Abstract
Abstract We consider a model in the context of martensitic materials in which hierarchical twinning near the habit plane (austenite-martensite interface) is a new and crucial ingredient. The model includes (1) a triple-well potential in local deviatoric (rectangular) strain, (2) strain gradient terms up to second order in strain and fourth order in gradient, and (3) all symmetry allowed compositional fluctuation-induced strain gradient terms. The last term favors branching of domain walls which enables communication between macroscopic and microscopic regions essential for shape memory. Below the transition temperature (T0) we obtain the conditions under which branching of twins is energetically favorable. Above T0 a hierarchy of branched domain walls also stabilizes tweed formation (criss-cross patterns of twins). External stress or pressure modulates (“patterns”) the spacing of domain walls. Results based on 2D time-dependent Ginzburg-Landau simulations are shown for twins, tweed and hierarchy formation.
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