基于细观方法的颗粒增强复合材料弹塑性分析

Elastoplastic Analysis of Particle Reinforced Composites Based on Meso Mechanical Method

针对高体积含量的颗粒增强复合材料 ,提出了一种细观结构模型 :将颗粒简化为同质、同尺寸的弹性圆球 ,两颗粒之间的连接基体简化为一弹塑性短圆柱体 ,并假设细观应力、应变和塑性区均为轴对称分布。基体和颗粒的变形行为分别简化为类似于弹性地基和弹性半空间 ,以此为基础 ,建立了反映一对颗粒法向和切向变形协调关系的两个积分方程。数值求解这两个方程 ,可得到一对颗粒间基体中细观应力的分布形式 ,从而建立颗粒对的细观弹塑性本构 ,采用平均化方法 ,进一步推导出材料宏观的应力 -应变关系。本文利用该模型对一种金属基复合材料的拉伸实验进行了模拟 。

A meso structure model of particle reinforced composites with large volume fraction is suggested. In this model, particles are assumed as identical elastic spheres, and the matrix linking two particles is viewed as an elastoplastic short column. Stress, strain and plastic zone in the matrix column are simplified as axisymmetrical distribution. Deformations of the matrix and the particles are depicted by an elastic foundation model and an elastic half space model respectively. Based on these assumptions, two integral equations representing deformation consistent conditions are given. By solving these two equations numerically, meso stresses are obtained and meso elastoplastic constitutive relations of a two particle linkage are deduced. Then the macro stress and strain relations are obtained by use of the average method. A unidirection tension test of an Al 2O 3/Al metal matrix composites is simulated by this model. Theoretical predictions agree well with the experimental observations.