A Damage-Coupled TMF Constitutive Model for Solder Alloy

This paper presents the development of a damage-coupled constitutive model to characterize the mechanical behavior of 63Sn-37Pb solder material under thermo-mechanical fatigue (TMF) loading. Based on the theory of damage mechanics, two internal state variables, known as the damage parameters, are introduced to characterize material degradation due to the change of material microstructures under load. Then, a damage effect tensor is proposed to define the effective stress for a damaged material. In general, there are two different kinds of damage accumulation depending upon the mode of loading: inelastic damage and fatigue damage. With the aid of irreversible thermodynamics, the damage evolution equations are established. A failure criterion is proposed based on the equivalent damage accumulation in materials. A test program to determine the material parameters is also presented. The damage model is implemented in a finite element program ABAQUS through its user-defined material subroutine UMAT. The model is applied to predict the behavior for 63Sn-37Pb solder alloy under monotonic tensile loading, load-controlled tensile creep loading and strain-controlled fatigue loading. The behavior of a notched specimen under monotonic tensile loading is also examined. The predicted failure mode and maximum load agree well with those measured experimentally.