Large-strain response of isotropic-hardening elastoplasticity with logarithmic rate: Swift effect in torsion

Abstract

Recently, a new Eulerian rate-type isotropic-hardening elastoplasticity model has been established by utilizing the newly discovered logarithmic rate. It has been proved that this model is unique among all isotropic hardening elastoplastic models with all possible objective corotational stress rates and other known objective stress rates by virtue of the self-consistency criterion: the hypoelastic formulation intended for elastic behaviour must be exactly integrable to deliver a hyperelastic relation. The simple shear response of this model has been studied and shown to be reasonable for both the shear and normal stress components. The objective of this work is to further study the large deformation response of this model, in particular, the secondorder effects, including the well-known Swift effect, in torsion of thin-walled cylindrical tubes with free ends. An analytical perturbation solution is derived, and numerical results are presented by means of the Runge±Kutta method. It is shown that the prediction of this model for the shear stress is in good accord with experimental data, but the predicted axial length change is negligibly small and much less than experimental data. This suggests that the strain-induced anisotropy may be the main cause of the Swift effect.

Innovative elastoplastic J2‐flow model incorporating cyclic and non‐cyclic failure effects of metals as inherent constitutive features

“…With the simplified conditions given in Equation (40), both the deformation gradient and the velocity gradient may be derived using the general forms given in [37,38]. Here, derivations are omitted and results are directly presented.…”

“…With the above results, the governing equations for the constrained torsion and the free torsion may be derived from the new elastoplastic constitutive equations (34)-(37) following the same procedures in [37,38]. In the next two subsections, such equations will be directly presented.…”

“…[15,16,34]. Simulation results have been restricted either to the constrained torsion case [35,36] or to the free torsion case [37][38][39] under monotonic loadings. Moreover, monotonic and cyclic Swift effects in the free torsion case have been studied in [40,41], and both the constrained torsion and the free torsion under monotonic loading conditions have been treated for the same samples and simulation results have been presented with two separate sets of parameter values in [34].…”

An accurate and explicit approach to modeling realistic hardening‐to‐softening transition effects of metals

“…Unlike the usually treated uniaxial stretching response, the simple shearing response display finite rotation effects and is accordingly of significance to disclosing an essential aspect of finite strain response features. In fact, much attention has been directed to this aspect (cf., e.g., [11–20]), as indicated in the introduction section. However, a complete study with realistic hardening and softening effects up to failure has long been unavailable.…”

“…That would especially be the case in the sense of accurately simulating realistic hardening and softening effects. In particular, early results (see, e.g., [11–13]) for simple shearing responses with finite rotation effects were found to be unreasonable and subsequent results (see, e.g., [14–20]) in this respect were shown to be qualitatively reasonable for certain limited cases of hardening.…”