裂纹稳态扩展下正交异性材料的动应力强度因子<I>K</I><SUB>Ⅲ</SUB>解答

裂纹稳态扩展下正交异性材料的动应力强度因子K_Ⅲ解答

摘要: 研究了无限大正交异性材料中半无限长Ⅲ型裂纹的动态扩展问题。裂纹尖端附近的应力和位移被表达为解析复函数的形式,而复函数可以表达为幂级数的形式,幂级数的系数由研究问题的边界条件来确定。这样就给出了裂纹尖端附近的应力分量和位移分量的简单近似表达式,由推导出的动应力分量和动位移分量可以退化为其在各向同性材料静态断裂问题中的情况。最后,裂纹扩展特性由裂纹几何参数和裂纹扩展速度来反映出来,相同的几何参数情况下,裂纹扩展愈快,裂纹尖端附近的最大应力分量和最大位移分量愈大。

Abstract: The dynamic propagation problem of semi-infinite mode Ⅲ crack in an orthotropic infinite body is investigated. The stresses and displacements near the crack tip are expressed as analytical complex functions, which can be represented in power series. The constant coefficients of the series are determined with boundary conditions. Simple approximate expressions for the stresses and displacements near the crack tip are developed. The expressions can be degenerated for static problems in isotropic materials. Finally, the crack propagation characteristics are represented with the mechanical properties of the orthotropic material and crack speeds. The faster the crack velocity, the greater the maximum values of the stresses and displacements near the crack tip.