Finite element simulations of microstructure evolution in stress-induced martensitic transformations

Ozsoy, Istemi B.; Babacan, N.

doi:10.1016/j.ijsolstr.2015.12.009

Cited by 7 publications

(6 citation statements)

References 59 publications

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“…of the transformation stress and stress hysteresis on the crystal orientation is in qualitative agreement with both experimental ( Gall et al, 2001; and numerical ( Ozsoy and Babacan, 2016 ) results.…”

Section: Article In Presssupporting

confidence: 84%

“…(12) and (13) JID: SAS [m5G;March 27, 2018;10:23 ] threshold characterizes the resistance against a moving interface caused by the interactions between the interface and the longrange stress field of various defects (e.g., vacancies, dislocations, subgrain boundaries), by the Peierls barrier, acoustic emission, etc. Almost every micromechanical theory of the phase transformation incorporates such a term ( Lim and McDowell, 2002;Levitas and Ozsoy, 2009a;Boyd and Lagoudas, 1996a;Levitas et al, 1999;Gillet et al, 1998;Ozsoy and Babacan, 2016;Patoor and Berveiller, 1997 ). In contrast, the traditional phase field theories ( Artemev et al,20 01; 20 0 0; Wang and Khachaturyan, 1997;Zhu et al, 2017;Cho et al, 2012;Idesman et al, 2008;Steinbach and Apel, 2006;Mosler et al, 2014;Schneider et al, 2015 ) neglect it, except ( Levitas and Lee, 2007;.…”

Section: Box 1 (Problem Formulation) Kinematicsmentioning

confidence: 99%

“…The width of diffuse interfaces is stabilized and determined by the local strain rate. Due to this dependency the width of diffuse interfaces is sensitive to the macrostrain rate (or displacement rate) and mesh size ( Ozsoy and Babacan, 2016;; Nemat- et al, 2005 ). While theoretically the problem is well posed and strain-rate regularized (similar to the viscoplastic regularization Beissel and Belytschko, 1996 ), when the loading or unload-ing rates approach zero to obtain a stationary solution the ratedependency disappears and the stationary solution associates with a sharp interface between two adjacent phases.…”

Section: Study Of Mesh-sensitivity Of Solutionsmentioning

confidence: 99%

“…This model was developed similarly to the phenomenological models for phase transformation but with strain softening during transformation instead of hardening (similar to elastoplastic models ( Beissel and Belytschko, 1996;Shaw and Kyriakides, 1997a ), which were used as ersatz models for the study of microstructure evolution). A more detailed micromechanical model which exhibits strain softening was developed in Levitas and Ozsoy (2009a,b) and implemented for finite element modeling of microstructure in Ozsoy and Babacan (2016) . Alternatively, to increase the sample size within the Ginzburg-Landau approach, the width of the interface, δ, is increased artificially to ∼ 1 μm while keeping the correct expression for interface energy, E ( Steinbach and Apel, 2006 ).…”

Section: Introductionmentioning

confidence: 99%

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Microscale phase field modeling of the martensitic transformation during cyclic loading of NiTi single crystal

Esfahani

Ghamarian

Levitas

et al. 2018

International Journal of Solids and Structures

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A microscale phase field model developed in Levitas et al. (2004) and Idesman et al. (2005) is slightly advanced for different and anisotropic elastic moduli of phases and is employed for the study of the stressinduced cubic-monoclinic phase transition in NiTi single crystal involving all 12 martensitic variants. The model is scale-independent, without the gradient term, and it is applicable for any scale greater than 100 nm. This model includes strain softening and the corresponding transformation strain localization, and it reproduces a discrete martensitic microstructure. The model only tracks finite-width interfaces between austenite and the mixture of martensitic variants, and does not consider the interfaces between martensitic variants. The model is implemented as a UMAT subroutine in a commercial finite element (FE) package, ABAQUS. Multiple problems for a uniaxial cyclic loading are solved to study the effect of mesh, strain rate, crystal orientation, different numbers of pre-existing nuclei, and the magnitude of the athermal threshold on the stress-strain responses as well as the microstructure evolution. The obtained results exhibit that the microstructure and global stress-strain responses are practically independent of mesh discretization and the applied strain rate for relatively small strain rates. While the presence of the initial nuclei in the sample decreases the nucleation stress, it slightly increases the total energy dissipation. The observed microstructure, the sudden drop in the stress-strain curve after initiation of the martensitic transformation, and the absence of a similar jump for the reverse phase transformation are in qualitative agreement with known experiments. Changing the crystallographic orientation of the sample varies the entire behavior, namely, the variants which are involved in the phase transformation, the morphology of the associated microstructure, the stress-strain curve, and the total dissipation. Athermal threshold, in addition to the expected increase in the magnitude of hysteresis, leads to some strain hardening for the direct phase transformation. a b s t r a c t A microscale phase field model developed in Levitas et al. (2004) and Idesman et al. ( 2005) is slightly advanced for different and anisotropic elastic moduli of phases and is employed for the study of the stressinduced cubic-monoclinic phase transition in NiTi single crystal involving all 12 martensitic variants. The model is scale-independent, without the gradient term, and it is applicable for any scale greater than 100 nm. This model includes strain softening and the corresponding transformation strain localization, and it reproduces a discrete martensitic microstructure. The model only tracks finite-width interfaces between austenite and the mixture of martensitic variants, and does not consider the interfaces between martensitic variants. The model is implemented as a UMAT subroutine in a commercial finite element (FE) package, ABAQUS. Multiple problems for a uniaxial cyclic loading are solved to st...

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Section: Article In Presssupporting

confidence: 84%

Section: Box 1 (Problem Formulation) Kinematicsmentioning

confidence: 99%

Section: Study Of Mesh-sensitivity Of Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Microscale phase field modeling of the martensitic transformation during cyclic loading of NiTi single crystal

Esfahani

Ghamarian

Levitas

et al. 2018

International Journal of Solids and Structures

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“…A phase-field model to simulate the transformation of lower bainite, including carbon diffusion and carbide formation was developed by Düsing and Mahnken (2016), and PF model was also used by Schmidt et al (2017) for martensitic transformation coupled with the heat equation. Ozsoy and Babacan (2016) used FEM for simulations of microstructure evolution in stress-induced martensitic transformations, and simulation of phase transformations during cooling of 55SiMnMo steel were realized based on FEM by Yan et al (2017). An interesting approach for modeling of phase transformations is also the use of neural networks.…”

Section: Introductionmentioning

confidence: 99%

Heat flow model based on lattice Boltzmann method for modeling of heat transfer during phase transformation

Łach

Svyetlichnyy

Straka

2019

HFF

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Purpose A fundamental principle of materials engineering is that the microstructure of a material controls the properties. The phase transformation is an important phenomenon that determines the final microstructure. Recently, many analytical and numerical methods were used for modeling of phase transformation, but some limitations can be seen in relation to the choice of the shape of growing grains, introduction of varying grain growth rate and modeling of diffusion phenomena. There are also only few comprehensive studies that combine the final microstructure with the actual conditions of its formation. Therefore, the objective of the work is a development of a new hybrid model based on lattice Boltzmann method (LBM) and cellular automata (CA) for modeling of the diffusional phase transformations. The model has a modular structure and simulates three basic phenomena: carbon diffusion, heat flow and phase transformation. The purpose of this study is to develop a model of heat flow with consideration of enthalpy of transformation as one of the most important parts of the proposed new hybrid model. This is one of the stages in the development of the complex model, and the obtained results will be used in a combined solution of heat flow and carbon diffusion during the modeling of diffusion phase transformations. Design/methodology/approach Different values of overheating/overcooling affect different values in the enthalpy of transformation and thus the rate of transformation. CA and LBM are used in the hybrid model in part related to heat flow. LBM is used for modeling of heat flow, while CA is used for modeling of the microstructure evolution during the phase transformation. Findings The use of LBM and CA in one numerical solution creates completely new possibilities for modeling of phase transformations. CA and LBM in comparison with commonly used approaches significantly simplify interface and interaction between different parts of the model, which operates in a common domain. The CA can be used practically for all possible processes that consist of nucleation and grains growth. The advantages of the LBM method can be well used for the simulation of heat flow during the transformation, which is confirmed by numerical results. Practical implications The developed heat flow model will be combined with the carbon diffusion model at the next stage of work, and the new complex hybrid model at the final stage will provide new solutions in numerical simulation of phase transformations and will allow comprehensive modeling of the diffusional phase transformations in many processes. Heating, annealing and cooling can be considered. Originality/value The paper presents the developed model of heat flow (temperature module), which is one of the main parts of the new hybrid model devoted to modeling of phase transformation. The model takes into account the enthalpy of transformation, and the connection with the model of microstructure evolution was obtained.

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Modeling of propagation of phase transformation fronts in NiTi under uniaxial tension

Jiang

Kyriakides

Landis

et al. 2017

European Journal of Mechanics - A/Solids

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Tension induced solid-state transformation in a nearly equiatomic NiTi results in inhomogeneous deformation with transformed and untransformed material coexisting. Strains of the order of 7% are recovered on unloading with the material reverting to its original phase. In a thin strip the two coexisting phases and deformation regimes are separated by inclined fronts monitored with digital image correlation. The fronts propagate along the strip until the transformation is completed with the stress remaining nearly unchanged. A recently developed constitutive model for the pseudoelastic behavior of NiTi is implemented in a finite element analysis used to simulate the strip experiment. The model is capable of addressing the tension/compression asymmetry by incorporating both the tensile and compressive responses of the material. Softening moduli are introduced over the extents of the plateaus of the tensile response at approximately the Maxwell stress levels. The numerical solution reproduced the closed hysteresis with the correct stress plateau levels and extents. Localized deformation initiates in a single narrow band of higher strain inclined to the axis of the strip. The high strain zone propagates initially with inclined fronts and subsequently with a crisscross pattern with the stress remaining essentially unchanged. The details of the front propagation are influenced by inplane moment caused by secondary kinking of the strip. The strip unloads by tracing a lower stress plateau developing a similar propagation of localization patterns. Overall, the numerical simulation captures the main features of the response and the associated localization configurations. The sensitivity of the solution to the mesh, the boundary conditions, and the softening moduli are discussed.

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Finite element simulations of microstructure evolution in stress-induced martensitic transformations

Cited by 7 publications

References 59 publications

Microscale phase field modeling of the martensitic transformation during cyclic loading of NiTi single crystal

Microscale phase field modeling of the martensitic transformation during cyclic loading of NiTi single crystal

Heat flow model based on lattice Boltzmann method for modeling of heat transfer during phase transformation

Modeling of propagation of phase transformation fronts in NiTi under uniaxial tension

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