Abstract：Carbon-fiber reinforced polymer(CFRP) materials are usually anisotropic. Therefore in the study of these materials, in regard to the constitutive relationship and equation of state(EOS), the anisotropic modification should be taken into account. Based on the relationship between the increments of stress and strain derived by the generalized Hook law and classical elastic-plastic theory, a three-dimensional constitutive model for CFRP anisotropic materials was established. The Tsai-Hill principle was used to calculate the plastic strain increment of anisotropic material while the Grüneisen EOS was used to depict the nonlinear relationship between the pressure and volume strain. A three-dimensional stress propagation process in carbon fiber reinforced phenol-formaldehyde resin (C/PF) during a flyer impact test was simulated by using an explicit FEM program. The results indicate that the constitutive model proposed is practical and able to demonstrate the mechanical properties of anisotropic materials. On account of introducing the generalized volume module and orthotropic correction terms, the pressure obtained by the proposed anisotropic model is lower than that in isotropic condition. The flyer plate speed was set to be 100 m/s to 3 000 m/s, and the calculation results indicate that with the increase of the flyer speed, the contribution of the correction terms to the pressure decreases and the anisotropic model tends to be consistent with isotropic model.
张昆，汤文辉，冉宪文. 正交各向异性CFRP材料的本构关系及其在平板撞击模拟中的应用[J]. 振动与冲击, 2019, 38(22): 101-116.
ZHANG Kun，TANG Wenhui，RAN Xianwen. Constitutive relationship of anisotropic CFRP material and its application in planar plate impact simulation. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(22): 101-116.
[1] Ryan S, Schaefer F, Riedel W. Numerical simulation of hypervelocity impact on CFRP/Al HC SP spacecraft structures causing penetration and fragment ejection[J]. International Journal of Impact Engineering. 2006;33(1):703-12.
[2] Zhengchun D, Mengrui Z, Zhiguo W, et al. Design and application of composite platform with extreme low thermal deformation for satellite. Composite Structures[J]. 2016;152(Supplement C):693-703.
[3] Clegg R, White D, Riedel W, et al. Hypervelocity impact damage prediction in composites: Part I—material model and characterization[J]. International Journal of Impact Engineering. 2006;33(1):190-200.
[4] Grujicic M, Pandurangan B, Koudela K, et al. A computational analysis of the ballistic performance of light-weight hybrid composite armors[J]. Applied Surface Science. 2006;253(2):730-45.
[5] Min S, Chen X, Chai Y, et al. Effect of reinforcement continuity on the ballistic performance of composites reinforced with multiply plain weave fabric[J]. Composites Part B: Engineering. 2016;90:30-6.
[6] Riedel W, Nahme H, White DM, et al. Hypervelocity impact damage prediction in composites: Part II—experimental investigations and simulations[J]. International Journal of Impact Engineering. 2006;33(1):670-80.
[7] Anderson CE, Cox P, Johnson G, et al. A constitutive formulation for anisotropic materials suitable for wave propagation computer programs—II[J]. Computational Mechanics. 1994;15(3):201-23.
[8] O'Donoghue PE, Anderson Jr CE, Friesenhahn GJ, et al. A constitutive formulation for anisotropic materials suitable for wave propagation computer programs[J]. Journal of composite materials. 1992;26(13):1860-84.
[9] Lukyanov, Alexander A. Anisotropic Materials Behavior Modeling Under Shock Loading[J]. Journal of Applied Mechanics. 2009;76(6):1089-94.
[10] Lukyanov AA. Constitutive behaviour of anisotropic materials under shock loading[J]. International Journal of Plasticity. 2008;24(1):140-67.
[11] Key CT, Schumacher SC. CTH reference manual: composite capability and technologies[R]. Sandia National Laboratories, 2009.
[12] Chen J, Allahdadi F, Sun C. A quadratic yield function for fiber-reinforced composites[J]. Journal of composite materials. 1997;31(8):788-811.
[13] Chen J, Allahdadi FA, Carney TC. High-velocity impact of graphite/epoxy composite laminates[J]. Composites science and technology. 1997;57(9-10):1369-79.
[14] 史艳莉, 吴建军. 各向异性屈服准则的发展及应用[J]. 锻压技术. 2006;31(1):99-103.
SHI Yan- li, WU Jian- jun. Development and the applications of anisotropic yield criterions[J]. Forging and Stamping Technology. 2006;31(1):99-103.
[15] 蒋邦海, 张若棋. 一种碳纤维织物增强复合材料的层间冲击拉伸力学性能实验研究[J]. 复合材料学报. 2005;22(5):107-12.
Jiang Banghai, Zhang Ruoqi. Experimental study on the inter laminar tensile properties for a kind of carbon fiber woven reinforced composite under impact loading[J]. ACTA MATERIAE COMPOSITAE SINICA. 2005;22(5):107-12.
[16] 蒋邦海, 张若棋. 一种碳纤维织物增强复合材料应变率相关的各向异性强度准则[J]. 爆炸与冲击. 2006;26(4):333-8.
Jiang Banghai, Zhang Ruoqi. Strain rate- dependent Tsai- Hill strength criteria for a carbon fiber woven reinforced composite[J]. Explosion and Shock Waves. 2006;26(4):333-8.
[17] 黄霞, 汤文辉, 蒋邦海. 平面应变各向异性本构关系及在应力波传播模拟中的应用[J]. 爆炸与冲击. 2010;30(4):383-9.
Huang Xia, Tang Wenhui, Jiang Banghai. Constitutive relation for anisotropic materials under plane-strain conditions and its application to stress-wave propagation simulation[J]. Explosion and Shock Waves. 2010; 30(4): 383-9.
[18] 黄霞, 汤文辉, 蒋邦海. 碳酚醛-铝板中二维X射线热击波数值模拟[J]. 航天器环境工程. 2011;28(1):41-45
Huang Xia, Tang Wenhui, Jiang Banghai. 2-D numerical simulation of thermal shock wave induced by X-ray irradiation in carbon fiber-reinforced phenolic aluminum target[J]. Spacecraft Environment Engineering. 2011; 28(1): 41-45
[19] 黄霞, 汤文辉, 蒋邦海, 等. 一种适用于各向异性材料的修正PUFF物态方程[J]. 计算物理. 2011;28(3):368-74.
Huang Xia, Tang Wenhui, Jiang Banghai, et al. A Modified PUFF Equation of State for Anisotropic Materials[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS. 2011; 28(3):368-74.
[20] Huang X, Tang W, Jiang B. A modified anisotropic PUFF equation of state for composite materials[J]. Journal of Composite Materials. 2012;46(5):499-506.
[21] Wicklein M, Ryan S, White D, Clegg R. Hypervelocity impact on CFRP: testing, material modelling, and numerical simulation[J]. International Journal of Impact Engineering. 2008;35(12):1861-9.
[22] 中国人民解放军国防科学技术大学. X射线三维热-力学效应模拟软件[P]. 中华人民共和国2016SR110024，2016.05.18.
