Rate-independent dissipation in phase-field modelling of displacive transformations

Tůma, Karel; Stupkiewicz, S.; Petryk, H.

doi:10.1016/j.jmps.2018.02.007

Cited by 17 publications

(9 citation statements)

References 63 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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“…Within this work, a small deformation framework is applied, so that there is no difference between the current, deformed configuration of

\mathcal {B}

, and its reference state. The evolution of both degrees of freedom is then obtained through thermodynamically consistent phase‐field modeling based on a micro‐force balance, as outlined in [2–4]. The resulting system of coupled partial differential equations

\begin{align} \bm{\nabla }\cdot \bm{\sigma } &= \bm{0} \ , \end{align}

\begin{align} M\;\!\dot{\eta } &= \mathcal {F}(\delta _{\eta }\widetilde{g}) \ , \end{align}

is subject to

\delta _{\eta }\widetilde{g}\!\cdot \!\mathcal {F}(\delta _{\eta }\widetilde{g}) \ge 0

in order to fulfill the dissipation inequality.…”

Section: Phase‐field Modeling Of Shape Memory Alloysmentioning

confidence: 99%

“…Although this formulation is physically justified and valid for many material systems, it could be inadequate for displacive phase transformations due to their essential rate‐independent feature as observed experimentally. In this context, a thermomechanically coupled—and variationally consistent—Allen–Cahn type phase‐field approach incorporating both rate‐dependent and ‐independent dissipation potentials, as introduced in [2], is proposed in this work. Incorporating a rate‐independent dissipation formulation provides a more realistic representation of the thermoelastic hysteresis behavior of SMAs and overcomes the limitations of typical phase‐field formulations.…”

Section: Introductionmentioning

confidence: 99%

Phase‐field modeling of stress‐ and temperature‐induced hysteresis behavior of shape memory alloys incorporating rate‐independent dissipation

El Khatib,

von Oertzen,

Patil

et al. 2023

Proc Appl Math and Mech

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Shape memory alloys (SMAs) are a unique class of multifunctional materials, which exhibit distinctive thermomechanical properties. They are primarily characterized by their ability to recover their original shape under stress and temperature‐controlled loading scenarios. This exceptional property is attributed to the phase transformation that occurs within these alloys, wherein SMAs undergo reversible transition between austenite and multi‐variant martensite phases. The phase transformation in SMAs during a complete load cycle results in a hysteresis, which represent the dissipated energy in the transformation cycle. More specifically, SMAs exhibit a rate‐independent response to a sufficiently slow loading, so that their cyclic response is characterized by a hysteresis loop that maintains a finite width even when the external loading rate approaches zero. Understanding and accurately predicting the rate‐independent hysteresis behavior of SMAs is therefore crucial for their efficient utilization in various engineering applications. In this regard, the phase‐field method has emerged as an appropriate modeling framework resolving the evolution of complex interface topologies as observed in phase‐transforming solids. However, the majority of already existing models typically rely on rate‐dependent formulations and thus remain incapable of reproducing thermoelastic hysteresis behavior at quasi‐static loading scenarios. To overcome this issue, a thermomechanically coupled—and variationally consistent—Allen–Cahn based phase‐field approach incorporating both rate‐dependent and ‐independent driving force formulations is introduced in this work. In order to demonstrate potential applications of the proposed model, two‐dimensional finite‐element simulations were performed to resolve the microstructure formation of twinned martensite in ZrO2. In addition, rate‐dependent and ‐independent stress‐ and temperature‐induced hysteresis curves are predicted qualitatively within the given approach, thus proving its adaptability. Furthermore, the influence of model specific parameters on resulting austenitic and martensitic start and finish temperatures is discussed for cyclic undercooling simulations. The proposed model is thus shown to serve as a valuable tool for the design and optimization of SMA‐based devices.

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“…In this approach, the complete evolution problem is formulated in a rate form as an (unconstrained) minimization problem, which is then consistently transformed into an incremental (time-discrete) problem, again in the form of a minimization problem. Consideration of the physical inequality constraints on the order parameters leads to a constrained minimization problem [19], see also [51] for the case with a mixed viscous and rate-independent dissipation. Here, we skip the formulation of the rate evolution problem and directly introduce the problem in an incremental setting.…”

Section: Incremental Energy Minimization Frameworkmentioning

confidence: 99%

“…Additional simulations are carried out for different values of , namely = 0.75, 2 and 4 nm, and the results are compared to those of our reference study (for = 1 nm). To keep a consistent rate of interface propagation as increases (decreases), the mobility parameter m must decrease (increase) by the respective factor, see the related discussion in [51]. Therefore, m = 1.33, 0.5 and 0.25 (MPa s) −1 are adopted, respectively, for computations with = 0.75, 2 and 4 nm.…”

Section: Parametric Studymentioning

confidence: 99%

Phase-field modeling of multivariant martensitic transformation at finite-strain: computational aspects and large-scale finite-element simulations

Tůma,

Rezaee-Hajidehi,

Hron

et al. 2020

Preprint

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Large-scale 3D martensitic microstructure evolution problems are studied using a finite-element discretization of a finite-strain phase-field model. The model admits an arbitrary crystallography of transformation and arbitrary elastic anisotropy of the phases, and incorporates Hencky-type elasticity, a penalty-regularized double-obstacle potential, and viscous dissipation. The finite-element discretization of the model is performed in Firedrake and relies on the PETSc solver library. The large systems of linear equations arising are efficiently solved using GMRES and a geometric multigrid preconditioner with a carefully chosen relaxation. The modeling capabilities are illustrated through a 3D simulation of the microstructure evolution in a pseudoelastic CuAlNi single crystal during nano-indentation, with all six orthorhombic martensite variants taken into account. Robustness and a good parallel scaling performance have been demonstrated, with the problem size reaching 150 million degrees of freedom.

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Rate-independent dissipation in phase-field modelling of displacive transformations

Cited by 17 publications

References 63 publications

Influence of Material Parameters on Martensitic Transformation and Its Sensitivity Analysis

Influence of Material Parameters on Martensitic Transformation and Its Sensitivity Analysis

Phase‐field modeling of stress‐ and temperature‐induced hysteresis behavior of shape memory alloys incorporating rate‐independent dissipation

Phase-field modeling of multivariant martensitic transformation at finite-strain: computational aspects and large-scale finite-element simulations

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