The limiting values of the Swift effect in hyperelastic-plastic materials exhibiting yield stress saturation

Abstract

The Swift effect is a well-known phenomenon that addresses the change in length of a cylindrical sample in free-end torsion or the generation of an axial force in fixed-end torsion. In this study, we focus on the latter case. For materials with yield stress saturation (common in metals or some polymers under specific conditions), it is reasonable to assume that the magnitude of the axial force and torque should reach a steady-state value with increasing torsional strain. The aim of this study is to establish the relationship between these values and the mechanical parameters of materials. We utilize a hyperelastic-plastic formulation based on the multiplicative decomposition of the deformation gradient tensor into elastic and plastic parts. The isotropic incompressible material model incorporates a general-form hyperelastic law, a yield condition, and a plastic potential in the form of arbitrary smooth functions of the deviatoric invariants J₂ and J₃. A new universal relationship for the limiting values of the components of the elastic deformation tensor under fixed-end torsion is derived. In general, the limiting values of axial stress and torque can be calculated by solving two pairs of algebraic equations. In specific cases, such as the von Mises, Drucker and Cazacu – Barlat plasticity models, simple formulas for these quantities are derived.