#### Vol. 4, No. 2, 2009

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Inelastic heat fraction evaluation for engineering problems involving dynamic plastic localization phenomena

### Patrice Longère and André Dragon

Vol. 4 (2009), No. 2, 319–349
##### Abstract

The evaluation of the temperature produced during adiabatic dissipative processes for a large class of engineering materials (metals and some polymers) remains a major subject of interest, notably in the fields of high-speed machining and impact dynamics. The hypothesis consisting in considering the proportion of plastic work dissipated as heat (quantified by the inelastic heat fraction $\beta$) as independent on the loading path is now recognized as highly simplistic. Experimental investigations have shown indeed the dependence of the inelastic heat fraction on strain, strain rate and the temperature itself. The theoretical studies available nowadays are not entirely conclusive on various features regarding the history dependence and the evolution of $\beta$. The present work attempts to provide a systematic approach to the temperature rise and the inelastic heat fraction evolution for a general loading within the framework of thermoelastic/viscoplastic standard modelling including a number of quantitative variants regarding strain hardening/thermal softening and thermomechanical coupling description. The theoretical results thus obtained are confronted with experimental data from the literature. An analysis of the effects of various model simplifications on the evaluation of temperature growth with regard to conditions for dynamic plastic localization occurrence is also carried out. It is shown that the value of critical shear strain at localization incipience is strongly dependent on the level of simplification admitted.

##### Keywords
thermomechanics, viscoplasticity, inelastic heat fraction, nonlinear modelling, dynamics, localization