一类弹粘塑性材料II型扩展裂纹的尖端场

为了研究粘性效应作用下的II型扩展裂纹尖端场,假设扩展裂纹尖端的粘性系数与塑性应变率的幂次成反比,通过量级匹配表明应力和应变均具有幂奇异性,奇异性指数由粘性系数中等效塑性应变率的幂指数唯一确定.引入Airy应力函数,求出了裂纹尖端应力和应变场的控制方程.选取适当的特征参数,给出了边界条件,对控制方程通过双参数打靶,进行了数值计算,求得了裂纹尖端的应力应变场.分析与计算结果表明粘性效应是裂纹尖端场的一个重要因素.

The field at the tip of mode II propagating crack in a class of elastic-viscoplastic materials

While investigating the field at the tip of a mode II propagating crack in a viscoplastic environment,we assumed that the viscosity coefficient at the propagating crack tip is inversely proportional to the power law of the plastic strain rate.It is known that stress and strain both possess power law singularities,and their singularities are uniquely determined by the exponent of equivalent plastic strain rate in the coefficient of viscousity.The governing equations of the stress and strain fields at the crack-tip were solved separately by means of Airy's stress function.Numerical calculations of the governing equations were carried out with appropriate characteristic parameters and the given boundary conditions,and from this the continuous stress-strain fields obtained at the crack-tip.The analytical and computational results verified that the viscosity effect is an important factor in crack-tip fields.