Damage mechanics constitutive model for Pb/Sn solder joints incorporating nonlinear kinematic hardening and rate dependent effects using a return mapping integration algorithm

Abstract

A thermodynamics-based damage mechanics rate dependent constitutive model is used to simulate experiments conducted on thin layer eutectic Pb/Sn solder joints. As compared to previous implementations of the model here we correct the difficulties introduced by the slow convergency rate of the Owen and Hinton (Owen, D.R.J., Hinton, E., 1980. Finite Element in Plasticity. Pineridge Press Limited, Swansea, UK) integration scheme. To this end, we time-integrated the model with a classical return mapping algorithm where rate dependency, nonlinear kinematic hardening of the Armstrong–Frederick type and damage effects are simultaneously coupled. The model is implemented into the commercial finite element code ABAQUS via its user material subroutine capability and validated against experimental results. We simulated monotonic shear, cyclic shear and fatigue shear experiments performed on homemade thin layer solder joints. The simulation results are in good agreement with the experiments and the model accurately describes the true behavior of Pb/Sn solder alloys. As a direct advantage of the new model implementation this can be used for axisymmetric and 3D simulations as opposed to the plain strain-only capability in the Owen and Hinton (Owen, D.R.J., Hinton, E., 1980. Finite Element in Plasticity. Pineridge Press Limited, Swansea, UK) integration scheme.