Micromechanism approach to model creep fatigue interaction in lead-tin alloy

An elasto-viscoplastic constitutive equation is derived for a lead-tin alloy used in the microelectronics industry. This crystalline material exhibits nonlinear characteristics, such as strain hardening and saturation phenomena, if the applied load is cyclic. The constitutive equations govern the microdeformations undergone by a representative volume of the material during mechanical loading. The model is based on an averaging procedure from the microlevel (grains and grain boundaries) to the overall level, followed by an evolution equation that determines the orientation and extension of the characteristic slip-crack system. The averaging process introduces two fundamental functions related to the current damage and hardening recovery of the material. Properties of the material that are seen on the microlevel (such as microcracks, slip bands, and voids) are incorporated into the analysis by a simple rheological model, made of spring, dashpot, and slider, which allows the overall response of the material to be rate-dependent and to match the experimental data for both tensile and cyclic loadings obtained at different strain rates.