Role of Constitutive Modeling on the Analysis of Shear Localization in Semi-Solid Deformation

This study presents an analytical framework to investigate the role of constitutive modeling in evaluating the instability of semi-solid deformation. Two constitutive models’ distinct conceptual foundations are considered. The first model characterizes mushy-state deformation as an interpolation between the behaviors of porous and cohesionless granular materials. The second model adopts the Norton-Hoff viscosity law to describe the rheology of semi-solid alloys. The evolution of small perturbations is examined in relation to key constitutive parameters. Both models predict that increased rate sensitivity mitigates the likelihood of shear localization, whereas higher strain rates tend to promote it. However, the models diverge in their predictions regarding the effect of cohesion. The viscosity-based model exhibits stronger agreement with recent X-ray tomography studies and experimental data from tests on ۷۰۷۵ aluminum alloy, indicating its superior capability in capturing semi-solid rheological behavior. Furthermore, this model predicts the existence of a critical strain rate, above which semi-solid deformation becomes unstable for a given cohesion degree. In contrast, the Zavaliangos model suggests that the tendency for localization increases with cohesion, an outcome that contradicts experimental findings. This discrepancy is substantiated through parameterization and quantitative analysis.

Keywords:

Shear localization , Semi-solid deformation , dilatancy , Perturbation analysis , constitutive model