I型裂纹尖端约束应力区模型及其解析解

Analytical solutions for the restraining stress zone model of mode I crack tip

考虑了I型裂纹尖端损伤区域内三种不同的约束应力分布形式,即右三角分布形式(情况A)、均匀分布形式(情况B)、左三角分布形式(情况C),并采用复变函数方法求得了应力强度因子与裂纹张开位移的解析解;在此基础上,通过数值计算得到了应力强度因子和裂纹张开位移随约束应力区长度、约束应力大小以及分布形式的变化规律。研究结果表明:随裂尖材料损伤程度的增加,裂尖损伤区内约束应力减小,应力强度因子和裂纹张开位移增大;约束应力的分布形式对应力强度因子和裂纹张开位移有显著影响;相对于其他区域,约束应力对裂纹尖端区域裂纹张开位移的影响较大。然而,对于裂尖损伤区域的形成与作用荷载、材料性质、构件几何尺寸之间的关系,还需要进行更为深入的研究。

Three different distributions of restraining stresses in mode I crack tip damaged zone are considered, in which Case A is the right triangular shape, Case B is the uniform distribution and Case C is the left triangular shape. By application of complex function approach, the analytical solutions of stress intensity factor(SIF) and crack opening displacement(COD) for above three different cases are derived. Variations of SIF and COD with the restraining stress zone length, the value and distribution type of restraining stresses are numerically calculated. Numerical results obtained show that the restraining stress decreases with the material damage. Accordingly, SIF and COD increase when the restraining stress decreases by the material damage. Moreover, the distribution type of restraining stresses has a pronounced influence on SIF and COD. Compared to other regions, restraining stress has a greater impact on COD of crack tip zone. It is pertinent to pay more attention on the relationship of crack tip damage zone versus applied load, material property and geometric size of structural members in the future work.