Analysis of elastic–plastic behavior and plastic front evaluation in spot welded joints

• A new analytical procedure for the elastic–plastic behavior of spot welded joints.
• Use of a theoretical equivalent model with an elastic compensation model.
• Good accuracy in the theoretical estimation of the evolution of plastic front.
• Results accuracy in terms of stiffness evaluation of spot welded joints in plasticity when load increases.
• Great advantages in elastic–plastic analysis of multi spot welded structures.

A new analytical procedure for the evaluation of the elastic–plastic stiffness behaviour and of the plastic front in spot welded joints is presented. The spot weld joint is modelled with a new theoretical model, a circular finite plate having variable thickness and with central rigid nugget. The closed form solution of the new reference theoretical model, while plasticity effect is considered, leads to the definition of a joint element useful to FE models of multi-spot structures. This solution allows to evaluate the variation of the stiffness of the spot nugget, when the finite plate is subjected to orthogonal load, while plasticity and moderate deflections are present. Furthermore, using the new analytical procedure it is possible to determine a good accuracy in the estimation of the evolution of plastic front, with the goal of studying the local behaviour of the junction, in terms of evaluation of plasticity radius and in terms of global stiffness of the joint. The procedure can be used as the basis to develop a spot weld element in FE analysis of multi spot welded structures, able to precisely evaluate both local and overall stiffness of spot joints, even when plasticity is accounted. The theoretical procedure leads to results that match those obtained analysing the actual spot weld region by reference FE models.