MICROSCOPIC DAMAGE MODEL CONSIDERING THE RESOLVED NORMAL STRESS ON CRYSTAL SLIP PLANE
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摘要: 材料内部的解理、滑移面剥离等细观损伤是引起宏观失效的根源, 从细观尺度研究损伤的发生和发展有助于深入认识材料的变形和失效过程. 本文基于晶体塑性理论, 从滑移系的受力和变形出发研究材料的细观损伤, 建立了考虑滑移面分解正应力的细观损伤模型, 为晶体材料解理断裂的分析提供了新方法. 首先, 在晶体弹塑性变形构型的基础上引入损伤变形梯度张量的概念, 从变形运动学着手建立了考虑损伤能量耗散的本构方程, 并推导了塑性流动方程与损伤演化方程; 然后, 建立了相应的数值计算方法, 给出了应力与状态变量的更新算法, 推导了Jacobian矩阵的表达式; 接着, 以$[100]$取向的单晶铜材料为例, 通过有限元计算与试验结果的对比, 并采用粒子群优化算法标定了11个材料细观参数; 最后, 将所提细观损伤模型应用于RVE单轴拉伸过程的模拟, 得到了考虑损伤影响的应力应变曲线, 并分析了材料的塑性流动与损伤演化过程. 结果表明, 本文所提模型能够计算材料在受载过程中的损伤累积效应, 合理反映晶体材料的细观损伤机理.Abstract: Studies show that the macroscopic failure of structure results from the microscopic damage within materials, such as cleavage and slip plane decohesion. Therefore, it is helpful to understand the deformation and failure process of materials by studying the damage evolution at micro-scale. Based on the crystal plasticity theory, the microscopic damage in material is studied by analyzing the stress and deformation of slip system, and the microscopic damage model is proposed to consider the resolved normal stress on crystal slip plane. This study provides a new approach for the analysis of cleavage fracture of crystalline materials. First, the gradient tensor of damage deformation is introduced in addition to the crystal elastic-plastic deformation configuration. The constitutive equation with damage energy dissipation is established from the deformation kinematics analysis, and the plastic flow equation and the damage evolution equation are derived. Second, the numerical method is established including the updating algorithm of stress and state variables and the derivation of Jacobian matrix. After that, the single crystal copper with $[100]$ orientation is studied as an example. Through comparing the results obtained by finite element computation and by experimental test, the 11 material microscopic parameters are calibrated using the particle swarm optimization algorithm. Finally, the proposed microscopic damage model is applied to the simulation of RVE under uniaxial tension. The curve of stress versus strain considering the damage effect is obtained, and the development of plastic flow and damage evolution are analyzed. The results show that the proposed model is able to compute the damage accumulation of materials and reasonably reflect the microscopic damage mechanism of crystalline materials.
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