裂尖具线性分布约束应力的运动裂纹模型及其解析解

摘要

The analytical solution of moving Griffith crack model with a constant speed is well known as Yoffe solution.For a static crack,its strip yielding model is well known as Dugdale model.It is found that when Dugdale model is generalized to the moving crack case,the crack opening displacement (COD)is discontinuous and approaches to positive and negative infinite at Rayleigh wave speed.Here,a restraining stress zone was attached to the crack tip while two speed effect functions were introduced assuming the restraining stress zone has a linear distribution.The complex function approach was employed to solve the problem.Analytical solutions of dynamic stress intensity factor (SIF)and crack opening displacement (COD)were then obtained.The new COD result was continuous and finite at Rayleigh wave speed.Some numerical results of COD were presented.Some valuable conclusions were obtained.%以恒定速度运动的Griffith裂纹解析解为著名的Yoffe解。静止裂纹的条状屈服模型即Dugdale模型，将其推广到运动裂纹模型时发现，当裂纹运动速度跨越Rayliegh波速时，裂纹张开位移COD趋于(∞，且表现为间断。通过在裂尖引入一个约束应力区及两个速度效应函数，假设约束应力为线性分布，采用复变函数方法，求得动态应力强度因子SIF与裂纹张开位移COD的解析解。新的结果，在Rayleigh波速下裂纹张开位移连续且为有限值。给出裂纹张开位移的一些数值结果，获得了一些有意义的结论。