基于裂纹尖端二阶弹性解的断裂过程区尺度

Fracture Process Zone Size Based on Secondary Elastic Crack Tip Stress Solution

基于Westergaard应力函数裂纹尖端二阶弹性解,推导了裂纹尖端微裂区的轮廓线和特征尺寸的解析表达式;采用幂函数模型描述的拉应变软化模型,确定了在最大拉应力强度理论和最大拉应变强度理论下断裂过程区(FPZ)临界值的解析表达式;将基于Westergaard应力函数一阶弹性解及二阶弹性解、Muskhelishvili应力函数和Duan-Nakagawa模型确定的FPZ临界值进行了比较。结果表明裂纹尖端微裂区和FPZ临界值随着Poisson比的减小而增加并逐渐趋近于应用最大拉应力强度理论确定的结果;二阶弹性解确定的裂纹尖端微裂区和FPZ临界值大于一阶弹性解的值;FPZ临界值随着拉应变软化指数的增加而增加;二阶弹性解确定的FPZ临界值的精度远高于一阶弹性解确定的值。

The contour and characteristic sizes of a micro-crack zone ahead of a fracture process zone （PFZ） were derived by the local solution based on Westergaard stress function with the secondary elastic crack tip stress. The critical sizes of FPZ were yielded out by the use of a power exponent tensile strain softening model under the maximum tensile stress criterion and the maximum tensile strain ~riterion. Based on the first elastic crack tip stress expression and the secondary elastic crack tip stress expression by Westergaard stress function, Mnskhel- ishvili stress function and Duan-Nakagawa model, the critical sizes of FPZ were compared. The discussions show that the size of a micro-crack zone and the critical size of FPZ increase with the decreasing Poisson ratio, and approach that of the maximum stress criterion. The contour and characteristic size of a micro-crack zone and the critical sizes of FPZ based on the seconda- ry elastic crack tip stress solution are bigger than the one based on the first elastic crack tip stress solution. The critical size of FPZ increases with the increasing tensile strain softening in- dex. The accuracy of critical size of FPZ based on the secondary elastic crack tip stress solution is much higher than the one based on the first elastic crack tip stress solution.