含空洞非线性材料的本构势和空洞扩展率

CONSTITUTIVE POTENTIAL FOR VOID-CONTAING NONLINEAR MATORIALS AND VOID GROWTH

本文基于体胞模型的解析分析,分析了含空洞非线性材料的宏观本构势,得到了各种幂硬化指数下宏观应力和基体平均流变应力之间的相关曲线.当基体是遵循经典塑性全量理论时,这些曲线方程就是一簇依赖于空洞体积比和硬化指数的屈服面方程.当基体是粘性体时,这些方程就是粘性约束方程.通过曲线拟合的方法,本文发展了修正的Gurson方程,使之适合于不同硬化指数的情况.最后本文计算了粘性体中空洞的相对扩展率,结果与已有体胞模型的数值模拟计算结果相当一致.

Based on an analysis of the deformation of an isolated void in a finite nonlinear viscous material, we estadlish th constitutive potentials for voided nonlinearly viscous materials, from which the related curves of the macroscopic stress, the average flow stress of the matrix material and the void volume fraction f are derived. However, the theory applies equally well to small strain, rate-independent J_2 deformation theory solid. By considering the effects of the strain-hardening directly, this paper modifies the Gurson constitutive model and makes it fit different strain-hardening com ponent. Finally, we obtain the void relative growthrates for the nonlinear materials anp compare these results with the numerical results of Budiansky et al~[7], Duva & Huchi nson~[8] and Duva~[9] respcctivcly.