A sharp interface model of compatible twin patterns in shape memory alloys

Abstract

The cubic-orthorhombic shape memory alloy system is studied using a sharp interface model based on the linear theory of compatible laminates. A computational method is developed to generate all possible compatible laminates for a given state of strain, and check whether these laminates satisfy exact compatibility conditions. The type of austenite-martensite interface that can form is dependent upon the detail of the martensite structure; the formation of flat and wedge-like austenite-martensite interfaces is explored. A full search is used to reveal the routes in strain space along which the two-phase structure can continuously evolve. A variety of laminate structures, some well known and some new, are reported. The methods developed are readily applied to other crystal systems, such as the tetragonal crystal system, in shape memory alloys or related materials.

Phase-field modeling of martensitic microstructure with inhomogeneous elasticity

“…This motivates many more research efforts being focus on developing models based on atomic descriptions to continuum frameworks for numerical simulations. [14][15][16][17][18] Among them, phase-field models are particularly popular due to no prior assumptions on the profiles and tracking of interfaces. [19][20][21][22][23] Advances in computer simulations include results from single crystals, 24,25 multilayers, 26,27 and polycrystals.…”

Effective time step analysis for the Allen–Cahn equation with a high‐order polynomial free energy

“…For the numerical solution to diffuse-interface systems, such as the AC equation, a sufficiently large number of grid points is required to discretize the phase interface layer. 17 As one way to properly compute the diffuse-interface even in relatively coarse grids for computational efficiency, the high-order polynomial free energy function was recently applied. 18,19 In particular, the authors in Reference 19 dealt with the use of the hAC equation especially focusing on the advantages of employing the high-order free energy function in applications.…”

“…As such, many scientific problems have been solved through the numerical application of the AC equation. For the numerical solution to diffuse‐interface systems, such as the AC equation, a sufficiently large number of grid points is required to discretize the phase interface layer 17 . As one way to properly compute the diffuse‐interface even in relatively coarse grids for computational efficiency, the high‐order polynomial free energy function was recently applied 18,19 .…”