Critical thought experiment to choose the driving force for interface propagation in inelastic materials

The problem of defining the driving force for interface propagation in inelastic materials is discussed. In most publications, the driving force coincides with the Eshelby driving force, i.e. it represents a total dissipation increment on the moving interface due to all the dissipative processes (phase transition (PT) and plasticity). Recently (Levitas, V.I., 1992a. Post-bifurcation Behaviour in Finite Elastoplasticity. Applications to Strain Localization and Phase Transitions. Universität Hannover. Insititut für Baumecharik and Numerische Mechanik, BNM-Bencht 1JP 585-LC, 92/5, Hannover; Int. J. Eng. Sci. 33 (1995) 921; Mech. Res. Commun. 22 (1995) 87; J. de Physique III 5 (1995) 173; J. De Physique III 5 (1995) 41; Int. J. Solids Struct. 35 (1998) 889], an alternative approach was developed in which the driving force represents the dissipation increment due to PT only, i.e. total dissipation minus plastic dissipation. The aim of this paper is to prove the contradictory character of application of the Eshelby driving force to inelastic materials. For this purposes, a problem on the interface propagation in a rigid–plastic half-space under homogeneous normal and shear stresses is solved using both definitions, along with the principle of the maximum the driving force. Finite strain theory is used. It appears that the first approach exhibits some qualitative contradictions, which are not observed in our approach. In particular, even for shape memory alloys, when transformation strain can be accommodated elastically (or even without internal stresses), maximization of the Eshelby driving force requires as much plasticity as possible. When applied shear stress tends to the yield stress in shear of a new phase, the driving force tends to infinity, i.e. PT has to always occur at the beginning of plastic flow. Note that in this paper plasticity means dislocation plasticity rather than plasticity due to twinning. Twinning during martensitic PT is the appearance of several martensitic variants which are in twin relation to each other. Consequently, for twinned martensite one has microheterogeneous transformation strain without plastic dissipation term, i.e. both approaches coincide.