Computer Simulation of Martensitic Transformation in Constrained Films

Seol, Dong Jin; Hu, Songyan; Li, Yong Li; Chen, Lei; Oh, Kyu Hwan

doi:10.4028/www.scientific.net/msf.408-412.1645

Cited by 19 publications

(15 citation statements)

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“…Bollada Garcke et al (1999); Kim et al (2006); Moelans et al (2008Moelans et al ( , 2009; Nestler (2005); Steinbach et al (1996); Steinbach and Pezzolla (1999); Tóth et al (2011aTóth et al ( ,b, 2015 where all the transformation paths lie within the ηi + ηj + η k = 1 plane. (b) Model used in Artemev et al (2000Artemev et al ( , 2001; Jin et al (2001); Levitas (2013a); Levitas and Preston (2002a,b); Li et al (2001); Seol et al (2002Seol et al ( , 2003, for which variant↔variant transformation paths cannot be described with a single order parameter and are not controlled. (c) & (d) Models with polar (c) and hyperspherical (d) order parameters (Levitas et al (2003(Levitas et al ( , 2013).…”

Section: Mpfa-imentioning

confidence: 99%

“…The authors in Refs. Artemev et al (2000Artemev et al ( , 2001; Jin et al (2001); Li et al (2001); Seol et al (2002Seol et al ( , 2003 considered N order parameters η i for a system with N variants, where each η i describes A ↔ M i transformations (η i = 0 in A and η i = 1 in M i ). Additional conditions for such a choice have been imposed in Levitas (2013a); Levitas and Preston (2002a,b) for small and large strains, which in particular include lattice instability conditions, and lead to more complex thermodynamic potentials and expressions for the transformation strains.…”

Section: Mpfa-iimentioning

confidence: 99%

“…Multiphase phase field approach to martensitic PTs. Besides various continuum studies of multivariant martensitic PTs within a sharp interface approach (Ball and James (1987); Levitas and Ozsoy (2009a,b); Petryk and Stupkiewicz (2010a,b); Roytburd (1974); Roytburd and Slutsker (2001)), the phase field approaches (also known as the Ginzburg-Landau approaches) have been widely used for studying microstructure evolution during martensitic PTs (Artemev et al (2000(Artemev et al ( , 2001(Artemev et al ( , 2005; Chen (2002); Clayton and Knap (2011a,b); Hildebrand and Miehe (2012); Idesman et al (2008); Jin et al (2001); Lei et al (2010); Levin et al (2013); Levitas and Javanbakht (2011); Levitas and Lee (2007); Levitas and Preston (2002a,b); Levitas et al (2003Levitas et al ( , 2013; Li et al (2001); Seol et al (2002Seol et al ( , 2003; ; ). The central idea in all the phase field approaches is to introduce the order parameters for describing the PTs in a continuous way.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nanoscale multiphase phase field approach for stress- and temperature-induced martensitic phase transformations with interfacial stresses at finite strains

Basak

Levitas

2018

Journal of the Mechanics and Physics of Solids

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A thermodynamically consistent, novel multiphase phase field approach for stress-and temperature-induced martensitic phase transformations at finite strains and with interfacial stresses has been developed. The model considers a single order parameter to describe the austenite↔martensitic transformations, and another N order parameters describing N variants and constrained to a plane in an N-dimensional order parameter space. In the free energy model coexistence of three or more phases at a single material point (multiphase junction), and deviation of each variant-variant transformation path from a straight line have been penalized. Some shortcomings of the existing models are resolved. Three different kinematic models (KMs) for the transformation deformation gradient tensors are assumed: (i) In KM-I the transformation deformation gradient tensor is a is a linear function of the Bain tensors for the variants. (ii) In KM-II the natural logarithms of the transformation deformation gradient is taken as a linear combination of the natural logarithm of the Bain tensors multiplied with the interpolation functions. (iii) In KM-III it is derived using the twinning equation from the crystallographic theory. The instability criteria for all the phase transformations have been derived for all the kinematic models, and their comparative study is presented. A large strain finite element procedure has been developed and used for studying the evolution of some complex microstructures in nanoscale samples under various loading conditions. Also, the stresses within variant-variant boundaries, the sample size effect, effect of penalizing the triple junctions, and twinned microstructures have been studied. The present approach can be extended for studying grain growth, solidifications, para↔ferro electric transformations, and diffusive phase transformations.

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Section: Mpfa-imentioning

confidence: 99%

Section: Mpfa-iimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nanoscale multiphase phase field approach for stress- and temperature-induced martensitic phase transformations with interfacial stresses at finite strains

Basak

Levitas

2018

Journal of the Mechanics and Physics of Solids

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“…The effect of clamping 13,14 and non-transforming layers 15,16 has been studied theoretically. However, the influence of geometry and size has not been systematically studied.…”

Section: Introductionmentioning

confidence: 99%

Microstructure and mechanical properties of constrained shape-memory alloy nanograins and nanowires

Bouville¹,

Ahluwalia²

2008

Acta Materialia

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We use the phase-field method to study the martensitic transformation at the nanoscale. For nanosystems such as nanowires and nanograins embedded in a stiff matrix, the geometric constraints and boundary conditions have an impact on martensite formation, leading to new microstructuressuch as dots aligned on a square lattice with axes along 01 -or preventing martensite formation altogether. We also perform tension tests on the nanowires. The stress-strain curves are very different from bulk results. Moreover, they are weakly affected by microstructures -the mechanical response of nanowires with different microstructures may be similar, while nanowires with the same microstructure may have a different mechanical behavior. We also observe that at the transition temperature, or slightly below it, the narrowest wires behave pseudoelastically whereas wider wires are in the memory-shape regime. Moreover the yield stress does not change monotonically with width: it has a minimum value at intermediate width.

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“…Elastic solutions are derived for both elastically anisotropic and isotropic thin films subject to the mixed stress-free and constraint boundary conditions. These thin film boundary conditions have been successfully applied to the phase-field simulation of the formation of martensitic domains [14][15][16]. Elastic solutions from thin film boundary conditions are employed in a 3-dimensional phase-field model.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional phase-field modeling of spinodal decomposition in constrained films

Seol

et al. 2003

Met. Mater. Int.

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The morphological evolution during spinodal decomposition in binary alloy thin films elastically constrained by substrates is studied. Elastic solutions, derived for both elastically isotropic and anisotropic thin films subject to mixed stress-free and constraint boundary conditions, are employed in a three-dimensional phasefield model to investigate the effect of coherency strain and substrate constraint on microstructural evolution. The temporal evolution of the Cahn-Hilliard equation under thin film boundary conditions is solved with a semi-implicit Fourier-spectral method. The phase separation with coherency strain in an elastically anisotropic film shows the behavior of surface-directed spinodal decomposition driven by the elastic energy effect. Negative elastic anisotropy in the cubic alloy causes the alignment of the phases along <100> elastically soft directions.

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Computer Simulation of Martensitic Transformation in Constrained Films

Cited by 19 publications

References 0 publications

Nanoscale multiphase phase field approach for stress- and temperature-induced martensitic phase transformations with interfacial stresses at finite strains

Nanoscale multiphase phase field approach for stress- and temperature-induced martensitic phase transformations with interfacial stresses at finite strains

Microstructure and mechanical properties of constrained shape-memory alloy nanograins and nanowires

Three-dimensional phase-field modeling of spinodal decomposition in constrained films

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