金属基纳米复合材料等效弹性模量的均匀化方法数值模拟

Numerical Simulation of Equivalent Elastic Modulus for Metal Matrix Nano-composite Materials Using Homogenization Method

均匀化理论利用位移场双尺度渐近展开建立有限元列式,本文将其与有限元通用程序相结合,应用于金属基复合材料的弹性本构数值模拟。通过对不同尺度增强相金属基复合材料等效模量的数值模拟,考察了均匀化方法的适用情况。数值计算结果表明,对常规尺度增强相金属基复合材料,均匀化方法可以较准确地预测其等效弹性模量;对纳米增强相金属基复合材料,该方法仍可给出较好的预测,但存在某种程度的系统偏差。通过对纳米尺度增强机理的分析讨论,认为纳米增强相与基体材料间的界面效应可能有别于连续介质假设,指出可以考虑采用离散原子-连续介质耦合模型改进数值模拟结果。

The homogenization method is well established on the basis of the double-scale asymptotic expansion of the displacement field. In conjunction with finite element method, it has been successfully applied to predict the macroscopic properties of metal matrix composite materials. Its adequacy was investigated through case studies for metal matrix composites reinforced with particulate of different size. Numerical simulation had been conducted to obtain the equivalent elastic modulus for composites. In comparison with experimental data, it is found that for normal metal matrix composites the homogenization method can give an excellent prediction. As, for nano-composites, this method works still well and produces satisfactory results of acceptable accuracy. Nevertheless, deviation to a certain degree from the experimental results has been observed. Viewing on the mechanism of the reinforcement in nanoscale, it is considered that the interface effects between the reinforcement and the metallic matrix for a nano-composite may be different from that for a normal composite. It is suggested that the atomistic-continuum interface coupling model may be the way for a further improvement.