Theoretical Framework for Modeling Spot Welds under Various Types of Loading Conditions

The theoretical framework and closed-form stress intensity factor solutions in terms of the structural stresses for spot welds under various types of loading conditions are presented based on elasticity theories and fracture mechanics. A mechanics description of loading conditions for a finite plate with a rigid inclusion is first presented. The loading conditions of interest are the resultant loads on the inclusion in a plate and the surface tractions on the lateral surface of a plate. The surface tractions on the lateral surface of the plate can be decomposed into a load-balanced part and a self-balanced part. The resultant loads on the inclusion and the self-balanced resultant loads on the lateral surface are then decomposed into various types of symmetric and anti-symmetric parts. Based on the elasticity theories, closed-form moment, force and stress solutions are derived for a plate with a rigid inclusion subjected to various types of loading conditions. Based on the J integral for a strip model, closed-form analytical stress intensity factor solutions for spot welds joining two sheets of equal thickness are derived in terms of the structural stresses around a rigid inclusion in a plate under various types of loading conditions. The closed-form solutions presented in this paper are used as the basis to develop new analytical stress intensity factor solutions for spot welds in various types of specimens presented in a subsequent paper.