flashes were used in the impact tests. The numerical simulations were run with the Autodyn code in two steps. In the first, the surface loads were determined for different impact velocities under assumed condition of interface defeat. In the second, these surface loads were applied to the targets in order to obtain critical states of damage and failure related to the transition between interface defeat and penetration, and the corresponding critical velocities. In the impact tests, interface defeat occurred below a transition velocity, which was significantly lower for the conical than for the cylindrical projectiles. Above the transition velocity, the initial penetration of conical projectiles differed markedly from that usually observed for cylindrical projectiles. It occurred along a cone-shaped surface crack, qualitatively corresponding to surface failure observed in the simulations. The transition velocity for the conical projectile was found to be close to the critical velocity associated with this surface failure.
[141]
LundbergP, WesterlingL, LundbergB.1996.
Influence of scale on the penetration of tungsten rods into steel-backed alumina targets
. International Journal of Impact Engineering, 18: 403-416.
As ballistic tests are often performed in reduced geometrical scale, the scaling laws are important for the interpretation of the results. In this study, we tested the validity of replica scaling, by which we mean that all geometrical dimensions are scaled uniformly, while the materials and the impact velocity are kept the same. Long tungsten projectiles with length-to-diameter ratio 15 were fired against unconfined alumina targets with steel backing. The tests were carried out with impact velocities 1500 m sand 2500 m s, and in three different scales with projectile lengths 30, 75 and 150 mm (diameters 2, 5 and 10 mm). The alumina targets were photographed by means of a high-speed camera, and the tungsten projectiles were photographed inside the alumina targets by means of flash radiography. Also, the residual penetrations in the steel backings were measured. The Johnson-Holmquist model for ceramic materials was implemented into the AUTODYN code, which was used for simulation of the experiments. The agreement between results of experiment and simulation was fair, and over the tested interval of scales replica scaling was found to be valid with reasonable accuracy.
Deformation behavior and its relationship to the penetration performance of high-velocity KE penetrator material//Proceedings of the 1990 Army Science conference
Abstract Lagrangian finite element codes with explicit time integration are extensively used for the analysis of structures subjected to explosive loading. Within these codes, numerous material models have been implemented. However, the development of a realistic but efficient concrete material model has proven complex and challenging.The plasticity concrete material model in the Lagrangian finite element code DYNA3D was assessed and enhanced. The main modifications include the implementation of a third, independent yield failure surface; removal of the tensile cutoff and extension of the plasticity model in tension; shift of the pressure cutoff; implementation of a three invariant formulation for the failure surfaces; determination of the triaxial extension to triaxial compression ratio as a function of pressure; shear modulus correction; and implementation of a radial path strain rate enhancement. These modifications insure that the response follows experimental observations for standard uniaxial, biaxial and triaxial tests in both tension and compression, as shown via single element analyses. The radial path strain rate enhancement insures constant enhancement for all those tests. As a full scale example, a standard dividing wall subjected to a blast load is analyzed and the effects of the modifications assessed.
[145]
Mcglaun JM, Thompson SL, Elrick MG.1990.
CTH: A three-dimensional shock wave physics code
. International Journal of Impact Engineering, 10: 351-360.
An experimental method to compare the ballistic efficiencies of different ceramics against long rod projectiles//Proceedings of the 11th International Symposium on Ballistics,
We report a direct observation of the ''streamline'' reversal of eroded rod material proposed by Allen and Rogers in 1961 [1]. Allen and Rogers suggested that the ''turning'' of high-velocity long-rod penetrator material at the target interface could be viewed as a reversal of the direction of a ''streamline'' with only a change of sign in the velocity. Allen and Rogers' streamline reversal model has two important consequences. First, the eroded debris has a speed of v=2u - v relative to the target, where v is the impact velocity and u is the speed of penetration of the rod relative to the target. Secondly, a consequence of v=2u - v is that the length of the rod debris, l, is given by the difference in the initial length of the rod, l, and the remaining length of the rod, l, i.e., l=l- l. Results of a time-resolved experiment for a tungsten penetrator into a polycarbonate target at 3.61 km/s and a corresponding numerical simulation are consistent with streamline reversal. Numerical simulations are then used in a parametric study to investigate the effects of various density ratios between penetrator and target materials.
[151]
Orphal DL, Anderson Jr. CE.2006.
The dependence of penetration velocity on impact velocity
. International Journal of Impact Engineering, 33: 546-554.
Recent experimental measurements show that eroding long-rod penetration velocity is a linear function of impact velocity over a very wide range of impact velocities and for an interesting range of rod–target material combinations. These experiments all show that U= a+ bV, where U and V are the penetration and impact velocity, respectively, and “ a” and “ b” are constants for given projectile and target materials. Numerical simulations also show that U= a+ bV. The accumulation of these results suggests that a linear relationship between penetration and impact velocity may be fundamental over a very large range of impact velocities. A linear relationship between penetration and impact velocity has a number of implications. Some implications of this result for the Tate–Alekseevskii model are briefly examined in this paper.
[152]
Orphal DL, Anderson Jr. CE, BehnerT, Templeton DW.2009.
Failure and penetration response of borosilicate glass during multiple short-rod impact
. International Journal of Impact Engineering, 36: 1173-1181.
In Anderson Jr CE, Orphal DL, Behner T, Templeton, DW [Failure and penetration response of borosilicate glass during short-rod impact. Int J Impact Eng 2009, doi:10.1016/ j.ijimpeng.2008.12.002.] it was demonstrated that the failure front (FF) produced by the penetration of a borosilicate glass target by a gold rod ceased to propagate a short time after the rod was fully eroded. This strongly suggests that progression of the FF is not described by a wave equation. Here it is shown that propagation of the FF is reinitiated if a second co-axial rod, spaced a distance from the first, impacts the glass at the bottom of the penetration channel. The experiments were performed in reverse ballistic mode with two short rods spaced apart. In some experiments both rods were gold; in other experiments, one rod was copper and the other gold. FF propagation was measured using high-speed photography; rod penetration was measured using multiple, independent flash X-rays. Much of the observed phenomenology can be modeled assuming that the rod, either first or second, “communicates” with the FF at a speed corresponding to the bulk sound speed of the undamaged glass.
[153]
Orphal DL, Anderson Jr. CE, Franzen RR, Babcock SM.1995.
Variation of crater geometry with projectile $L/D$ for $L/D \leq 1$
. International Journal of Impact Engineering, 17: 595-604.
Abstract A series of hydrocode calculations and terminal ballistics experiments were performed to investigate the penetration mechanics of projectiles with L/D 1. Projectile L/D ranged from 132 to 1; impact velocity ranged from 1.5 to 5 km/s. Projectiles were tungsten or tungsten alloy, targets were RHA. The paper concentrates on the effect of projectile L/D on the size and geometry of the target crater. Normalized crater depth (or penetration) increases with decreasing projectile L/D and achieves a maximum at about LD=18 for 1.5 km/s and 116 for 3 km/s, and then decreases with further decrease in L/D. For 5 km/s, PL increases with decreasing L/D over the entire range studied. PL scales with impact velocity as PL Vf(LD) where, we believe, f(LD) approaches 2 as L/D 0. The ratio of crater to projectile diameter DcD decreases with decreasing L/D and approaches a value of 1 as L/D approaches zero for all velocities studied. The crater shape measured by PDc decreases with decreasing L/D; i.e., as L/D decreases, the crater changes from approximately hemispherical for LD = 1 to a very shallow disk shape. The kinetic energy required per unit crater volume, KEVc, increases with decreasing L/D for LD < 14. That is, cratering efficiency decreases with decreasing projectile L/D. For the impacts studied, KEVc increases from about 5 kJ/cm3 to 12 kJ/cm3 as projectile L/D is reduced from 1 to 132.
[154]
Orphal DL, Anderson Jr. CE, Franzen RR, Walker JD, Schneidewind PN, Majerus ME.1993.
Impact and penetration by $L/D\leq 1$ projectiles
. International Journal of Impact Engineering, 14: 551-560.
Calculations of steel target penetration by L/D ≤ 1 tungsten and tungsten alloy projectiles have been extended to ja:math over the velocity range 1.5 to 5 km/s. The ratio of crater to projectile diameter tends to 1 as L/D decreases over this entire velocity range. For impact velocities of 1.5 and 3 km/s, penetration depth normalized by projectile length, P/L, increases with decreasing projectile L/D up to a maximum value and then decreases for still lower L/D. Experiments at impact velocities of 2 and 3 km/s confirm these results. For 5 km/s impact velocity, the calculations show P/L increasing with decreasing projectile L/D over the entire range ja:math . The projectile L/D for which the maximum P/L occurs appears to depend on the impact velocity. P/L generally scales with impact velocity as P/L 65 v f(L/D) where f(L/D) ranges from 0 for a long rod to, we believe, 2 in the limit as projectile L/D approaches zero. The calculations show for ja:math ; for ja:math ; and for ja:math , the new results give P/L 65 v 1.9 .
[155]
Orphal DL, Franzen RR.1990.
Penetration mechanics and performance of segmented rods against metal targets
. International Journal of Impact Engineering, 10: 427-438.
Terminal ballistic experiments confirm theoretical predictions that a segmented rod will penetrate a semi-infinite metal target deeper than a continuous rod of the same material and having equal mass, diameter and velocity. For copper segmented rods impacting aluminum targets and tantalum segmented rods impacting 4340 (BHN 300) steel, penetration depths of at least 50 percent greater than that for a corresponding continuous rod are measured at impact velocities of 4 to 5 km/s. Spacing between segments of only about 2.5 segment diameters or more are required to achieve these results. Reducing the Li/D of the segments to less than 1 improves the penetration efficiency of a segmented rod. For segmented rods with segment L i/D < 1, experiments suggest that penetration may increase with impact velocity rate greater than V 2 3.
[156]
Orphal DL, Franzen RR.1997.
Penetration of confined silicon carbide targets by tungsten long rods at impact velocities from 1.5 to 4.6km/s
. International Journal of Impact Engineering, 19: 1-13.
Forty terminal ballistics experiments were performed to measure the penetration of simple confined boron carbide targets by long tungsten rods. Impact velocities ranged from 1.5 to about 5.0km/s. The experiments were performed in the reverse ballistic mode using a two-stage light-gas gun. For tests with velocities 1.493≤v≤2.767km/s, the penetrator diameter was 1.02mm (0.040inch). For tests with impact velocities v≥2.778km/s the penetrator diameter was 0.762mm (0.030 inch). For tests in the velocity range 2.335 < v< 2.761 km/s both penetrator sizes were used. The length-to-diameter ratio for the penetrator was L/D = 20 for all but the three highest velocity tests; in these three tests L/D = 15. Primary instrumentation for these experiments was four independently timed, 450 kV flash X-rays. These X-rays provided four views of the penetrator-target interaction during the penetration event from which he following data were determined: p = penetration depth as a function of time, L
Five small scale reverse ballistic tests were performed to examine the effects of a thin-walled surrounding tube and/or lexan spacers between segments on the penetration mechanics and performance of tantalum segmented rods against steel targets. Impact velocity was 4.5–5 km/s. The data, although few, suggest that such structures as surrounding tubes and segment spacers do not necessarily degrade the penetration performance of segmented rods.
In designing targets for laboratory long-rod penetration tests, the question of lateral confinement often arises, How wide should the target be to exert enough confinement? For ceramic targets, the problem is enhanced as ceramics are usually weak in tension and therefore have less self-confinement capability. At high velocities the problem is enhanced even more as the crater radius and the extent of the plastic zone around it are larger. Recently we used the quasistatic cavity expansion model to estimate the resistance of ceramic targets and its dependence on impact velocity [1]. We validated the model by comparing it to computer simulations in which we used the same strength model. Here we use the same approach to address the problem of lateral confinement. We solved the quasistatic cavity expansion problem in a cylinder with a finite outside radius b at which
[162]
Piekutowski AJ.1996.
Formation and description of debris clouds produced by hypervelocity impact. National Aeronautics and Space Administration
We performed a series of depth-of-penetration experiments using 7.11-mm-diameter, 71.12-mm-long, ogive-nose steel projectiles and 254-mm-diameter, 6061-T6511 aluminum targets. The projectiles were made from vacuum-arc remelted (VAR) 4340 steel (R c 38) and AerMet 100 steel (R c 53), had a nominal mass of 0.021 kg, and were launched using a powder gun or a two-stage, light gas gun to striking velocities between 0.5 and 3.0 km/s. Since the tensile yield strength of AerMet 100 (R c 53) steel is about 1.5 times greater than VAR 4340 (R c 38) steel, we were able to demonstrate the effect of projectile strength on ballistic performance. Post-test radiographs of the targets showed three different regions of penetrator response as the striking velocity increased: (1) the projectiles remained rigid and visibly undeformed; (2) the projectiles deformed during penetration without nose erosion, deviated from the target centerline, and exited the side of the target or turned severely within the target; and (3) the projectiles eroded during penetration and lost mass. To show the effect of projectile strength, we present depth-of-penetration data as a function of striking velocity for both types of steel projectiles at striking velocities ranging from 0.5 and 3.0 km/s. In addition, we show good agreement between the rigid-projectile penetration data and a cavityexpansion model.
Some modifications to the Holmquist ohnson ook (HJC) model (1993) for concrete under impact loading conditions are proposed. First, the pressure-shear behaviour is enhanced by including the influence of the third deviatoric stress invariant to take into account the substantial shear strength difference between the tensile and compressive meridians. Second, the modelling of strain-rate sensitivity is slightly changed so that the strain-rate enhancement factor goes to unity for zero strain rate. Third, three damage variables describing the tensile cracking, shear cracking and pore compaction mechanisms are introduced. A critical review of the constitutive model with alternative proposals for parameter identification is given. The model parameters are obtained for two concrete qualities, and perforation of concrete slabs is considered numerically and compared with experimental results from the literature. Ballistic limit assessments with deviations under 8% when compared to the experimental results are obtained, indicating that the modified version of the HJC concrete model represents a good compromise between simplicity and accuracy for large-scale computations of concrete plates impacted by projectiles.
[165]
Rajendran AM.1994.
Modeling the impact behavior of AD85 ceramic under multiaxial loading
. International Journal of Impact Engineering, 15: 749-768.
This report presents an advanced constitutive model to describe the complex behavior of ceramic materials under impact loading conditions. The governing equations utilize a set of microphysically based constitutive relationships to model deformation and damage processes in a ceramic. The total strain is decomposed into elastic, plastic, and microcracking components. The model parameters for AD85 ceramic were determined using the data from split Hopkinson bar (SHB) and bar-on-bar experiments under uniaxial stress state and plate impact experiment under uniaxial strain state. To further validate the generality of the model parameters, modeling of a diagnostic ballistic experiment in which a steel projectile impacted an AD85 ceramic front-faced thick aluminum plate was considered. In this experiment, stress histories were measured in the target by embedded manganin and carbon stress gauges. The results from the numerical simulations of the ballistic experiment using a shock wave propagation based finite element code successfully matched the measured stress history.
[166]
Rajendran AM, Grove DJ.1996.
Determination of Rajendran-Grove Ceramic Constitutive Model Constants/
This paper presents a methodology to determine the constitutive/damage model constants for silicon carbide for penetration modeling applications. The ceramic constitutive model describes the total strain as the sum of elastic, plastic, and microcracking components. There are effectively nine model constants to be determined. Six constants are adequate to describe the microcracking strain. The pulverized ceramic strength is described through one constant. The plastic strain description involves two which can be determined from a flow stress vs. strain rate plot. By matching the measured velocity vs. time or stress vs. time profiles from plate impact experiments with numerical simulations, the microcracking model constants can be determined. The fracture toughness value is available in material handbooks. In a two dimensional hydrocode analysis, the pulverized ceramic strength model parameter is adjusted to match the measured depth of penetration in a ballistic test.
Ballistic tests are performed by shooting both tungsten fiber/bulk metallic glass W/Zr58Ti13Cu17Ni12 composite rods (composite rod) and tungsten heavy alloy rods (95W rod) into 30CrMnMo target. The composite rod exhibits self-sharpening behaviors, and its matrix damages and fibers break are limited in a thin, narrow area, which is defined as “edge layer”. Penetrating depth of composite rods is 50% deeper than the depth of 95W rods with same dimension size.
[169]
RosenbergZ.1993.
On the relation between the Hugoniot elastic limit and the yield strength of brittle materials
The ricochet of eroding long rods, from inclined steel targets, is investigated by a series of three-dimensional (3D) numerical simulations. These are compared with the predictions of our, previously published, analytical model for ricochet. The agreement between simulation results and model predictions is excellent, strongly enhancing our simple ricochet model. We also highlight several aspects of our model which are derived from its simple closed form. One of these is the fact that ricochet of long rods can take place only at velocities and obliquities which are higher than certain threshold values. Otherwise, the process involves rod bending and sliding along the target impact face.
[171]
RosenbergZ, AshuachY, YeshurunY, DekelE.2009.
On the main mechanisms for defeating AP projectiles, long rods and shaped charge jets
. International Journal of Impact Engineering, 36: 588-596.
Some of the important mechanisms for defeating various projectiles and shaped charge are reviewed in this paper. These mechanisms are based on the compressive strength of the target material (its inherent resistance to penetration) and on the asymmetrical forces which it exerts on the threat, through proper geometrical arrangements. We discuss the basic features of the resistance to penetration, starting with the classical analysis of the cavity expansion process in elasto-plastic solids. This property of the target is responsible for the deceleration of hard cored projectiles and for the erosion of long rods, under normal impact conditions. We then discuss the asymmetrical interaction of armor piercing (AP) projectiles, long rods and shaped charge jets with inclined plates (stationary and moving). These asymmetric forces, exerted on the impacting threat, are responsible for their deflection and breakup. Our work combines experimental observations with numerical simulations and engineering models, which highlight the basic mechanisms behind these complex situations. This understanding is necessary for optimizing the performance of any armor design against a given threat.
[172]
RosenbergZ, DekelE.1994a.
The relation between the penetration capability of long rods and their length to diameter ratio
. International Journal of Impact Engineering, 15: 125-129.
Recent experimental studies, on the penetration of long rods into semi-infinite steel targets, reveal some features which cannot be predicted by the conventional 1-D penetration model of Alekseevskii and Tate. This paper presents experimental results together with 2-D simulations which were performed in order to investigate this discrepancy. Specifically we are interested in the question of whether the normalized penetration curve—P/L (P is penetration depth, L is penetrator length)—is dependent on penetrator's length to diameter ratio in the range of L/D = 10–40. Both experimental and simulation results show a decrease of about 15% between P/L values for L/D = 10 and 20 rods as well as for L/D = 20 and 30. These, rather large, differences are discussed in terms of material parameters which are resonsible for the discrepancy between the 1-D model and both experiment and simulation. Moreover, we have simulated the penetration of long rods having zero yield strength. Our results show that for large aspect ratios (L/D > 30) these weaker rods penetrate more than those with their full yield strength. This crossover phenomenon is both counterintuitive as well as opposed to the predictions of the 1-D model for this combination of rod-target materials.
[173]
RosenbergZ, DekelE.1994b.
A critical examination of the modified Bernoulli equation using two-dimensional simulations of long rod penetrators
. International Journal of Impact Engineering, 15: 711-720.
Abstract The modified Bernoulli equation is examined through a series of two-dimensional simulations of long rods penetrating semi-infinite targets. These are copper, aluminium and tungsten alloy rods having zero strength with length-to-diameter ratios of 20. The targets are steel and tungsten alloy with yield strengths in the range of 0 2 GPa. Impact velocities were varied between 1 and 7 km/s. Each simulation results in a definite value for the steady-state penetration velocity, which is substituted in the modified Bernoulli equation to derive an effective resistance to penetration (Rt). The dependence of Rt on target yield strength, impact velocity and projectile and target characteristics is determined.
[174]
RosenbergZ, DekelE.1996.
A computational study of the influence of projectile strength on the performance of long-rod penetrators
. International Journal of Impact Engineering, 18: 671-677.
Two-dimensional numerical simulations were used to explore the penetration capability of long-rods as a function of their strength. Tungsten alloy rods of varying strengths were ‘shot’ at semi-infinite armor steel targets in the velocity range of 1.4–2.2 km/s. It is found that penetration depths versus penetrator strength curves have a maximum which depends on the impact velocity. This effect which, to our best knowledge, has not been reported previously can be explained, at least qualitatively, by considering the deceleration of the rear part of the rod, as its strength increases. This deceleration can lead to a substantial decrease in the velocity of the rear part of the penetrator with the result that its penetration capability is reduced beyond that of a nondecelerating penetrator. The deceleration is a direct consequence of the elastic waves travelling along the back part of the rod with an amplitude which is equal to the strength of the penetrator material.
[175]
RosenbergZ, DekelE.1998.
A computational study of the relations between material properties of long-rod penetrators and their ballistic performance
. International Journal of Impact Engineering, 21: 283-296.
The paper summarizes a series of two-dimensional numerical simulations which were performed to study the effects of material properties on the terminal ballistics of long-rod penetrators. Our focus was on the properties of the rod material, unlike recent works which concentrated on a target properties. We varied almost all the relevant parameters within a large range of values in order to study the separate effects of each one. These parameters included: compressive and tensile strengths, elastic moduli, melting temperatures and the maximum equivalent plastic strain (failure strain) of the rod material. Most of the simulations were performed for an actual experiment with 300 mm tungsten-alloy long-rod, impacting a semi-infinite steel target. The simulations show that the mechanical and thermal softening mechanisms are the most dominant, as far as the depth of penetration is concerned. In contrast, the elastic moduli and spall strength have a negligible effect as far as penetration depth is concerned.
[176]
RosenbergZ, DekelE.1999.
On the role of nose profile in long-rod penetration
. International Journal of Impact Engineering, 22: 551-557.
The superiority of depleted uranium on tungsten-alloy penetrators has recently been assigned to the self-sharpening mechanism, at the tip of the DU rods, due to the adiabatic shear failure which this material experiences. The purpose of the work presented here was to further investigate the role of deformed nose profile on the deep penetrations of long rods into semi-infinite targets. This was achieved through a series of 2-D numerical simulations and several perforation experiments where we recovered and examined the residual penetrators. The simulations were performed for rigid tungsten-alloy rods having five different nose shapes with the density and elastic properties of tungsten alloys. For the normal impact experiments we chose three rod materials: a tungsten alloy, a copper and a titanium alloy. The residual rods (after perforation of finite thickness targets) were imaged by flash X-ray and softly recovered using sand boxes. As expected, the nose shapes of these rods were very different from each other.
[177]
RosenbergZ, DekelE.2000.
Further examination of long rod penetration: the role of penetrator strength at hypervelocity impacts
. International Journal of Impact Engineering, 24: 85-102.
2D numerical simulations were performed in order to further investigate the role of penetrator strength in the interaction of long rods and semi-infinite targets. These simulations are used to highlight the reasons for several discrepancies between existing data and the well-known 1D model for penetration. In particular, the nature of the secondary penetration of high-density rods, the hydrodynamic limits of high-strength rods, and the predicted maxima in their penetration curves are discussed. The causes for these discrepancies are established by additional numerical simulations which explore the validity of the penetrator strength parameter in the analytical model as a physical entity. It is shown that this is, indeed, the weakest part of the model since it is strongly dependent on both the impact velocity of the rod and its length-to-diameter ratio.
[178]
RosenbergZ, DekelE.2001a.
More on the secondary penetration of long rods
. International Journal of Impact Engineering, 26: 639-649.
The secondary penetration of long rods, impacting semi-infinite metallic targets, has been investigated since the early 60's, both experimentally and analytically. Several models have been proposed for the extra penetration which is achieved by these rods at the later stages of the process. However, the models are of limited applicability since they cover only limited regimes of the relevant parameters. In order to further understand the phenomenon of secondary penetration, we performed a large number of numerical simulations using the PISCES 2 DELK code. These simulations dealt with the relevant parameters in large ranges of variability, such as: the rod impact velocity, its aspect ratio (L/D), as well as the densities and strengths of rod and target material. We show that the semi-empirical formulations do not account for the whole range of these parameters. Our simulations show that the strength of the rod has a major influence on the values of the secondary penetrations. In addition, these values are strongly dependent on L/D and target strength.
[179]
RosenbergZ, DekelE.2001b.
Material similarities in long-rod penetration mechanics
. International Journal of Impact Engineering, 25: 361-372.
The process of long-rod penetration into thick metallic targets is examined through a series of two-dimensional simulations. The aim of the research presented here is to uncover the inherent material similarities in this process. In particular, the search is for non-dimensional parameters which account for the depth of penetration, such as the density ratio, and the relative strengths of penetrator and target. The simulation results are in accord with existing empirical data, shedding more light on the penetration process and emphasizing the difficulties in achieving an overall normalization procedure for this process.
[180]
RosenbergZ, DekelE.2003.
Numerical study of the transition from rigid to eroding-rod penetration
The behavior of rigid long rods, during deep penetration into thick metallic targets, is quite different from that of eroding rods. These differences are discussed in the present paper, through a series of 2D numerical simulations, compared with experimental data, on steel rods impacting aluminum targets. Special emphasis is placed on the threshold impact velocity, where the rods are starting to deform. At these velocities, penetration depths of the rods decrease substantially, and we were trying to account for these reductions in our simulations. We also study the effect of rod aspect ratio (L/D) on its penetration efficiency (P/L), as well as the role of rod and target strengths and their density ratio ( _p/ _t) on this efficiency.
[181]
RosenbergZ, DekelE.2004.
On the role of material properties in the terminal ballistics of long rods
. International Journal of Impact Engineering, 30: 835-851.
The terminal ballistics of long-rod penetrators is a very complex field of research involving high pressure physics, continuum mechanics, material science and high strain rate phenomena. The research in this field is advanced through experimental data collection, engineering models, and numerical simulations. In the present paper, we summarize some of our recent work which is focused on determining the important material parameters in the interaction of long rods with various targets (both stationary and moving). Our basic goal is to be able to account for various phenomena encountered in the experiments, rather than reproduce the data very accurately. We achieve this goal by using the minimal set of material parameters which is needed in order to highlight the basic features in the interaction. We also show how 3D numerical simulations help to establish a simple model for the complex interaction between a tungsten alloy rod and a moving steel plate.
[182]
RosenbergZ, DekelE.2008.
A numerical study of the cavity expansion process and its application to long-rod penetration mechanics
. International Journal of Impact Engineering, 35: 147-154.
The paper describes a series of 2D numerical simulations which followed the cavity expansion process in an elasto- plastic solid. The results from these simulations, in terms of cavity wall motion as a function of the applied pressures inside the cavity, highlighted several issues concerning cavity expansion process and the terminal ballistics of both rigid and eroding long rods. These issues include the form of the relation between the dynamic radial stress on the cavity wall and its velocity, which can be written in a simple, normalized form, at least for the materials we simulated here. Also, the difference between target resistance to the penetration of rigid and eroding-rod penetration, was quantified with a series of simulations in which the pressures in the cavity were applied on an angular section, rather than on its whole surface. Finally, we explored the inherent differences between spherical and cylindrical cavity expansion processes, which can be helpful for analytical models of the penetration of rigid rods with different nose shapes.
[183]
RosenbergZ, DekelE.2010.
On the deep penetration of deforming long rods
. International Journal of Solids & Structures, 47: 238-250.
A series of 2D numerical simulations was performed in order to follow various features in the penetration mechanics of deforming long rods. In particular, we were interested in the threshold velocity which marks the transition from rigid to deforming rod and the resulting depths of penetration around this transition velocity. We simulated various cases in which we varied the yield strengths of the rod and the target, as well as their densities and the nose shape of the rod. With the results of these simulations we constructed a rather simple model which accounts for the threshold velocity from rigid to deforming rod behavior. This model predictions are in good agreement with both our simulations and with experimental data for various rods and targets.
One of the most complex processes, in the field of terminal ballistics, is that of yawed impact of long rods. In spite of many experimental observations, and some analytical modeling, a clear picture of this issue is still lacking. In order to gain some insight into the operating mechanisms, we developed a simple engineering model which considers the yawed rod as a series of small disks. We then define the effective length and diameter of the rod by considering those disks which are going to hit the initial crater which is opened by the impact. We also performed a series of 3D numerical simulations with various L/D tungsten alloy rods impacting a steel target, at yaws in the full range of 0-90^circ. We analyzed the results of these simulations in terms of the normalized penetration (P/D), where D is the rod diameter, and looked for systematic trends in the results for the various rods. The agreement between our model predictions and both experimental data and simulation results is quite good. Based on this agreement we can highlight some new features of the penetration process of yawed rods.
A series of terminal ballistics experiments and 2-D simulations, with small scale tungsten alloy penetrators, was performed in order to quantify the ballistic efficiency of confined ceramic tiles. The data includes both depth of penetration (DOP), into thick steel backing and X-ray shadowgraphs during the penetration process. Impact velocities ranged between 1.25 to 3.0 km/s. The size of the tiles varied in order to check their performance as a function of thickness and lateral dimensions. We found that the differential ballistic efficiency of alumina tiles is practically independent on impact velocity and tile thickness, within the ranges of velocity and thicknesses, investigated here. A detailed simulation study, using the Eulerian processor of the PISCES 2-D ELK code, was performed in order to better understand the interaction between long-rods and ceramic tiles, and particularly, to adjust a proper failure criterion to the tiles. We found that a simple version of the Johnson-Holmquist model, with a single parameter, is fairly adequate to account for most of the data. These include: lateral confinement, tile thickness and impact velocity influence on the penetration depth. We used the code to further investigate the influence of lateral dimensions on tile performance.
Penetration of Tungsten-Alloy rods into composite ceramic targets: Experiments and 2-D Simulations//Proceedings of the APS conference on Shock Waves in Condensed Matter
This paper investigates the interaction of long-rod penetrators with thick ceramic tiles, sandwiched between steel plates, through several model experiments and 2-D simulations. Experimental data from low velocity penetrations have been used to calibrate the relevant properties of the ceramic specimens. The influence of increasing impact velocity on tile performance was then investigated through data and simulations of shaped charge jets penetrating the ceramic. We found that the ballistic efficiency of the ceramic tile is lower against high velocity (5 km/s) long-rods, in contrast with the common thesis that their improved performance against shaped charge jets is the result of their enhanced strength. On the other hand, our simulations clearly show that, for high strength ceramics, there is a radial motion of metal and ceramic debris towards the penetration axis. This effect is, probably, the main reason for the considerable improvement in the performance of ceramic tiles against shaped charge jets.
[189]
RosenbergZ, KreifR, DekelE.1997b.
A note on the geometric scaling of long-rod penetration
. International Journal of Impact Engineering, 19: 277-283.
The paper describes a set of experiments with copper and tungsten alloy long-rods, which were aimed at finding the sources of non-scaling effects recently discovered in terminal ballistics. Our basic assumption was that geometrical scaling should hold for ductile penetrators (like copper) and that any deviation from this scaling should be attributed to brittle failure mechanisms at the penetrator's head. Our experimental results support this assumption as far as the depth of penetration into steel of two penetrators, differing by a factor of 2, is considered. Thus, copper penetrators scaled well, within experimental error, while a difference of about 10% was found between the depth of penetration of 1:2 and 1:4 tungsten alloy penetrators. We also present two-dimensional simulations, which were performed with the PISCES 2DELK code, in order to determine lateral edge effects. These simulations enabled us to choose the right size for our “infinite” targets, avoiding any influence from their lateral-free surface.
[190]
RosenbergZ, MarmorE, MayselessM.1990.
On the hydrodynamic theory of long-rod penetration
. International Journal of Impact Engineering, 10: 483-486.
The hydrodynamic theory of long-rod penetration is reexamined by applying the modified Bernoulli equation to the forces acting on both sides of the moving rod-target interface. Using a ratio of 2 for the effective cross sectional areas of the mushroomed and rigid parts of the rod, it is shown that analytical expressions can be used to calculate the resistance to target penetration. The analytical expression used to calculate this resistance is the cylindrical cavity expansion, which yields resistance values of 3 4 times the compressive yield strength of the target material. Calculations based on our model show good agreement with experimental data, for steel and tungsten long rods penetrating various steel targets.
[191]
RosenbergZ, TsaliahJ.1990.
Applying Tate's model for the interaction of long rod projectiles with ceramic targets
. International Journal of Impact Engineering, 9: 247-251.
The penetration of ceramic tiles by long rod penetrators is discussed in terms of the modified hydrodynamic theory of A. Tate which was developed for thick metallic targets. The resistance of the tile to penetration is determined with the threshold velocity for the penetration of a very large ceramic block. According to Tate's theory, the threshold impact velocity for a given projectile (with a well defined strength) depends only on the tile's resistance to penetration. We show here that using three different projectiles (copper, steel and tungsten) resulted in the same value for this parameter for thick alumina tiles. This fact strongly enhances the idea of applying Tate's theory to ceramics. A different set of experiments, with relatively thin tiles bonded to thick steel plates, was performed determining penetration depths of the long rods into the steel backing. These were compared with predictions based on Tate's model using the values for the penetration resistance, which were determined by thick tile experiments. The good agreement can be considered as a further confirmation of our main thesis. Resistance of penetration parameters ( R t) were determined for other ceramics (silicon carbide, titanium diboride, etc.) by measuring the penetration depths of the long rod projectile into the thick backing and using Tate's model with R t as a parameter.
[192]
RosenbergZ, YeshurunY, MayselessM.1989.
On the ricochet of long rod projectiles//Proceedings of the 11th international symposium on ballistics
Ballistic tests with armor piercing projectiles on different ceramic tiles are presented. The tests were conducted using the thick-backing configuration, which is a new experimental technique to evaluate ballistic efficiencies of ceramic tiles. The residual penetration of the projectile into a thick metallic backing plate, which supports the ceramic tile, is measured. It is shown that the ballistic efficiencies of the different tiles increase monotonically with their normalized effective strength. This strength parameter is defined as the average of the static and dynamic compressive strengths divided by the density of the ceramic. A simple analysis is presented which accounts for the linear dependence of the ballistic efficiency on the normalized effective strength.
[194]
SadanandanS, Hetherington JG.1997.
Characterisation of ceramic/steel and ceramic/aluminium armours subjected to oblique impact
. International Journal of Impact Engineering, 19: 811-819.
This paper investigates the performance of alumina/5083 aluminium, and alumina/Grade 43A steel armours when subjected to oblique impact by 7.62 mm Swedish FFV Armour Piercing, and U.K. Ball ammunition. It also describes the failure mechanism of composite targets and highlights the differences in Ball and AP attacks. It was found that the ballistic limit velocity ( V 50 ) increased with obliquity. In the majority of cases a weight penalty was incurred when such armour was inclined to attack. The results obtained were compared with predictions from both theoretical and empirical models and showed reasonable correlation. The theoretical model is based on an assumed failure mechanism which describes the observed deformation patterns. The empirical relationships are based on root cosine and root secant expressions [i.e. (AD(06)AD(n) = cos0.5 06), and (V50(θ)V50(n) = sec0.5 06)] and provide an effective tool in armour design.
[195]
SatapathyS.2001.
Dynamic spherical cavity expansion in brittle ceramics
. International Journal of Solids & Structures, 38: 5833-5845.
In this paper we derived the pressure required to open a spherical cavity in an infinite brittle ceramic at a constant speed. The ceramic material is assumed to crack upon reaching its elastic limit. Subsequent failure of the cracked material due to compressive failure renders pulverization of the material. The pulverized material is assumed to follow a Mohr oulomb type constitutive behavior. The results show that at high cavity expansion speeds the comminuted region outruns the cracked region, i.e. the cracked region disappears. At very high cavity expansion speeds the comminuted zone propagation speed saturates at a level slightly below the longitudinal wave speed. Limited comparison with experimental penetration resistance shows reasonable agreement between theory and experiment.
[196]
Satapathy SS, Bless SJ.2000.
Cavity expansion resistance of brittle materials obeying a two-curve pressure--shear behavior
We derived a closed-form solution for the pressure required to open a spherical or a cylindrical cavity in brittle materials which demonstrate a two-curve pressure hear behavior. The material is allowed to crack under tension and fail under shear; only both failure modes result in comminution. Since the cavity expansion pressure is closely related to the penetration resistance of a target material, this solution identifies the material parameters that are important in impact and penetration problems. It is found that cracking and comminution can be prevented when a large enough confinement pressure is present, and the resulting high cavity expansion resistance could explain the intriguing phenomenon of interface defeat. The effects of dilatancy, and shear strength of comminuted ceramic on cavity expansion pressure are explicitly revealed.
[197]
Segletes SB, Walters WP.2003.
Extensions to the exact solution of the long-rod penetration/erosion equations
. International Journal of Impact Engineering, 28: 363-376.
The exact solution to the long-rod penetration equations is revisited, in search of improvements to the solution efficiency, while simultaneously enhancing the understanding of the physical parameters that drive the solution. Substantial improvements are offered in these areas. The presentation of the solution is simplified in a way that more tightly unifies the special- and general-case solutions to the problem. Added computational efficiencies are obtained by expressing the general-case solution for penetration and implicit time in terms of a series of Bessel functions. Other extensions and efficiencies are addressed, as well.
Experimental and numerical investigation of the ricocheting of projectiles from metallic surfaces//Proceedings of the 6th international symposium on ballistics
The protection capability of a flying steel plate against obliquely impacting tungsten heavy alloy long‐rod penetrators was simulated using the NET3D code as a function of plate velocity ranging from 610.5 to 0.5 km/sec at an obliquity of 60°. The negativity in plate velocity was assigned if the plate had a velocity component in the direction of penetrator progress. Based on the residual kinetic energy of the penetrator after perforating the plate, the protection capability of the plate increased as the plate velocity decreased to a negative value at both a normal ordnance velocity (1.5 km/sec) and a hypervelocity (2.5 km/sec) impact. The defeat capability of the oblique plate increased as the impact velocity increased in the plate velocity range studied in this work. The interaction mechanisms between the penetrator and steel plate, responsible for these results, were investigated. The physical meaning of the results obtained in this work were discussed in the light of sensor‐activated and reactive armours.
[200]
Silsby GF.1984.
Penetration of semi-infinite steel targets by tungsten rods at 1.3 to 4.5km/s//Proceedings of the 8th International Symposium on
Ballistics.
[201]
Silsby GF, Roszak RJ, Giglio-TosL.1983.
BRL's 50mm high pressure powder gun for terminal ballistic testing-the first year's experience
. Ballistic Research Laboratory Report No. BRL-MR-03236.
A simplified approximate model considering rod/target material's compressibility is proposed for hypervelocity penetration. We study the effect of shockwaves on hypervelocity penetration whenever the compressibility of the rod is much larger, analogously, and much less than that of the target, respectively. The results show that the effect of shockwaves is insignificant up to 12 km/s, so the shockwave is neglected in the present approximate model. The Murnaghan equation of state is adopted to simulate the material behaviors in penetration and its validity is proved. The approximate model is finally reduced to an equation depending only on the penetration velocity and a simple approximate solution is achieved. The solution of the approximate model is in agreement with the result of the complete compressible model. In addition, the effect of shockwaves on hypervelocity penetration is shown to weaken material's compressibility and reduce the interface pressure of the rod/target, and thus the striking/protective performance of the rod/target is weakened, respectively. We also conduct an error analysis of the interface pressure and penetration efficiency. With a velocity change of 1.6 times the initial sound speed for the rod or target, the error of the approximate model is very small. For metallic rod-target combinations, the approximate model is applicable even at an impact velocity of 12 km/s.
[203]
Song WJ, Chen XW, ChenP.
2017b. The effects of compressibility and strength on penetration of long rod and jet
We further consider the effect of rod strength by employing the compressible penetration model to study the effect of compressibility on hypervelocity penetration. Meanwhile, we define different instances of penetration efficiency in various modified models and compare these penetration efficiencies to identify the effects of different factors in the compressible model. To systematically discuss the effect of compressibility in different metallic rod-target combinations, we construct three cases, i.e., the penetrations by the more compressible rod into the less compressible target, rod into the analogously compressible target, and the less compressible rod into the more compressible target. The effects of volumetric strain, internal energy, and strength on the penetration efficiency are analyzed simultaneously. It indicates that the compressibility of the rod and target increases the pressure at the rod/target interface. The more compressible rod/target has larger volumetric strain and higher internal energy. Both the larger volumetric strain and higher strength enhance the penetration or anti-penetration ability. On the other hand, the higher internal energy weakens the penetration or anti-penetration ability. The two trends conflict, but the volumetric strain dominates in the variation of the penetration efficiency, which would not approach the hydrodynamic limit if the rod and target are not analogously compressible. However, if the compressibility of the rod and target is analogous, it has little effect on the penetration efficiency.
Researchers at the U.S. Army Ballistic Research Laboratory (BRL) have conducted a combined experimental and numerical research program in high-velocity penetration aimed at increasing the understanding of penetration mechanics over the striking velocity range between 1.5 and 4 km/s. A judicious combination of ballistic tests and large-scale simulations have been used to evaluate the performance of a family of both monolithic and segmented penetrators against semi-infinite rolled homogeneous armor (RHA). The results of the experimental and numerical programs are discussed.
[206]
Steinberg DJ.1987.
Constitutive model used in computer simulation of time-resolved, shock-wave data
. International Journal of Impact Engineering, 5: 603-611.
We have designed a constitutive model for use with high-speed, hydrodynamic computer codes. The model, valid at high-deformation rates, accounts for pressure and temperature dependence of the yield strength and shear modulus, work hardening, pressure-dependent melting, Bauschinger and strain-rate effects, and spall. There are a minimum number of parameters needed to implement the model, and most can be determined without recourse to shock-wave data. At Lawrence Livermore National Laboratory, we assembled a library of these material properties for 44 metals, alloys, mixtures, and compounds. Shock and release data from plate-impact experiments for Be, U, Ta, Cu, 1100-0, and 6061-T6 Al, with peak stresses from 6.4 to 230 GPa, are successfully compared against calculations.
[207]
Steinberg DJ, Cochran SG, Guinan MW.1980.
A constitutive model for metals applicable at high-strain rate
A model, applicable at high‐strain rate, is presented for the shear modulus and yield strength as functions of equivalent plastic strain, pressure, and internal energy (temperature). The parameters needed to implement the model have been determined for 14 metals. Using this model, hydrodynamic computer simulations have been successful in reproducing measured stress and free‐surface‐velocity–vs–time data for a number of shock‐wave experiments.
[208]
Steinberg DJ, Lund CM.1989.
A constitutive model for strain rates from 0.0001 to 1,000,000/s
The relationships between target material properties and the target strength term in the analytic representation of impact is examined. For ductile materials hardness is closely related to the magnitude of the strength term. It is shown that the key parameters correlating microhardness measurements in ceramics are similar to those for ductile materials. However, the strength terms that have been measured in ballistic tests are much lower than the values that would be predicted on the basis of the indentation measurements. It is found that the penetration resistance depends on the fracture toughness, where the ratio of the measured target strength term to the hardness increases with the fracture toughness of the target.
[210]
Stilp AJ, HohlerV.1990.
Experimental methods for terminal ballistics and impact physics//High Velocity Impact Dynamics
On the occasion of the Distinguished Scientist Award presentation at HVIS 1992, the technical and scientific promotion of the Impact Physics Division at EMI in the field of aeroballistics, free flight dynamics, terminal ballistics and impact physics is described. This development is closely related to the work of the recipients. The activities began in the late fifties when a small pressurized ballistic range with a gas gun was built. The problems to construct a well working facility with observation stations are reported that arose, at those early times, from the lack of experience, money and suitable locations. In the mid-sixties, the experimental possibilities were extended by building a two-stage light gas gun that could also be used as a gun tunnel. These facilities have been the foundation for research in the field of free flight aerodynamics, such as the study of near and far wakes behind a blunt hypersonic body or the study of shock wave boundary layer interactions. In 1972, th e division took the first step into terminal ballistics and, because of increasing interest, impact physics became the main research area. The division grew and with it the instrumentation. Today, diverse gas guns, powder guns and two-stage light gas guns are in operation. One topic of main interest during the years has been the penetration of rod shaped projectiles. Here the best-known result may be mentioned, the so-called 'Hohler-Stilp S-shaped penetration curves`. In addition to this, many other topics have been investigated that can be summarized under the title "penetration mechanics and impact physics". Based on a well developed launching technique and instrumentation, problems were investigated at low velocities of a few hundred m/s, at ordnance velocities and especially at hypervelocities up to 10 km/s. It has been recognized that dynamic material behavior and microstructural effects play an important role in understanding the interaction of projectiles with targets. Therefore , a VISAR, an electronic raster microscope, a Hopkinson bar and further equipment have been installed. Basing on the work of a period of more than 20 years, EMI has come into contact with national and foreign institutions and has become a partner for many cooperations.
[212]
SubramanianR, Bless SJ.1995.
Penetration of semi-infinite AD995 alumina targets by tungsten long rod penetrators from 1.5 to 3.5km/s
. International Journal of Impact Engineering, 17: 807-816.
In tests in which the ratio of target diameter to penetrator diameter was reduced to 15, R t , dropped by 30% to 50%. When a steel coverplate was used, total interface defeat occurred at 1.5 km/s.
[213]
SubramanianR, Bless SJ, CazamiasJ, BerryD.1995.
Reverse impact experiments against tungsten rods and results for aluminum penetration between 1.5 and 4.2km/s
. International Journal of Impact Engineering, 17: 817-824.
Reverse impact experiments against 0.76 mm diameter L/D = 20 tungsten rods have been conducted with a 38 mm diameter launch tube, two-stage light-gas gun using four 450 kV flash X-rays to measure penetration rates. Techniques for projectile construction, sample placement, alignment, and radiography are described. Data for penetration rate, consumption velocity, and total penetration were obtained for 28 mm diameter 6061-T651 aluminum cylinders at impact velocities between 1.5 and 4.2 km/s. It was found that penetration velocity was a linear function of impact velocity over this velocity range. Above 2 km/s impact velocity, penetration was completely hydrodynamic. There was substantial secondary penetration, and the total penetration increased linearly with impact velocity over the range 1.5 to 2.5 km/s.
[214]
TateA.1967.
A theory for the deceleration of long rods after impact
. Journal of the Mechanics & Physics of Solids, 15: 387-399.
A modified hydrodynamic theory which takes some account of strength effects is used to predict the deceleration of a long rod after striking a target. The results are then compared with experimental data from X-ray observations.
[215]
TateA.1969.
Further Results in the Theory of Long Rod Penetration
. Journal of the Mechanics & Physics of Solids, 17: 141-150.
T he theory of long rod penetration as given in a previous paper by the author is extended to take account of the deformation of a soft rod against a rigid target and the penetration of a rigid projectile into a soft target. It is shown that it is theoretically possible to have a decrease in depth of penetration with increasing impact velocity, and a method for deducing the average radius of the hole is given. The theory is compared with experimental results.
[216]
TateA.1979.
A simple estimate of the minimum target obliquity required for the ricochet of a high speed long rod projectile. Journal of Physics. D
Abstract A simple model for the minimum obliquity required to induce ricochet of a high speed long rod projectile from a thick target plate is suggested.
[217]
TateA.1986.
Long rod penetration models & mdash: Part II. Extensions to the hydrodynamic theory of penetration
. International Journal of Mechanical Sciences, 28: 599-612.
The modified hydrodynamic theory of penetration is extended to take account of the transient, plastic-wave dominated and after-flow phases of penetration. It is also indicated how a more detailed flow field model of the primary phase of penetration leads to the modified Bernoulli equation and a relationship between the dynamic yield strength and the strength factors R t and Y p. The effect of the decelerative motion on the modified Bernoulli equation is also briefly examined. Finally, the theory is compared with experimental results of previous papers.
[218]
TateA, Green K EB, Chamberlain PG, Baker RG.1978.
Model scale experiments on long rod penetrators//Proceedings of 4th International Symposium on Ballistics, Monterey
Sophisticated numerical models are increasingly used to analyze complex physical processes such as concrete structures subjected to high-impulsive loads. Among other influencing factors for a realistic and reliable analysis, it is essential that the material models are capable of describing the material behaviour at the pertinent scale level in a realistic manner. One of the widely used concrete material models in impact and penetration analysis, the RHT model, covers essentially all macro features of concrete-like materials under high strain rate loading. However, the model was found to exhibit undesirable performance under certain loading conditions and some of the modeling issues have been discussed within a recent review paper by the authors. The present paper provides a more in-depth evaluation of the RHT model and proposes modifications to the model formulation to enhance the performance of the model as implemented in the hydrocode AUTODYN. The modifications include Lode-angle dependency of the residual strength surface, tensile softening law and the dynamic tensile strength function. The improvement of the performance of the modified RHT model is demonstrated using numerical sample tests, and further verified via simulations of two series of physical experiments of concrete penetration/perforation by steel projectiles. The results demonstrate an overall improvement of the simulation with the modified RHT model. In particular, the depth of penetration, projectile exit velocity and the crater size are predicted more favourably as compared to the test data. It is also shown that the modeling of the concrete tensile behaviour can affect sensibly the predicted perforation response (e.g., the projectile exit velocity), as is generally expected when the impact velocity exceeds the ballistic limit.
[220]
WalkerD, Anderson Jr CE.1991.
The Wilkins' computational ceramic model for CTH. SwRI Report,
As the aspect ratio (L/D) of a projectile decreases and the projectile becomes more disk like, the penetration mode changes. A model for the penetration of low L/D projectiles has been developed to explain and predict the low L/D penetration event. The model divides the penetration into two phases: first a flyer plate type impact, and second, a crater growth phase. Calculations provided insight into the physical mechanism involved. Shortly after impact, the projectile enters a long period of constant velocity penetration. This behavior leads to the depth of penetration scaling with projectile diameter. A large crater grows in the target, and the projectile travels into a debris filled crater as a free body. The velocity is frozen in when release waves arrive from the free surface. In the model, the crater in the target is analyzed by assuming plastic constitutive response, with the motion caused by an impulsive load due to the impact. The final depth of penetration is obtained by combining a one-dimensional depth of penetration and a plastic target cratering response. The model compares well with both large scale numerical simulations and experimental data.
[222]
Walker JD.1999.
An analytical velocity field for back surface bulging//Proceedings of the 18th international symposium on ballistics
, Lancaster: Technomic Publishing Co.:1239-1246.
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Walker JD.2001.
Ballistic limit of fabrics with resin//Proceedings of the 19th International Symposium on Ballistics
Tunsten into steel penetration including velocity, $L/D$, and impact inclination effects//Proceedings of the 19th international symposium on ballistics
,Interlaken Switzerland: 1133-1139.
[225]
Walker JD, Anderson Jr. CE.1994.
The influence of initial nose shape in eroding penetration
. International Journal of Impact Engineering, 15: 139-148.
The effect of projectile nose shape on penetration is examined numerically using the nonlinear, large deformation wavecode CTH. In particular, the impact of a tungsten alloy, long rod projectile into a 4340 steel target is investigated for three different nose shapes: blunt, hemispherical, and conical. The pressures are sufficiently high that erosion of the projectile begins immediately upon impact. The decays of the shocks are examined, as are the resulting material flow fields. Later-time effects are also explored, such as how the nose shape affects penetration, and how long each case takes to arrive at a quasi-steady-state flow configuration in which the tungsten-steel interface is completely determined by eroding plastic flow.
[226]
Walker JD, Anderson Jr. CE.1995.
A time-dependent model for long-rod penetration
. International Journal of Impact Engineering, 16: 19-48.
The one-dimensional, quasi-steady-state, modified Bernoulli theory of Tate [ J. Mech. Phys. Solids , 15 , 287 (1967)] is often used to examine long-rod penetration into semi-infinite targets. In general., the time histories of penetration predicted by the Tate model can be in good agreement with those computed from numerical simulations. However, discrepancies exist between the model and numerical simulations at the beginning and at the end of penetration. From insights provided by numerical simulations, assumptions are made concerning the velocity and stress profiles in the projectile and the target. Using these assumptions, the time-dependent, cylindrically-symmetric, axial momentum equation is explicitly integrated along the centerline of the projectile and target to provide the equation of motion. The model requires the initial interface velocity hich can be found, for example, from the shock jump conditions-and material properties of the projectile and target to compute the time history of penetration. Agreement between the predictions of this one-dimensional, time-dependent penetration model are in good agreement with experimental results and numerical simulations.
[227]
WaltersW, WilliamsC, NormandiaM.2006.
An explicit solution of the Alekseevski--Tate penetration equations
. International Journal of Impact Engineering, 33: 837-846.
The Alekseevski–Tate equations are typically used to predict the penetration, penetration velocity, rod velocity, and rod length of long rod penetrators and similar projectiles impacting targets. These nonlinear equations were originally solved numerically and more recently by the exact analytical solution of Walters and Segletes. However, due to the nonlinear nature of the equations, the penetration was obtained implicitly as a function of time, so that an explicit functional dependence of the penetration on material properties was not obtained. The current paper obtains the velocities, length, and penetration as an explicit function of time by employing a perturbation solution of the nondimensional Alekseevski–Tate equations. Simple (algebraic) analytical equations are given. Perturbation solutions of the Alekseevski–Tate equations were first undertaken by Forrestal et al., up to the first–order, and good agreement with the exact solutions was shown for relatively short times. In retrospect, this solution was only valid for penetrators impacting weak targets. The current study obtains a third-order perturbation solution and includes both penetrator and target strength terms, and is applicable for strong targets. The paper compares the exact solution to the perturbation solutions, and a typical comparison between the exact and approximate solutions for a tungsten rod impacting a semi-infinite steel armor target is shown. Also, alternate ways are investigated to normalize the governing equations in order to obtain an optimum perturbation parameter. In most cases, the third-order perturbation solution shows good agreement with the exact solution of the Alekseevski–Tate equations. In addition, simple equations based on the first–order perturbation solution are presented, which are accurate for the perforation of finite thickness (short penetration time) targets.
[228]
Walters WP, Segletes SB.1991.
An exact solution of the long rod penetration equations
. International Journal of Impact Engineering, 11: 225-231.
An exact solution is presented for the long rod penetration equations first formulated by Alekseevski in 1966 and independently by Tate in 1967. This analytical solution allows a faster and easier solution of the penetration equations, since stability considerations associated with any numerically integrated solutions are avoided. Additionally, an analytical solution provides greater insight into the penetration mechanism than a comparable numerically integrated solution.
[229]
Wang XM, Zhao GZ, Shen PH, Zha HZ.1995.
High velocity impact of segmented rods with an aluminum carrier tube
. International Journal of Impact Engineering, 17: 915-923.
Abstract In this paper, we apply the method of ballistic test to investigate the history and mechanism of the tungsten alloy segmented rod with aluminium carrier tube and corresponding continuous rod penetrating into semi-infinite steel target at velocities from 1.8 to 2.0 km / s. The length to diameter ratio of the segmented rod is 1 (LD = 1), the ratios of length of spacing between segments to diameter (s/d) are 0.5, 1.0 and 2.0 respectively. The results show that the power of penetration of the segmented rod with carrier tube is obviously higher then that of the corresponding continuous rod with carrier tube. Raising of the impact velocity, suitably increasing of the length of spacing between segments and filling the spacing with non-metallic material, etc. all can increase the penetrating power of the segmented rod. When impact velocity is 2.0 km / s, s / d=2.0, the penetrating power of the segmented rod is 10% higher than that of the corresponding continuous rod, if the spacing is filled with glass steel (non-metallic material), the power will be 20% higher. In this paper, we present a simplified model of based on hydrodynamics and penetrating mechanics. This model can properly describe the whole penetrating process of segmented rod penetrating into semi-infinite target. The shape of the crater and depth of penetration, etc. calculated are in good agreement with the results obtained by experiments.
[230]
WeerheijmJ, Van Doormaal J C A M.2007.
Tensile failure of concrete at high loading rates: New test data on strength and fracture energy from instrumented spalling tests
. International Journal of Impact Engineering, 34: 609-626.
For the numerical prediction of the response of concrete structures under extreme dynamic loading, like debris impact and explosions, reliable material data and material models are essential. TNO-PML and the Delft University of Technology collaborate in the field of impact dynamics and concrete modelling. Recently, TNO-PML developed an alternative Split Hopkinson Bar test methodology which is based on the old principle of spalling, but equipped with up-to-date diagnostic tools and to be combined with advanced numerical simulations. Data on dynamic tensile strength and, most important, on fracture energy at loading rates up to 1000 GPa/s are obtained. The paper describes the test and measurement set-up, presents the new test data and the analysis of the test results. In addition, a rate-dependent softening curve is given which is based on the integrated findings so far.
[231]
Wen HM, HeY, LanB.2010.
Analytical model for cratering of semi-infinite metallic targets by long rod penetrators
. Science China (Technological Sciences), 53: 3189-3196.
Analytical model is presented herein to predict the diameter of crater in semi-infinite metallic targets struck by a long rod penetrator. Based on the observation that two mechanisms such as mushrooming and cavitation are involved in cavity expansion by a long rod penetrator, the model is constructed by using the laws of conservation of mass, momentum, energy, together with the u-v relationship of the newly suggested 1D theory of long rod penetration (see Lan and Wen, Sci China Tech Sci, 2010, 53(5): 1364 1373). It is demonstrated that the model predictions are in good agreement with available experimental data and numerical simulations obtained for the combinations of penetrator and target made of different materials.
[232]
Wen HM, HeY, LanB.2011.
A combined numerical and theoretical study on the penetration of a jacketed rod into semi-infinite targets
. International Journal of Impact Engineering, 38: 1001-1010.
A combined numerical and theoretical study is conducted herein on the penetration of semi-infinite targets by jacketed rods with different r j 0/ r c 0 ratios where r j 0 and r c 0 are the radii of the jacket and the core, respectively. The numerical results show that for smaller r j 0/ r c 0 ratios the u– v relationship changes only a little compared to that of unitary long rod penetrator of the same core material, hence, the u– v relationship of unitary (homogeneous) long rod penetration is also applicable for jacketed rod penetration. Model for cratering in semi-infinite targets by jacketed rods is then suggested by using the laws of conversation of mass, momentum and energy, together with the u– v relationship of unitary (homogeneous) long rod penetration and an analytical model for predicting the depth of penetration has also been given for jacketed long rods penetrating semi-infinite targets in co-erosion mode. A new criterion for transition from bi-erosion to co-erosion is proposed. It transpires that the present model is in good agreement with the experimental observations for EN24 steel jacketed tungsten alloy long rods penetrating semi-infinite armor steel targets in terms of crater diameter and penetration depth.
[233]
Wen HM, LanB.2010.
Analytical models for the penetration of semi-infinite targets by rigid, deformable and erosive long rods
Segmented and telescopic projectiles are designed to make efficient use of the higher impact velocities achievable with new acceleration techniques. This concept has been found to work against steel armour. In this study, we compare the penetration capability into an alumina target for these unconventional projectiles with that of a homogeneous projectile. The influence of segment separation distance and core-to-tube diameter ratio were simulated for the impact velocities 2.5, 3.0 and 3.5 km/s. The simulated final penetrations are compared to test results for one type of each of the homogeneous, segmented and telescopic projectiles at 2.5 and 3.0 km/s. Both simulations and tests show that the unconventional projectiles have better penetration capability than a homogeneous projectile with the same initial geometry.
[235]
WesterlingL, LundbergP, LundbergB.2001.
Tungsten long-rod penetration into confined cylinders of boron carbide at and above ordnance velocities
. International Journal of Impact Engineering, 25: 703-714.
The purpose was to investigate the influence of impact velocity and confinement on the resistance of boron carbide targets to the penetration of tungsten long-rod projectiles. Experimental tests with impact velocities from 1400 to 2600 m/s were performed using a two-stage light-gas gun and a reverse impact technique. The targets consisted of boron carbide cylinders confined by steel tubes of various thicknesses. Simulations were carried out using the AUTODYN-2D code and Johnson olmquist's constitutive model with and without damage evolution. The experimental results show that the penetration process had different character in three different regions. At low-impact velocities, no significant penetration occurred. At high-impact velocities, the relation between penetration velocity and impact velocity was approximately linear, and the penetration was steady and symmetrical. In between, there was a narrow transition region of impact velocities with intermittent and strongly variable penetration velocity. In the lower part of this region, extended lateral flow of the projectile took place on the surface of the target. The influence of confinement on penetration velocity was found to be small, especially at high-impact velocities. The simulated results for penetration velocity versus impact velocity agreed fairly well with the experimental results provided damage evolution was suspended below the transition region.
[236]
YazivD, RosenbergG, PatrtomY.
Differential ballistic efficiency of applique armour
This paper presents a new analytical model developed to simulate ballistic impact of projectiles on ceramic/metal add-on armours. The model is based on Tate and Alekseevskii’s equation for the projectile penetration into the ceramic tile, whilst the response of the metallic backing is modelled following the ideas of Woodward’s and den Reijer’s models. The result is a fully new analytical model that has been checked with data of residual mass and residual velocity of real fire tests of medium caliber projectiles on ceramic/metal add-on armours. Agreement observed between experimental and analytical results confirmed the validity of the model. Therefore, the model developed can be a useful tool for optimisation of ceramic/metal armour design.
[239]
Zhang LS, Huang FL.2004.
Model for long-rod penetration into semi-infinite targets
. Journal of Beijing Institute of Technology, 13: 285-289.
Based on the equation of momentum conservation, an improved equation for the quisi-steady penetration of a long rod into homogeneous semi-infinite targets has been derived, assuming that the flow interface between the rod material and the target material is hemispherical and that the normal pressure on the interface is defined by the dynamic spherical cavity expansion. The equation has a form similar to the Tate equation, and the parameters in this equation have definite physical senses and practical values.
[240]
ZhangX, SerjoueiA, SridharI.2017.
Criterion for interface defeat to penetration transition of long rod projectile impact on ceramic armor
Numerical studies were conducted on the ballistic performance of alumina ceramic (AD95) tiles based on depth of penetration method, when subjected to normal impact of tungsten long rod projectiles at velocities ranging from 1100 to 2000 ms-1. The residual depth on after-effect target was derived in each case, and the ballistic efficiency factor was determined using the corresponding penetration depth on medium carbon steel. Anti-penetration experiment study of the AD95 ceramic tiles to tungsten long rod projectiles has been carried out to verify the accuracy of numerical simulation model. The result shows that numerical simulation results agree well with the corresponding experiment results and AD95 ceramic has excellent ballistic performance than medium carbon steel. The ballistic efficiency factor increases with velocity increasing when impact velocity lower than 1300 ms-1, and when it was higher than 1300 ms-1 the ballistic efficiency factor has almost no difference.
[243]
ZhaoJ, Chen XW, Jin FN, XuY.2010.
Depth of penetration of high-speed penetrator with including the effect of mass abrasion
. International Journal of Impact Engineering, 37: 971-979.
Mass abrasion is observed on the nose of projectile when a projectile strikes concrete target at high velocity. To evaluate the influence of the mass abrasion on the depth of penetration (DOP) limit, the relationship between the nose factor of the residual projectile after abrasion and the initial impact velocity is suggested according to the experimental data. Based on the dynamic cavity expansion theory, with considering the effects of varying nose factor and mass of projectile, a modified model is proposed to calculate the depth of penetration of kinetic energy penetrator. The model predicts that a theoretical maximum DOP exists due to the mass abrasion of the projectile. The model is checked by the different experimental data.
[244]
ZhouH, Wen HM.2003.
Penetration of bilinear strain-hardening targets subjected to impact by ogival-nosed projectiles
. Theory and Practice of Energetic Materials, 5: 933-942.
A theoretical study is presented herein on the penetration of ductile metal targets subjected to impact by ogival-nosed projectiles. The targets are made of bilinear strain-hardening materials with incompressibility. The paper consists of two parts. The first part is dynamic spherical cavity expansion model; the second is the penetration equations derived using the model. Closed-form solutions are obtained both for forces acting on the projectile nose and the depth of penetration. It is shown that the theoretical predictions are in good agreement with the available penetration data for aluminum targets subjected to impact by ogival-nosed as well as spherical-nosed projectiles.
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
... 自20世纪七八十年代起, 长杆高速侵彻领域开展了大量实验.西德恩斯特马赫研究所 (Ernst Mach Institute, EMI)的Hohler和Stilp(1977)开展的$L / D =10$钨合金长杆弹侵彻半无限厚装甲钢靶的实验成为后来检验理论模型和数值模拟的标准.Silsby(1984)进行了更大长径比 $(L/ D = 32)$和更大尺寸的实验.Hohler和Stilp(1987)总结了已发表的实验数据,讨论了侵彻深度、弹坑半径等与撞击速度、弹靶材料以及长径比的关系.其中提出的长径比效应后来成为长杆侵彻一个相当重要的特征效应.美国陆军弹道研究实验室 (Ballistic Research Laboratory,BRL)的Sorensen等(1991)总结了钨合金连续和分段长杆侵彻轧制均质钢(Rolled Homogeneous Armor, RHA)的全尺寸与半尺寸实验.美国西南研究院 (Southwest Research Institute, SwRI)的Anderson等(1992a)编辑了侵彻数据库,对此前开展的终点弹道实验数据进行了较全面的搜集整理. ...
... 开展的$L / D =10$钨合金长杆弹侵彻半无限厚装甲钢靶的实验成为后来检验理论模型和数值模拟的标准.Silsby(1984)进行了更大长径比 $(L/ D = 32)$和更大尺寸的实验.Hohler和Stilp(1987)总结了已发表的实验数据,讨论了侵彻深度、弹坑半径等与撞击速度、弹靶材料以及长径比的关系.其中提出的长径比效应后来成为长杆侵彻一个相当重要的特征效应.美国陆军弹道研究实验室 (Ballistic Research Laboratory,BRL)的Sorensen等(1991)总结了钨合金连续和分段长杆侵彻轧制均质钢(Rolled Homogeneous Armor, RHA)的全尺寸与半尺寸实验.美国西南研究院 (Southwest Research Institute, SwRI)的Anderson等(1992a)编辑了侵彻数据库,对此前开展的终点弹道实验数据进行了较全面的搜集整理. ...
... 进行了更大长径比 $(L/ D = 32)$和更大尺寸的实验.Hohler和Stilp(1987)总结了已发表的实验数据,讨论了侵彻深度、弹坑半径等与撞击速度、弹靶材料以及长径比的关系.其中提出的长径比效应后来成为长杆侵彻一个相当重要的特征效应.美国陆军弹道研究实验室 (Ballistic Research Laboratory,BRL)的Sorensen等(1991)总结了钨合金连续和分段长杆侵彻轧制均质钢(Rolled Homogeneous Armor, RHA)的全尺寸与半尺寸实验.美国西南研究院 (Southwest Research Institute, SwRI)的Anderson等(1992a)编辑了侵彻数据库,对此前开展的终点弹道实验数据进行了较全面的搜集整理. ...
... 总结了已发表的实验数据,讨论了侵彻深度、弹坑半径等与撞击速度、弹靶材料以及长径比的关系.其中提出的长径比效应后来成为长杆侵彻一个相当重要的特征效应.美国陆军弹道研究实验室 (Ballistic Research Laboratory,BRL)的Sorensen等(1991)总结了钨合金连续和分段长杆侵彻轧制均质钢(Rolled Homogeneous Armor, RHA)的全尺寸与半尺寸实验.美国西南研究院 (Southwest Research Institute, SwRI)的Anderson等(1992a)编辑了侵彻数据库,对此前开展的终点弹道实验数据进行了较全面的搜集整理. ...
Analytical models for penetration mechanics: A review
1
2017
... 国际上在长杆高速侵彻领域比较活跃的有Hohler和Stilp, Anderson,Orphal以及Rosenberg等研究组, 其所著的综述 (Anderson 2003, 2017;Orphal 2006; Stilp & Hohler 1995)和专著 (Rosenberg & Dekel 2012)侧重于介绍各自在该领域的工作进展.国内学者对长杆高速侵彻问题的研究起步较晚,但对于一些特定材料与特殊问题的研究已取得一些有意义的成果.陈小伟和陈裕泽对长杆高速侵彻陶瓷靶问题撰写了代表性综述 (陈小伟等 2006), 同时陈小伟教授课题组还在长杆高速侵彻理论 (Jiao & Chen 2018)、界面击溃效应 (Li & Chen 2017; Li et al. 2014,2015b; 李继承等 2011a, 2011b)、纤维增强金属玻璃长杆弹 (Chen et al.2015, Li et al. 2015a,李继承等 2011c, 陈小伟等 2012, 王杰等 2014)、分段杆 (郎林等 2011)和可压缩性 (Song et al. 2017a, 2017b,2018)等方面开展了一系列研究.中国科学技术大学文鹤鸣教授课题组开展了长杆侵彻的一维理论和模拟研究(He & Wen 2013; Lan & Wen 2010; Lu & Wen 2018; Wen & Lan 2010; Wen et al. 2010, 2011; Zhou & Wen 2003; 兰彬等 2008, 2009),北京理工大学黄风雷教授团队对长杆侵彻陶瓷靶、金属靶和混凝土靶开展了实验、模拟和理论研究(Zhang & Huang 2004, 张连生等 2005, 李志康和黄风雷 2010,李金柱等 2014, Li et al. 2017),南京理工大学张先锋教授课题组研究了长杆高速撞击陶瓷靶和界面击溃效应(Zhang & Li 2010; Zhang et al. 2011; 谈梦婷等 2016, 2017,2018),解放军理工大学方秦教授课题组开展了长杆高速侵彻的实验和理论分析(Kong et al. 2016b; Kong et al. 2017b, 2017c; 孔祥振等 2017;翟阳修等 2017). ...
Long-rod penetration into intact and pre-damaged SiC ceramic
3
2008
... 流体动力学理论最大的不足在于未考虑材料强度,虽然在此基础上改进的Allen-Rogers模型引入了靶体强度,但由于模型中的定常状态和不可压流体的两个假设,实验结果与模型预测仍存在偏差. Anderson和Orphal(2008)利用逆向弹道实验数据和基于CTH程序的模拟结果与流体动力学理论模型进行对比,发现在高达4km/s的速度下实验和模拟的结果仍明显低于模型预测,且在4km/s时材料强度依然存在. Anderson 和Orphal (Anderson & Orphal 2008, Orphal 2006, Orphal & Anderson 1999)通过模拟证实了不可压流体假设对模型预测的影响,随着撞击速度的提高, 可压缩性的影响增加.虽然部分实验结果与流体动力学理论预测接近, 但Orpha(2006)认为这是由于模型的过高预测和模型未考虑的第3阶段侵彻相抵消的结果.若考虑定常侵彻外还包含第3阶段侵彻,更高速度下总侵彻深度应该超过流体极限. ...
... 利用逆向弹道实验数据和基于CTH程序的模拟结果与流体动力学理论模型进行对比,发现在高达4km/s的速度下实验和模拟的结果仍明显低于模型预测,且在4km/s时材料强度依然存在. Anderson 和Orphal (Anderson & Orphal 2008, Orphal 2006, Orphal & Anderson 1999)通过模拟证实了不可压流体假设对模型预测的影响,随着撞击速度的提高, 可压缩性的影响增加.虽然部分实验结果与流体动力学理论预测接近, 但Orpha(2006)认为这是由于模型的过高预测和模型未考虑的第3阶段侵彻相抵消的结果.若考虑定常侵彻外还包含第3阶段侵彻,更高速度下总侵彻深度应该超过流体极限. ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
Interface defeat of long rods impacting oblique silicon carbide
5
2011
... 弹体通常由高密度金属 (钨、贫化铀)及其合金制成, 靶体材料差异较大,从传统金属到陶瓷 (Anderson & Morris 1992; Anderson & Royal-Timmons 1997; Behner et al. 2006; Hohler et al. 1995, Li et al. 2017, Orphal & Franzen 1997; Orphal et al. 1996, 1997;Rosenberg et al. 1995, 1997a; Subramanian & Bless 1995;Subramanian et al. 1995; Westerling et al. 2001)、玻璃 (Anderson & Holmquist 2013; Anderson et al. 2009, 2011a; Behner et al. 2008; Hohler et al. 1993; Orphal et al. 2009)以及混凝土 (Gold et al. 1996, Kong et al. 2017c, Nia et al. 2014)和编织物 (Walker 2001)等复合材料的抗侵彻性能均有实验报道. 对于直接弹道实验,需设计弹托并安装弹托回收装置 (Lundberg et al. 1996);而对于小尺寸逆向弹道实验, 需在靶体外加装密闭装置 (Kong et al.2017c, Subramanian et al. 1995) (如图6所示). 此外, 靶体尺寸(Franzen et al. 1997, Littlefield et al. 1997, Lundberg et al.1996, Rosenberg & Dekel 2000, Rosenberg et al.1997b)、约束形式 (Anderson & Royal-Timmons 1997, Partom & Littlefield 1995, Subramanian & Bless 1995,Westerling et al. 2001)和金属覆盖板 (Anderson & Royal-Timmons 1997, Subramanian & Bless 1995)等也是实验需要特别关注的问题. ...
Time-resolved penetration into glass: Experiments and computations
2
2011
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
... 自20世纪七八十年代起, 长杆高速侵彻领域开展了大量实验.西德恩斯特马赫研究所 (Ernst Mach Institute, EMI)的Hohler和Stilp(1977)开展的$L / D =10$钨合金长杆弹侵彻半无限厚装甲钢靶的实验成为后来检验理论模型和数值模拟的标准.Silsby(1984)进行了更大长径比 $(L/ D = 32)$和更大尺寸的实验.Hohler和Stilp(1987)总结了已发表的实验数据,讨论了侵彻深度、弹坑半径等与撞击速度、弹靶材料以及长径比的关系.其中提出的长径比效应后来成为长杆侵彻一个相当重要的特征效应.美国陆军弹道研究实验室 (Ballistic Research Laboratory,BRL)的Sorensen等(1991)总结了钨合金连续和分段长杆侵彻轧制均质钢(Rolled Homogeneous Armor, RHA)的全尺寸与半尺寸实验.美国西南研究院 (Southwest Research Institute, SwRI)的Anderson等(1992a)编辑了侵彻数据库,对此前开展的终点弹道实验数据进行了较全面的搜集整理. ...
... 弹体通常由高密度金属 (钨、贫化铀)及其合金制成, 靶体材料差异较大,从传统金属到陶瓷 (Anderson & Morris 1992; Anderson & Royal-Timmons 1997; Behner et al. 2006; Hohler et al. 1995, Li et al. 2017, Orphal & Franzen 1997; Orphal et al. 1996, 1997;Rosenberg et al. 1995, 1997a; Subramanian & Bless 1995;Subramanian et al. 1995; Westerling et al. 2001)、玻璃 (Anderson & Holmquist 2013; Anderson et al. 2009, 2011a; Behner et al. 2008; Hohler et al. 1993; Orphal et al. 2009)以及混凝土 (Gold et al. 1996, Kong et al. 2017c, Nia et al. 2014)和编织物 (Walker 2001)等复合材料的抗侵彻性能均有实验报道. 对于直接弹道实验,需设计弹托并安装弹托回收装置 (Lundberg et al. 1996);而对于小尺寸逆向弹道实验, 需在靶体外加装密闭装置 (Kong et al.2017c, Subramanian et al. 1995) (如图6所示). 此外, 靶体尺寸(Franzen et al. 1997, Littlefield et al. 1997, Lundberg et al.1996, Rosenberg & Dekel 2000, Rosenberg et al.1997b)、约束形式 (Anderson & Royal-Timmons 1997, Partom & Littlefield 1995, Subramanian & Bless 1995,Westerling et al. 2001)和金属覆盖板 (Anderson & Royal-Timmons 1997, Subramanian & Bless 1995)等也是实验需要特别关注的问题. ...
An examination of deviations from hydrodynamic penetration theory
1
2008
... 二维计算程序诞生于20世纪60年代, 并于七八十年代发展成熟 (Anderson 1987). 美国桑迪亚国家实验室 (Sandia National Laboratories,SNL)的二维欧拉流体动力学程序CSQ是最早用来模拟长杆侵彻问题的工具,也是三维流体动力学程序CTH的前身(McGlaun 1990). Anderson等 (Anderson & Orphal 2003,2008; Anderson & Walker 1991; Anderson et al. 1993, 1995,1996, 1999b)利用CTH对长杆侵彻作了一系列的模拟,其中Anderson和Walker(1991)对$L /D=10$钨合金长杆以1.5km/s侵彻RHA的模拟得到了比Alekseevskii-Tate模型更贴近实验的结果,他们分析了产生差异的原因,并在此基础上提出了一个与时间相关的理论模型 (Walker & Anderson 1995). 以色列防务技术研究院RAFAEL公司的Rosenberg等(Rosenberg & Dekel 1994a, 1996, 1998, 1999, 2000, 2003;Rosenberg et al. 1995, 1997a, 1998)运用2D欧拉程序PISCES2DELK进行了一系列数值模拟,分析了弹头形状、长径比、弹靶强度以及其他材料参数等因素对长杆侵彻的影响.通过数值模拟, 侵彻过程中的压力、速度和几何等细节信息得以获得.然而, 数值模拟结果与计算方法和材料本构的选取密切相关,且相关参数的选取也具有较强的人为性,故其准确性往往需要与实验和理论对比来验证. ...
Re-examination of the evidence for a failure wave in SiC penetration experiments
1
2006
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
Failure and penetration response of borosilicate glass during short-rod impact
1
2009
... 弹体通常由高密度金属 (钨、贫化铀)及其合金制成, 靶体材料差异较大,从传统金属到陶瓷 (Anderson & Morris 1992; Anderson & Royal-Timmons 1997; Behner et al. 2006; Hohler et al. 1995, Li et al. 2017, Orphal & Franzen 1997; Orphal et al. 1996, 1997;Rosenberg et al. 1995, 1997a; Subramanian & Bless 1995;Subramanian et al. 1995; Westerling et al. 2001)、玻璃 (Anderson & Holmquist 2013; Anderson et al. 2009, 2011a; Behner et al. 2008; Hohler et al. 1993; Orphal et al. 2009)以及混凝土 (Gold et al. 1996, Kong et al. 2017c, Nia et al. 2014)和编织物 (Walker 2001)等复合材料的抗侵彻性能均有实验报道. 对于直接弹道实验,需设计弹托并安装弹托回收装置 (Lundberg et al. 1996);而对于小尺寸逆向弹道实验, 需在靶体外加装密闭装置 (Kong et al.2017c, Subramanian et al. 1995) (如图6所示). 此外, 靶体尺寸(Franzen et al. 1997, Littlefield et al. 1997, Lundberg et al.1996, Rosenberg & Dekel 2000, Rosenberg et al.1997b)、约束形式 (Anderson & Royal-Timmons 1997, Partom & Littlefield 1995, Subramanian & Bless 1995,Westerling et al. 2001)和金属覆盖板 (Anderson & Royal-Timmons 1997, Subramanian & Bless 1995)等也是实验需要特别关注的问题. ...
On the hydrodynamic approximation for long-rod penetration
1
1999
... 二维计算程序诞生于20世纪60年代, 并于七八十年代发展成熟 (Anderson 1987). 美国桑迪亚国家实验室 (Sandia National Laboratories,SNL)的二维欧拉流体动力学程序CSQ是最早用来模拟长杆侵彻问题的工具,也是三维流体动力学程序CTH的前身(McGlaun 1990). Anderson等 (Anderson & Orphal 2003,2008; Anderson & Walker 1991; Anderson et al. 1993, 1995,1996, 1999b)利用CTH对长杆侵彻作了一系列的模拟,其中Anderson和Walker(1991)对$L /D=10$钨合金长杆以1.5km/s侵彻RHA的模拟得到了比Alekseevskii-Tate模型更贴近实验的结果,他们分析了产生差异的原因,并在此基础上提出了一个与时间相关的理论模型 (Walker & Anderson 1995). 以色列防务技术研究院RAFAEL公司的Rosenberg等(Rosenberg & Dekel 1994a, 1996, 1998, 1999, 2000, 2003;Rosenberg et al. 1995, 1997a, 1998)运用2D欧拉程序PISCES2DELK进行了一系列数值模拟,分析了弹头形状、长径比、弹靶强度以及其他材料参数等因素对长杆侵彻的影响.通过数值模拟, 侵彻过程中的压力、速度和几何等细节信息得以获得.然而, 数值模拟结果与计算方法和材料本构的选取密切相关,且相关参数的选取也具有较强的人为性,故其准确性往往需要与实验和理论对比来验证. ...
A penetration model for metallic targets based on experimental data
An analytical model for dwell and interface defeat
3
2005
... Lundberg等(2000)在分析钨和镆长杆侵彻陶瓷靶时发现了此现象,后续的实验和模拟 (Behner et al. 2011; Anderson & Walker 2005; Andersson et al. 2007; Lundberg & Lundberg 2005;Lundberg et al. 2006, 2013)验证了这一现象. Lundberg等(2000)提出了可能出现该现象的压力范围并得到了转变速度的区间,该转变速度取决于陶瓷靶的材料属性, 且其为小尺寸时受尺寸律影响(Lundberg et al. 2013). Li等(2015b)分析了界面击溃的速度上限与长杆侵彻的速度下限,进而确定了转变速度的范围.对于界面击溃转变速度问题的研究将在后文详细论述. ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
... Anderson等 (Anderson & Walker 2005, Behner et al. 2008,Behner et al. 2011, Holmquist et al.2010)在实验和模拟中也发现了上述现象. Li等(2015b)由此定义了长杆撞击陶瓷靶的3种变形模式,撞击过程中弹体头阴影部分为转变区,曲线由Alekseevskii-Tate模型计算得部和尾部速度的典型变化方式见图3. ...
... 由早期实验数据分析可看出, 弹靶密度对侵彻深度影响显著.最直观的认识就是长杆高速侵彻的流体动力学极限即为弹靶密度比$1/\mu$. 然而Anderson等 (Anderson et al. 1992b, Anderson & Morris et al. 1992)总结实验数据发现,弹密度和靶密度对侵彻深度的贡献是不一样的,靶体密度与弹体密度相比对侵彻的影响较小, 如图15所示. ...
Influence of confinement on the transition velocity of silicon carbide//Proceedings of the 23rd international symposium on ballistics,
6
2007
... Lundberg等(2000)在分析钨和镆长杆侵彻陶瓷靶时发现了此现象,后续的实验和模拟 (Behner et al. 2011; Anderson & Walker 2005; Andersson et al. 2007; Lundberg & Lundberg 2005;Lundberg et al. 2006, 2013)验证了这一现象. Lundberg等(2000)提出了可能出现该现象的压力范围并得到了转变速度的区间,该转变速度取决于陶瓷靶的材料属性, 且其为小尺寸时受尺寸律影响(Lundberg et al. 2013). Li等(2015b)分析了界面击溃的速度上限与长杆侵彻的速度下限,进而确定了转变速度的范围.对于界面击溃转变速度问题的研究将在后文详细论述. ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
Penetration dynamics and interface defeat capability of silicon carbide against long Rod impact
5
2011
... Lundberg等(2000)在分析钨和镆长杆侵彻陶瓷靶时发现了此现象,后续的实验和模拟 (Behner et al. 2011; Anderson & Walker 2005; Andersson et al. 2007; Lundberg & Lundberg 2005;Lundberg et al. 2006, 2013)验证了这一现象. Lundberg等(2000)提出了可能出现该现象的压力范围并得到了转变速度的区间,该转变速度取决于陶瓷靶的材料属性, 且其为小尺寸时受尺寸律影响(Lundberg et al. 2013). Li等(2015b)分析了界面击溃的速度上限与长杆侵彻的速度下限,进而确定了转变速度的范围.对于界面击溃转变速度问题的研究将在后文详细论述. ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
... Anderson等 (Anderson & Walker 2005, Behner et al. 2008,Behner et al. 2011, Holmquist et al.2010)在实验和模拟中也发现了上述现象. Li等(2015b)由此定义了长杆撞击陶瓷靶的3种变形模式,撞击过程中弹体头阴影部分为转变区,曲线由Alekseevskii-Tate模型计算得部和尾部速度的典型变化方式见图3. ...
... Lundberg等 (Lundberg & Lundberg 2005; Lundberg et al. 2000,2006; Westerling et al. 2001)和Anderson等 (Anderson et al. 2011a,Behner et al. 2011)讨论了金属盖板对提高界面击溃转变速度的作用:盖板一方面扩大杆弹头部面积从而分散初始载荷,另一方面延长杆弹材料对陶瓷靶的作用时间从而可避免撞击面产生的拉伸应力导致靶板过早失效. ...
Penetration and failure of lead and borosilicate glass against rod impact
4
2008
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
... , 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
... Anderson等 (Anderson & Walker 2005, Behner et al. 2008,Behner et al. 2011, Holmquist et al.2010)在实验和模拟中也发现了上述现象. Li等(2015b)由此定义了长杆撞击陶瓷靶的3种变形模式,撞击过程中弹体头阴影部分为转变区,曲线由Alekseevskii-Tate模型计算得部和尾部速度的典型变化方式见图3. ...
Protective properties of finite-extension ceramic targets against steel and copper projectiles//Proceedings of the 27th International Symposium on Ballistics, Freiburg, Germany
Inelastic deformation and energy dissipation in ceramics: A mechanism-based constitutive model
1
2008
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
Experimental test of the theory of penetration by metallic jets
The influence of experimental design on depth-of-penetration (DOP) test results and derived ballistic efficiencies
3
1997
... 目前长杆高速侵彻实验大多采用直接弹道实验 (direct ballistictest)和小尺寸逆向弹道实验 (small-scale reverse ballistictest)的方法来进行 (Franzen et al. 1997).直接弹道技术最有代表性的是陶瓷抵抗长杆弹侵彻实验中的侵彻深度(depth of penetration, DOP)方法 (Anderson & Royal-Timmons 1997, Hohler et al. 1995),该方法通过对附在陶瓷后的金属靶剩余侵彻深度的精确测量来反映陶瓷靶的抗侵彻能力(如图5所示). 直接弹道实验的优势在于实验尺寸与实际应用更接近,但靶体尺寸过大会导致不能使用 X射线记录时程信息,故每次实验只能得到一个剩余侵彻深度.小尺寸逆向弹道实验则是通过靶体反向撞击弹体,能利用闪光X射线摄影同时记录侵彻过程的时间和空间信息,但是该实验技术对靶体直径有限制, 只能做小尺寸实验 (陈小伟和陈裕泽 2006). ...
... DOP实验示意图 (Franzen et al. 1997) ...
... 弹体通常由高密度金属 (钨、贫化铀)及其合金制成, 靶体材料差异较大,从传统金属到陶瓷 (Anderson & Morris 1992; Anderson & Royal-Timmons 1997; Behner et al. 2006; Hohler et al. 1995, Li et al. 2017, Orphal & Franzen 1997; Orphal et al. 1996, 1997;Rosenberg et al. 1995, 1997a; Subramanian & Bless 1995;Subramanian et al. 1995; Westerling et al. 2001)、玻璃 (Anderson & Holmquist 2013; Anderson et al. 2009, 2011a; Behner et al. 2008; Hohler et al. 1993; Orphal et al. 2009)以及混凝土 (Gold et al. 1996, Kong et al. 2017c, Nia et al. 2014)和编织物 (Walker 2001)等复合材料的抗侵彻性能均有实验报道. 对于直接弹道实验,需设计弹托并安装弹托回收装置 (Lundberg et al. 1996);而对于小尺寸逆向弹道实验, 需在靶体外加装密闭装置 (Kong et al.2017c, Subramanian et al. 1995) (如图6所示). 此外, 靶体尺寸(Franzen et al. 1997, Littlefield et al. 1997, Lundberg et al.1996, Rosenberg & Dekel 2000, Rosenberg et al.1997b)、约束形式 (Anderson & Royal-Timmons 1997, Partom & Littlefield 1995, Subramanian & Bless 1995,Westerling et al. 2001)和金属覆盖板 (Anderson & Royal-Timmons 1997, Subramanian & Bless 1995)等也是实验需要特别关注的问题. ...
An upper limit for the penetration performance of segmented rods with segment-$L/D \leq 1$
1994
New analytical model of expansion of spherical cavity in brittle material based on the concepts of mechanics of compressible porous and powder materials
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
Predicting the penetration of long rods into semi-infinite metallic targets
4
2013
... 国际上在长杆高速侵彻领域比较活跃的有Hohler和Stilp, Anderson,Orphal以及Rosenberg等研究组, 其所著的综述 (Anderson 2003, 2017;Orphal 2006; Stilp & Hohler 1995)和专著 (Rosenberg & Dekel 2012)侧重于介绍各自在该领域的工作进展.国内学者对长杆高速侵彻问题的研究起步较晚,但对于一些特定材料与特殊问题的研究已取得一些有意义的成果.陈小伟和陈裕泽对长杆高速侵彻陶瓷靶问题撰写了代表性综述 (陈小伟等 2006), 同时陈小伟教授课题组还在长杆高速侵彻理论 (Jiao & Chen 2018)、界面击溃效应 (Li & Chen 2017; Li et al. 2014,2015b; 李继承等 2011a, 2011b)、纤维增强金属玻璃长杆弹 (Chen et al.2015, Li et al. 2015a,李继承等 2011c, 陈小伟等 2012, 王杰等 2014)、分段杆 (郎林等 2011)和可压缩性 (Song et al. 2017a, 2017b,2018)等方面开展了一系列研究.中国科学技术大学文鹤鸣教授课题组开展了长杆侵彻的一维理论和模拟研究(He & Wen 2013; Lan & Wen 2010; Lu & Wen 2018; Wen & Lan 2010; Wen et al. 2010, 2011; Zhou & Wen 2003; 兰彬等 2008, 2009),北京理工大学黄风雷教授团队对长杆侵彻陶瓷靶、金属靶和混凝土靶开展了实验、模拟和理论研究(Zhang & Huang 2004, 张连生等 2005, 李志康和黄风雷 2010,李金柱等 2014, Li et al. 2017),南京理工大学张先锋教授课题组研究了长杆高速撞击陶瓷靶和界面击溃效应(Zhang & Li 2010; Zhang et al. 2011; 谈梦婷等 2016, 2017,2018),解放军理工大学方秦教授课题组开展了长杆高速侵彻的实验和理论分析(Kong et al. 2016b; Kong et al. 2017b, 2017c; 孔祥振等 2017;翟阳修等 2017). ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
... Anderson等 (Anderson & Walker 2005, Behner et al. 2008,Behner et al. 2011, Holmquist et al.2010)在实验和模拟中也发现了上述现象. Li等(2015b)由此定义了长杆撞击陶瓷靶的3种变形模式,撞击过程中弹体头阴影部分为转变区,曲线由Alekseevskii-Tate模型计算得部和尾部速度的典型变化方式见图3. ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
Modeling prestressed ceramic and its effect on ballistic performance
2
2005
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
A Computational Constitutive Model for Glass Subjected to Large Strains, High Strain Rates and High Pressures
1
2011
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
A computational constitutive model for concrete subjected to large strains, high strain rates and high pressures//Proceedings of 14th international symposium on Ballistics, Quebec, Canada
1
1993
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
Penetration of concrete targets using a modified Holmquist-Johnson-Cook material model
1
2013
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
Approximate solutions of the Alekseevskii--Tate model of long-rod penetration
4
2018
... 国际上在长杆高速侵彻领域比较活跃的有Hohler和Stilp, Anderson,Orphal以及Rosenberg等研究组, 其所著的综述 (Anderson 2003, 2017;Orphal 2006; Stilp & Hohler 1995)和专著 (Rosenberg & Dekel 2012)侧重于介绍各自在该领域的工作进展.国内学者对长杆高速侵彻问题的研究起步较晚,但对于一些特定材料与特殊问题的研究已取得一些有意义的成果.陈小伟和陈裕泽对长杆高速侵彻陶瓷靶问题撰写了代表性综述 (陈小伟等 2006), 同时陈小伟教授课题组还在长杆高速侵彻理论 (Jiao & Chen 2018)、界面击溃效应 (Li & Chen 2017; Li et al. 2014,2015b; 李继承等 2011a, 2011b)、纤维增强金属玻璃长杆弹 (Chen et al.2015, Li et al. 2015a,李继承等 2011c, 陈小伟等 2012, 王杰等 2014)、分段杆 (郎林等 2011)和可压缩性 (Song et al. 2017a, 2017b,2018)等方面开展了一系列研究.中国科学技术大学文鹤鸣教授课题组开展了长杆侵彻的一维理论和模拟研究(He & Wen 2013; Lan & Wen 2010; Lu & Wen 2018; Wen & Lan 2010; Wen et al. 2010, 2011; Zhou & Wen 2003; 兰彬等 2008, 2009),北京理工大学黄风雷教授团队对长杆侵彻陶瓷靶、金属靶和混凝土靶开展了实验、模拟和理论研究(Zhang & Huang 2004, 张连生等 2005, 李志康和黄风雷 2010,李金柱等 2014, Li et al. 2017),南京理工大学张先锋教授课题组研究了长杆高速撞击陶瓷靶和界面击溃效应(Zhang & Li 2010; Zhang et al. 2011; 谈梦婷等 2016, 2017,2018),解放军理工大学方秦教授课题组开展了长杆高速侵彻的实验和理论分析(Kong et al. 2016b; Kong et al. 2017b, 2017c; 孔祥振等 2017;翟阳修等 2017). ...
A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures//Proceedings of the 7th International Symposium on Ballistics:
2
1983
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
An improved computational constitutive model for brittle materials
3
1994
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
Response of aluminum nitride (including a phase change) to large strains, high strain rates, and high pressures
Conversion of 3D distorted elements into meshless particles during dynamic deformation
1
2003
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
An algorithm to automatically convert distorted finite elements into meshless particles during dynamic deformation
... 不同算法的数值模拟结果.(a)网格自适应算法对WHA长杆侵彻有约束陶瓷靶的模拟结果 (Ortiz 1996),(b)有限元和粒子耦合的算法对钨长杆侵彻钢靶的模拟结果 (Johnson et al. 2002) ...
Modified K & C model for cratering and scabbing of concrete slabs under projectile impact
1
2017
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
Numerical predictions of cratering and scabbing in concrete slabs subjected to projectile impact using a modified version of HJC material model
1
2016
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
Critical Impact Yaw for Long-Rod Penetrators
2
2016
... 国际上在长杆高速侵彻领域比较活跃的有Hohler和Stilp, Anderson,Orphal以及Rosenberg等研究组, 其所著的综述 (Anderson 2003, 2017;Orphal 2006; Stilp & Hohler 1995)和专著 (Rosenberg & Dekel 2012)侧重于介绍各自在该领域的工作进展.国内学者对长杆高速侵彻问题的研究起步较晚,但对于一些特定材料与特殊问题的研究已取得一些有意义的成果.陈小伟和陈裕泽对长杆高速侵彻陶瓷靶问题撰写了代表性综述 (陈小伟等 2006), 同时陈小伟教授课题组还在长杆高速侵彻理论 (Jiao & Chen 2018)、界面击溃效应 (Li & Chen 2017; Li et al. 2014,2015b; 李继承等 2011a, 2011b)、纤维增强金属玻璃长杆弹 (Chen et al.2015, Li et al. 2015a,李继承等 2011c, 陈小伟等 2012, 王杰等 2014)、分段杆 (郎林等 2011)和可压缩性 (Song et al. 2017a, 2017b,2018)等方面开展了一系列研究.中国科学技术大学文鹤鸣教授课题组开展了长杆侵彻的一维理论和模拟研究(He & Wen 2013; Lan & Wen 2010; Lu & Wen 2018; Wen & Lan 2010; Wen et al. 2010, 2011; Zhou & Wen 2003; 兰彬等 2008, 2009),北京理工大学黄风雷教授团队对长杆侵彻陶瓷靶、金属靶和混凝土靶开展了实验、模拟和理论研究(Zhang & Huang 2004, 张连生等 2005, 李志康和黄风雷 2010,李金柱等 2014, Li et al. 2017),南京理工大学张先锋教授课题组研究了长杆高速撞击陶瓷靶和界面击溃效应(Zhang & Li 2010; Zhang et al. 2011; 谈梦婷等 2016, 2017,2018),解放军理工大学方秦教授课题组开展了长杆高速侵彻的实验和理论分析(Kong et al. 2016b; Kong et al. 2017b, 2017c; 孔祥振等 2017;翟阳修等 2017). ...
... 弹体通常由高密度金属 (钨、贫化铀)及其合金制成, 靶体材料差异较大,从传统金属到陶瓷 (Anderson & Morris 1992; Anderson & Royal-Timmons 1997; Behner et al. 2006; Hohler et al. 1995, Li et al. 2017, Orphal & Franzen 1997; Orphal et al. 1996, 1997;Rosenberg et al. 1995, 1997a; Subramanian & Bless 1995;Subramanian et al. 1995; Westerling et al. 2001)、玻璃 (Anderson & Holmquist 2013; Anderson et al. 2009, 2011a; Behner et al. 2008; Hohler et al. 1993; Orphal et al. 2009)以及混凝土 (Gold et al. 1996, Kong et al. 2017c, Nia et al. 2014)和编织物 (Walker 2001)等复合材料的抗侵彻性能均有实验报道. 对于直接弹道实验,需设计弹托并安装弹托回收装置 (Lundberg et al. 1996);而对于小尺寸逆向弹道实验, 需在靶体外加装密闭装置 (Kong et al.2017c, Subramanian et al. 1995) (如图6所示). 此外, 靶体尺寸(Franzen et al. 1997, Littlefield et al. 1997, Lundberg et al.1996, Rosenberg & Dekel 2000, Rosenberg et al.1997b)、约束形式 (Anderson & Royal-Timmons 1997, Partom & Littlefield 1995, Subramanian & Bless 1995,Westerling et al. 2001)和金属覆盖板 (Anderson & Royal-Timmons 1997, Subramanian & Bless 1995)等也是实验需要特别关注的问题. ...
... );而对于小尺寸逆向弹道实验, 需在靶体外加装密闭装置 (Kong et al.2017c, Subramanian et al. 1995) (如图6所示). 此外, 靶体尺寸(Franzen et al. 1997, Littlefield et al. 1997, Lundberg et al.1996, Rosenberg & Dekel 2000, Rosenberg et al.1997b)、约束形式 (Anderson & Royal-Timmons 1997, Partom & Littlefield 1995, Subramanian & Bless 1995,Westerling et al. 2001)和金属覆盖板 (Anderson & Royal-Timmons 1997, Subramanian & Bless 1995)等也是实验需要特别关注的问题. ...
... 除部分DOP实验 (Lundberg et al. 1996, Kong et al.2017c)使用高速摄影记录弹坑数据外,目前在长杆高速侵彻实验中最普遍使用的诊断技术为闪光X射线摄影.在小尺寸逆向弹道实验中,可以从X光照片中读出每个瞬时的侵彻深度、弹体剩余长度和弹体碎片长度,其他物理量在此基础上计算即可求得 (Subramanian et al. 1995). ...
A residual velocity predictive model for long rod penetrators
Theoretical analysis of projectile-target interface defeat and transition to penetration by long rods due to oblique impacts of ceramic targets
5
2017
... 国际上在长杆高速侵彻领域比较活跃的有Hohler和Stilp, Anderson,Orphal以及Rosenberg等研究组, 其所著的综述 (Anderson 2003, 2017;Orphal 2006; Stilp & Hohler 1995)和专著 (Rosenberg & Dekel 2012)侧重于介绍各自在该领域的工作进展.国内学者对长杆高速侵彻问题的研究起步较晚,但对于一些特定材料与特殊问题的研究已取得一些有意义的成果.陈小伟和陈裕泽对长杆高速侵彻陶瓷靶问题撰写了代表性综述 (陈小伟等 2006), 同时陈小伟教授课题组还在长杆高速侵彻理论 (Jiao & Chen 2018)、界面击溃效应 (Li & Chen 2017; Li et al. 2014,2015b; 李继承等 2011a, 2011b)、纤维增强金属玻璃长杆弹 (Chen et al.2015, Li et al. 2015a,李继承等 2011c, 陈小伟等 2012, 王杰等 2014)、分段杆 (郎林等 2011)和可压缩性 (Song et al. 2017a, 2017b,2018)等方面开展了一系列研究.中国科学技术大学文鹤鸣教授课题组开展了长杆侵彻的一维理论和模拟研究(He & Wen 2013; Lan & Wen 2010; Lu & Wen 2018; Wen & Lan 2010; Wen et al. 2010, 2011; Zhou & Wen 2003; 兰彬等 2008, 2009),北京理工大学黄风雷教授团队对长杆侵彻陶瓷靶、金属靶和混凝土靶开展了实验、模拟和理论研究(Zhang & Huang 2004, 张连生等 2005, 李志康和黄风雷 2010,李金柱等 2014, Li et al. 2017),南京理工大学张先锋教授课题组研究了长杆高速撞击陶瓷靶和界面击溃效应(Zhang & Li 2010; Zhang et al. 2011; 谈梦婷等 2016, 2017,2018),解放军理工大学方秦教授课题组开展了长杆高速侵彻的实验和理论分析(Kong et al. 2016b; Kong et al. 2017b, 2017c; 孔祥振等 2017;翟阳修等 2017). ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
... 以上研究均针对长杆正碰撞陶瓷靶的界面击溃现象,实际应用中斜碰撞更加普遍, 不少研究者已对陶瓷靶斜撞击进行了一系列的研究 (Anderson et al. 2011a, Hetherington & Lemieux 1994, Hohler et al. 2001, Lee, 2003, Li & Chen 2017, Sadanandan & Hetherington 1997, Zaera & Sánchez-Gálvez 1998). ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
On the transition from interface defeat to penetration in the impact of long rod onto ceramic targets
6
2015
... 国际上在长杆高速侵彻领域比较活跃的有Hohler和Stilp, Anderson,Orphal以及Rosenberg等研究组, 其所著的综述 (Anderson 2003, 2017;Orphal 2006; Stilp & Hohler 1995)和专著 (Rosenberg & Dekel 2012)侧重于介绍各自在该领域的工作进展.国内学者对长杆高速侵彻问题的研究起步较晚,但对于一些特定材料与特殊问题的研究已取得一些有意义的成果.陈小伟和陈裕泽对长杆高速侵彻陶瓷靶问题撰写了代表性综述 (陈小伟等 2006), 同时陈小伟教授课题组还在长杆高速侵彻理论 (Jiao & Chen 2018)、界面击溃效应 (Li & Chen 2017; Li et al. 2014,2015b; 李继承等 2011a, 2011b)、纤维增强金属玻璃长杆弹 (Chen et al.2015, Li et al. 2015a,李继承等 2011c, 陈小伟等 2012, 王杰等 2014)、分段杆 (郎林等 2011)和可压缩性 (Song et al. 2017a, 2017b,2018)等方面开展了一系列研究.中国科学技术大学文鹤鸣教授课题组开展了长杆侵彻的一维理论和模拟研究(He & Wen 2013; Lan & Wen 2010; Lu & Wen 2018; Wen & Lan 2010; Wen et al. 2010, 2011; Zhou & Wen 2003; 兰彬等 2008, 2009),北京理工大学黄风雷教授团队对长杆侵彻陶瓷靶、金属靶和混凝土靶开展了实验、模拟和理论研究(Zhang & Huang 2004, 张连生等 2005, 李志康和黄风雷 2010,李金柱等 2014, Li et al. 2017),南京理工大学张先锋教授课题组研究了长杆高速撞击陶瓷靶和界面击溃效应(Zhang & Li 2010; Zhang et al. 2011; 谈梦婷等 2016, 2017,2018),解放军理工大学方秦教授课题组开展了长杆高速侵彻的实验和理论分析(Kong et al. 2016b; Kong et al. 2017b, 2017c; 孔祥振等 2017;翟阳修等 2017). ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
Numerical simulations of oblique-angle penetration by deformable projectiles into concrete targets
1
2009
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
On the penetration of high strength steel rods into semi-infinite aluminium alloy targets
3
2018
... 国际上在长杆高速侵彻领域比较活跃的有Hohler和Stilp, Anderson,Orphal以及Rosenberg等研究组, 其所著的综述 (Anderson 2003, 2017;Orphal 2006; Stilp & Hohler 1995)和专著 (Rosenberg & Dekel 2012)侧重于介绍各自在该领域的工作进展.国内学者对长杆高速侵彻问题的研究起步较晚,但对于一些特定材料与特殊问题的研究已取得一些有意义的成果.陈小伟和陈裕泽对长杆高速侵彻陶瓷靶问题撰写了代表性综述 (陈小伟等 2006), 同时陈小伟教授课题组还在长杆高速侵彻理论 (Jiao & Chen 2018)、界面击溃效应 (Li & Chen 2017; Li et al. 2014,2015b; 李继承等 2011a, 2011b)、纤维增强金属玻璃长杆弹 (Chen et al.2015, Li et al. 2015a,李继承等 2011c, 陈小伟等 2012, 王杰等 2014)、分段杆 (郎林等 2011)和可压缩性 (Song et al. 2017a, 2017b,2018)等方面开展了一系列研究.中国科学技术大学文鹤鸣教授课题组开展了长杆侵彻的一维理论和模拟研究(He & Wen 2013; Lan & Wen 2010; Lu & Wen 2018; Wen & Lan 2010; Wen et al. 2010, 2011; Zhou & Wen 2003; 兰彬等 2008, 2009),北京理工大学黄风雷教授团队对长杆侵彻陶瓷靶、金属靶和混凝土靶开展了实验、模拟和理论研究(Zhang & Huang 2004, 张连生等 2005, 李志康和黄风雷 2010,李金柱等 2014, Li et al. 2017),南京理工大学张先锋教授课题组研究了长杆高速撞击陶瓷靶和界面击溃效应(Zhang & Li 2010; Zhang et al. 2011; 谈梦婷等 2016, 2017,2018),解放军理工大学方秦教授课题组开展了长杆高速侵彻的实验和理论分析(Kong et al. 2016b; Kong et al. 2017b, 2017c; 孔祥振等 2017;翟阳修等 2017). ...
... 此外, Wen等 (Lan & Wen 2010, Lu & Wen 2018, Wen & Lan 2010)从一维长杆高速侵彻模型出发,定义了刚性弹侵彻临界速度$V_{\rm R} $和侵蚀弹侵彻临界速度$V_{\rm H}$, 对长杆弹侵彻的不同模式开展了一系列研究. ...
... Lan-Wen模型首次给出了弹靶界面出现流动区的条件,即弹靶界面上剪应力远小于静水压时材料行为由强度控制转变为静水压控制,并建立了高速侵彻与空腔膨胀理论之间的联系.特别针对弹体强度大于靶体阻力的情况,Lan-Wen模型可描述刚体侵彻、变形体侵彻和消蚀侵彻3种不同长杆弹侵彻模式的相互转化(Lu & Wen 2018, Wen & Lan 2010).通过对临界侵彻速度和式(35)的合理取值,Lan-Wen模型与不同弹靶组合的实验结果吻合较好. ...
Influence of length scale on the transition from interface defeat to penetration in unconfined ceramic targets
4
2013
... Lundberg等(2000)在分析钨和镆长杆侵彻陶瓷靶时发现了此现象,后续的实验和模拟 (Behner et al. 2011; Anderson & Walker 2005; Andersson et al. 2007; Lundberg & Lundberg 2005;Lundberg et al. 2006, 2013)验证了这一现象. Lundberg等(2000)提出了可能出现该现象的压力范围并得到了转变速度的区间,该转变速度取决于陶瓷靶的材料属性, 且其为小尺寸时受尺寸律影响(Lundberg et al. 2013). Li等(2015b)分析了界面击溃的速度上限与长杆侵彻的速度下限,进而确定了转变速度的范围.对于界面击溃转变速度问题的研究将在后文详细论述. ...
... 提出了可能出现该现象的压力范围并得到了转变速度的区间,该转变速度取决于陶瓷靶的材料属性, 且其为小尺寸时受尺寸律影响(Lundberg et al. 2013). Li等(2015b)分析了界面击溃的速度上限与长杆侵彻的速度下限,进而确定了转变速度的范围.对于界面击溃转变速度问题的研究将在后文详细论述. ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
Transition between interface defeat and penetration for tungsten projectiles and four silicon carbide materials
7
2005
... Lundberg等(2000)在分析钨和镆长杆侵彻陶瓷靶时发现了此现象,后续的实验和模拟 (Behner et al. 2011; Anderson & Walker 2005; Andersson et al. 2007; Lundberg & Lundberg 2005;Lundberg et al. 2006, 2013)验证了这一现象. Lundberg等(2000)提出了可能出现该现象的压力范围并得到了转变速度的区间,该转变速度取决于陶瓷靶的材料属性, 且其为小尺寸时受尺寸律影响(Lundberg et al. 2013). Li等(2015b)分析了界面击溃的速度上限与长杆侵彻的速度下限,进而确定了转变速度的范围.对于界面击溃转变速度问题的研究将在后文详细论述. ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
Impact of metallic projectiles on ceramic targets: Transition between interface defeat and penetration
8
2000
... Lundberg等(2000)在分析钨和镆长杆侵彻陶瓷靶时发现了此现象,后续的实验和模拟 (Behner et al. 2011; Anderson & Walker 2005; Andersson et al. 2007; Lundberg & Lundberg 2005;Lundberg et al. 2006, 2013)验证了这一现象. Lundberg等(2000)提出了可能出现该现象的压力范围并得到了转变速度的区间,该转变速度取决于陶瓷靶的材料属性, 且其为小尺寸时受尺寸律影响(Lundberg et al. 2013). Li等(2015b)分析了界面击溃的速度上限与长杆侵彻的速度下限,进而确定了转变速度的范围.对于界面击溃转变速度问题的研究将在后文详细论述. ...
... )验证了这一现象. Lundberg等(2000)提出了可能出现该现象的压力范围并得到了转变速度的区间,该转变速度取决于陶瓷靶的材料属性, 且其为小尺寸时受尺寸律影响(Lundberg et al. 2013). Li等(2015b)分析了界面击溃的速度上限与长杆侵彻的速度下限,进而确定了转变速度的范围.对于界面击溃转变速度问题的研究将在后文详细论述. ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
... 通过对钨和钼长杆侵彻不同陶瓷的实验与对应的数值模拟, Lundberg等(Lundberg et al. 2000, Westerling et al.2001)发现在无明显侵彻发生的低速区和侵彻速度与撞击速度呈线性的高速区之间,存在狭窄的转变速度区. 转变区内弹体先驻留 (dwell)一段时间 (如图34), 之后以更低的速度侵彻靶体. ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
... 除部分DOP实验 (Lundberg et al. 1996, Kong et al.2017c)使用高速摄影记录弹坑数据外,目前在长杆高速侵彻实验中最普遍使用的诊断技术为闪光X射线摄影.在小尺寸逆向弹道实验中,可以从X光照片中读出每个瞬时的侵彻深度、弹体剩余长度和弹体碎片长度,其他物理量在此基础上计算即可求得 (Subramanian et al. 1995). ...
An experimental study of penetration resistance of ceramic armour subjected to projectile impact
Deformation behavior and its relationship to the penetration performance of high-velocity KE penetrator material//Proceedings of the 1990 Army Science conference
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
CTH: A three-dimensional shock wave physics code
3
1990
... 二维计算程序诞生于20世纪60年代, 并于七八十年代发展成熟 (Anderson 1987). 美国桑迪亚国家实验室 (Sandia National Laboratories,SNL)的二维欧拉流体动力学程序CSQ是最早用来模拟长杆侵彻问题的工具,也是三维流体动力学程序CTH的前身(McGlaun 1990). Anderson等 (Anderson & Orphal 2003,2008; Anderson & Walker 1991; Anderson et al. 1993, 1995,1996, 1999b)利用CTH对长杆侵彻作了一系列的模拟,其中Anderson和Walker(1991)对$L /D=10$钨合金长杆以1.5km/s侵彻RHA的模拟得到了比Alekseevskii-Tate模型更贴近实验的结果,他们分析了产生差异的原因,并在此基础上提出了一个与时间相关的理论模型 (Walker & Anderson 1995). 以色列防务技术研究院RAFAEL公司的Rosenberg等(Rosenberg & Dekel 1994a, 1996, 1998, 1999, 2000, 2003;Rosenberg et al. 1995, 1997a, 1998)运用2D欧拉程序PISCES2DELK进行了一系列数值模拟,分析了弹头形状、长径比、弹靶强度以及其他材料参数等因素对长杆侵彻的影响.通过数值模拟, 侵彻过程中的压力、速度和几何等细节信息得以获得.然而, 数值模拟结果与计算方法和材料本构的选取密切相关,且相关参数的选取也具有较强的人为性,故其准确性往往需要与实验和理论对比来验证. ...
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
An experimental method to compare the ballistic efficiencies of different ceramics against long rod projectiles//Proceedings of the 11th International Symposium on Ballistics,
Numerical predictions of ballistic limits for concrete slabs using a modified version of the HJC concrete model
1
2008
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
Modeling the impact behavior of AD85 ceramic under multiaxial loading
1
1994
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
Determination of Rajendran-Grove Ceramic Constitutive Model Constants/
1
1996
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
Impact studies of five ceramic materials and pyrex
Penetration of Tungsten-Alloy rods into composite ceramic targets: Experiments and 2-D Simulations//Proceedings of the APS conference on Shock Waves in Condensed Matter
4
1998
... 二维计算程序诞生于20世纪60年代, 并于七八十年代发展成熟 (Anderson 1987). 美国桑迪亚国家实验室 (Sandia National Laboratories,SNL)的二维欧拉流体动力学程序CSQ是最早用来模拟长杆侵彻问题的工具,也是三维流体动力学程序CTH的前身(McGlaun 1990). Anderson等 (Anderson & Orphal 2003,2008; Anderson & Walker 1991; Anderson et al. 1993, 1995,1996, 1999b)利用CTH对长杆侵彻作了一系列的模拟,其中Anderson和Walker(1991)对$L /D=10$钨合金长杆以1.5km/s侵彻RHA的模拟得到了比Alekseevskii-Tate模型更贴近实验的结果,他们分析了产生差异的原因,并在此基础上提出了一个与时间相关的理论模型 (Walker & Anderson 1995). 以色列防务技术研究院RAFAEL公司的Rosenberg等(Rosenberg & Dekel 1994a, 1996, 1998, 1999, 2000, 2003;Rosenberg et al. 1995, 1997a, 1998)运用2D欧拉程序PISCES2DELK进行了一系列数值模拟,分析了弹头形状、长径比、弹靶强度以及其他材料参数等因素对长杆侵彻的影响.通过数值模拟, 侵彻过程中的压力、速度和几何等细节信息得以获得.然而, 数值模拟结果与计算方法和材料本构的选取密切相关,且相关参数的选取也具有较强的人为性,故其准确性往往需要与实验和理论对比来验证. ...
... 近年来长杆高速侵彻领域的数值模拟研究主要集中在以下几个方面:弹靶材料参数对侵彻深度的影响 (Anderson et al. 1992b, 1993, 1999a;Forrestal & Longcope 1990; Kong et al. 2017b; Li et al.2015a; Rosenberg & Dekel 1998, 2000, 2001b, 2004),长径比效应 (Anderson et al. 1995, 1996; Orphal et al. 1993, 1995;Rosenberg & Dekel 1994a; Walker 1999), 侵彻末段作用机理(Anderson & Orphal 2003; Orphal 1997; Rosenberg & Dekel 2000, 2001a), 陶瓷靶抗长杆侵彻机理 (Li et al. 2017;Rosenberg et al. 1995, 1997b, 1998; Zhang et al. 2011; 蒋东等 2010; 谈梦婷等 2016).大量数值模拟工作都与实验结果和理论分析相互印证以期具有说服力. ...
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
On the ricochet of long rod projectiles//Proceedings of the 11th international symposium on ballistics
Experimental and numerical investigation of the ricocheting of projectiles from metallic surfaces//Proceedings of the 6th international symposium on ballistics
Constitutive model used in computer simulation of time-resolved, shock-wave data
2
1987
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
A constitutive model for metals applicable at high-strain rate
1
1980
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
A constitutive model for strain rates from 0.0001 to 1,000,000/s
1
1989
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
Material properties determining the resistance of ceramics to high velocity penetration
1989
Experimental methods for terminal ballistics and impact physics//High Velocity Impact Dynamics
... 除部分DOP实验 (Lundberg et al. 1996, Kong et al.2017c)使用高速摄影记录弹坑数据外,目前在长杆高速侵彻实验中最普遍使用的诊断技术为闪光X射线摄影.在小尺寸逆向弹道实验中,可以从X光照片中读出每个瞬时的侵彻深度、弹体剩余长度和弹体碎片长度,其他物理量在此基础上计算即可求得 (Subramanian et al. 1995). ...
A theory for the deceleration of long rods after impact
Modifications of RHT material model for improved numerical simulation of dynamic response of concrete
1
2010
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
The Wilkins' computational ceramic model for CTH. SwRI Report,
1
1991
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
A model for penetration by very low aspect ratio projectiles
3
1999
... 近年来长杆高速侵彻领域的数值模拟研究主要集中在以下几个方面:弹靶材料参数对侵彻深度的影响 (Anderson et al. 1992b, 1993, 1999a;Forrestal & Longcope 1990; Kong et al. 2017b; Li et al.2015a; Rosenberg & Dekel 1998, 2000, 2001b, 2004),长径比效应 (Anderson et al. 1995, 1996; Orphal et al. 1993, 1995;Rosenberg & Dekel 1994a; Walker 1999), 侵彻末段作用机理(Anderson & Orphal 2003; Orphal 1997; Rosenberg & Dekel 2000, 2001a), 陶瓷靶抗长杆侵彻机理 (Li et al. 2017;Rosenberg et al. 1995, 1997b, 1998; Zhang et al. 2011; 蒋东等 2010; 谈梦婷等 2016).大量数值模拟工作都与实验结果和理论分析相互印证以期具有说服力. ...
Tunsten into steel penetration including velocity, $L/D$, and impact inclination effects//Proceedings of the 19th international symposium on ballistics
2001
The influence of initial nose shape in eroding penetration
1994
A time-dependent model for long-rod penetration
4
1995
... 长杆侵彻中弹靶变形模式示意图$(v$为弹尾(刚体)速度即撞击速度,$u$为弹头 (流体)速度即侵彻速度) (Walker & Anderson 1995) ...
... 二维计算程序诞生于20世纪60年代, 并于七八十年代发展成熟 (Anderson 1987). 美国桑迪亚国家实验室 (Sandia National Laboratories,SNL)的二维欧拉流体动力学程序CSQ是最早用来模拟长杆侵彻问题的工具,也是三维流体动力学程序CTH的前身(McGlaun 1990). Anderson等 (Anderson & Orphal 2003,2008; Anderson & Walker 1991; Anderson et al. 1993, 1995,1996, 1999b)利用CTH对长杆侵彻作了一系列的模拟,其中Anderson和Walker(1991)对$L /D=10$钨合金长杆以1.5km/s侵彻RHA的模拟得到了比Alekseevskii-Tate模型更贴近实验的结果,他们分析了产生差异的原因,并在此基础上提出了一个与时间相关的理论模型 (Walker & Anderson 1995). 以色列防务技术研究院RAFAEL公司的Rosenberg等(Rosenberg & Dekel 1994a, 1996, 1998, 1999, 2000, 2003;Rosenberg et al. 1995, 1997a, 1998)运用2D欧拉程序PISCES2DELK进行了一系列数值模拟,分析了弹头形状、长径比、弹靶强度以及其他材料参数等因素对长杆侵彻的影响.通过数值模拟, 侵彻过程中的压力、速度和几何等细节信息得以获得.然而, 数值模拟结果与计算方法和材料本构的选取密切相关,且相关参数的选取也具有较强的人为性,故其准确性往往需要与实验和理论对比来验证. ...
Tensile failure of concrete at high loading rates: New test data on strength and fracture energy from instrumented spalling tests
1
2007
... 材料本构的选择对模拟结果有较大影响.目前在长杆高速侵彻金属靶的模拟中最广泛使用的是Johnson-Cook本构模型(Johnson & Cook 1983), 而在更高的撞击速度下,考虑材料可压缩性和剪切模量的Steinberg模型 (Steinberg 1987,Steinberg et al. 1980, Steinberg & Lund 1989)能更准确地描述冲击波高压状态下的材料特征. 对于脆性材料,需要对裂纹区和粉碎区进行更恰当的模拟.陶瓷靶材需要分别对完善材料和粉碎区失效材料的压缩强度进行描述,并引入在0到1之间变化的损伤函数. JH模型 (Holmquist & Johnson 2005, 2011; Johnson & Holmquist 1994)是目前使用最广泛的陶瓷本构模型, 此外还有Wilkins模型 (McGlaun et al. 1990, Walker & Anderson 1991)、Rajendran-Grove(RG)模型 (Rajendran 1994, Rajendran & Grove 1996)和Deshpande-Evans (DE)模型 (Deshpande & Evans 2008).混凝土靶则主要采用考虑应变率效应和体积压缩的HJC模型 (Holmquist et al. 1993)及其改进模型 (Islam et al. 2013, Kong et al. 2016a, Liu et al. 2009, Polanco-Loria et al. 2008, Tu & Lu 2010)以及考虑不同表面强度和损伤函数的K & C模型 (Malvar et al.1997)及其改进模型 (Kong et al. 2017a, Weerheijm & VanDoormaal 2007). ...
Analytical model for cratering of semi-infinite metallic targets by long rod penetrators
4
2010
... 国际上在长杆高速侵彻领域比较活跃的有Hohler和Stilp, Anderson,Orphal以及Rosenberg等研究组, 其所著的综述 (Anderson 2003, 2017;Orphal 2006; Stilp & Hohler 1995)和专著 (Rosenberg & Dekel 2012)侧重于介绍各自在该领域的工作进展.国内学者对长杆高速侵彻问题的研究起步较晚,但对于一些特定材料与特殊问题的研究已取得一些有意义的成果.陈小伟和陈裕泽对长杆高速侵彻陶瓷靶问题撰写了代表性综述 (陈小伟等 2006), 同时陈小伟教授课题组还在长杆高速侵彻理论 (Jiao & Chen 2018)、界面击溃效应 (Li & Chen 2017; Li et al. 2014,2015b; 李继承等 2011a, 2011b)、纤维增强金属玻璃长杆弹 (Chen et al.2015, Li et al. 2015a,李继承等 2011c, 陈小伟等 2012, 王杰等 2014)、分段杆 (郎林等 2011)和可压缩性 (Song et al. 2017a, 2017b,2018)等方面开展了一系列研究.中国科学技术大学文鹤鸣教授课题组开展了长杆侵彻的一维理论和模拟研究(He & Wen 2013; Lan & Wen 2010; Lu & Wen 2018; Wen & Lan 2010; Wen et al. 2010, 2011; Zhou & Wen 2003; 兰彬等 2008, 2009),北京理工大学黄风雷教授团队对长杆侵彻陶瓷靶、金属靶和混凝土靶开展了实验、模拟和理论研究(Zhang & Huang 2004, 张连生等 2005, 李志康和黄风雷 2010,李金柱等 2014, Li et al. 2017),南京理工大学张先锋教授课题组研究了长杆高速撞击陶瓷靶和界面击溃效应(Zhang & Li 2010; Zhang et al. 2011; 谈梦婷等 2016, 2017,2018),解放军理工大学方秦教授课题组开展了长杆高速侵彻的实验和理论分析(Kong et al. 2016b; Kong et al. 2017b, 2017c; 孔祥振等 2017;翟阳修等 2017). ...
... 此外, Wen等 (Lan & Wen 2010, Lu & Wen 2018, Wen & Lan 2010)从一维长杆高速侵彻模型出发,定义了刚性弹侵彻临界速度$V_{\rm R} $和侵蚀弹侵彻临界速度$V_{\rm H}$, 对长杆弹侵彻的不同模式开展了一系列研究. ...
... Lan-Wen模型首次给出了弹靶界面出现流动区的条件,即弹靶界面上剪应力远小于静水压时材料行为由强度控制转变为静水压控制,并建立了高速侵彻与空腔膨胀理论之间的联系.特别针对弹体强度大于靶体阻力的情况,Lan-Wen模型可描述刚体侵彻、变形体侵彻和消蚀侵彻3种不同长杆弹侵彻模式的相互转化(Lu & Wen 2018, Wen & Lan 2010).通过对临界侵彻速度和式(35)的合理取值,Lan-Wen模型与不同弹靶组合的实验结果吻合较好. ...
Criterion for interface defeat to penetration transition of long rod projectile impact on ceramic armor
1
2017
... Hauver等(1992)最早将上述现象称为界面击溃 (interface defeat),而Rosenberg和Tsaliah(1990)早前发现的陶瓷开始侵彻的阈值速度$V_{\rm c} $被定义为界面击溃向长杆侵彻转变的临界速度. 此后, Lundberg等(Andersson et al. 2007; Lundberg & Lundberg 2005; Lundberg et al. 2000, 2006,2013)分别对界面击溃转变速度以及不同陶瓷材料、长杆弹头部形状和尺寸效应对界面击溃效应的影响开展了一系列实验、理论和模拟研究.Johnson和Holmquist (Holmquist & Johnson 2003, 2005; Johnson & Holmquist 1994; Johnson et al.2003)提出了描述陶瓷材料动力学响应的本构模型,并运用CTH程序模拟了陶瓷靶界面击溃. Anderson等 (Anderson & Walker 2005; Anderson et al. 2006, 2008, 2011b; Behner et al.2006, 2008, 2011; Holmquist et al.2010)对界面击溃的理论分析模型、约束、失效波和预破坏对界面击溃的影响以及界面斜击溃进行了分析.Li等 (Li & Chen 2017, Li et al. 2014,2015b)针对不同弹体头形和斜击溃提出了理论分析模型并对界面击溃转变速度进行了分析.谈梦婷等(2016)通过数值模拟研究了不同弹体头形、盖板厚度和预应力对界面击溃的影响.Zhang等(2017)结合陶瓷锥裂纹模型和翼型裂纹扩展模型建立了陶瓷靶界面击溃的损伤演化模型. ...
On the comparison of the ballistic performance of 10% zirconia toughened alumina and 95% alumina ceramic target
1
2010
... 国际上在长杆高速侵彻领域比较活跃的有Hohler和Stilp, Anderson,Orphal以及Rosenberg等研究组, 其所著的综述 (Anderson 2003, 2017;Orphal 2006; Stilp & Hohler 1995)和专著 (Rosenberg & Dekel 2012)侧重于介绍各自在该领域的工作进展.国内学者对长杆高速侵彻问题的研究起步较晚,但对于一些特定材料与特殊问题的研究已取得一些有意义的成果.陈小伟和陈裕泽对长杆高速侵彻陶瓷靶问题撰写了代表性综述 (陈小伟等 2006), 同时陈小伟教授课题组还在长杆高速侵彻理论 (Jiao & Chen 2018)、界面击溃效应 (Li & Chen 2017; Li et al. 2014,2015b; 李继承等 2011a, 2011b)、纤维增强金属玻璃长杆弹 (Chen et al.2015, Li et al. 2015a,李继承等 2011c, 陈小伟等 2012, 王杰等 2014)、分段杆 (郎林等 2011)和可压缩性 (Song et al. 2017a, 2017b,2018)等方面开展了一系列研究.中国科学技术大学文鹤鸣教授课题组开展了长杆侵彻的一维理论和模拟研究(He & Wen 2013; Lan & Wen 2010; Lu & Wen 2018; Wen & Lan 2010; Wen et al. 2010, 2011; Zhou & Wen 2003; 兰彬等 2008, 2009),北京理工大学黄风雷教授团队对长杆侵彻陶瓷靶、金属靶和混凝土靶开展了实验、模拟和理论研究(Zhang & Huang 2004, 张连生等 2005, 李志康和黄风雷 2010,李金柱等 2014, Li et al. 2017),南京理工大学张先锋教授课题组研究了长杆高速撞击陶瓷靶和界面击溃效应(Zhang & Li 2010; Zhang et al. 2011; 谈梦婷等 2016, 2017,2018),解放军理工大学方秦教授课题组开展了长杆高速侵彻的实验和理论分析(Kong et al. 2016b; Kong et al. 2017b, 2017c; 孔祥振等 2017;翟阳修等 2017). ...
Numerical study on anti-penetration process of alumina ceramic (AD95) to tungsten long rod projectiles
3
2011
... 国际上在长杆高速侵彻领域比较活跃的有Hohler和Stilp, Anderson,Orphal以及Rosenberg等研究组, 其所著的综述 (Anderson 2003, 2017;Orphal 2006; Stilp & Hohler 1995)和专著 (Rosenberg & Dekel 2012)侧重于介绍各自在该领域的工作进展.国内学者对长杆高速侵彻问题的研究起步较晚,但对于一些特定材料与特殊问题的研究已取得一些有意义的成果.陈小伟和陈裕泽对长杆高速侵彻陶瓷靶问题撰写了代表性综述 (陈小伟等 2006), 同时陈小伟教授课题组还在长杆高速侵彻理论 (Jiao & Chen 2018)、界面击溃效应 (Li & Chen 2017; Li et al. 2014,2015b; 李继承等 2011a, 2011b)、纤维增强金属玻璃长杆弹 (Chen et al.2015, Li et al. 2015a,李继承等 2011c, 陈小伟等 2012, 王杰等 2014)、分段杆 (郎林等 2011)和可压缩性 (Song et al. 2017a, 2017b,2018)等方面开展了一系列研究.中国科学技术大学文鹤鸣教授课题组开展了长杆侵彻的一维理论和模拟研究(He & Wen 2013; Lan & Wen 2010; Lu & Wen 2018; Wen & Lan 2010; Wen et al. 2010, 2011; Zhou & Wen 2003; 兰彬等 2008, 2009),北京理工大学黄风雷教授团队对长杆侵彻陶瓷靶、金属靶和混凝土靶开展了实验、模拟和理论研究(Zhang & Huang 2004, 张连生等 2005, 李志康和黄风雷 2010,李金柱等 2014, Li et al. 2017),南京理工大学张先锋教授课题组研究了长杆高速撞击陶瓷靶和界面击溃效应(Zhang & Li 2010; Zhang et al. 2011; 谈梦婷等 2016, 2017,2018),解放军理工大学方秦教授课题组开展了长杆高速侵彻的实验和理论分析(Kong et al. 2016b; Kong et al. 2017b, 2017c; 孔祥振等 2017;翟阳修等 2017). ...
... 近年来长杆高速侵彻领域的数值模拟研究主要集中在以下几个方面:弹靶材料参数对侵彻深度的影响 (Anderson et al. 1992b, 1993, 1999a;Forrestal & Longcope 1990; Kong et al. 2017b; Li et al.2015a; Rosenberg & Dekel 1998, 2000, 2001b, 2004),长径比效应 (Anderson et al. 1995, 1996; Orphal et al. 1993, 1995;Rosenberg & Dekel 1994a; Walker 1999), 侵彻末段作用机理(Anderson & Orphal 2003; Orphal 1997; Rosenberg & Dekel 2000, 2001a), 陶瓷靶抗长杆侵彻机理 (Li et al. 2017;Rosenberg et al. 1995, 1997b, 1998; Zhang et al. 2011; 蒋东等 2010; 谈梦婷等 2016).大量数值模拟工作都与实验结果和理论分析相互印证以期具有说服力. ...
