THE LOCALIZATION OF PLASTIC-DEFORMATION IN THERMOPLASTIC SOLIDS

The main objective of this paper is the investigation of the influence of thermomechanical couplings and thermal softening effects on adiabatic shear band localization criteria for finite rate-independent deformation of an elastic-plastic body. The constitutive equations for thermoelastic-plastic J2-flow theory are formulated within a framework of the rate type covariance structure with internal state variables. Two alternative descriptions are presented. Both constitutive structures formulated are invariant with respect to diffeomorphisms and are materially isomorphic. Particular attention is focused on the coupling phenomena generated by the internal heat resulting from internal dissipation. An identification procedure has been developed which permits the determination of the exact form of the evolution equation for the internal state variable vector. A set of coupled evolution equations for the Kirchhoff stress tensor and for temperature is investigated. The assumption that the thermodynamic process considered is adiabatic permits the elimination of the rate of temperature and gives the fundamental evolution equation for the Kirchhoff stress tensor. This important result allows the use of the standard bifurcation method in the examination of the adiabatic shear band localization criteria. For the particular elastic properties of the material and for some simplified case of the coupling effects the criteria for adiabatic shear band localization are obtained in exact analytical form. Discussions of the influence of thermomechanical couplings, thermal expansion, thermal plastic softening effects and the covariance terms on the localization criteria are presented.