裂纹体分析的权函数理论与应用: 回顾和展望

断裂力学是工程材料和结构的疲劳与断裂分析、损伤容限设计和结构完整性评定的理论基础. 应力强度因子作为线弹性裂纹尖端奇异场的单一表征参量和裂纹扩展驱动力, 在裂纹体的断裂力学分析中发挥着关键作用. 权函数法为复杂受载裂纹体的应力强度因子求解计算提供了强有力的解析工具, 不但具有远高于各类数值解法的计算效率, 而且精度可靠, 使用方便. 本文结合笔者团队在权函数法方面的长期研究工作, 对该方法自20世纪70年代初提出至今半个世纪以来, 国际断裂界在二维和三维权函数理论与应用方面的主要研究进展作了回顾和评述, 并对其未来发展提出了展望. 主要内容涵盖: 当前国际断裂界广泛应用的3种二维裂纹解析权函数法简介和以格林函数为基准的验证评价; 三维裂纹问题的片条合成权函数法和点载荷权函数法; 权函数法在复杂受载裂纹体的应力强度因子和裂纹张开位移等关键力学参量计算、内聚力/桥连等裂纹模型分析、共线多裂纹权函数理论及其在剩余强度预测等方面的应用, 以及复杂裂纹几何的工程化权函数分析和权函数法的反向应用问题. 

Weight function theory and applications for crack analysis: A review and outlook

Fracture mechanics is the theoretical foundation for fatigue and fracture analyses of engineering materials and structures, damage tolerance design, and structural integrity assessment. Being the single characterizing parameter of the linear elastic crack tip singular stress/strain field and the crack deriving force, the stress intensity factor (SIF) plays a vital role in fracture mechanics analysis. The weight function method (WFM) is a powerful method for the determination of SIFs for cracks under complex load conditions, with remarkable computational efficiency and reliable solution accuracy, and is easy to use. Combined with the authors’ teamwork on WFM research in the past several decades, this article presents a comprehensive review of the historical developments of various WFMs over the past 50 years and also a brief outlook. The main topics include: a brief introduction of three types of analytical weight function approaches for 2D crack problems and accuracy verification based on Green’s functions; the slice synthesis weight function method and the point weight function method for 3D crack problems; various practical applications of WFMs, including determination of the key fracture mechanics parameters of SIFs and crack opening displacements under complex loadings, cohesive/bridging model analyses, WFM for multiple collinear cracks and residual strength prediction of panels containing multiple site damage, engineering weight function approaches to complex crack configurations, and inverse application of WFM for the determination of stress distributions in un-cracked bodies.