Cubic to tetragonal martensitic transformation in a thin film elastically constrained by a substrate

Abstract

A 3-dimensional phase-field model is developed to describe the cubic to tetragonal martensitic phase transformation in a thin film attached to a substrate. Elasticity solutions are derived for both elastically anisotropic and isotropic thin films with arbitrary domain structures, subject to the mixed boundary conditions for stressfree and constrained states. The model is applied to an Fe-31%Ni alloy system. The nucleation process as well as the final domain structure strongly depends on the substrate constraint. At a smaller undercooling, the increased strain energy effect results in a lower volume fraction of martensite, a finer domain structure and a longer nucleation period.

Interface propagation and microstructure evolution in phase field models of stress-induced martensitic phase transformations

“…This correspondence between phase transformation and thermoelasticity equations has important computational consequences: finite element thermoelasticity codes can be used, after some minor modifications, for phase-field model simulations of phase transformations. In contrast to approaches based on the spectral (fast Fourier transform) method Curnoe and Jacobs, 2001a,b;Jacobs et al, 2003;Jin et al, 2001;Lookman et al, 2003a,b;Rasmussen et al, 2001;Seol et al, 2003;Wang and Khachaturyan, 1997;Wang et al, 2001), the finite element approach allows us to easily expand the treatment to heterogeneous materials, large strains, arbitrary boundary conditions, and complex material models. Because the potential (42), (43) accurately describes the important features of martensitic phase transformations, we expect that our calculated microstructure evolution in this study is more realistic than that predicted by other approaches Curnoe and Jacobs, 2001a,b;Jacobs et al, 2003;Jin et al, 2001;Lookman et al, 2003a,b;Rasmussen et al, 2001;Seol et al, 2003;Shenoy et al, 1999;Wang and Khachaturyan, 1997;Wang et al, 2001).…”

“…Despite significant success in modeling microstructure formation in Artemev et al (2001), Curnoe andJacobs (2001a,b), Jacobs et al (2003), Jin et al (2001), Levitas and Preston (2002a,b), Levitas et al (2003), Levitas and Lee (2007), Lookman et al (2003a,b), Rasmussen et al (2001), Seol et al (2003), Shenoy et al (1999), Wang and Khachaturyan (1997), and Wang et al (2001), and here, the phase field approach has a major drawback: it does not include an athermal resistance to interface motion. This resistance is analogous to dry friction in classical mechanics.…”

“…In this paper we will focus on martensitic or diffusionless transformations (Ahluwalia et al, 2003;Artemev et al, 2001;Curnoe and Jacobs, 2001a,b;Jacobs et al, 2003;Jin et al, 2001;Levitas and Preston, 2002a,b;Levitas et al, 2003;Levitas and Lee, 2007;Lookman et al, 2003a,b;Rasmussen et al, 2001;Seol et al, 2003;Shenoy et al, 1999;Wang et al, 2001). Deformation of the crystal lattice of the austenite, A, the high-temperature phase, into the martensite, M, the low temperature phase, can be described by the transformation strain tensor e t (also called the Bain strain or spontaneous strain).…”

“…However, in the phase field approach these internal variables describe material instabilities, such as the instabilities of a crystal lattice responsible for solid-solid phase transformations, twin and dislocation nucleation, melting, fracture and so on. Some theories of martensitic phase transformations employ order parameters related to transformation strains Levitas and Preston, 2002a,b;Levitas et al, 2003;Levitas and Lee, 2007;Seol et al, 2003;Shenoy et al, 1999;Wang and Khachaturyan, 1997;Wang et al, 2001), while the order parameters in other models are the components of the strain tensor responsible for lattice instability (Curnoe and Jacobs, 2001a,b;Jacobs et al, 2003;Lookman et al, 2003a,b;Rasmussen et al, 2001). The thermodynamic (Landau) potential is typically a polynomial in the order parameters with multiple minima (as in Fig.…”

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

“…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.…”