A phase field model for martensitic transformations with a temperature‐dependent separation potential

Schmidt, Simon; Plate, Carolin; Müller, Regina; Müller, Ralf; Meiser, Jerome; Urbassek, Herbert M.

doi:10.1002/pamm.201610229

Cited by 6 publications

(3 citation statements)

References 3 publications

(8 reference statements)

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“…As suggested in [15] and [4] the phase separation potential is considered to be temperature dependent. For the parameter identification and for the sake of simplicity we consider here only one martensitic orientation, without being limited to one orientation variant.…”

Section: Configurational Forcesmentioning

confidence: 99%

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

2017

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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.

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Section: Configurational Forcesmentioning

confidence: 99%

“…The parameters for A have been obtained using data from molecular dynamics simulations [16,17,18,15]. The method of least squares is used to fit a 6th grade polynomial to the MD data points for the Landau polynomial.…”

Section: Configurational Forcesmentioning

confidence: 99%

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

2017

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“…Solid-solid phase transformations in iron, iron alloys, and steels are relevant in many branches of technology. Modeling of these phase transformations occurs on the level of atomistic (molecular dynamics) simulation [1,2], ab-initio calculations [3], or phase-field simulations [4,5]. For the case of atomistic simulations based on molecular dynamics or Monte Carlo, the interatomic interaction potentials governing the interaction between Fe atoms and between Fe and the alloying atoms is of fundamental importance.…”

Section: Introductionmentioning

confidence: 99%

Effect of Alloying Elements on the α-γ Phase Transformation in Iron

Meiser

Urbassek

2019

Materials

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Small concentrations of alloying elements can modify the α - γ phase transition temperature T c of Fe. We study this effect using an atomistic model based on a set of many-body interaction potentials for iron and several alloying elements. Free-energy calculations based on perturbation theory allow us to determine the change in T c introduced by the alloying element. The resulting changes are in semi-quantitative agreement with experiment. The effect is traced back to the shape of the pair potential describing the interaction between the Fe and the alloying atom.

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Heat Conduction in a Phase Field Model for Martensitic Transformation

Schmidt

Müller

2017

Proc Appl Math and Mech

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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]:

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A phase field model for martensitic transformations with a temperature‐dependent separation potential

Cited by 6 publications

References 3 publications

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

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

Effect of Alloying Elements on the α-γ Phase Transformation in Iron

Heat Conduction in a Phase Field Model for Martensitic Transformation

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