具有界面相的球形粒子在无限大基体中的应力集中分析

STRESS CONCENTRATION ANALYSIS OF A SPHERICAL PARTICLE WITH AN INTERPHASE EMBEDDED IN AN INFINITE ELASTIC MATRIX

研究了无限大基体内具有界面相的球形粒子在轴对称载荷作用下的应力场 ,并与线弹簧界面模型的情形进行了比较 ,对粒子 界面相以及界面相 基体两个界面的应力集中系数以及粒子内部的应力集中系数进行了分析 .研究了应力三轴度、界面相厚度以及三相的模量对应力集中系数的影响 .结果表明 ,对给定的模量和界面相厚度值 ,存在一个临界应力三轴度值 .若应力三轴度小于此临界值 ,则界面相 基体界面的应力集中系数大于粒子 界面相界面的应力集中系数 ;否则 ,前者会小于后者 .所做的应力分析可以为颗粒增强复合材料的强韧化设计提供一定参考 .

The stress field in an infinite matrix containing a spherical particle with an interphase under axisymmetric loading is studied and compared with the linear spring interface model. A detailed analysis of the stress concentration factors at the two interfaces and inside the particle is given. The effects of the stress triaxiality, the interphase thickness and the moduli of the three phases on the stress concentration factors are investigated. The results show that for a set of moduli and the interphase thickness there exists a critical value of the stress triaxiality. If the stress triaxiality is smaller than the critical value, the stress concentration factor at the interphase/matrix interface is larger than that at the particle/interphase interface. Otherwise, the former is smaller than the latter. The present analyses may provide some guidelines for the toughening design of particle-reinforced composite materials.