正交各向异性板周期张开型平行裂纹的应力分析

Analysis of stress of periodically opened parallel cracks in orthotropic plate

通过构造适当的Westergaard应力函数,采用复变方法和待定系数法对正交各向异性纤维增强复合材料板的周期张开型平行裂纹尖端附近的应力场进行力学分析.在无穷远处对称拉伸载荷的作用下,利用双曲函数的周期性,修正常规的应力强度因子定义,得到用n表示的周期张开型裂纹尖端的应力强度因子及用修正的应力强度因子表示的周期张开型裂纹尖端附近的应力场的显式解析表达式.此外,应力场的大小与材料弹性常数有关,这是正交各向异性材料不同于各向同性材料的特征.由于裂纹的周期分布,应力强度因子的大小取决于形状因子.结果表明,当裂纹间距趋于无限大时,退化为含单个中心裂纹正交异性纤维增强复合材料板的结果,并且所得的解析解能更好地体现裂纹的周期性.

By constructing proper Westergaard^s stress function, the stress field around the tip of periodi- cally opened parallel cracks in orthotropic fiber-reinforced composite plate subjected to the load of symmet- ric tension at infinity was analyzed mechanically by using complex variable function method and approach of undermined coefficients. The conventional definition of stress intensity factor was revised by using the periodicity of the hyperbdie function. The explicit analytic expressions of the stress fields with n as stress intensity factor and also with the revised stress intensity factor were finally obtained. In addition, the scope of stress field was related to the elasticity constant of the materials which was the feature of ortho- tropic materials different from the isotropic materials. Due to the periodicity of crack distribution, the stress intensity factor would be determined by the shape factor. The result showed that when the interval of the cracks approached to infinity, the orthotropic fiber-reinforced composite plate would be degenerated into one with a single central crack, and the analytic solution obtained would well reflect the periodicity of the crack.