基于能量释放率理论的三维应力强度因子显式闭合解

Explicit Closed-Form Solutions for Three-Dimensional Stress Intensity Factors Based on the Energy Release Rate Theory

基于能量差率基本原理,以非穿透裂纹深度的相对值作为控制裂纹虚比例扩展的无量纲几何参量,构造求解裂纹张开位移幅值的伯努利微分方程,导出以裂纹绝对尺寸和相对尺寸为参数的裂纹张开位移幅值表达式,得到有限大体非穿透裂纹三维应力强度因子闭合解。并给出无量纲应力强度因子与各种相对尺寸参数关系的显式表达式,计算结果与Newman的有限元分析结果基本一致。该方法在工程结构损伤容限与耐久性设计应用中更加便捷、高效。

To solve the crack opening displacement amplitude,the Bernoulli non-liner differential equa-tion based on the energy release rate principle is established,where the relative depth of non-throughcrack is defined as a dimensionless geometric variable to control the virtual proportional crack growth. Theequation of crack opening displacement amplitude is thus expressed with parameters of absolute and rela-tive crack dimensions. A closed form solution for three-dimensional stress intensity factors in a finite bodyis then obtained. Finally,the explicit expression of the relationship between the dimensionless stress inten-sity factor and the relative crack parameter is given. The results agree well with those obtained with the con-ventional finite element method,while this method is more convenient and efficient in engineering structur-al damage tolerance and durability design applications.