A thermodynamic framework for coupled multiphase Ginzburg-Landau/Cahn-Hilliard systems for simulation of lower bainitic transformation

Düsing, Martin; Mahnken, Rolf

doi:10.1007/s00419-016-1161-5

Cited by 13 publications

(8 citation statements)

References 26 publications

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“…The thermodynamic framework presented in [3] based on a microforce balance as introduced by Gurtin [1] is extended here for deformable continua. Therefore, the balance laws read…”

Section: Governing Equationsmentioning

confidence: 99%

Simulation of upper and lower bainitic transformation with a coupled phase field/diffusion/deformation framework

Düsing

Mahnken

2018

Proc Appl Math and Mech

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In materials science one distinguishes between upper and lower bainite which grow due to different quenching processes. The temperature influences significantly the diffusion of carbon and therefore the resulting microstructure. The growth direction of the corresponding phase depends strongly on the eigenstrains of the transformation. In this work we describe this phase transformation process with different diffusion mechanisms and a coupling of the phase field method with deformations due to eigenstrains. Numerical examples demonstrate the expected behaviour.

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“…The thermodynamic framework presented in [3] based on a microforce balance as introduced by Gurtin [1] is extended here for deformable continua. Therefore, the balance laws read…”

Section: Governing Equationsmentioning

confidence: 99%

Simulation of upper and lower bainitic transformation with a coupled phase field/diffusion/deformation framework

Düsing

Mahnken

2018

Proc Appl Math and Mech

Self Cite

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“…In this work a thermodynamic framework as presented in [2] is used to derive a set of partial differential equations to model the above mentioned phase transformations and the diffusion of carbon. The choice of constitutive equations defines the characteristics of the model.…”

Section: Governing Equationsmentioning

confidence: 99%

“…The constitutive equations cannot be chosen arbitrarily, however, they have to fulfill certain restrictions which are imposed by the second law of thermodynamics. Details can be found in [2].…”

Section: Governing Equationsmentioning

confidence: 99%

“…where q ij are the phase energy coefficients, ρ g is a coupling factor and h ij are the interfacial energy densities which are not presented here for the sake of brevity [2]. The potential energy functions g ij are double well potentials to separate areas of different phases, which read…”

Section: Governing Equationsmentioning

confidence: 99%

“…we end up with evolution equations for the phase-field order parameters φ i and the concentration c. For the sake of brevity we skip the evolution equations of the phase fields (details see [2]) and present the diffusion equation without detailed Helmholtz energy expressionṡ…”

Section: Governing Equationsmentioning

confidence: 99%

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A coupled phase transformation and solute diffusion model for bainitic transformation

Düsing

Mahnken

2017

Proc Appl Math and Mech

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The concept of generalized stresses for computational manufacturing and beyond

et al. 2016

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Computational manufacturing aims at predicting the physical state of a part, structure or respectively its components resulting from a production process. Applicants of computational manufacturing expect reliable and predictive simulation results for various physical effects. Therefore, extended continuum models become increasingly important in modern field theories of materials. To this end, Gurtin and Forest propose the concept of generalized stresses, which shows a strong link between extended continuum mechanics in macroscopic modelling and phase field models in mesoscopic modelling. In this exposition, the concept of generalized stresses is exploited to three different scenarios of computational manufacturing: 1. Micromorphic elasticity considering rotational as well as deformable microstructural effects motivated for a cold box sand in a casting process. 2. Visco‐plasticity coupled to gradient phase transformation at large strains with applications to a cutting process and a hybrid forming process, each showing phase transformations and TRIP‐effects. 3. Multiphase field modelling coupled to Cahn‐Hilliard diffusion to simulate the complex lower bainite transformation in steel as a mesoscopic application of computational manufacturing. Each prototype model is illustrated by a representative finite‐element simulation. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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A thermodynamic framework for coupled multiphase Ginzburg-Landau/Cahn-Hilliard systems for simulation of lower bainitic transformation

Cited by 13 publications

References 26 publications

Simulation of upper and lower bainitic transformation with a coupled phase field/diffusion/deformation framework

Simulation of upper and lower bainitic transformation with a coupled phase field/diffusion/deformation framework

A coupled phase transformation and solute diffusion model for bainitic transformation

The concept of generalized stresses for computational manufacturing and beyond

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