双向应力场中表面裂纹应力强度因子的权函数法

Improved point load weight function for stress intensity factor of surface cracks under two-dimensional stress field

半椭圆表面裂纹是船舶等焊接结构中常见的损伤形式,计算裂纹尖端应力强度因子是结构损伤容限设计的前提,权函数法是求解复杂应力场中应力强度因子的有效手段之一。本文基于一种集中力载荷权函数统一形式,通过三维有限元建模计算了裂纹半长比a/c=0.05~1.0、裂纹深度比a/T=0.01~0.8的表面裂纹应力强度因子,并将其作为参考解,得到一组形状适用范围更广的有限厚度平板表面裂纹最深点和表面点的二维权函数。权函数的准确性通过在裂纹面上施加最高六阶的双向变化应力载荷进行验证,权函数法结果与有限元法相比求解误差在10%以内。文中所提出的权函数为复杂焊接结构表面裂纹扩展分析奠定了基础。

Semi-elliptical surface cracks always occur in the welded structures such as ships, and the stress intensity factor analysis for such cracks is of major importance in damage tolerance design. The weight function method is useful to determine stress intensity factors under complex stress field. In this paper, practical formula of general point load weight function for surface cracks in finite thickness plate is developed based on the expression initially proposed by Wang et al. In order to overcome the limitation of applicable range on crack shape, three-dimensional finite element analyses were performed to calculate the stress intensity factors for surface cracks with aspect ratio a/c=0.05-1.0 and crack depth-to-thickness ratio a/T= 0.01-0.8. The unknown parameters in general form can be determined from reference stress intensity factor solutions. The derived weight functions are then validated against available stress intensity factors at surface and deepest points under several two-dimensional stress distributions up to sixth order, and the differences between weight function and FEM are mainly less than 10%, showing a fairly good accuracy. The proposed weight function may also provide an efficient approach to evaluate the surface fatigue crack growth in welded structures subjected to complicated stress fields due to stress concentration and welding.