一种弹芯用聚碳酸酯的动态力学性能研究及本构关系
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摘要
为了研究一种弹芯用聚碳酸酯材料在冲击作用下的动态力学响应,利用材料试验机和SHPB装置对该材料在不同应变率条件下动静态压缩性能进行测试分析,获得了该聚碳酸酯材料不同应变率下的应力应变曲线,试验结果表明:聚碳酸酯材料的压缩过程呈现明显的黏弹性现象,其动静态屈服强度和模量随着应变率的增加而变大,塑性阶段表现为应变软化与应变硬化相互作用的结果,且不同应变率下塑性阶段的应力应变曲线切向模量近似相等;基于试验结果建立了描述聚碳酸酯材料大变形力学行为的黏弹塑性本构模型,并得到了该材料的本构方程。对比分析显示,该模型可以较准确地描述聚碳酸酯材料动静态压缩行为。
In order to study dynamic response of polycarbonate material for bullet cores under impact, static and dynamic state compressive performances of the material under different strain rates were tested and analyzed with a material testing machine and SHPB device to obtain stress-strain curves of polycarbonate under different stain rates. The test results showed that the compression process of polycarbonate material reveals obvious viscoelastic phenomenon; with increase in strain rate, its static and dynamic state yield strengths and elastic moduli increase; its plastic stage is the result of interaction between strain softening and strain hardening, and its plastic stress-strain curves' tangential moduli under different strain rates approximately equal. Based on the test results, a visco-elastoplastic constitutive model describing polycarbonate material's large deformation mechanical behavior was established, and this material's constitutive equations were obtained. The contrastive analysis showed that the model can more correctly describe dynamic and static state compression behaviors of polycarbonate material.
In order to study dynamic response of polycarbonate material for bullet cores under impact, static and dynamic state compressive performances of the material under different strain rates were tested and analyzed with a material testing machine and SHPB device to obtain stress-strain curves of polycarbonate under different stain rates. The test results showed that the compression process of polycarbonate material reveals obvious viscoelastic phenomenon; with increase in strain rate, its static and dynamic state yield strengths and elastic moduli increase; its plastic stage is the result of interaction between strain softening and strain hardening, and its plastic stress-strain curves' tangential moduli under different strain rates approximately equal. Based on the test results, a visco-elastoplastic constitutive model describing polycarbonate material's large deformation mechanical behavior was established, and this material's constitutive equations were obtained. The contrastive analysis showed that the model can more correctly describe dynamic and static state compression behaviors of polycarbonate material.
引文
[1] PAULUS G, CHANTERET P Y, WOLLMANN E. PELE: A new penetrator-concept for the generation of lateral effects[C]//21st International Symposium on Ballistics. Adelaide, Australia: IBC, 2004.
[2] KESBERG G, SCHIRM V, KERK S. PELE-the future ammunition concept[C]//21st International Symposium on ballistics. Adelaide, Australia: IBC, 2004.
[3] 陈春晓, 彭刚, 冯家臣, 等. PELE 弹芯用改性 PA1010 工程塑料动态力学性能研究[J]. 塑料工业, 2015, 43(10): 87-90. CHEN Chunxiao,PENG Gang,FENG Jiachen,et al. Study on the dynamic mechanical properties of modified PA1010 engineering plastic for PELE penetrator core[J]. China Plastics Industry,2015,43(10):87-90.
[4] 涂胜元, 王军波, 安振涛. 壳体和内芯的材料特性对PELE侵彻后效的影响[J]. 中北大学学报, 2009, 30(3): 213-216. TU Shengyuan, WANG Junbo, AN Zhentao. Influence of the material characteristic of shell and coreon the penetration after effect of PELE[J]. Journal of North University of China, 2009, 30(3): 213-216.
[5] 尹建平, 王志军, 魏继允. 装填材料密度对侵彻膨胀弹终点效应的影响[J]. 中北大学学报(自然科学版), 2011, 32(6): 671-675. YIN Jianping, WANG Zhijun, WEI Jiyun. Influence of filling material density on terminal effect of PELE projectile[J]. Journal of North University of China(Natural Science Edition), 2011, 32(6):671-675.
[6] 朱建生, 赵国志, 杜忠华. 装填材料对PELE效应的影响[J]. 弹道学报, 2007, 19(2): 62-65. ZHU Jiansheng, ZHAO Guozhi, DU Zhonghua. Influence of the filling material on the PELE effect[J]. Journal of Ballistics, 2007, 19(2):62-62.
[7] 蒋建伟, 张谋, 门建兵, 等. 不同内核材料 PELE 弹丸对多层靶穿甲实验研究[J]. 北京理工大学学报, 2010, 30(9): 1009-1012. JIANG Jianwei, ZHANG Mou, MEN Jianbing, et al. Experimental study on multi-layered target penetration of PELE with different cores[J]. Transactions of Beijing Institute of Technology, 2010, 30(9):1009-1012.
[8] 惠旭龙,白春玉,葛宇静,等. 2A16铝合金中应变率力学性能研究[J]. 振动与冲击,2017,36(19):66-70. HUI Xulong, BAI Chunyu, GE Yujing, et al. Dynamic property of 2A16 aluminum alloy under intermediate strain rate[J].Journal of Vibration and Shock,2017,36(19):66-70.
[9] MULLIKEN A D, BOYCE M C. Mechanics of the rate-dependent elastic-plastic deformation of glassy polymers from low to high strain rates[J]. International Journal of Solids and Structures, 2006, 43(5): 1331-1356.
[10] RICHETON J, SCHLATTER G, VECCHIO K S, et al. A unified model for stiffness modulus of amorphous polymers across transition temperatures and strain rates[J]. Polymer, 2005, 46(19): 8194-8201.
[11] RICHETON J, AHZI S, VECCHIO K S, et al. Influence of temperature and strain rate on the mechanical behavior of three amorphous polymers: characterization and modeling of the compressive yield stress[J]. International Journal of Solids and Structures, 2006, 43(7): 2318-2335.
[12] RICHETON J, AHZI S, VECCHIO K S, et al. Modeling and validation of the large deformation inelastic response of amorphous polymers over a wide range of temperatures and strain rates[J]. International Journal of Solids and Structures, 2007, 44(24): 7938-7954.
[13] SENDEN D J A, KROP S, VAN DOMMELEN J A W, et al. Rate-and temperature-dependent strain hardening of polycarbonate[J]. Journal of Polymer Science, Part B: Polymer Physics, 2012, 50(24): 1680-1693.
[14] SAFARI K H, ZAMANI J, FERREIRA F J, et al. Constitutive modeling of polycarbonate during high strain rate deformation[J]. Polymer Engineering & Science, 2013, 53(4): 752-761.
[15] LU Y B, LI Q M. Dynamic behaviour of polymers at high strain-rates based on split Hopkinson pressure bar tests[J]. International Journal of Impact Engineering, 2010, 38(1): 41.
[16] 胡文军, 唐录成, 张方举, 等. 聚碳酸酯冲击压缩的实验研究[J]. 高分子材料科学与工程, 2006, 22(6): 165-168. HU Wenjun, TANG Lucheng, ZHANG Fangju, et al. Experimental study of polycarbonate’s impact compression[J]. Polymer Materials Science & Engineering, 2006, 22(6):165-168.
[17] 胡文军, 张方举, 田常津, 等. 聚碳酸酯的动态应力应变响应和屈服行为[J]. 材料研究学报, 2007, 21(4): 439-443. HU Weijun, ZHANG Fangju, TIAN Changjin, et al. Dynamic stress-strain response and yield behavior of polycarbonate[J]. Chinese Journal of Materials Research, 2007, 21(4):439-443.
[18] 唐志平. 横观各向同性材料动态力学性能试验中的试件最佳尺寸[J]. 爆炸与冲击, 1985(2):3-12. TANG Zhiping. Optimum size of transversal isotropic specimen in dynamic testing using the split hopkinson pressure bar[J]. Explosion and Shock Waves, 1985(2):3-12.
[19] YU P, YAO X, HAN Q, et al. A visco-elastoplastic constitutive model for large deformation response of polycarbonate over a wide range of strain rates and temperatures[J]. Polymer, 2014, 55(25): 6577-6593.
[20] WANG H, ZHANG Y, HUANG Z, et al. Experimental and modeling study of the compressive behavior of PC/ABS at low, moderate and high strain rates[J]. Polymer Testing, 2016, 56: 115-123.
[2] KESBERG G, SCHIRM V, KERK S. PELE-the future ammunition concept[C]//21st International Symposium on ballistics. Adelaide, Australia: IBC, 2004.
[3] 陈春晓, 彭刚, 冯家臣, 等. PELE 弹芯用改性 PA1010 工程塑料动态力学性能研究[J]. 塑料工业, 2015, 43(10): 87-90. CHEN Chunxiao,PENG Gang,FENG Jiachen,et al. Study on the dynamic mechanical properties of modified PA1010 engineering plastic for PELE penetrator core[J]. China Plastics Industry,2015,43(10):87-90.
[4] 涂胜元, 王军波, 安振涛. 壳体和内芯的材料特性对PELE侵彻后效的影响[J]. 中北大学学报, 2009, 30(3): 213-216. TU Shengyuan, WANG Junbo, AN Zhentao. Influence of the material characteristic of shell and coreon the penetration after effect of PELE[J]. Journal of North University of China, 2009, 30(3): 213-216.
[5] 尹建平, 王志军, 魏继允. 装填材料密度对侵彻膨胀弹终点效应的影响[J]. 中北大学学报(自然科学版), 2011, 32(6): 671-675. YIN Jianping, WANG Zhijun, WEI Jiyun. Influence of filling material density on terminal effect of PELE projectile[J]. Journal of North University of China(Natural Science Edition), 2011, 32(6):671-675.
[6] 朱建生, 赵国志, 杜忠华. 装填材料对PELE效应的影响[J]. 弹道学报, 2007, 19(2): 62-65. ZHU Jiansheng, ZHAO Guozhi, DU Zhonghua. Influence of the filling material on the PELE effect[J]. Journal of Ballistics, 2007, 19(2):62-62.
[7] 蒋建伟, 张谋, 门建兵, 等. 不同内核材料 PELE 弹丸对多层靶穿甲实验研究[J]. 北京理工大学学报, 2010, 30(9): 1009-1012. JIANG Jianwei, ZHANG Mou, MEN Jianbing, et al. Experimental study on multi-layered target penetration of PELE with different cores[J]. Transactions of Beijing Institute of Technology, 2010, 30(9):1009-1012.
[8] 惠旭龙,白春玉,葛宇静,等. 2A16铝合金中应变率力学性能研究[J]. 振动与冲击,2017,36(19):66-70. HUI Xulong, BAI Chunyu, GE Yujing, et al. Dynamic property of 2A16 aluminum alloy under intermediate strain rate[J].Journal of Vibration and Shock,2017,36(19):66-70.
[9] MULLIKEN A D, BOYCE M C. Mechanics of the rate-dependent elastic-plastic deformation of glassy polymers from low to high strain rates[J]. International Journal of Solids and Structures, 2006, 43(5): 1331-1356.
[10] RICHETON J, SCHLATTER G, VECCHIO K S, et al. A unified model for stiffness modulus of amorphous polymers across transition temperatures and strain rates[J]. Polymer, 2005, 46(19): 8194-8201.
[11] RICHETON J, AHZI S, VECCHIO K S, et al. Influence of temperature and strain rate on the mechanical behavior of three amorphous polymers: characterization and modeling of the compressive yield stress[J]. International Journal of Solids and Structures, 2006, 43(7): 2318-2335.
[12] RICHETON J, AHZI S, VECCHIO K S, et al. Modeling and validation of the large deformation inelastic response of amorphous polymers over a wide range of temperatures and strain rates[J]. International Journal of Solids and Structures, 2007, 44(24): 7938-7954.
[13] SENDEN D J A, KROP S, VAN DOMMELEN J A W, et al. Rate-and temperature-dependent strain hardening of polycarbonate[J]. Journal of Polymer Science, Part B: Polymer Physics, 2012, 50(24): 1680-1693.
[14] SAFARI K H, ZAMANI J, FERREIRA F J, et al. Constitutive modeling of polycarbonate during high strain rate deformation[J]. Polymer Engineering & Science, 2013, 53(4): 752-761.
[15] LU Y B, LI Q M. Dynamic behaviour of polymers at high strain-rates based on split Hopkinson pressure bar tests[J]. International Journal of Impact Engineering, 2010, 38(1): 41.
[16] 胡文军, 唐录成, 张方举, 等. 聚碳酸酯冲击压缩的实验研究[J]. 高分子材料科学与工程, 2006, 22(6): 165-168. HU Wenjun, TANG Lucheng, ZHANG Fangju, et al. Experimental study of polycarbonate’s impact compression[J]. Polymer Materials Science & Engineering, 2006, 22(6):165-168.
[17] 胡文军, 张方举, 田常津, 等. 聚碳酸酯的动态应力应变响应和屈服行为[J]. 材料研究学报, 2007, 21(4): 439-443. HU Weijun, ZHANG Fangju, TIAN Changjin, et al. Dynamic stress-strain response and yield behavior of polycarbonate[J]. Chinese Journal of Materials Research, 2007, 21(4):439-443.
[18] 唐志平. 横观各向同性材料动态力学性能试验中的试件最佳尺寸[J]. 爆炸与冲击, 1985(2):3-12. TANG Zhiping. Optimum size of transversal isotropic specimen in dynamic testing using the split hopkinson pressure bar[J]. Explosion and Shock Waves, 1985(2):3-12.
[19] YU P, YAO X, HAN Q, et al. A visco-elastoplastic constitutive model for large deformation response of polycarbonate over a wide range of strain rates and temperatures[J]. Polymer, 2014, 55(25): 6577-6593.
[20] WANG H, ZHANG Y, HUANG Z, et al. Experimental and modeling study of the compressive behavior of PC/ABS at low, moderate and high strain rates[J]. Polymer Testing, 2016, 56: 115-123.