动态裂纹尖端塑性区的解析解

Analytic solutions on plastic zone of dynamic crack tip

基于动态裂纹尖端应力场方程和Hill屈服准则,确定裂纹尖端塑性区的表达式,给出平面应力条件下Ⅰ/Ⅱ复合型动态裂纹尖端塑性区的解析解,分析了不同裂纹扩展速度下裂纹尖端塑性区的形状和大小。结果表明,Hill准则适用于正交异性材料和各向同性材料裂纹尖端塑性区的估算;裂纹扩展速度越快,裂纹尖端塑性区的范围越大,裂纹尖端塑性区的形状变化越大;Ⅰ型裂纹和Ⅱ型裂纹尖端塑性区的形状关于裂纹面对称;复合型裂纹尖端塑性区的范围和形状与m有关;对于同型裂纹,与正交异性材料相比,各向同性材料裂纹尖端塑性区的范围较大。

Based on the dynamic crack tip stress field equations and Hill yield criterion, the expression for crack tip plastic zone was determined. An analytic solution to I / II mixed mode dynamic crack tip plastic zone under plane stress state was also presented. The shape and size of the crack tip plastic zone at different crack propagation velocity were analyzed. The results show that Hill yield criterion is applicable to estimating the crack tip plastic zone of both orthotropie material and isotropic material. The faster the cracks spread, the bigger the shape and size change of the crack tip plastic zone. The shape of I mode and II mode crack tip plastic zone is symmetrical about the crack plane. The shape and size of the mixed mode crack tip plastic zone have relations with m value. Compared with orthotropic material, the size of crack tip plastic zone of isotropic material is bigger for the same crack mode.