Two-dimensional weight function of stress intensity factors for surface cracks emanating from weld toes of butt-welded plates

Abstract

The two-dimensional weight function method, which is proposed by Wang and Glinka (2009), is adopted here to calculate stress intensity factors for surface cracks emanating from weld toes of butt-welded plates with different toe angles. Two-dimensional point load weight function is derived based on reference stress intensity factors and accurate stress distribution on virtual crack face obtained from comprehensive finite element analyses. The obtained weight function is validated against finite element calculations and shows high accuracy. Explicit fitted empirical formulae are obtained for semi-elliptical surface cracks with wide ranges of crack aspect ratio $0.2⩽a/c⩽1.0$, crack depth ratio $0.2⩽a/B⩽0.9$, crack angular parameter $0.05⩽2\varphi /\pi ⩽0.95$, at weld toes with toe angles $\phi =0^{°}\text{,}{15}^{°}\text{,}{30}^{°},{45}^{°}$ and toe radius ratio $r/B=0.0,0.1,0.2,0.3$ for quick fatigue crack growth prediction in engineering structures providing a foundation for durability and damage tolerance design. It is shown that sharp transition ($r/B=0.0$) between the weld toe and the base metal will lead to a significant increase of weight function coefficient M at the front of shallow cracks ($a/B\text{= 0.02}$) near the surface.