幂软化材料动态裂纹尖端的弹塑性场

Dynamic Fields Near a Propagating Crack-tip in a Strain-damage Material

采用塑性动力学方程,对应变损伤材料平而应力动态裂纹尖端场进行了渐近分析。假定材料服从J_2流动理论,且损伤规律以幂律应变软化的规律给出,其结果表明:在裂纹尖端附近,应力和应变分别具有如下的奇异性:σ/(1n R/r)^(-n/n+1),∈～(1n R/r)^(1/n+1),并且通过数值计算给出了裂纹尖端附近的应力分布。而对于n=1情况下,即损伤规律服从反比例关系,本文对平面应变问题和Ⅲ型反平面剪切问题进行了研究。给出了动态弹塑性场的渐近解,揭示了场的渐近特性。

Based on plastic-dynamic equations, the asymptotic behaviour of the near-tip fields for a plane stress tensile crack propagating in a strain-damage material has been studied in this paper. It is assumed that the medium obeys the J_2 flow theory and damage rule is given asymptotically in a form like power-law strain softening. It is shown that the stress and strain singularites given are of the orders (lnR/r)^(-n/(n+1))and(lnR/r)^(1+(n+1)) respectively. The stress distribution surrounding the crack tip is given numerically, When n=1, the damage rule is given asymptotically in a form like inverse ratio strain softening, for the plane strain problem and antiplane shear problem the detailed research is given and asymptotic solutions of the dynamic elastoplastic field are derived. The asymptotic behaviour of the field is revealed.