基于应变梯度晶体塑性理论的金属微柱轴向压缩有限元分析

Finite element analysis of metal micropillar compression based on strain gradient crystal plasticity theory

微压缩实验研究发现,随着微柱直径减小,以剪切带形式表征的非均匀塑性变形会愈加明显。为了考察应变梯度对微柱塑性行为的影响,构建了一种适用于切线模量算法的低阶应变梯度理论模型。该模型提出了包含塑性应变与应变梯度的塑性硬化模量表达式,建立了应变梯度增量与剪切应变增量之间的线性显式关系。通过对上述模型进行有限元实现,模拟了Ni单晶微柱的轴向压缩过程,并将预测结果与一种基于向前欧拉算法的低阶应变梯度塑性模型计算结果进行了比较,检验了理论模型的合理性与算法的可靠性。研究表明,Ni微柱在轴向压缩过程中产生的应变梯度,能够较为显著地提高塑性变形过程中的应变硬化率。

Micro-compression shows that non-uniform deformation in terms of shear bands becomes more and more remarkable as the micropillar diameter decreases.In order to evaluate the effect of strain gradient on the mechanical response of micropillar plasticity,an alternative lower-order strain gradient plasticity model appropriate for the tangent modulus method is established.The linear relation between the increment of strain gradient and shear strain increment is proposed,a concrete expression of plastic strain hardening modulus incorporating both the total shear strain and strain gradient is established,and accordingly a numerical solution of the model using an explicit approach is presented.Following that,three-dimensional finite element analysis of the proposed model is performed to simulate the compression of Ni micropillar.The validity of the model as well as it’s the accuracy of the solution is demonstrated by comparison with those from a mechanism-based strain gradient plasticity model using forward Euler method.It is found that the strain gradient produced in microcomression could cause a significant increase in the strain hardening rate.