Multiple twinning and variant-variant transformations in martensite: Phase-field approach

Abstract

A phase-field theory of transformations between martensitic variants and multiple twinning within martensitic variants is developed for large strains and lattice rotations. It resolves numerous existing problems. The model, which involves just one order parameter for the description of each variant-variant transformation and multiple twinnings within each martensitic variant, allows one to prescribe the twin interface energy and width, and to introduce interface stresses consistent with the sharp interface limit. A finite-element approach is developed and applied to the solution of a number of examples of twinning and combined austenitemartensite and martensite-martensite phase transformations (PTs) and nanostructure evolution. A similar approach can be developed for reconstructive, electric, and magnetic PTs. A phase-field theory of transformations between martensitic variants and multiple twinning within martensitic variants is developed for large strains and lattice rotations. It resolves numerous existing problems. The model, which involves just one order parameter for the description of each variant-variant transformation and multiple twinnings within each martensitic variant, allows one to prescribe the twin interface energy and width, and to introduce interface stresses consistent with the sharp interface limit. A finite-element approach is developed and applied to the solution of a number of examples of twinning and combined austenite-martensite and martensitemartensite phase transformations (PTs) and nanostructure evolution. A similar approach can be developed for reconstructive, electric, and magnetic PTs.

Thermodynamically consistent phase field theory of phase transformations with anisotropic interface energies and stresses

“…The developed PFA is applicable to melting or solidification [9-14, 30, 43], sublimation, amorphization, and can be generalized for solid-solid PTs [1-6, 8, 32, 61], twinning [15,16], grain growth [17], fracture [54,62], and interaction of cracks and dislocations with PTs [63][64][65][66][67][68][69][70][71][72], for which the interface energy depends on interface orientation of crystals from both its sides. It also has to be generalized for fully large strain formulation [35] and multivariant martensitic transformations and multiphase materials [73].…”

“…The phase field approach (PFA) is routinely utilized for the simulation of various firstorder phase transformations (PTs), including martensitic PTs [1][2][3][4][5][6][7][8], melting [9][10][11][12][13][14], twinning [15,16], and grain growth [17]. In PFA, the energy density of the system depends on the so-called order parameters η i , i = 1, 2, ..., n, and their gradients, in addition to the strain tensor and temperature.…”

Multiphase phase field theory for temperature- and stress-induced phase transformations

“…For three phases, when constraint is explicitly eliminated, the theory in [3,14,13] is completely consistent with the two-phase theory and produces proper PT criteria. However, due to the constraint, for more than three phases, these theories cannot produce correct PT criteria.…”

“…Due to some problems found in [14], the nonlinear constraint for the hyperspherical order parameters was substituted with the linear constraint of the type η i = 1, which, however, does not include A or melt [14,13]. For three phases, when constraint is explicitly eliminated, the theory in [3,14,13] is completely consistent with the two-phase theory and produces proper PT criteria.…”

A coupled kinetic Monte Carlo–finite element mesoscale model for thermoelastic martensitic phase transformations in shape memory alloys

“…The limited length (e.g., 10-30 nanometers) and time (e.g., nanoseconds) scales accessed by such MD studies are not directly comparable to those (e.g., hundreds of nanometers [49] to micrometers in size and milliseconds [17] to minutes in time) involved in existing experimental measurements of SMAs. There are also some finite element [50][51][52][53][54][55] and phase field [56][57][58][59][60] models for SMAs, which can incorporate much larger scales in the constitutive laws describing material energy during transformation. However, continuum models sometimes cannot predict reverse transformation, and more generally tend to lack connections between simulated scales and those intrinsic to martensitic transformation in SMAs, which are essential for understanding defect-transformation interactions.…”