Dislocation density and twinning-related constitutive modeling of substructural evolution in Sn-5Sb-0.5(Ag/Cu) alloys under monotonic deformation

Abstract

The development of a numerical model and experimental evaluation of microstructural evolution during the deformation of such materials are of pronounced significance. In the current work, evolutions of the substructure in three Sn alloys, namely Sn-5Sb, Sn-5Sb-0.5Ag, and Sn-5Sb-0.5Cu, were investigated using a dislocation density constitutive equation. The mechanical behavior of such alloys has been assessed, taking advantage of Ag and Cu addition and substructure-based factors like dislocation density, size, and misorientation. A comprehensive constitutive equation was developed for modeling the flow behavior of Sn-based alloy through the substructure-based tensile response of the material. It has been perceived that Cu is more in effect to improve the strength of Sn than Ag and Sn-5Sb-0.5Cu alloy is with enhanced work hardening rate during the tensile state of deformation. Dislocation density formulation results have direct implications on the capability to explicitly model the superimposed effect of dislocation densities and subgrain boundaries on the macroscopic mechanical properties of polycrystals. A numerical description of twinning stress in studied BCT alloys is described by the dislocation production kinetic model considering dislocation pile-up as the dominant mechanism. The developed slip-twinning transition model is incorporated into the deformation maps to identify the twinning domain.