A micromechanical model considering dislocation density based intra-granular backstress under cyclic loading

Cyclic loading experiments of the Sn-3.0Ag-0.5Cu solder alloy at a wide range of temperatures and strain rates are conducted. The influence of both temperature and strain rate are investigated. A micromechanical constitutive model based on the dislocation density theory is proposed for polycrystalline materials under cyclic loadings. The dislocation storage and annihilation mechanisms during strain path changes are considered by introducing the reversible dislocations. Based on Eshelby's inclusion analysis, a dislocation density related slip system level intra-granular backstress model is developed to describe the Bauschinger effect. The differences between the proposed backstress model and the traditional Armstrong-Frederick model are discussed. Combined with the small strain elastic plastic self-consistent model, the developed model is successfully applied to describe the cyclic stress-strain curves of body-centered tetragonal structured Sn-3.0Ag-0.5Cu alloy and modified 9Cr-1Mo steel with a body-centered cubic structure.