基于空穴聚集的高应变率低应力三轴性拉伸断裂机理研究
|
摘要
本论文以典型的延性金属材料——纯铜为研究对象，研究高应变率低应力三轴性拉伸断裂及有关的高应变率本构方程。主要创新点如下：
1）计及第三偏应力不变量（罗德角）效应[Bai. Int. J. plasticity24,1071(2008)]，确定调整典型延性金属材料—纯铜的热粘塑本构方程，适于描述纯铜杆与板条的大变形：
为分析和预估高应变率低应力三轴性对典型延性金属材料—纯铜拉伸断裂的影响，计及罗德角效应，由经优化的Hopkinson拉伸试验的第一次冲击拉伸脉冲，合理确定了纯铜杆件/板条材料的热粘塑本构方程。通过比较高速摄影记录与数值模拟纯铜杆件/板条试件在Hopkinson拉伸试验的多次冲击拉伸下包括非局部化颈缩的大变形，调整所确定的热粘塑本构方程，适于描述纯铜杆与板条的大变形。
2）研究了纯铜杆件动态非局部化颈缩，验证了Batra[Int. J. Impact Eng.34,448(2007)]的热粘塑失稳判据：
由于惯性、热软化及应变率硬化，杆件动态非局部化颈缩比准静态更为复杂，一直存在不同论点。采用高速摄影记录纯铜杆试件在Hopkinson拉伸试验中变形的全过程，发现试件表面上的皱褶对应于试件发生非局部化颈缩，由此从实验上确定了杆件发生非局部化颈缩的临界应变。采用上述调整确定的纯铜杆材料热粘塑本构方程，按Batra最近基于摄动理论导出的热粘塑失稳判据所估算的临界应变与实验确定值基本一致，从而证实了Batra热粘塑失稳判据的有效性。
3）发展了一种独特的局部应变受控高应变率低应力三轴性冲击拉伸断裂试验方法：
在我们所发明的高速冲击拉伸试验装置上，对多根纯铜杆试件设置特制夹具，控制纯铜杆试件不同的局部延伸，在同一冲击拉伸速度下，得到试件变形过程不同阶段的实验结果，取得冲击拉伸杆颈缩与断裂“凝固化”了的过程信息。扫描电镜对“凝固化”过程的分析，揭示了空穴增长与聚集机理：稳定的空穴聚集由于主空穴的相互接近；失稳的空穴聚集由于空穴间基体的颈缩和剪切。
4）提出了一种计及特征空穴动态演化的数值模拟方法:
引入Ragab[Eng. Fract. Mech.71,1515(2004)]由实验确定的特征空穴，采用上述调整确定的纯铜杆材料的热粘塑本构方程，提出了一种计及特征空穴动态演化的数值模拟方法。分析和预估了应变率及应力三轴性对Hopkinson拉伸试验及上述高速冲击拉伸试验中试件的变形和断裂的影响。此种数值模拟揭示了颈缩区特征空穴的演化过程以及应力三轴性与应变率变化，结合扫描电镜观测分析，试图解释实验现象。颈缩区边界附近的微空穴数量与大小大于颈缩区中心处，纯铜杆试件的断裂可能由边界发展到内部，此现象可以解释Alves等[J. Mech. Phys.Solids47,643(1999)]提出的疑问：虽然应力三轴性在颈缩区中心最大，为什么断裂总是从颈缩的外边界发生？
5）基于空穴形状演化，提出了一种空穴动态失稳判据:
提出了一种动态计算纯铜空穴单元模型，分析和预估冲击拉伸纯铜杆件的断裂应变及临界冲击拉伸速度。讨论了基于准静态数值计算的空穴失稳准则[Pardoen et al., J.Mech. Phys. Solids48,2467(2000). Benzerga, J. Mech. Phys. Solids50,1331(2002)]，提出了一种基于空穴形状演化的动态失稳判据。采用此动态失稳判据预估的Hopkinson拉伸试验及上述高速冲击拉伸实验中纯铜杆的冲击拉伸断裂应变与实验值基本一致。采用此种判据预估的纯铜临界冲击拉伸速度也与利用上述高速冲击拉伸断裂试验装置得到的实验临界冲击拉伸速度。
6）发展了一种研究空穴簇动态聚集机理的方法，提出了一种动态空穴聚集判据：
为了直接观测空穴簇的增长与聚集，采用Hopkinson拉伸试验装置，研究纯铜板条上预置空穴簇在多次冲击拉伸脉冲下的演化过程。采用高速摄影记录这些预置空穴簇的动态增长、聚集及聚集后的演化过程。采用上述调整确定的纯铜板条材料本构方程以及空穴聚集判据，数值模拟预置空穴簇的演化过程，提出了一种依赖于应力三轴性及应变率的空穴聚集判据，试图揭示空穴聚集过程。比较在纯铜板条试件一定平均应变下实验记录的与数值模拟的空穴聚集后图像，可检验空穴聚集判据的有效性。数值模拟中，也采用了由我们局域化了的Thomason[Ductile fracture of metals (PergamonPress,1990), Fatigue Frac Eng Matter Struc.21,1105(1998)]及Brown-Embury判据[Proceeding of3rd international conference on strength of metals and alloys1973.p.164~173.]。结果表明，我们提出的依赖于应力三轴性和应变率的空穴失稳判据能够描述空穴聚集过程，局域化了的Thomason和Brown-Embury空穴聚集判据在一定程度上也能与空穴聚集过程相一致。
In this doctoral dissertation, typical ductile metal-pure copper is the main reseach object.This dissertation mainly studies ductile tension fraction and related constitutive equationunder high strain rate and low stress triaxiality. The following are the innovations in thisdissertation:
1) Thermoviscoplastic constitutive equations of typical ductile material-a pure copperwere determined and adjusted with considering the third deviatoric stress invariant (Lodeangle parameter) dependence [Bai et al. Int. J. plasticity24,1071(2008)] to describe largerstrain of the pure copper bars and sheets:
In order to analyse and predict the effect of high strain rate and low stress triaxialityon tension fracture of bars and sheets made of typical ductile material-a pure copper, welldefined thermoviscoplastic constitutive equations of the pure copper were determined fromthe first tension loading in the optimized tensile split Hopkinson bar (TSHB) tests for copperbars and sheets, considering the third deviatoric stress invariant (Lode angle parameter)dependence. In order to describe large strain of pure copper bars and sheets, the determinedthermoviscoplastic constitutive equations were adjusted in numerically simulating the largedeformations including the diffuse necking of pure copper bars and sheets generated by themulti-tension loading in TSHB tests and recorded by a high speed camera.
2) The dynamic diffuse necking of pure copper bars was investigated with verifyingBatra criterion [Int. J. Impact Eng.34,448(2007)] for thermoviscoplastic instability:
It was found that the surface wrinkles on pure copper bars recorded by the high speedcamera in TSHB tests were connected to the diffuse necking which are more complexphenomena than in static case due to inertia, thermal softening and strain rate hardening andneed well understanding. The instability criterion for homogeneous simple tensiledeformations of a thermoviscoplastic bar presented recently by Batra et al with perturbationmethod was verified by the comparison between the recorded strain at which the surfacewrinkles on pure copper bars occur and the estimated strains according to Batra criterion andour adjusted theomoviscoplastic constitutive equation for pure copper bars.
3) A novel fracture testing under high strain rate and low stress triaxiality tension wasdeveloped to interrupt the test at different levels of deformation:
It was realized to interrupt, isolate and identify the various stages of the dynamicfracture process of pure copper bars under impact tension, by using our designed high-speed tensile facility (HSTF) tests in which multiple-bars with special fixture were tested andcontrolled at different levels of elongation in a single test. It was shown that diffuse neckingof bars developed into localized necking, and voids within the necking zone nucleated, grewand coalesced as the controlled elongation increased. Different mechanisms of voidcoalescence in pure copper were observed from scanning electron microscopical (SEM)investigation: stable coalescence through impingement of primary voids; unstable coalescencethrough necking and shearing of the primary intrevoid ligament.
4) A numerical simulation method was presented with involving dynamic evolution ofa characteristic void:
A numerical simulation method with a characteristic void identified by Ragab[Eng.Fract. Mech.71,1515(2004)] experimentally was presented by using our adjustedthermoviscoplastic constitutive equation for pure copper bar to analyse and predict the effectsof strain rate and stress triaxiality on tension deformation and fracture of pure copper bars inTSHB tests and interrupted HSTF tests. The variations of stress triaxiality and strain rate withtime in necking zone computed with the numerical simulation method were connected to theSEM investigation for recovered localized necking zones. It was found that although thestress triaxiality is a maximum in the middle of the necking zone, void evolution at a positionnear the surface of minimum cross-section of the necking zone was more severe than in themiddle of the necking zone, which may be connected with the finding discussed by Alves[J.Mech. Phys. Solids47,643(1999)]“a crack started to run probably from the notch root,certainly not from the middle where the triaxiality is a maximum.”
5) A dynamic void instability criterion was presented based on void shape evolution:
A dynamically computational void cell model was presented for pure copper toanalyse and predicted the localized fracture strains and the critical impact velocity in tensionof pure copper bars. The instability criteria obtained from quasi static numerical simulation[Pardoen et al., J. Mech. Phys. Solids48,2467(2000). Benzerga, J. Mech. Phys. Solids50,1331(2002)]were discussed and a dynamic void instability criterion based on void shapeevolution was presented, which predicted the fracture strains consistent with the experimentalresults of pure copper bars in TSHB tests and the critical impact velocity of pure copper intension consistent with the experiments in HSTF tests.
6) A method for investigating the dynamic coalescence mechanism of void cluster wasdeveloped with proposing a dynamic criterion for void coalescence:
In order to visualize void growth and coalescence in a controlled matter, the dynamicgrowth, coalescence and evolution post coalescence of drilled simplest cluster voids in purecopper sheets subjected to the multi-tension loading in the TSHB tests were recorded by the high speed camera and simulated by using our adjusted constitutive equation of the purecopper and the different criteria for void coalescence. This study presented a stress triaxialityand strain rate (STSR) dependent failure criterion for void coalescence to reveal the voidcoalescence process. The experimentally recorded void evolution at a certain average strain ofpure copper sheets were compared with the numerically simulated results, which involved theSTSR dependent failure criterion, the localized Thomason criterion[Ductile fracture of metals(Pergamon Press,1990), Fatigue Frac Eng Matter Struc.21,1105(1998)] and Brown-Embury criterion[Proceeding of3rd international conference on strength of metals and alloys1973. p.164~173.]. The validity of void coalescence criteria was assessed: the STSRdependent failure criterion could be used to describe the void coalescence process while thelocalized Thomason criterion and Brown-Embury criterion for void cluster could also matchthe process of void coalescence to a certain extent.
1）计及第三偏应力不变量（罗德角）效应[Bai. Int. J. plasticity24,1071(2008)]，确定调整典型延性金属材料—纯铜的热粘塑本构方程，适于描述纯铜杆与板条的大变形：
为分析和预估高应变率低应力三轴性对典型延性金属材料—纯铜拉伸断裂的影响，计及罗德角效应，由经优化的Hopkinson拉伸试验的第一次冲击拉伸脉冲，合理确定了纯铜杆件/板条材料的热粘塑本构方程。通过比较高速摄影记录与数值模拟纯铜杆件/板条试件在Hopkinson拉伸试验的多次冲击拉伸下包括非局部化颈缩的大变形，调整所确定的热粘塑本构方程，适于描述纯铜杆与板条的大变形。
2）研究了纯铜杆件动态非局部化颈缩，验证了Batra[Int. J. Impact Eng.34,448(2007)]的热粘塑失稳判据：
由于惯性、热软化及应变率硬化，杆件动态非局部化颈缩比准静态更为复杂，一直存在不同论点。采用高速摄影记录纯铜杆试件在Hopkinson拉伸试验中变形的全过程，发现试件表面上的皱褶对应于试件发生非局部化颈缩，由此从实验上确定了杆件发生非局部化颈缩的临界应变。采用上述调整确定的纯铜杆材料热粘塑本构方程，按Batra最近基于摄动理论导出的热粘塑失稳判据所估算的临界应变与实验确定值基本一致，从而证实了Batra热粘塑失稳判据的有效性。
3）发展了一种独特的局部应变受控高应变率低应力三轴性冲击拉伸断裂试验方法：
在我们所发明的高速冲击拉伸试验装置上，对多根纯铜杆试件设置特制夹具，控制纯铜杆试件不同的局部延伸，在同一冲击拉伸速度下，得到试件变形过程不同阶段的实验结果，取得冲击拉伸杆颈缩与断裂“凝固化”了的过程信息。扫描电镜对“凝固化”过程的分析，揭示了空穴增长与聚集机理：稳定的空穴聚集由于主空穴的相互接近；失稳的空穴聚集由于空穴间基体的颈缩和剪切。
4）提出了一种计及特征空穴动态演化的数值模拟方法:
引入Ragab[Eng. Fract. Mech.71,1515(2004)]由实验确定的特征空穴，采用上述调整确定的纯铜杆材料的热粘塑本构方程，提出了一种计及特征空穴动态演化的数值模拟方法。分析和预估了应变率及应力三轴性对Hopkinson拉伸试验及上述高速冲击拉伸试验中试件的变形和断裂的影响。此种数值模拟揭示了颈缩区特征空穴的演化过程以及应力三轴性与应变率变化，结合扫描电镜观测分析，试图解释实验现象。颈缩区边界附近的微空穴数量与大小大于颈缩区中心处，纯铜杆试件的断裂可能由边界发展到内部，此现象可以解释Alves等[J. Mech. Phys.Solids47,643(1999)]提出的疑问：虽然应力三轴性在颈缩区中心最大，为什么断裂总是从颈缩的外边界发生？
5）基于空穴形状演化，提出了一种空穴动态失稳判据:
提出了一种动态计算纯铜空穴单元模型，分析和预估冲击拉伸纯铜杆件的断裂应变及临界冲击拉伸速度。讨论了基于准静态数值计算的空穴失稳准则[Pardoen et al., J.Mech. Phys. Solids48,2467(2000). Benzerga, J. Mech. Phys. Solids50,1331(2002)]，提出了一种基于空穴形状演化的动态失稳判据。采用此动态失稳判据预估的Hopkinson拉伸试验及上述高速冲击拉伸实验中纯铜杆的冲击拉伸断裂应变与实验值基本一致。采用此种判据预估的纯铜临界冲击拉伸速度也与利用上述高速冲击拉伸断裂试验装置得到的实验临界冲击拉伸速度。
6）发展了一种研究空穴簇动态聚集机理的方法，提出了一种动态空穴聚集判据：
为了直接观测空穴簇的增长与聚集，采用Hopkinson拉伸试验装置，研究纯铜板条上预置空穴簇在多次冲击拉伸脉冲下的演化过程。采用高速摄影记录这些预置空穴簇的动态增长、聚集及聚集后的演化过程。采用上述调整确定的纯铜板条材料本构方程以及空穴聚集判据，数值模拟预置空穴簇的演化过程，提出了一种依赖于应力三轴性及应变率的空穴聚集判据，试图揭示空穴聚集过程。比较在纯铜板条试件一定平均应变下实验记录的与数值模拟的空穴聚集后图像，可检验空穴聚集判据的有效性。数值模拟中，也采用了由我们局域化了的Thomason[Ductile fracture of metals (PergamonPress,1990), Fatigue Frac Eng Matter Struc.21,1105(1998)]及Brown-Embury判据[Proceeding of3rd international conference on strength of metals and alloys1973.p.164~173.]。结果表明，我们提出的依赖于应力三轴性和应变率的空穴失稳判据能够描述空穴聚集过程，局域化了的Thomason和Brown-Embury空穴聚集判据在一定程度上也能与空穴聚集过程相一致。
In this doctoral dissertation, typical ductile metal-pure copper is the main reseach object.This dissertation mainly studies ductile tension fraction and related constitutive equationunder high strain rate and low stress triaxiality. The following are the innovations in thisdissertation:
1) Thermoviscoplastic constitutive equations of typical ductile material-a pure copperwere determined and adjusted with considering the third deviatoric stress invariant (Lodeangle parameter) dependence [Bai et al. Int. J. plasticity24,1071(2008)] to describe largerstrain of the pure copper bars and sheets:
In order to analyse and predict the effect of high strain rate and low stress triaxialityon tension fracture of bars and sheets made of typical ductile material-a pure copper, welldefined thermoviscoplastic constitutive equations of the pure copper were determined fromthe first tension loading in the optimized tensile split Hopkinson bar (TSHB) tests for copperbars and sheets, considering the third deviatoric stress invariant (Lode angle parameter)dependence. In order to describe large strain of pure copper bars and sheets, the determinedthermoviscoplastic constitutive equations were adjusted in numerically simulating the largedeformations including the diffuse necking of pure copper bars and sheets generated by themulti-tension loading in TSHB tests and recorded by a high speed camera.
2) The dynamic diffuse necking of pure copper bars was investigated with verifyingBatra criterion [Int. J. Impact Eng.34,448(2007)] for thermoviscoplastic instability:
It was found that the surface wrinkles on pure copper bars recorded by the high speedcamera in TSHB tests were connected to the diffuse necking which are more complexphenomena than in static case due to inertia, thermal softening and strain rate hardening andneed well understanding. The instability criterion for homogeneous simple tensiledeformations of a thermoviscoplastic bar presented recently by Batra et al with perturbationmethod was verified by the comparison between the recorded strain at which the surfacewrinkles on pure copper bars occur and the estimated strains according to Batra criterion andour adjusted theomoviscoplastic constitutive equation for pure copper bars.
3) A novel fracture testing under high strain rate and low stress triaxiality tension wasdeveloped to interrupt the test at different levels of deformation:
It was realized to interrupt, isolate and identify the various stages of the dynamicfracture process of pure copper bars under impact tension, by using our designed high-speed tensile facility (HSTF) tests in which multiple-bars with special fixture were tested andcontrolled at different levels of elongation in a single test. It was shown that diffuse neckingof bars developed into localized necking, and voids within the necking zone nucleated, grewand coalesced as the controlled elongation increased. Different mechanisms of voidcoalescence in pure copper were observed from scanning electron microscopical (SEM)investigation: stable coalescence through impingement of primary voids; unstable coalescencethrough necking and shearing of the primary intrevoid ligament.
4) A numerical simulation method was presented with involving dynamic evolution ofa characteristic void:
A numerical simulation method with a characteristic void identified by Ragab[Eng.Fract. Mech.71,1515(2004)] experimentally was presented by using our adjustedthermoviscoplastic constitutive equation for pure copper bar to analyse and predict the effectsof strain rate and stress triaxiality on tension deformation and fracture of pure copper bars inTSHB tests and interrupted HSTF tests. The variations of stress triaxiality and strain rate withtime in necking zone computed with the numerical simulation method were connected to theSEM investigation for recovered localized necking zones. It was found that although thestress triaxiality is a maximum in the middle of the necking zone, void evolution at a positionnear the surface of minimum cross-section of the necking zone was more severe than in themiddle of the necking zone, which may be connected with the finding discussed by Alves[J.Mech. Phys. Solids47,643(1999)]“a crack started to run probably from the notch root,certainly not from the middle where the triaxiality is a maximum.”
5) A dynamic void instability criterion was presented based on void shape evolution:
A dynamically computational void cell model was presented for pure copper toanalyse and predicted the localized fracture strains and the critical impact velocity in tensionof pure copper bars. The instability criteria obtained from quasi static numerical simulation[Pardoen et al., J. Mech. Phys. Solids48,2467(2000). Benzerga, J. Mech. Phys. Solids50,1331(2002)]were discussed and a dynamic void instability criterion based on void shapeevolution was presented, which predicted the fracture strains consistent with the experimentalresults of pure copper bars in TSHB tests and the critical impact velocity of pure copper intension consistent with the experiments in HSTF tests.
6) A method for investigating the dynamic coalescence mechanism of void cluster wasdeveloped with proposing a dynamic criterion for void coalescence:
In order to visualize void growth and coalescence in a controlled matter, the dynamicgrowth, coalescence and evolution post coalescence of drilled simplest cluster voids in purecopper sheets subjected to the multi-tension loading in the TSHB tests were recorded by the high speed camera and simulated by using our adjusted constitutive equation of the purecopper and the different criteria for void coalescence. This study presented a stress triaxialityand strain rate (STSR) dependent failure criterion for void coalescence to reveal the voidcoalescence process. The experimentally recorded void evolution at a certain average strain ofpure copper sheets were compared with the numerically simulated results, which involved theSTSR dependent failure criterion, the localized Thomason criterion[Ductile fracture of metals(Pergamon Press,1990), Fatigue Frac Eng Matter Struc.21,1105(1998)] and Brown-Embury criterion[Proceeding of3rd international conference on strength of metals and alloys1973. p.164~173.]. The validity of void coalescence criteria was assessed: the STSRdependent failure criterion could be used to describe the void coalescence process while thelocalized Thomason criterion and Brown-Embury criterion for void cluster could also matchthe process of void coalescence to a certain extent.
引文
[1] Batra R C, Wei Z G. Shear band spacing in thermoviscoplastic materials [J]. Int. J. ImpactEng.2006,32(6):947-967.
[2] Batra R C, Wei Z G. Instability strain and shear band spacing in simple tensile/compressivedeformations of thermoviscoplastic materials [J]. Int. J. Impact Eng.,2007,34(3):448-463.
[3] Tonks D L, Zurek, A K, Thissel W R, Void Coalesence model for ductile damage. Shockcompression of condensed Matter,2001[C], edited by M. D. Furnish, N. N. Thadhani, Y.Horie, American institute of physics,2002.
[4] Bai Y L, Xia M F, Ke F J, et al. Statistical microdamage mechanics and damage fieldevolution [J]. Theo. Appl. Frac. Mech.,2001,37(1-3):1-10.
[5] Pardoen T, Hutchinson J W, An extended model for void growth and Coalescence [J]. J.Mech. Phys. Solids,2000,48:2467-2512.
[6] Gurson, A L. Continuum theory of ductile rupture by void nucleation and growth, Part I—Yield criteria and flow rules for porous ductile media [J]. J. Eng. Mater. Tech.,1977,99:2–15.
[7] Thomason P F. Ductile Fracture of Metals [M]. Oxford: Pergamon Press,1990
[8] Benzerga A A. Micromechanics of coalescence in ductile fracture [J]. J. Mesh. phys. solids,2002,50:1331-1362.
[9] Ragab A R. A model for ductile fracture based on internal necking of spheroidal voids [J].Acta Mater.,2004,54:3997-1009.
[10] Bandsta J P, Koss D A. Simulation of growth and coalescence of voids during ductilefracture [J]. Mater. Sci. Eng. A,2004,387-389:399-403.
[11] Bandstra J P, Koss D A. Modeling the ductile fracture process of void coalescence by void-sheet formation [J]. Mater. Sci. Eng. A,2001,319-321:490-495.
[12] Bandstra J P, Koss D A, Geltmacher A, et al. Modeling void coalescence during ductilefracture of a steel [J]. Mater. Sci. Eng. A,2004,366(2):269-281.
[13] Bandstra J P, Koss D A. On the influence of void clusters on void growth and coalescenceduring ductile fracture [J]. Acta Mater.,2008,56(16):4429-4439.
[14] Orsini V C, Zikry M A. Void growth and interaction in crystalline materials [J]. Int. J.Plasticity,2001,17()10:1393-1417.
[15] Potirniche G. P, Hearndon J L, Horstemeyer M F, et al. Lattice orientation effects on voidgrowth and coalescence in fcc single crystals [J]. Int. J. Plasticity,2006,22(5):921-942.
[16] Yang M., Dong X H. Simulation of lattice orientation effects on void growth andcoalescence by crystal plasticity [J]. Acta Metallurgica Sinica (English Letters),2009,22.
[17] Ragab A R. Application of an extended void growth model with strain hardening and voidshape evolution to ductile fracture under axisymmetric tension [J]. Eng. Fract. Mech.,2004,71:1515-1534.
[18] Niordson C F. Void growth to coalescence in a non-local material [J]. Euro. J. Mech.A/Solids,2008,27:222-233.
[19] Fabregue D, Pardoen T. A constitutive model for elastoplastic solids containing primary andsecondary voids [J]. J. Mech. Phys. Solids,2008,56:719-741
[20] Lassance D, Scheyvaerts F, Pardoen T. Growth and Coalescence of penny-shaped voids inmetallic alloys [J]. Eng. Fract. Mech.,2006,73:1009-1034.
[21] Gotoh M, Yamashita M. Chaotic behavior of an elastoplastic bar in tensile test over a widerange of strain rate: a numerical investigation [J]. Int. J. Mech. Sci.,2000,42:1593-1606.
[22] Rusinek A, Zaera R, Klepaczko J R, et al. Analysis of inertia and scale effects on dynamicneck formation during tension of sheet steel [J]. Acta Mater.,2005,53:5387-5400.
[23] Sturges J L, Cole B N. The flying wedge: a method for high strain rate tensile testing. part1:Reasons for its development and general description [J]. Int. J. Impact Eng,2001,25:256-264.
[24] Barton D C. Determination of the high strain rate fracture properties of ductile materialsusing a combined experimental/numerical approach [J]. Int. J. Impact Eng.,2004,30:1147-1159.
[25] Hu JinWei, Jin YanHui, Chen Danian, et al. Measurement of critical impact velocity ofcopper in tension [J]. Chin. Phys. Lett.,2008,25(3):1049-1051.
[26] Jia S, Povirk G L. Modeling the effects of hole distribution in perforatedaluminum sheets II: minimum strength failure paths [J]. Int. J. Solids and Struc,2002,39(9):2533-2545.
[27] Weck A, Wilkinson D S. Experimental investigation of void coalescence in metallic sheetscontaining laser drilled holes [J]. Acta Mater.,2008,56(8):1774-1784.
[28] Weck A, Wilkinson D S, Maire E. Observation of void nucleation, growth and coalescencein a model metal matrix composite using X-ray tomography [J]. Mater. Sci. Eng. A,2008,488(1-2):435-445.
[29] Weck A, Wilkinson D S, Maire E, et al. Visualization by X-ray tomography of void growthand coalescence leading to fracture in model materials [J]. Acta Mater.2008,56(12):2919-2928.
[30] Smerd R, Winkler S, Salisbury C, et al. High strain rate tensile testing of automotivealuminum alloy sheet [J]. Int. J. Impact Eng.,2005,32(1-4):541-560.
[31] Wei X C, Fu R Y, Li L. Tensile deformation behavior of cold-rolled TRIP-aided steels overlarge range of strain rates [J]. Mate. Sci. Eng. A,2007,465(1-2):260-266.
[32] Huang C G, Chen S Y, Duan Z P. Real-time measurement on deformation fields of notchedsamples under impact tension [J]. Int. J. Impact Eng.,2005,31:329-339.
[33] Rittel D, Wang Z G, Dorogoy A. Geometrical imperfection and adiabatic shear banding [J].Int. J. Impact Eng.,2008,35(11):1280-1292.
[34] Wright T W, Ramesh K T. Statistically informed dynamics of void growth in rate dependentmaterials [J]. Int. J. Impact Eng.,2009,36(10-11):1242-1249.
[35] Ma D F, Chen D N, Wu S X, et al. An interrupted tensile testing at high strain rates for purecopper bars[J]. J. Appl. Phy.,2010,108:114902(1-13).
[36] Ma D F, Chen D N, Wu S X, et al. A dynamic investigation of observable void growth andcoalescence in pure copper sheets [J]. J. Appl. Phy.,2011,094905(1-17)
[37] Ma D F, Chen D N, Wu S X, et al. Analysis of thermoviscoplastic effects on dynamic neckformation during tension of copper bar [J]. Int. J. Nonlinear Sci. Num. Simulation,2011.Accepted.
[38]贾存威，侯延军，陈大年等. Hopkinson拉杆试验的优化与高导无氧铜拉伸本构关系的确定[J].固体力学学报,32(1):57-62.
[39]吴善幸，陈大年，张铎，马东方等.圆柱壳体冲击平板靶的实验与数值研究[J].工程力学,2010,27(3):10-14.
[40] Wu S X, Chen D N, Ma D F et al. The influences of constitutive models on the collapses ofOFHC copper cylindrical shells under impact compression[J]. Advanced Mater. Res.,2011,179:691-696.
[41] Bai Y L, Werzbicki T. A new model of metal plasticity and fracture with pressure and Lodedependence [J]. Int. J. plasticity,2008,24:1071-1096.
[42] Ma D F, Hou Y J, Chen D N, et al.A novel impact tension testing for OFHC copper barsunder local strain controlled[J].Chinese Phy. Letters,2011,28(1):016201.
[43] Joun M S, Choi I., Eom J G, et al. Finite element analysis of tensile testing with emphasis onnecking [J]. Computational Mater. Sci.,2007,41:63-69.
[44]马东方，陈大年，吴善幸等.高导无氧铜动态本构关系对于单轴冲击拉伸下空穴增长和失稳的影响[J].兵工学报,2009,30:74-79.
[45]陈大年,吴善幸,王焕然,马东方等.冲击载荷下延性材料的动态本构关系与动态断裂[J].兵工学报,2010,31(6):725-734.
[46]吴善幸，马东方,陈大年等.冲击拉伸下含孔高导无氧铜板中空穴增长与聚集的实验与数值研究[J].兵工学报,2009,30:134-138.
[47]陈大年,胡金伟,金扬辉等.高导无氧铜的临界冲击拉伸速度[J].爆炸与冲击,2009,29(2):113-118.
[48]马东方,侯延军,陈大年,等.高导无氧铜杆的冲击拉伸断裂系列实验以及基于样本体积单元的分析[J].爆炸与冲击,2011,31(4):385-391.
[49] Ma D F, Deng G T, Chen D N, et al. A visualized investigation of void growth andcoalescence in pure copper sheets under impact tension[J]. Advanced Mater. Res.,2011,317-319:1717-1724.
[50] Ma D F, Chen D N, Wu S X et al. Dynamic Experimental verification of void coalescencecriteria[J]. Mater. Sci. Eng. A,2012,533:96-106.
[51]金杨辉，贾存威，陈大年，马东方，吴善幸，王焕然。高导无氧铜杆在高应变率拉伸下的颈缩与断裂研究[J].应用力学学报，2009,26(4):776-782.
[52] Brown M, Embury D. Proceeding of3rdinternational conference on strength of metals andalloys [C]. London: Institute of Metals,1973.
[53]张学言.岩土塑性力学[M].北京：人民交通出版社，1993.
[54]郑颖人，沈珠江，龚晓南.岩土塑性力学原理：广义塑性力学[M].北京：中国建筑工业出版社，2002.
[55] Bardet J.Lode dependences for isotropic pressure-sensitive elastoplastic materials [J]. J. Appl.Mech, Transactions ASME,1990,57(3):498-506.
[56] Menetrey P, Willam K. Triaxial failure criterion for concrete and its generalization [J]. ACIStruc. J,1995,92:311-318.
[57] Wilson C D. A critical reexamination of classical metal plasticity [J]. J. Appl. Mech,Transactions ASME,2002,69(1):63-68.
[58] Richmond O, Spitzig W A. Theoretical and Applied Mechanics, Proceedings of the15thInternational Congress of Theoretical and Applied Mechanics [C]. Toronto: Ont., Canada.North-Holland Publ. Co.,1980.
[59] Gurson A L. Plastic flow and fracture behavior of ductile materials incorporating voidnucleation, growth and interaction[D]. Brown University,1975.
[60] Needleman A, Tvergaard V. An analysis of ductile rupture in notched bars [J]. J. Mech. Phy.Solids,1984,32(6):461-490.
[61] Cazacu O, Plunkeet B, Barlat F. Orthotropic yield criterion for hexagonal closed packedmetals [J]. Int. J. Plasticity,2006,22(7):1171-1194.
[62]陈大年，范春雷，胡金伟等.高导无氧铜的高压与高应变率本构关系研究.物理学报，2009，58(4):2612-2618.
[63] Johnson G R, Holmquist, T J. Evaluation of cylinder-impact test data for constitutive modelconstants[J]. J. Appl. Phys.,1988,64:3901~3910.
[64]吴善幸.冲击荷载下纯铜的本构关系与结构失稳研究[D].西安：西北工业大学航空学院，2011.
[65] Johnson GR, Cook WH. A constitutive model and data for metals subjected to large strains,high strain-rates and high temperatures. Proceedings of seventh international symposium onBallistics [C], The Hague, The Netherlands, April1983.
[66] Zerilli F J, Armstrong R W. Dislocation-mechanics-based constitutive relations for materialdynamics calculations[J]. J. Appl. Phy.,1987,61:1816-1825.
[67] Rule W K, Jones S E. A revised form for the Johnson-Cook strength model [J]. Int. J. ImpactEng.,1998,21:609~624.
[68] Chen DN, Fan CL, Xie SG., Hu JW, Wu SX, Wang HR. Study on constitutive relations andspall models for oxygen-free high-conductivity copper under planar shock tests [J]. J.Appl.Phy.,2007,101:063532:1~9.
[69] Kolsky H. Stress waves in solids [M]. New York: Dover publications,1963.
[70]贾存威. Hopkinson拉杆试验的优化与高导无氧铜本构关系及拉伸断裂研究[D].宁波：宁波大学机械工程与力学学院,2009.
[71] Hu X, Daehn GS. Effect of velocity on flow localization in tension [J]. Acta Mater,1996,44:1021-33
[72] Klepaczko J R. True direct split Hopkinson bar for tension tests of sheet metals, ISGMP-LPMM [J]. Internal report for Sollac, Meta:1995
[73] Waryoba D R, Kalu P N, Crooks R. Grain-boundary structure of oxygen-free high-conductivity (OFHC) copper subjected to severe plastic deformation and annealing [J]. Mater.Sci. Eng. A,2008,494:47–51.
[74] Singh B N, Edwards D J, Toft P. Effect of neutron irradiation and post-irradiation annealingon microstructure and mechanical properties of OFHC-copper [J]. J. Nuclear Mater,2001,299:205-218.
[75] Wu X J, Gorham D A. Stress Equilibrium in the Split Hopkinson Pressure Bar Test, Journalof Physics IV France, Colloque C3, Supplement au Journal de Physique Ⅲ d`aout1997,7:C3-91-C3-96
[76]王立礼.应力波基础[M].北京：国防工业出版社，2005.
[77]侯延军.冲击拉伸下纯铜杆的受录受控变形研究[D].宁波：宁波大学机械工程与力学学院,2010.
[78] Hallquist, J O. LS-DYNA Keywords Use’s Manual (Version970). USA: LSTC, April2003
[79] Klepaczko J R. True direct split Hopkinson bar for tension tests of sheet metals, ISGMP-LPMM. Internal report for Sollac, Meta:1995.
[80] Huh H, Kang WJ, Han SS. A tension split Hopkinson bar for investigating the dynamicbehavior of sheet metals [J]. Exp Mesh.,2002,42:8-17.
[81] Nicholas, T. Tensile testing of materials at high rates of strain [J]. Exp. Mech.,1981, X:177-185.
[82] Stabb GH, Gilat A. A direct-tension split Hopkinson bar for high strain-rate testing [J]. Exp.Mech.1991, X:232-5.
[83] Verleysen P, Benedict V, Verstraete T, et al. Numerical study of the influence of thespecimen geometry on split Hopkinson bar tensile test results [J]. Lat. Am. J. Solids Struct.,2009,6:285-298.
[84]吴桂英，张泽华.拉压性能不同金属材料的非经典塑性本构理论及实验研究[J].力学学报，1989,21:70-77.
[85]滕志斌，忻元华，滕博等.新编金属材料手册[M].北京：金盾出版社，2006
[86] Considerè M. L’emploi du fer et Lacier dans Les Constructions [J]. Ann Des Ponts etChausses,1885,9:574.
[87] Hart E W. Theory of the tensile test [J]. Acta Metallurgica,1967,15:351-355.
[88] Kocks U F, Jonas J J, Mecking H. The development of strain-rate gradients [J]. ActaMetallurgica,1979,27:419-432.
[89] Dumoulin D, Tabourot L, Chappuis C, et al. Determination of the equivalent stress–equivalent strain relationship of a copper sample under tensile loading [J]. J. Mater.Processing Tech.,2003,133:79-83.
[90] Joun M S, Eom J G, Lee M C. A new method for acquiring true stress-strain curves over alarge range of strains using a tensile test and finite element method[J]. Mech. Mater.,2008,40:586-593.
[91] McClintock F A. A criterion for ductile fracture by growth of holes [J]. J. Appl. Mech.,1968,35:363–371.
[92] Rice J R, Tracey D M. On the ductile enlargement of voids in triaxial stress fields [J]. J.Mech. Phys. Solids,1969,17:201–217.
[93] Needleman A. Void Growth in an Elastic-Plastic Medium [J]. J. Appl. Mech.,1972,39(4):964-970.
[94] Koplik J, Needleman A. Void growth and coalescence in porous plastic solids [J]. Int. J.Solids Struct.,1988,24:835–853.
[95] Mcmeeking R M, Hom C L. Finite element analysis of void growth in elastic-plasticmaterials [J]. Int. J. Fract.,1990,42:1-19.
[96] Hom C L, McMeeking R M. Three-dimensional void growth before a blunting crack tip [J]. J.Mech. Phys. Solids,1989,37(3):39-415.
[97] Kuna M, Sun D Z. Three-dimensional cell model analyses of void growth in ductilematerials [J]. Int. J. Fract.,1996,81:235-258.
[98] Tvergaard V. Material failure by void growth to coalescence. In: Advances in AppliedMechanics[M]. New York: Academic Press,1990.
[99] Hom C L, McMeeking R M. Void growth in elastic-plastic materials [J]. J. Appl. Mech.,1989,56:309-316.
[100] Bridgman P W. Studies in large plastic flow and fracture[M]. New York: McGraw-Hill BookCompany,1952.
[101] Chen W H. Necking of a bar [J]. Int. J. Solids struct.,1971,7:685-717.
[102] Needleman A. A numerical study of necking in circular cylindrical bar [J]. J. Mech. Phys.Solids,1972,20:111-127.
[103] Norris D M, Moran B, Scudder J K, et al. A computer simulation of the tension test [J]. J.Mech. Phys. Solids,1978,126:1-19.
[104] Chen L G. Necking in uniaxial tension [J]. Int. J. Mech. Sci.,1983,25:47-57.
[105] Alves M, Jones N. Influence of hydrostatic stress on failure of axisymmetric notchedspecimens [J]. J Mech Phys Solids.1999,47:643-667.
[106] Van Stone R H, Cox T B, Low J R, et al. Microstructural aspects of fracture by dimplerupture [J]. Int. Met. Rev.,1985,30:157–79.
[107] Garrison W M, Moody N R. Ductile fracture[J]. J. Phys. Chem. Solids,1987,48(11):1035–74.
[108] Tvergaard V. Influence of voids on shear band instabilities under plane strain conditions [J].Int. J. Frac.,1981,17:389–407.
[109] Faleskog J, Shih C F. Micromechanics of coalescence—I. Synergistic effects of elasticity,plastic yielding and multi-size-scale voids [J]. J. Mech. Phys. Solids,1997,45:21–45.
[110] Needleman A, Tvergaard V. An analysis of ductile rupture modes at a crack tip [J]. J. Mech.Phys. Solids,1987,35:151–183.
[111] McClintock F A. Local criteria for ductile fracture [J]. Int. J. Frac.,1968,4:103-130.
[112] Thomason P F. Ductile fracture by the growth and coalescence of microvoids of non-uniformsize and spacing [J]. Acta Metall. Mater.,1993,41:2127-2134.
[113] Bilby B A, Howard I C, Li Z H. Prediction of the first spinning cylinder test using ductiledamage theory [J]. Fatigue Frac. Eng. Mater. Struc.,1993,16:1–20.
[114] Xia L, Shih C F. Ductile crack growth—I. A numerical study using computational cellswith microstructurally-based length scales [J]. J. Mech. Phys. Solids,1995,43:233–259.
[115] Xia L, Shih C F. Ductile crack growth—II. Void nucleation and geometry effects onmacroscopicfracture behaviour [J]. J. Mech. Phys. Solids,1995,43:1953–1981.
[116] Xia L, Shih C F, Hutchinson J W. A computational approach to ductile crack growth underlarge scale yielding conditions[J]. J. Mech. Phys. Solids,1995,43:389–413.
[117] Ruggieri C, Panontin T L, Dodds R H. Numerical modeling of ductile crack growth in3-Dusing computational cell elements [J]. Int. J. Frac.,1996,82:67–95.
[118] Gao X, Faleskog J, Shih C F. Cell model for nonlinear fracture analysis—II. Fracture-process calibration and verification [J]. Int. J. Frac.,1998,89:374–386.
[119] Tvergaard V. On localization in ductile materials containing voids [J]. Int. J. Frac.,1982,18:237–251.
[120] Kim J, Gao X S, Srivatsan T S. Modeling of void growth in ductile solids: effects of stresstriaxiality and initial porosity [J]. Eng. Frac. Mech.,2004,71:379-400.
[121] Curran DR, Seaman L, Shockey DA. Dynamic failure of solids. Phys. Reports1987,147:253-388.
[122] Ortiz M, Molinari A. Effect of strain hardening and rate sensitivity on the dynamic growth ofa void in a plastic material [J]. J. Appl. Mech.1992,59:48-53.
[123] Tong W, Ravichandran G. Inertial effects on void growth in porous viscoplastic materials [J].J. Appl. Mech.1995,62:633-639.
[124] Wu XY, Ramesh, KT, Wright TW. The dynamic growth of a single void in a viscoplasticmaterial under transient hydyostatic loading. J. Mech. Phys. Solids2003,51:1-26
[125] Gologanu M, Leblond J B. Approximate models for ductile metals containing non-sphericalvoids-Case of axisymmetric prolate ellipsoidal cavities [J]. J. Mech. Phys. Solids,1993,41(11):1723-1754.
[126] Mann H C, High-velocity tension-impact tests[J]. Proceedings ASTM,1936,36:85-108
[127] Clark DS. The influence of impact velocity on the tensile characteristics of some aircraftmetals and alloys. Technical Note No.868, National Advisory Committee for Aeronautics,October1942.
[128] Duwez PE, Clark DS. An experimental study of the propagation of plastic deformationunder conditions of longitudinal impact. Proceedings, Am. Soc. Testing Mats.1947,47:502.
[129] Clark DS, Duwez PE. Discussion of the forces acting in tension impact tests of materials [J].J. Appl. Mech.,1948,15(3): A243.
[130] Clark DS, Wood DS. The tensile impact properties of some metals and alloys [J].Transactions, Am. Soc. Metals.,1950,42:45.
[131] Clark DS, Wood. DS. The influence of specimen dimension and shape on the results intension impact testing [J]. Proceedings ASTM,1950,50:577-585.
[132] Wood WW. Experimental determination of shear modulus of laminated fiber-reinforcedcomposites [J]. Experimental Mech.,1967,7(10):441-446.
[133]陈大年,尹志华.对膨胀壳体失稳的一种简化处理[J].爆炸与冲击,1999,19:193-198.
[134]金扬辉.高导无氧铜杆件的颈缩断裂与临界冲击拉伸速度研究[D]。浙江宁波：宁波大学，2008.
[2] Batra R C, Wei Z G. Instability strain and shear band spacing in simple tensile/compressivedeformations of thermoviscoplastic materials [J]. Int. J. Impact Eng.,2007,34(3):448-463.
[3] Tonks D L, Zurek, A K, Thissel W R, Void Coalesence model for ductile damage. Shockcompression of condensed Matter,2001[C], edited by M. D. Furnish, N. N. Thadhani, Y.Horie, American institute of physics,2002.
[4] Bai Y L, Xia M F, Ke F J, et al. Statistical microdamage mechanics and damage fieldevolution [J]. Theo. Appl. Frac. Mech.,2001,37(1-3):1-10.
[5] Pardoen T, Hutchinson J W, An extended model for void growth and Coalescence [J]. J.Mech. Phys. Solids,2000,48:2467-2512.
[6] Gurson, A L. Continuum theory of ductile rupture by void nucleation and growth, Part I—Yield criteria and flow rules for porous ductile media [J]. J. Eng. Mater. Tech.,1977,99:2–15.
[7] Thomason P F. Ductile Fracture of Metals [M]. Oxford: Pergamon Press,1990
[8] Benzerga A A. Micromechanics of coalescence in ductile fracture [J]. J. Mesh. phys. solids,2002,50:1331-1362.
[9] Ragab A R. A model for ductile fracture based on internal necking of spheroidal voids [J].Acta Mater.,2004,54:3997-1009.
[10] Bandsta J P, Koss D A. Simulation of growth and coalescence of voids during ductilefracture [J]. Mater. Sci. Eng. A,2004,387-389:399-403.
[11] Bandstra J P, Koss D A. Modeling the ductile fracture process of void coalescence by void-sheet formation [J]. Mater. Sci. Eng. A,2001,319-321:490-495.
[12] Bandstra J P, Koss D A, Geltmacher A, et al. Modeling void coalescence during ductilefracture of a steel [J]. Mater. Sci. Eng. A,2004,366(2):269-281.
[13] Bandstra J P, Koss D A. On the influence of void clusters on void growth and coalescenceduring ductile fracture [J]. Acta Mater.,2008,56(16):4429-4439.
[14] Orsini V C, Zikry M A. Void growth and interaction in crystalline materials [J]. Int. J.Plasticity,2001,17()10:1393-1417.
[15] Potirniche G. P, Hearndon J L, Horstemeyer M F, et al. Lattice orientation effects on voidgrowth and coalescence in fcc single crystals [J]. Int. J. Plasticity,2006,22(5):921-942.
[16] Yang M., Dong X H. Simulation of lattice orientation effects on void growth andcoalescence by crystal plasticity [J]. Acta Metallurgica Sinica (English Letters),2009,22.
[17] Ragab A R. Application of an extended void growth model with strain hardening and voidshape evolution to ductile fracture under axisymmetric tension [J]. Eng. Fract. Mech.,2004,71:1515-1534.
[18] Niordson C F. Void growth to coalescence in a non-local material [J]. Euro. J. Mech.A/Solids,2008,27:222-233.
[19] Fabregue D, Pardoen T. A constitutive model for elastoplastic solids containing primary andsecondary voids [J]. J. Mech. Phys. Solids,2008,56:719-741
[20] Lassance D, Scheyvaerts F, Pardoen T. Growth and Coalescence of penny-shaped voids inmetallic alloys [J]. Eng. Fract. Mech.,2006,73:1009-1034.
[21] Gotoh M, Yamashita M. Chaotic behavior of an elastoplastic bar in tensile test over a widerange of strain rate: a numerical investigation [J]. Int. J. Mech. Sci.,2000,42:1593-1606.
[22] Rusinek A, Zaera R, Klepaczko J R, et al. Analysis of inertia and scale effects on dynamicneck formation during tension of sheet steel [J]. Acta Mater.,2005,53:5387-5400.
[23] Sturges J L, Cole B N. The flying wedge: a method for high strain rate tensile testing. part1:Reasons for its development and general description [J]. Int. J. Impact Eng,2001,25:256-264.
[24] Barton D C. Determination of the high strain rate fracture properties of ductile materialsusing a combined experimental/numerical approach [J]. Int. J. Impact Eng.,2004,30:1147-1159.
[25] Hu JinWei, Jin YanHui, Chen Danian, et al. Measurement of critical impact velocity ofcopper in tension [J]. Chin. Phys. Lett.,2008,25(3):1049-1051.
[26] Jia S, Povirk G L. Modeling the effects of hole distribution in perforatedaluminum sheets II: minimum strength failure paths [J]. Int. J. Solids and Struc,2002,39(9):2533-2545.
[27] Weck A, Wilkinson D S. Experimental investigation of void coalescence in metallic sheetscontaining laser drilled holes [J]. Acta Mater.,2008,56(8):1774-1784.
[28] Weck A, Wilkinson D S, Maire E. Observation of void nucleation, growth and coalescencein a model metal matrix composite using X-ray tomography [J]. Mater. Sci. Eng. A,2008,488(1-2):435-445.
[29] Weck A, Wilkinson D S, Maire E, et al. Visualization by X-ray tomography of void growthand coalescence leading to fracture in model materials [J]. Acta Mater.2008,56(12):2919-2928.
[30] Smerd R, Winkler S, Salisbury C, et al. High strain rate tensile testing of automotivealuminum alloy sheet [J]. Int. J. Impact Eng.,2005,32(1-4):541-560.
[31] Wei X C, Fu R Y, Li L. Tensile deformation behavior of cold-rolled TRIP-aided steels overlarge range of strain rates [J]. Mate. Sci. Eng. A,2007,465(1-2):260-266.
[32] Huang C G, Chen S Y, Duan Z P. Real-time measurement on deformation fields of notchedsamples under impact tension [J]. Int. J. Impact Eng.,2005,31:329-339.
[33] Rittel D, Wang Z G, Dorogoy A. Geometrical imperfection and adiabatic shear banding [J].Int. J. Impact Eng.,2008,35(11):1280-1292.
[34] Wright T W, Ramesh K T. Statistically informed dynamics of void growth in rate dependentmaterials [J]. Int. J. Impact Eng.,2009,36(10-11):1242-1249.
[35] Ma D F, Chen D N, Wu S X, et al. An interrupted tensile testing at high strain rates for purecopper bars[J]. J. Appl. Phy.,2010,108:114902(1-13).
[36] Ma D F, Chen D N, Wu S X, et al. A dynamic investigation of observable void growth andcoalescence in pure copper sheets [J]. J. Appl. Phy.,2011,094905(1-17)
[37] Ma D F, Chen D N, Wu S X, et al. Analysis of thermoviscoplastic effects on dynamic neckformation during tension of copper bar [J]. Int. J. Nonlinear Sci. Num. Simulation,2011.Accepted.
[38]贾存威，侯延军，陈大年等. Hopkinson拉杆试验的优化与高导无氧铜拉伸本构关系的确定[J].固体力学学报,32(1):57-62.
[39]吴善幸，陈大年，张铎，马东方等.圆柱壳体冲击平板靶的实验与数值研究[J].工程力学,2010,27(3):10-14.
[40] Wu S X, Chen D N, Ma D F et al. The influences of constitutive models on the collapses ofOFHC copper cylindrical shells under impact compression[J]. Advanced Mater. Res.,2011,179:691-696.
[41] Bai Y L, Werzbicki T. A new model of metal plasticity and fracture with pressure and Lodedependence [J]. Int. J. plasticity,2008,24:1071-1096.
[42] Ma D F, Hou Y J, Chen D N, et al.A novel impact tension testing for OFHC copper barsunder local strain controlled[J].Chinese Phy. Letters,2011,28(1):016201.
[43] Joun M S, Choi I., Eom J G, et al. Finite element analysis of tensile testing with emphasis onnecking [J]. Computational Mater. Sci.,2007,41:63-69.
[44]马东方，陈大年，吴善幸等.高导无氧铜动态本构关系对于单轴冲击拉伸下空穴增长和失稳的影响[J].兵工学报,2009,30:74-79.
[45]陈大年,吴善幸,王焕然,马东方等.冲击载荷下延性材料的动态本构关系与动态断裂[J].兵工学报,2010,31(6):725-734.
[46]吴善幸，马东方,陈大年等.冲击拉伸下含孔高导无氧铜板中空穴增长与聚集的实验与数值研究[J].兵工学报,2009,30:134-138.
[47]陈大年,胡金伟,金扬辉等.高导无氧铜的临界冲击拉伸速度[J].爆炸与冲击,2009,29(2):113-118.
[48]马东方,侯延军,陈大年,等.高导无氧铜杆的冲击拉伸断裂系列实验以及基于样本体积单元的分析[J].爆炸与冲击,2011,31(4):385-391.
[49] Ma D F, Deng G T, Chen D N, et al. A visualized investigation of void growth andcoalescence in pure copper sheets under impact tension[J]. Advanced Mater. Res.,2011,317-319:1717-1724.
[50] Ma D F, Chen D N, Wu S X et al. Dynamic Experimental verification of void coalescencecriteria[J]. Mater. Sci. Eng. A,2012,533:96-106.
[51]金杨辉，贾存威，陈大年，马东方，吴善幸，王焕然。高导无氧铜杆在高应变率拉伸下的颈缩与断裂研究[J].应用力学学报，2009,26(4):776-782.
[52] Brown M, Embury D. Proceeding of3rdinternational conference on strength of metals andalloys [C]. London: Institute of Metals,1973.
[53]张学言.岩土塑性力学[M].北京：人民交通出版社，1993.
[54]郑颖人，沈珠江，龚晓南.岩土塑性力学原理：广义塑性力学[M].北京：中国建筑工业出版社，2002.
[55] Bardet J.Lode dependences for isotropic pressure-sensitive elastoplastic materials [J]. J. Appl.Mech, Transactions ASME,1990,57(3):498-506.
[56] Menetrey P, Willam K. Triaxial failure criterion for concrete and its generalization [J]. ACIStruc. J,1995,92:311-318.
[57] Wilson C D. A critical reexamination of classical metal plasticity [J]. J. Appl. Mech,Transactions ASME,2002,69(1):63-68.
[58] Richmond O, Spitzig W A. Theoretical and Applied Mechanics, Proceedings of the15thInternational Congress of Theoretical and Applied Mechanics [C]. Toronto: Ont., Canada.North-Holland Publ. Co.,1980.
[59] Gurson A L. Plastic flow and fracture behavior of ductile materials incorporating voidnucleation, growth and interaction[D]. Brown University,1975.
[60] Needleman A, Tvergaard V. An analysis of ductile rupture in notched bars [J]. J. Mech. Phy.Solids,1984,32(6):461-490.
[61] Cazacu O, Plunkeet B, Barlat F. Orthotropic yield criterion for hexagonal closed packedmetals [J]. Int. J. Plasticity,2006,22(7):1171-1194.
[62]陈大年，范春雷，胡金伟等.高导无氧铜的高压与高应变率本构关系研究.物理学报，2009，58(4):2612-2618.
[63] Johnson G R, Holmquist, T J. Evaluation of cylinder-impact test data for constitutive modelconstants[J]. J. Appl. Phys.,1988,64:3901~3910.
[64]吴善幸.冲击荷载下纯铜的本构关系与结构失稳研究[D].西安：西北工业大学航空学院，2011.
[65] Johnson GR, Cook WH. A constitutive model and data for metals subjected to large strains,high strain-rates and high temperatures. Proceedings of seventh international symposium onBallistics [C], The Hague, The Netherlands, April1983.
[66] Zerilli F J, Armstrong R W. Dislocation-mechanics-based constitutive relations for materialdynamics calculations[J]. J. Appl. Phy.,1987,61:1816-1825.
[67] Rule W K, Jones S E. A revised form for the Johnson-Cook strength model [J]. Int. J. ImpactEng.,1998,21:609~624.
[68] Chen DN, Fan CL, Xie SG., Hu JW, Wu SX, Wang HR. Study on constitutive relations andspall models for oxygen-free high-conductivity copper under planar shock tests [J]. J.Appl.Phy.,2007,101:063532:1~9.
[69] Kolsky H. Stress waves in solids [M]. New York: Dover publications,1963.
[70]贾存威. Hopkinson拉杆试验的优化与高导无氧铜本构关系及拉伸断裂研究[D].宁波：宁波大学机械工程与力学学院,2009.
[71] Hu X, Daehn GS. Effect of velocity on flow localization in tension [J]. Acta Mater,1996,44:1021-33
[72] Klepaczko J R. True direct split Hopkinson bar for tension tests of sheet metals, ISGMP-LPMM [J]. Internal report for Sollac, Meta:1995
[73] Waryoba D R, Kalu P N, Crooks R. Grain-boundary structure of oxygen-free high-conductivity (OFHC) copper subjected to severe plastic deformation and annealing [J]. Mater.Sci. Eng. A,2008,494:47–51.
[74] Singh B N, Edwards D J, Toft P. Effect of neutron irradiation and post-irradiation annealingon microstructure and mechanical properties of OFHC-copper [J]. J. Nuclear Mater,2001,299:205-218.
[75] Wu X J, Gorham D A. Stress Equilibrium in the Split Hopkinson Pressure Bar Test, Journalof Physics IV France, Colloque C3, Supplement au Journal de Physique Ⅲ d`aout1997,7:C3-91-C3-96
[76]王立礼.应力波基础[M].北京：国防工业出版社，2005.
[77]侯延军.冲击拉伸下纯铜杆的受录受控变形研究[D].宁波：宁波大学机械工程与力学学院,2010.
[78] Hallquist, J O. LS-DYNA Keywords Use’s Manual (Version970). USA: LSTC, April2003
[79] Klepaczko J R. True direct split Hopkinson bar for tension tests of sheet metals, ISGMP-LPMM. Internal report for Sollac, Meta:1995.
[80] Huh H, Kang WJ, Han SS. A tension split Hopkinson bar for investigating the dynamicbehavior of sheet metals [J]. Exp Mesh.,2002,42:8-17.
[81] Nicholas, T. Tensile testing of materials at high rates of strain [J]. Exp. Mech.,1981, X:177-185.
[82] Stabb GH, Gilat A. A direct-tension split Hopkinson bar for high strain-rate testing [J]. Exp.Mech.1991, X:232-5.
[83] Verleysen P, Benedict V, Verstraete T, et al. Numerical study of the influence of thespecimen geometry on split Hopkinson bar tensile test results [J]. Lat. Am. J. Solids Struct.,2009,6:285-298.
[84]吴桂英，张泽华.拉压性能不同金属材料的非经典塑性本构理论及实验研究[J].力学学报，1989,21:70-77.
[85]滕志斌，忻元华，滕博等.新编金属材料手册[M].北京：金盾出版社，2006
[86] Considerè M. L’emploi du fer et Lacier dans Les Constructions [J]. Ann Des Ponts etChausses,1885,9:574.
[87] Hart E W. Theory of the tensile test [J]. Acta Metallurgica,1967,15:351-355.
[88] Kocks U F, Jonas J J, Mecking H. The development of strain-rate gradients [J]. ActaMetallurgica,1979,27:419-432.
[89] Dumoulin D, Tabourot L, Chappuis C, et al. Determination of the equivalent stress–equivalent strain relationship of a copper sample under tensile loading [J]. J. Mater.Processing Tech.,2003,133:79-83.
[90] Joun M S, Eom J G, Lee M C. A new method for acquiring true stress-strain curves over alarge range of strains using a tensile test and finite element method[J]. Mech. Mater.,2008,40:586-593.
[91] McClintock F A. A criterion for ductile fracture by growth of holes [J]. J. Appl. Mech.,1968,35:363–371.
[92] Rice J R, Tracey D M. On the ductile enlargement of voids in triaxial stress fields [J]. J.Mech. Phys. Solids,1969,17:201–217.
[93] Needleman A. Void Growth in an Elastic-Plastic Medium [J]. J. Appl. Mech.,1972,39(4):964-970.
[94] Koplik J, Needleman A. Void growth and coalescence in porous plastic solids [J]. Int. J.Solids Struct.,1988,24:835–853.
[95] Mcmeeking R M, Hom C L. Finite element analysis of void growth in elastic-plasticmaterials [J]. Int. J. Fract.,1990,42:1-19.
[96] Hom C L, McMeeking R M. Three-dimensional void growth before a blunting crack tip [J]. J.Mech. Phys. Solids,1989,37(3):39-415.
[97] Kuna M, Sun D Z. Three-dimensional cell model analyses of void growth in ductilematerials [J]. Int. J. Fract.,1996,81:235-258.
[98] Tvergaard V. Material failure by void growth to coalescence. In: Advances in AppliedMechanics[M]. New York: Academic Press,1990.
[99] Hom C L, McMeeking R M. Void growth in elastic-plastic materials [J]. J. Appl. Mech.,1989,56:309-316.
[100] Bridgman P W. Studies in large plastic flow and fracture[M]. New York: McGraw-Hill BookCompany,1952.
[101] Chen W H. Necking of a bar [J]. Int. J. Solids struct.,1971,7:685-717.
[102] Needleman A. A numerical study of necking in circular cylindrical bar [J]. J. Mech. Phys.Solids,1972,20:111-127.
[103] Norris D M, Moran B, Scudder J K, et al. A computer simulation of the tension test [J]. J.Mech. Phys. Solids,1978,126:1-19.
[104] Chen L G. Necking in uniaxial tension [J]. Int. J. Mech. Sci.,1983,25:47-57.
[105] Alves M, Jones N. Influence of hydrostatic stress on failure of axisymmetric notchedspecimens [J]. J Mech Phys Solids.1999,47:643-667.
[106] Van Stone R H, Cox T B, Low J R, et al. Microstructural aspects of fracture by dimplerupture [J]. Int. Met. Rev.,1985,30:157–79.
[107] Garrison W M, Moody N R. Ductile fracture[J]. J. Phys. Chem. Solids,1987,48(11):1035–74.
[108] Tvergaard V. Influence of voids on shear band instabilities under plane strain conditions [J].Int. J. Frac.,1981,17:389–407.
[109] Faleskog J, Shih C F. Micromechanics of coalescence—I. Synergistic effects of elasticity,plastic yielding and multi-size-scale voids [J]. J. Mech. Phys. Solids,1997,45:21–45.
[110] Needleman A, Tvergaard V. An analysis of ductile rupture modes at a crack tip [J]. J. Mech.Phys. Solids,1987,35:151–183.
[111] McClintock F A. Local criteria for ductile fracture [J]. Int. J. Frac.,1968,4:103-130.
[112] Thomason P F. Ductile fracture by the growth and coalescence of microvoids of non-uniformsize and spacing [J]. Acta Metall. Mater.,1993,41:2127-2134.
[113] Bilby B A, Howard I C, Li Z H. Prediction of the first spinning cylinder test using ductiledamage theory [J]. Fatigue Frac. Eng. Mater. Struc.,1993,16:1–20.
[114] Xia L, Shih C F. Ductile crack growth—I. A numerical study using computational cellswith microstructurally-based length scales [J]. J. Mech. Phys. Solids,1995,43:233–259.
[115] Xia L, Shih C F. Ductile crack growth—II. Void nucleation and geometry effects onmacroscopicfracture behaviour [J]. J. Mech. Phys. Solids,1995,43:1953–1981.
[116] Xia L, Shih C F, Hutchinson J W. A computational approach to ductile crack growth underlarge scale yielding conditions[J]. J. Mech. Phys. Solids,1995,43:389–413.
[117] Ruggieri C, Panontin T L, Dodds R H. Numerical modeling of ductile crack growth in3-Dusing computational cell elements [J]. Int. J. Frac.,1996,82:67–95.
[118] Gao X, Faleskog J, Shih C F. Cell model for nonlinear fracture analysis—II. Fracture-process calibration and verification [J]. Int. J. Frac.,1998,89:374–386.
[119] Tvergaard V. On localization in ductile materials containing voids [J]. Int. J. Frac.,1982,18:237–251.
[120] Kim J, Gao X S, Srivatsan T S. Modeling of void growth in ductile solids: effects of stresstriaxiality and initial porosity [J]. Eng. Frac. Mech.,2004,71:379-400.
[121] Curran DR, Seaman L, Shockey DA. Dynamic failure of solids. Phys. Reports1987,147:253-388.
[122] Ortiz M, Molinari A. Effect of strain hardening and rate sensitivity on the dynamic growth ofa void in a plastic material [J]. J. Appl. Mech.1992,59:48-53.
[123] Tong W, Ravichandran G. Inertial effects on void growth in porous viscoplastic materials [J].J. Appl. Mech.1995,62:633-639.
[124] Wu XY, Ramesh, KT, Wright TW. The dynamic growth of a single void in a viscoplasticmaterial under transient hydyostatic loading. J. Mech. Phys. Solids2003,51:1-26
[125] Gologanu M, Leblond J B. Approximate models for ductile metals containing non-sphericalvoids-Case of axisymmetric prolate ellipsoidal cavities [J]. J. Mech. Phys. Solids,1993,41(11):1723-1754.
[126] Mann H C, High-velocity tension-impact tests[J]. Proceedings ASTM,1936,36:85-108
[127] Clark DS. The influence of impact velocity on the tensile characteristics of some aircraftmetals and alloys. Technical Note No.868, National Advisory Committee for Aeronautics,October1942.
[128] Duwez PE, Clark DS. An experimental study of the propagation of plastic deformationunder conditions of longitudinal impact. Proceedings, Am. Soc. Testing Mats.1947,47:502.
[129] Clark DS, Duwez PE. Discussion of the forces acting in tension impact tests of materials [J].J. Appl. Mech.,1948,15(3): A243.
[130] Clark DS, Wood DS. The tensile impact properties of some metals and alloys [J].Transactions, Am. Soc. Metals.,1950,42:45.
[131] Clark DS, Wood. DS. The influence of specimen dimension and shape on the results intension impact testing [J]. Proceedings ASTM,1950,50:577-585.
[132] Wood WW. Experimental determination of shear modulus of laminated fiber-reinforcedcomposites [J]. Experimental Mech.,1967,7(10):441-446.
[133]陈大年,尹志华.对膨胀壳体失稳的一种简化处理[J].爆炸与冲击,1999,19:193-198.
[134]金扬辉.高导无氧铜杆件的颈缩断裂与临界冲击拉伸速度研究[D]。浙江宁波：宁波大学，2008.