A phase field model for martensitic transformation coupled with the heat equation

Abstract

In order to consider temperature dependency in a phase field model for martensitic transformations a temperature dependent phase separation potential is introduced. The kinematics and the energetic setup underlying the phase transformation are briefly explained. Parameters are identified using molecular dynamics (MD) simulations. The kinetics of the phase field model are in good agreement with those of the MD simulations. Further, the effect of temperature on the microstructure evolution is studied for varying initial austenite contents.

Phase field model for the martensitic transformation: comparison of the Voigt/Taylor and Khachaturyan approach

“…The parameter A can be related to the temperature T [44]. The proportional constants α grad and β ch can be chosen to represent measures for the interfacial width L and the energy density G, which is attributed to the interface…”

“…In the following, we present the Khachaturyan and the Voigt/Taylor homogenizational approach discussing this issue. For the Khachaturyan approach [7], we closely follow [44,46]. For the interface, we suppose that (14) holds.…”

“…As a result, the free energy is crucial for the evolution of the martensite phases. In [44,46] a temperature-dependent energy functional is discussed. However, the temperature diffusion and the MT live in different time frames; therefore, the transience of the temperature is neglected.…”

Martensitic transformation at a crack under mode I and II loading

“…A simple implementation by additive decomposition is given in equation (6). Notice that this allows to reuse the previously defined scalar function s. Given n = 1, the interpolation in equation (5) simplifies to the scalar phase field case. In our model a linear function s is used.…”

“…The model relies on minimization of the energy E = V ψ dV , which is additively split up ψ = ψ el ( ∼ ε, φ) + ψ ch (φ) + ψ grad (∇φ) into the elastic energy potential ψ el , the chemical energy ψ ch , and a gradient term ψ grad . The choice of the chemical energy [5,7] is motivated by molecular dynamic simulations [3,6]. A small strain setting is assumed, where the total strain is the sum of the elastic and the transformation induced strain: ∼ ε = ∼ ε el + ∼ ε tr (φ).…”