Temperature at the Phase Boundary during Quasi-Static Motions of a Two-PhaseThermoelastic Bar

摘要

In this paper, a thermo-mechanical problem involving a finite bar is considered.It is assumed that the bar initially consists of two phases, one of which was obtained from the other by a martensitic phase transformation. It is also assumed that both phases of the bar have thermoelastic constitutive behavior. The two-phase bar is subject to different temperatures at each boundary and to a boundary traction. A quasi-static thermo-mechanical process is considered and the temperature, static equilibrium positions, and quasi-static motions of the phase boundary are studied as the material coefficients, temperature boundary conditions, and end loading are varied. Martensitic phase transformations are diffusionless solid-solid phase transformations which have continuous displacements, with possible discontinuous strains, at their phase boundary. They are also characterized by the parent and product phases having different crystal structures, or at least different crystal orientations, and by the product phase having a shape deformation relative to the undeformed parent phase, which corresponds to an unstressed undeformed state of that product phase. The high-temperature phase of a material that can undergo such a transformation is usually referred to as the austenite phase of the material, and the low-temperature phase that can be created from the austenite by a martensitic phase transformation is usually referred to as the martensite phase of the material.