Collapse load for a crack in a plate with a mismatched welded joint

The accuracy of flaw assessment techniques for welded joints is directly related to the accurate estimate of the yield collapse load. A careful finite element limit analysis can provide a very good and reliable assessment of the collapse load. Unfortunately, such an analysis is normally time-consuming and requires a substantial effort in order to validate the finite element calculations. In this paper we apply the classical upper bound theorem of plasticity to develop simplified solutions for a through crack in a tensile plate with a mismatched welded joint. The weld configuration is idealised as a simple sandwich model and the collapse load is derived analytically from a solution of an extreme-value problem. The theoretical solutions are then verified by independent finite element calculations. The proposed solutions seem to be very effective and accurate and can be easily generalized for many other weld geometries and loading conditions.