A meso-scale damage evolution model for cyclic fatigue of viscoplastic materials

This study presents an approach to predict the degree of material degradation and the resulting changes in elastic, plastic and creep constitutive properties of viscoplastic materials, during cyclic loading in micro-scale applications. The objective of the study is to address the initiation and growth of homogeneous meso-scale damage, in the form of distributions of micro-cracks and micro-voids, due to cyclic, plastic (rate-independent inelastic) and creep (rate-dependent inelastic) deformations in viscoplastic materials and to evaluate the resulting changes in the effective meso-scale elastic, plastic and creep constitutive properties. An energy partitioning damage evolution (EPDE) model is proposed to describe the viscoplastic damage evolution. Development of the EPDE model constants is then demonstrated for a Pb-free solder, based on cyclic fatigue test data. Application of the EPDE model is demonstrated for solder joint fatigue during thermal cycling of a ball grid array (BGA) electronic assembly. A 3D viscoplastic finite element analysis is conducted, and damage evolution is modeled using a successive initiation (SI) technique reported earlier by the authors. In this approach, the local (meso-scale) material properties are progressively degraded and highly damaged sections of the macro-scale structure are ultimately eliminated, using the EPDE model. Prediction of damage initiation and propagation is presented both with and without property updating, for comparison purposes. The analysis shows that the EPDE model can realistically capture the softening observed during cyclic loading.