Partitioned cyclic fatigue damage evolution model for Pb-free solder materials

This study presents an approach to predict the degree of material degradation and the resulting changes in constitutive properties during cyclic loading in viscoplastic materials in micro-scale applications. The objective in the modeling approach is to address the initiation and growth of distributed micro-damage, in the form of micro-cracks and micro-voids, as a result of cyclic, plastic and creep deformations of material. This study extends an existing micromechanics-based approach, developed for unified viscoplastic models [Wen, et al, 20011, which uses dislocation mechanics to predict damage due to distributed micro-scale fatigue crack initiation [Mura and Nakasone, 1990]. In the present study, the approach is extended to a partitioned viscoplastic framework, because the micro-scale mechanisms of deformation and damage are different for plastic and creep deformation. In this approach, the model constants for estimating cyclic damage evolution are allowed to be different for creep and plastic deformations. A partitioned viscoplastic constitutive model is coupled with an energy partitioning (E-P) damage model [Oyan and Dasgupta, 1992] to assess fatigue damage evolution due to cyclic elastic, plastic and creep deformations. Wen's damage evolution model is extended to include damage evolution due to both plastic and creep deformations. The resulting progressive degradation of elastic, plastic and creep constitutive properties are continuously assessed and updated. The approach is implemented on a viscoplastic Pb-free solder. Dominant deformation modes in this material are dislocation slip for plasticity and diffusion-assisted dislocation climb/glide for creep. The material's behavior shows a good correlation with the proposed damage evolution model. Damage evolution constants for plastic and creep deformation were obtained for this Pb-free solder from load drop data collected from the mechanical cycling experiments at different temperatures. The amount of cyclic damage is evaluated and compared with experiment.