The Equilibrium Motion of the Martensitic Interface in Thick-Walled Infinite Austenitic Plate

Abstract

i) Consider the microregion R(t) subdivided (in actual configuration) by strong discontinuity interface S(t) into parent-phase portion R ₁(t) (high-temperature phase-austenite (A)) and product phase portion (low temperature phase-martensite (M)) R ₂ ·A → M phase transition (p.t.) is regarded as the coherent one, i.e., displacement and temperature T are continuous, whereas deformation gradient F, velocity v, and Cauchy’s stress σ experience jump discontinuities at S(t). The jump in some physical quantity ψ at the interface is denoted by [ψ]= ψ₁ — ψ₂, where indexes 1 and 2 indicate a property of parent phase and product phase, respectively. When, at generic instant t, the reference configuration is so chosen that the parent phase particles are identified by their position in the current configuration at that time (region R ₁) then the geometric and kinematical compatibilities relations become {fy(1)|46-1} and, for a quasistatic situation, the equation of balance of internal energy u, mechanical equilibrium equation, and Clausius-Duhem inequality at the interface S can be written in the following form [1] {fy(2)|46-2} {fy(3)|46-3}