Elastic strain energy density decomposition in failure of ductile materials under combined torsion-tension

Nikos P Andrianopoulos,Vasileios M Manolopoulos

doi:10.1186/s40712-014-0016-5

Nikos P Andrianopoulos, Vasileios M Manolopoulos

Open Access

https://doi.org/10.1186/s40712-014-0016-5

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Abstract

The constitutive behavior and failure of ductile materials are described in the present work for a general case of loading in terms of the secant moduli, which depend on the first (dilatational) and second (deviatoric) strain invariants. This approach exposes the distinct behavior of materials to the equivalent normal and shear stresses. The secant moduli enable the establishment of two (instead of one) constitutive equations necessary for the complete description of these materials. Emphasis is given in the accuracy of the resulting constitutive equations in terms of their predictions relative to actual experimental data for two materials systems. Failure predictions, according to T-criterion, are derived for two materials under combined torsion and tension, which are in good agreement with experimental data. Finally, the associated failure surfaces in a stress space are presented as well.

Highlights

The importance of strain energy density and in particular the distortional part of it relative to material failure was understood, conjectured and postulated, as early as in the era of Maxwell (1937) and others (Hencky 1924; Huber 1904)
Strain energy, supplied to the material via some generalized loading, can be additively decomposed into two parts: the elastic and the inelastic one; the elastic strain energy is recoverable upon removing the load due to the fact that the materials remained elastic throughout its loading; the plastic strain energy is unrecoverable that, when the load is removed, yields a permanent strain known as plastic strain
The lack of hydrostatic tension or compression data is a barrier in defining the exact form of p = p(Θ) and the exact value of the critical dilatational strain energy density TV,0

Summary

Introduction

The importance of strain energy density and in particular the distortional part of it relative to material failure was understood, conjectured and postulated, as early as in the era of Maxwell (1937) and others (Hencky 1924; Huber 1904). In case of failure of materials, the only available resource is elastic strain energy, stored into the material through elastic (linear or not) deformations. Elastic deformations exist from the very first load step until the last one From this point of view, the amount of plastic work has no causative role in failure because it is the outcome of the action of available strain energy. Plastic work is a result of this action and cannot be the cause of other processes, including failure. It is a type of specific failure per se.

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