Effect of weld geometry on the limit load of a cracked specimen under tension

The accuracy of the defect assessment methods strongly depends on the accuracy of limit load solutions. Usually, many parameters classify welded structures. Therefore, parametric analysis of such structures may be time-consuming. The upper bound theorem supplies an efficient method for reducing lengthy calculations. The mathematical features of this theorem allow for accurate estimations of the limit load to be found using rather simple kinematically admissible velocity fields. In the case of highly undermatched welded joints, the known singular velocity behavior near the bi-material interface can be taken into account to choose a kinematically admissible velocity field satisfying some features of the real velocity field. The present article provides such a solution for V-bevel butt welds containing a crack of quite an arbitrary shape. The welded joint is subject to tension. The solution consists of two steps. The first step determines the limit load of the specimen with no crack. This step requires the numerical minimization of a function of one variable. The second step accounts for the crack, assuming that the solution for the uncracked specimen is known. This step is purely analytical. The accuracy of the solution is confirmed by comparison with a solution for a particular geometry of the weld found using Riemann’s method. The effect of the weld geometry on the limit load is revealed.