Closed-form structural stress and stress intensity factor solutions for spot welds in square plates under opening loading conditions

Abstract

Closed-form structural stress and stress intensity factor solutions for spot welds in square plates under opening loading conditions are investigated here. First, the existing analytical axisymmetric solutions for a rigid inclusion in a circular plate with simply supported and clamped outer edges are reviewed. Then the results of axisymmetrical finite element analyses for a rigid inclusion in a circular plate are presented. The results indicate that the finite element model with one element across the plate thickness is an appropriate model to investigate the structural stress solutions for a rigid inclusion in a square plate to avoid the local effect of the reaction force due to the constraint applied to the rigid inclusion. Next, the results of three-dimensional finite element analyses for a rigid inclusion in a square plate with simply supported and clamped outer edges are presented. The results indicate that, as the ratio of the plate width to the rigid inclusion diameter becomes large about 6, the structural stress solutions along the circumference of the rigid inclusion become almost uniform. Approximate equivalent radius solutions are then determined in order to use the analytical structural stress solutions for a rigid inclusion in a circular plate to calculate the structural stress solutions along the circumference of the rigid inclusion in a square plate. Then, the results of three-dimensional finite element analyses for spot welds between square plates of different thicknesses and materials are presented. The results indicate that the computational stress intensity factor solutions agree well with those based on the structural stress solutions with the equivalent radius. Based on the closed-form structural stress solutions, complete sets of the normalized stress intensity factor solutions for spot welds between square plates of different thicknesses and materials under opening loading conditions are presented for combinations of steel, aluminum and magnesium sheets and combinations of aluminum and copper sheets for convenient engineering applications.