裂纹表面线性分布力作用下I型应力强度因子的解析解

对于I型裂纹,考虑到裂纹表面受线性分布约束应力作用,利用复变函数方法,从两个基本的解析函数出发,推导出应力强度因子(SIF)和裂纹张开位移(COD)的解析解.数值计算了3种形式的应力分布,即右梯形分布(情况I)、均匀分布(情况II)和左梯形分布(情况III).通过对3种形式的应力强度因子和裂纹张开位移进行对比,发现裂纹表面约束应力的分布形式和位置对应力强度因子和裂纹张开位移有很大影响;随着约束应力区远离裂纹中心,应力强度因子减小,而裂纹中心张开位移随之增大.

Analytical solution of stress intensity factor of a mode I crack with linearly distributed stresses

Restraining stresses with a linear distribution are applied to the surfaces of a mode I crack. By application of complex function approach and two basic analytical functions, the stress intensity factor （SIF） and crack opening displacement （COD） are derived. The stress distribution in three cases are calculated numerically. Case I is the right trapezium shape. Case II is the uniform distribution. Case III is the left trapezium shape. The variations of SIF and COD in three cases are compared. The numerical results show that the distribution type and position of restraining stress zone have a large influence on SIF and COD. With the increase of distance of restraining stress zone to the crack center, SIF decreases while COD at the crack center increases.