J-integral and limit load analysis of semi-elliptical surface cracks in plates under bending

Abstract

Systematic detailed linear and non-linear finite element (FE) analyses are performed for semi-elliptical surface cracks in plates under bending. Limit load (moment) solutions are obtained from the FE J results via the reference stress method. The FE results show that the Newman and Raju stress intensity factor equation is reasonably accurate and the Yagawa et al. J solution may significantly under estimate J for bending load. The relationship between J and the limit load is found to be dependent on the ratio a/ t and a/ c, where a and c are the depth and the half-length of the crack and t is the plate thickness. For a/ t≤0.5 with a/ c=0.2, J for any position along a crack front can be predicted by the reference stress method using a single limit load value except for the points very close to the plate surface. For all other cases, it can only be approximately estimated by the reference stress method because a limit load value that can satisfy all the FE J solutions along the crack front cannot be found. However, for all the cases examined, the maximum J along the crack front can be well predicted by the reference stress method when a proper global limit load is used. The Goodall and Webster global limit load equation is extended to any crack depth. The limit load data obtained in this paper can be well reproduced by the extended equation.