Phase-field modeling of martensitic microstructure with inhomogeneous elasticity

Chen, H. Z.; Shu, Y. C.

doi:10.1063/1.4796098

Cited by 11 publications

(6 citation statements)

References 62 publications

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“…Anisotropy, the habit is a constant plane, which is consistent with the classic WLR and BM theory . In the last few decades, the phase field method has shown tremendous capabilities of predicting Martensitic phase transformation . When the martensite transformation model is solved based on the phase field method, the values of various parameters will directly affect the final calculation results.…”

Section: Introductionsupporting

confidence: 72%

Influence of Material Parameters on Martensitic Transformation and Its Sensitivity Analysis

Gao

et al. 2019

steel research int.

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Accurate acquisition of the microscopic representation of the martensite transformation process is the key to obtaining the best performance of the material, it is of great significance in the field of quenching of iron-based materials and material design. The martensite transformation process is affected by a variety of material parameters, quantitative analysis of the influence degree, and sensitivity of various parameters on martensite transformation is the key to accurately grasp the transformation mechanism of martensite. This paper combines the phase-field with the finite element method, a mathematical model for the transformation of martensite from metastable to steady state is established and the model is solved. Accurately reveal the law of energy field variation during martensite transformation and obtain the influence of energy field and interference between martensite and analyze the influence of phase field parameters on martensite. On this basis, the sensitivity and correlation degree of various parameters to the martensite transformation process are evaluated by orthogonal test. This study lays an important theoretical foundation for effectively revealing and mastering the essence of martensite transformation law. It can find effective ways to influence the martensite transformation law, obtain optimal parameters, and improve the mechanical properties of materials.

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Section: Introductionsupporting

confidence: 72%

Influence of Material Parameters on Martensitic Transformation and Its Sensitivity Analysis

Gao

et al. 2019

steel research int.

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“…is the algorithmically consistent phase-inherent effective stiffness tensor (in terms of t), which, by the discussion of Eqs. (23) and (24), is symmetric and positive (semi-)definite.…”

Section: Implementation Of the Phase-inherent Visco-elastic Modelmentioning

confidence: 99%

“…A slightly different procedure is proposed by Khachaturyan [21], who suggests to use the VT scheme for elastic strains, and to treat inelastic strains by the RS scheme. More recently, the Hashin-Shtrikman bounds [22] (HS, which are second-order bounds while VT and RS are first-order bounds) have been applied by Chen and Shu [23] to simulate martensitic phase transformations. Durga et al [24] examined how VT and RS schemes lead to excess stress, strain and elastic energy in diffuse interfaces.…”

Section: Introductionmentioning

confidence: 99%

Phase-inherent linear visco-elasticity model for infinitesimal deformations in the multiphase-field context

Schwab

Reiter

Herrmann

et al. 2020

Adv. Model. and Simul. in Eng. Sci.

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A linear visco-elasticity ansatz for the multiphase-field method is introduced in the form of a Maxwell-Wiechert model. The implementation follows the idea of solving the mechanical jump conditions in the diffuse interface regions, hence the continuous traction condition and Hadamard’s compatibility condition, respectively. This makes strains and stresses available in their phase-inherent form (e.g. $$\varepsilon ^{\alpha }_{ij}$$ ε ij α , $$\varepsilon ^{\beta }_{ij}$$ ε ij β ), which conveniently allows to model material behaviour for each phase separately on the basis of these quantities. In the case of the Maxwell-Wiechert model this means the introduction of phase-inherent viscous strains. After giving details about the implementation, the results of the model presented are compared to a conventional Voigt/Taylor approach for the linear visco-elasticity model and both are evaluated against analytical and sharp-interface solutions in different simulation setups.

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“…There are different methods used for the modeling of the microstructure evolution in technological processes. The models based on cellular automata (CA) (Łach and Svyetlichnyy, 2014; Zhu et al , 2016), Monte Carlo Potts (Rodgers et al , 2017; Tan et al , 2017), the finite element method (Torabian et al , 2016; Umbrello et al , 2016), the phase-field method (Chen and Shu, 2013; Koyama, 2008), the level set method (Hallberg, 2013; Scholtes et al , 2016) and the vertex models (Barrales Mora, 2010; Tamaki et al , 2015) are among them. The application of the CA models for the simulation of the different phenomena in the materials has been significantly increased these days.…”

Section: Introductionmentioning

confidence: 99%

Development of hybrid model for modeling of diffusion phase transformation

Łach

Svyetlichnyy

2020

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Purpose Some functional properties of engineering materials, i.e. physical, mechanical and thermal ones, depend directly on the microstructure, which is a result of processes occurring in the material during the forming and thermomechanical processing. The proper microstructure can be obtained in many cases by the phase transformation. This phenomenon is one of the most important processes during hot forming and heat treatment. The purpose of this paper is to develop a new comprehensive hybrid model for modeling diffusion phase transformations. A problem has been divided into several tasks and is carried out on several stages. The purpose of this stage is a development of the structure of a hybrid model, development of an algorithm used in the diffusion module and one-dimensional heat flow and diffusion modeling. Generally, the processes of phase transformations are studied well enough but there are not many tools for their complex simulations. The problems of phase transformation simulation are related to the proper consideration of diffusion, movement of phase boundaries and kinetics of transformation. The proposed new model at the final stage of development will take into account the varying grain growth rate, different shape of growing grains and will allow for proper modeling of heat flow and carbon diffusion during the transformation in many processes, where heating, annealing and cooling can be considered (e.g. homogenizing and normalizing). Design/methodology/approach One of the most suitable methods for modeling of microstructure evolution during the phase transformation is cellular automata (CA), while lattice Boltzmann method (LBM) suits for modeling of diffusion and heat flow. Then, the proposed new hybrid model is based on CA and LBM methods and uses high performing parallel computations. Findings The first simulation results obtained for one-dimensional modeling confirm the correctness of interaction between LBM and CA in common numerical solution and the possibility of using these methods for modeling of phase transformations. The advantages of the LBM method can be used for the simulation of heat flow and diffusion during the transformation taking into account the results obtained from the simulations. LBM creates completely new possibilities for modeling of phase transformations in combination with CA. Practical implications The studies are focused on diffusion phase transformations in solid state in condition of low cooling rate (e.g. transformation of austenite into ferrite and pearlite) and during the heating and annealing (e.g. transformation of the ferrite-pearlite structure into austenite, the alignment of carbon concentration in austenite and growth of austenite grains) in carbon steels within a wide range of carbon content. The paper presents the comprehensive modeling system, which can operate with the technological processes with phase transformation during heating, annealing or cooling. Originality/value A brief review of the modeling of phase transformations and a description of the structure of a new CA and LBM hybrid model and its modules are presented in the paper. In the first stage of model implementation, the one-dimensional LBM model of diffusion and heat flow was developed. The examples of simulation results for several variants of modeling with different boundary conditions are shown.

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Phase-field modeling of martensitic microstructure with inhomogeneous elasticity

Cited by 11 publications

References 62 publications

Influence of Material Parameters on Martensitic Transformation and Its Sensitivity Analysis

Influence of Material Parameters on Martensitic Transformation and Its Sensitivity Analysis

Phase-inherent linear visco-elasticity model for infinitesimal deformations in the multiphase-field context

Development of hybrid model for modeling of diffusion phase transformation

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