Modeling of failure near spot welds in lap-shear specimens based on a plane stress rigid inclusion analysis

In this paper, the failure mechanism of resistance spot welds in dual-phase steel lap-shear specimens is investigated based on experimental observations, two-dimensional elasticity theories and two-dimensional finite element analyses. Optical micrographs of the cross sections of spot welds in lap-shear specimens of a dual-phase steel before and after failure are first examined to understand the failure mechanism. The experimental results suggest that under lap-shear loading conditions, a necking failure is initiated near the middle of the nugget circumference in the base metal and then the failure propagates along the nugget circumference in the sheet to final fracture. Based on the stress function approach of the elasticity theory, an analytic solution for an infinite plate containing a rigid inclusion subjected to a resultant shear force is developed and used to investigate the stress and strain distributions near the nugget in lap-shear specimens. The results of the elastic analytic solution and those of a two-dimensional elastic finite element analysis indicate that the initial yielding starts on the two side edges of the inclusion in the sheet. However, the results of a two-dimensional elastic–plastic finite element analysis indicate that as the applied displacement increases, the maximum equivalent plastic strain shifts from the two side edges of the inclusion to the middle of the inclusion along the inclusion circumference in the sheet. The computational results suggest that the location of the initial necking failure should occur near the middle of the nugget circumference in the sheet as observed in experiments based on the forming limit diagram (FLD) for ductile sheet metals.