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建立了一种速率相关的晶体塑性模型的显示积分算法。该晶体塑性模型将速度梯度张量分解为晶格和塑性部分来描述运动学,并利用亚弹性方程和Jaumann应力率计算柯西应力。该晶体塑性模型及新提出的显示积分算法已被用于一种商业有限元程序,并模拟了多晶的单轴压缩和轧制实验过程。实验结果表明,该晶体塑性模型的显示积分算法具有很高的精确性和可靠性。相对利用乘法分解变形梯度张量方法建立的超弹黏塑性模型及其对应的显示积分算法,该亚弹性模型的显示积分算法除了速度稍快外,其精确性与超弹性模型是一样的。
A display integral algorithm of rate-dependent crystal plasticity model is established. The crystal plasticity model decomposes the velocity gradient tensor into lattice and plastic sections to describe the kinematics and calculates the Cauchy stress using the sub-elastic equation and the Jaumann stress rate. The crystal plastic model and the newly proposed display integral algorithm have been used in a commercial finite element program and simulated the polyaxial uniaxial compression and rolling experimental process. Experimental results show that the integral model of the crystal plastic model has high accuracy and reliability. Compared with the hyperelastic visco-plastic model established by the method of multiplicative decomposition and deformation gradient tensor and its corresponding display integral algorithm, the display integral algorithm of the elastic model shows the same accuracy as the hyperelastic model, except for slightly faster velocity.