基于晶体塑性有限元方法的不同变形状态下织构演化预测

摘要

提出一种以线性方程组为控制方程的显式晶体塑性模型.该模型可用高斯全主元消去法直接求解,无需任何迭代.提出基于晶体学坐标系的求解流程以减少由于变形中晶粒旋转而额外增加的计算量.建立晶体塑性有限元模型,并将预测结果与试验结果进行对比,验证该模型在织构演化预测方面的可靠性.该模型被用于预测不同变形状态下的织构演化,而这些不同的变形状态是通过调整Z和Y方向上的加载速度比(K)实现的.实验结果表明:该模型在织构演化预测方面是可靠的(在压缩、拉伸、简单剪切和平面应变压缩过程中的预测结果与试验吻合良好)和高效的(比隐式模型快100多倍)；随着k值的增大,强织构由与法向(ND)成±35°角向{111}面上的丝织构转变,且织构强度增大；当应变速率在0.1～100 s-1之间增大时,织构强度迅速降低,而当应变速率在l00～7xl04 s-1之间增大时,织构强度缓慢减小,这表明该模型在模拟超高应变速率变形时也是数值稳定的.%An explicit model controlled by a linear equations set was developed.This model was directly solved by the complete pivot GAUSSIAN elimination method without any iteration.In addition,crystallographic-system based solving procedure was proposed to reduce the additional calculation caused by grain rotation.By establishing crystal plasticity finite element model (CPFEM),the model was verified by comparing the predicted texture to the experimental results.Then,the model was applied to predict textures under different deformatior states achieved by adjusting the ratio (k) of the loading velocities in Z and Y directions.The results show that the model is reliable in texture prediction (good agreement with the experiments in compression,tension,simple shear and plane-strain compression) and much more efficient (more than 100 times) than the implicit model; with the increasing of k,the strong texture progresses from ±35° to normal direction to fiber texture in the {111} plane and enhances in intensity; the texture intensity drops dramatically when the strain rate increases from 0.1 s-1 to 100 s-1,while drops slowly when the strain rate increases from 100 s-1 to 7× 104 s-1,which indicates the computational stability of the model for simulation of ultra-high strain rate deformation.