Pattern formation during cubic to orthorhombic martensitic transformations in shape memory alloys

Gao, Yipeng; Zhou, Ning; Wang, Dongqi; Wang, Y.

doi:10.1016/j.actamat.2014.01.012

Cited by 44 publications

(27 citation statements)

References 50 publications

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“…However, as discussed by Gao et al, 41) there is one-to-one correspondence between the OR and invariant plane orientation. Hence, the OR can be determined if the invariant plane normal is predicted by the phase-field simulation based on the microelasticity theory.…”

Section: Slip Distribution In the α′ Phasementioning

confidence: 94%

Phase-field Simulation of Habit Plane Formation during Martensitic Transformation in Low-carbon Steels

Tsukada

Kojima²,

Koyama

et al. 2015

ISIJ International

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The origin of the habit plane of the martensite phase (α ′) in low-carbon steels is elucidated by threedimensional phase-field simulations. The cubic → tetragonal martensitic transformation and the evolution of dislocations with Burgers vector a α ′ /2〈111〉 α ′ in the evolving α ′ phase are modeled simultaneously. By assuming a static defect in the undercooled parent phase (γ ), we simulate the heterogeneous nucleation in the martensitic transformation. The transformation progresses with the formation of the stress-accommodating cluster composed of the three tetragonal domains of the α ′ phase. With the growth of the α ′ phase, the habit plane of the martensitic cluster emerges near the (111) γ plane, whereas it is not observed in the simulation in which the slip in the α ′ phase is not considered. We observed that the formation of the (111) γ habit plane, which is characteristic of the lath martensite that contains a high dislocation density, is attributable to the slip in the α ′ phase during the martensitic transformation.

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Section: Slip Distribution In the α′ Phasementioning

confidence: 94%

Phase-field Simulation of Habit Plane Formation during Martensitic Transformation in Low-carbon Steels

Tsukada

Kojima²,

Koyama

et al. 2015

ISIJ International

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“…Phase field (PhF) simulation of different types of first-order solid-solid phase transformations is a widely used and validated simulation methodology [31][32][33][34][35][36][37][38][39][40][41][42]. PhF is employed here using the Ginzburg-Landau (GL) type polynomial energy function.…”

Section: Phase Field (Phf) Simulation Methodsmentioning

confidence: 99%

Linking simulations and experiments for the multiscale tracking of thermally induced martensitic phase transformation in NiTi SMA

Gur

Frantziskonis

2016

Modelling Simul. Mater. Sci. Eng.

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Martensitic phase transformation in NiTi shape memory alloys (SMA) occurs over a hierarchy of spatial scales, as evidenced from observed multiscale patterns of the martensitic phase fraction, which depend on the material microstructure and on the size of the SMA specimen. This paper presents a methodology for the multiscale tracking of the thermally induced martensitic phase transformation process in NiTi SMA. Fine scale stochastic phase field simulations are coupled to macroscale experimental measurements through the compound wavelet matrix method (CWM). A novel process for obtaining CWM fine scale wavelet coefficients is used that enhances the effectiveness of the method in transferring uncertainties from fine to coarse scales, and also ensures the preservation of spatial correlations in the phase fraction pattern. Size effects, well-documented in the literature, play an important role in designing the multiscale tracking methodology. Molecular dynamics (MD) simulations are employed to verify the phase field simulations in terms of different statistical measures and to demonstrate size effects at the nanometer scale. The effects of thermally induced martensite phase fraction uncertainties on the constitutive response of NiTi SMA is demonstrated.

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“…The elastic strain energy associated with the shear transformation strain is formulated using the Khachatruyan and Shatalov's microelasticity theory [38]. A stress-free boundary condition is applied in this investigation [32,[39][40], and the elastic strain energy is given by:…”

Section: Microelasticity Theorymentioning

confidence: 99%

Multiscale modelling of the morphology and spatial distribution of θ′ precipitates in Al-Cu alloys

2017

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A multiscale approach based on the phase-field model is developed to simulate homogeneous and heterogeneous formation of θ' precipitates during high temperature ageing in Al-Cu alloys. The model parameters that determine the different energy contributions (chemical free energy, interfacial energy, lattice parameters, elastic constants) were obtained from either computational thermodynamics databases or from first-principles density functional theory and molecular statics simulations. From the information, the evolution and equilibrium morphology of the θ' precipitates is simulated in 3D using the phase-field model. The model was able to reproduce the evolution of the different orientation variants of plate-like shaped θ' precipitates with orientation relationship (001)θ'//(001)α and [100]θ'//[100]α during homogeneous nucleation as well as the heterogeneous nucleation on dislocations, leading to the formation of precipitate arrays. Heterogeneous nucleation on pre-existing dislocation(s) was triggered by the interaction energy between the dislocation stress field and the stress-free transformation strain associated to the nucleation of the θ' precipitates. Moreover, the mechanisms controlling the evolution of the morphology and the equilibrium aspect ratio of the precipitates were ascertained. All the predictions of the multiscale model were in good agreement with experimental data. (J. LLorca) 2 IntroductionPrecipitation hardening is well-established as one of the most efficient strategies to increase the yield strength of metallic alloys [1][2][3]. Precipitates are normally intermetallic particles with sizes in the range from a few to a few hundred nm which appear during ageing. They hinder the glide of dislocations that have to by-pass or shear the precipitates, increasing the critical resolved shear stress to move the dislocation in the slip plane. The strengthening effect of the precipitates depends on a number of factors, which include their size, shape [4][5][6][7] and spatial distribution [8][9][10][11]. Precipitation hardened alloys are usually subjected after casting to a homogenization treatment above the solvus temperature followed by quenching, which leads to a supersatured solid solution of the solute atoms. Afterwards, precipitation is promoted by ageing the alloy at intermediate temperatures (sometimes in combination with mechanical deformation) and the final precipitate structure can be controlled up to some extent from the ageing temperature and time [2][3]12]. In general, it is accepted that the highest hardening is provided by uniform distributions of precipitates with large aspect ratio but the optimum combination of precipitate size, shape and spatial distribution depends on many factors, including the actual number of slip systems, the critical resolved shear stress of each system, the presence of other deformation mechanisms (such as twinning), etc. Thus, the design of novel precipitation hardened alloys and the optimization of the current ones is based on the ability to determine the precip...

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Pattern formation during cubic to orthorhombic martensitic transformations in shape memory alloys

Cited by 44 publications

References 50 publications

Phase-field Simulation of Habit Plane Formation during Martensitic Transformation in Low-carbon Steels

Phase-field Simulation of Habit Plane Formation during Martensitic Transformation in Low-carbon Steels

Linking simulations and experiments for the multiscale tracking of thermally induced martensitic phase transformation in NiTi SMA

Multiscale modelling of the morphology and spatial distribution of θ′ precipitates in Al-Cu alloys

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