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.
Metallic materials often exhibit a complex microstructure with varying material properties in the different phases. Of major importance in mechanical engineering is the evolution of the austenitic and martensitic phases in steel. The martensitic transformation can be induced by heat treatment or by plastic surface deformation at low temperatures. A two dimensional elastic phase field model for martensitic transformations considering several martensitic orientation variants to simulate the phase change at the surface is introduced in [1]. However here, only one martensitic orientation variant is considered for the sake of simplicity. The separation potential is temperature dependent. Therefore, the coefficients of the Landau polynomial are identified by results of molecular dynamics (MD) simulations for pure iron [2]. The resulting separation potential is applied to analyse the mean interface velocity with respect to temperature and load. The interface velocity is computed by use of the dissipative part to the configurational forces balance as suggested in [3]. The model is implemented in the finite element code FEAP using standard 4-node elements with bi-linear shape functions. A phase field model is used to determine the solution of the martensitic transformation (MT). In this model, two allotropes are of interest: the body cubic centered (bcc, ϕ = 1) martensitic, and the face cubic centered (fcc, ϕ = 0) austentic phase. The model relies on minimisation of the total free energy F [1] :
We study the martensitic transformation with a phase field model, where we consider the Bain transformation path in a small strain setting. For the order parameter, interpolating between an austenitic parent phase and martensitic phases, we use a Ginzburg-Landau evolution equation, assuming a constant mobility. In [1], a temperature dependent separation potential is introduced. We use this potential to extend the model in [2], by considering a transient temperature field, where the temperature is introduced as an additional degree of freedom. This leads to a coupling of both the evolution equation of the order parameter and the mechanical field equations (in terms of thermal expansion) with the heat equation. The model is implemented in FEAP as a 4-node element with bi-linear shape functions. Numerical examples are given to illustrate the influence of the temperature on the evolution of the martensitic phase. A phase field model is used to study the martensitic transformation (MT). We couple the phase field with the heat equation. The order parameter φ scales between the austenitic parent phase (fcc, φ = 0) and one martensitic orientation variant (bcc, φ = 1). The total free energy readswhere we introduce the temperature dependency by the phase separation potential ψ sep [1] and the coupling with the mechanics by the elastic energy W in terms of eigenstrain [3]. The gradient energy density ψ grad accounts for the surface energy.Here, G and L are related to the characteristic interface energy density and the length of the transiton zone as shown in [4]. The total strain is additively split up:considering linear elastic small strain, transformational eigenstrain and thermal expansion, respectively. The coefficient of thermal expansion α and the eigenstrain ε 0 bcc are assumed to be constant. This leads to a time dependent Ginzburg-Landau equation, the equilibrium balance and the heat equation as set of field equations:The mobility M , the density ρ, the heat capacity c and the thermal conductivity k are held constant. Therefore, the change of the order parameter in timeφ is proportional to the variational derivative of the total free energy E with respect to the order parameter φ itself. Temperature DependencyTemperature dependency is introduced on the one hand by thermal expansion, on the other hand by a temperature dependent separation potential. As given in (2) the phase separation potential is proportional to a Landau polynomial. Using the conditions that the local and global minima are at φ = 0 and φ = 1, the initially four paramaters of the Landau polynomial f can be reduced to two independent parameters [5]:
Austenitic TRansformation Induced Plasticity (TRIP) steels offer an outstanding combination of formability and strength. Using Electron Backscatter Diffraction (EBSD) technique, the grain orientation and morphology of f.c.c. and b.c.c. phases can be clearly detected in initial state and at definite strains [2]. In order to qualify the driving mechanisms of phase transformations occuring during deformation of metastable austenites, e.g. TRIP steels, a phase field model is used. For the modelling, we follow [6]. The field equations are solved using the finite element method with bi-linear shape functions and 4-node elements. Features of this model are demonstrated by illustrative numerical examples.
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