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Numerical study for damage of carbon fiber reinforced resin matrix laminates related to strain rates
PENG Liang, HUANG Wenbo, MAO Wei, ZHAO Meiying
College of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China
Received: 2016-11-03; Accepted: 2016-12-02; Published online: 2016-12-22 17:50
Foundation item: National Natural Science Foundation of China (11502205)
Corresponding author. ZHAO Meiying, E-mail:zhaomeiying@nwpu.edu.cn
Abstract: In order to study the effect of high strain rate loading on the deformation and failure of carbon fiber reinforced resin matrix composites, a numerical damage model, in which the stiffness and strength of composite material were modified by the strain rate correction method, was established in consideration of the strain rate effect. The in-plane failure behavior of the laminar structure under different strain rate conditions was simulated and compared with the literature experiment. The results show that the numerical model constructed in this paper can effectively predict the failure characteristics of the resin base plate structure under different strain rate conditions, and has high accuracy in predicting the stiffness and strength hardening phenomenon. For the specimen dominated by 0° and 90° layer, because of the quasi-linear mechanical properties, the numerical model obtains high accuracy in strength prediction; however, for ±45° layer dominant specimen, it exhibits the characteristics of strong nonlinear damage under different strain rate conditions, so the model has some errors in its strength prediction.
Key words: composite     laminates     strain rate effect     Hashin criteria     damage evolution

1 材料本构模型建立 1.1 考虑应变率的本构关系

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 损伤模式 等效位移 等效应力 纤维拉伸 纤维压缩 基体拉伸 基体压缩

 参数 数值 E11/GPa 119.8 E22=E33/GPa 10.5 ν12=ν13 0.297 5 ν23 0.48 G12=G13/GPa 5.2 G23/GPa 3.7 XT/GPa 1.805 XC/ GPa 1.338 YT/ GPa 0.05 YC/GPa 0.204 ST=SC/GPa 0.13 AS 2.3 BS 0.2 CS 3.1 Am 1.85 Bm 0.5 Cm 1.3 注：AS，BS，CS-强度应变率效应参数值；Am，Bm，Cm-模量应变率效应参数值。

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1.2 损伤判据

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1.3 损伤模型

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df=(1-dft)(1-dfc) 为纤维断裂的全局损伤变量, dftdfc分别为纤维拉伸、压缩对应的损伤演化变量；dm= (1-dmt)(1-dmc) 为基体破坏的全局损伤变量，dmtdmc分别为基体拉伸、压缩相对应的损伤演化变量。

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 图 1 VUMAT子程序流程图 Fig. 1 Flowchart of VUMAT subroutine
2 模型验证

 图 2 复合材料层板拉伸试件尺寸[6]与有限元模型 Fig. 2 Dimension[6] and finite element model of composite laminated tensile specimen

 MPa 等效参数 Knn Kss Ktt 数值 250 000 121 100 121 100 注：Knn-法向刚度；Kss-1方向刚度；Ktt-2方向刚度。

 MPa 破坏模式 法向 1方向 2方向 界面强度 102 50 50

 图 3 [(45/-45)4]s层板结构在不同应变率条件下实验[6]与数值仿真断口形貌对比 Fig. 3 Comparison of fracture morphology between experiment[6] and numerical simulation under different strain rates for [(45/-45)4]s laminate structure

 图 4 不同应变率条件下试件实验与数值仿真结果 Fig. 4 Results of experiment and numerical simulation of specimens under different strain rates
3 结论

1) 纤维增强树脂基复合材料在不同应变率载荷作用下，其力学性能，特别是横向、剪切力学性能存在有明显应变率效应。

2) 本文以应变率作为修正因子，对材料刚度与极限强度进行修正，并结合Hashin准则与连续损伤模型，构建了考虑应变率效应的复合材料各向异性力学模型；该模型可准确描述层板结构在不同应变率条件下的破坏特征，并在材料刚度与最大应力计算中表现出较高精度。

3) 由于复合材料断裂应力水平由材料破坏模式与各模式下材料断裂能联合控制，因此本文所提出模型在材料损伤过程的预测中仍存在一定误差。

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#### 文章信息

PENG Liang, HUANG Wenbo, MAO Wei, ZHAO Meiying

Numerical study for damage of carbon fiber reinforced resin matrix laminates related to strain rates

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(4): 694-700
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0846