Equations of Coupled Thermo-Plasticity

Abstract

The interaction of temperature and deformation during plastic flow appears in various forms. A thermal field influences the material properties, modifies the extent of plastic zones and results in ratchetting during cyclic heating etc., but also the deformation induces changes in the temperature distribution. From the stress analysis point of view the thermal effects in plasticity can be studied at two levels, depending on whether uncoupled or coupled theories of thermomechanical response have to be employed. The most technologically important problems regarding ratchetting, stresses in welding, residual stresses after quenching, design of reactor fuel elements etc. can be satisfactorily studied within an uncoupled theory. In such an approach the temperature enters the stress-strain relation through the thermal dilatation only, and possibly influences the material constants. The heat conduction equation and the relations governing the stress field are considered separately. These problems were described in Sections 9, 10 and 15. There exist, however, many instances when coupling of thermal and deformation states is of importance. We mention here stability analysis for metal forming, catastrophic shear during machining, and fatigue (Sluzalec 1990b).