正交各向异性单向复合材料裂纹尖端塑性区求解

基于复合材料力学基本理论,推导了Tsai-Hill准则、Hoffman准则和Tsai-Wu准则在平面问题下的一般表达式,在平面应力和应变状态下,得到复合材料中心裂纹板裂纹尖端塑性区的解析解.结果表明,基于Tsai-Wu准则得到的Ⅰ型、Ⅱ型和Ⅰ/Ⅱ复合型裂纹裂尖塑性区范围最小.平面应变状态下的裂尖塑性区范围小于平面应力状态下的裂尖塑性区范围.裂纹倾角β对复合材料裂尖塑性区范围和形状有明显影响,不同值得到的塑性区结果差别很大.不论是平面应力还是平面应变条件,裂纹尖端塑性区域都随着裂纹倾角的增大而增大.

Solutions to the crack tip plastic zone of orthotropic unidirectional composites

Based on mechanics of composite materials, Tsai-Hill yield criterion, Hoffman yield criterion and Tsai-Wu yield criterion expressions were derived under plane stress and strain conditions. The analysis solutions of mode Ⅰ, mode Ⅱ and mixed mode Ⅰ/Ⅱ crack tip plastic zone were gained. The results show that the size of crack tip plastic zone based on Tsai-Wu yield criterion is the smallest in the case of plane stress. The size of crack tip plastic zone under plane strain condition is less than that under plane stress condition for Tsai-Hill criterion and Hoffman criterion. The crack inclination angle β affects the size and shape of crack tip plastic zone obviously, and the difference between crack tip plastic zone results is great for different value of parameter β.