碳纤维增强树脂基类复合材料通常具有力学性能的正交各向异性，因此在对该类材料的动态力学性能研究中，其本构关系及物态方程必须考虑正交各向异性的修正。本文从经典的正交各向异性弹性本构方程出发，以某型碳纤维增强酚醛树脂材料为研究对象，引入Tsai-Hill准则描述材料的塑性行为，采用Grüneisen物态方程描述压力与体应变之间的非线性关系，建立了正交各向异性材料的三维弹塑性本构模型。并采用显式有限元方法，对三维条件下平板撞击问题中的应力波传播过程进行了模拟。研究表明，本文所建立的三维本构模型能够合理呈现出材料的各向异性力学特性。对于靶板中平台压力，由于广义体积模量及正交各向异性修正项的引入，得到的压力相对于各向同性模型偏低。本文设定飞片以100 m/s至3000 m/s的速度撞击静止靶板，对计算结果的数值分析发现随着飞片速度上升，正交各向异性模型中修正项对压力的贡献减小。最终正交各向异性模型趋近于各向同性模型。
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.
关键词
正交各向异性材料 /
本构关系 /
物态方程 /
平板撞击 /
显式有限元
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Key words
anisotropic material /
constitutive model /
equation-of-state /
planar plate impact /
explicit FEM
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