A phase field approach with a reaction pathways-based potential to model reconstructive martensitic transformations with a large number of variants

•We propose a modeling of martensitic phase transformations based onpathway tree.•The pathway tree is obtained by duplication of elementary pathways.•Successive transformations and subsequent numerous variants are easily defined.•This method is applied to 2D square-to-hexagonal transformation with 123 variants.•Simple traction shows that up to five successive transformations are generated.

A pathway tree is constructed by recursively duplicating a single reconstructive martensitic transformation path with respect to lattice symmetries and point-group rotations. An energy potential built on this pathway is implemented in a phase-field technique in large strain framework, with the transformational strain as the order parameter. A specific splitting between non-dissipative elastic behavior and the dissipative evolution of the order parameter allows for the modeling of acoustic waves during rapid transformations. A simple toy-model transition from hexa- to square-lattice successfully demonstrates the possibility to model reconstructive martensitic transformations for a large number of variants (more than one hundred). Pure traction applied to our toy-model shows that variants can nucleate into previously created variants, with a hierarchical nucleation of variants spanning over five levels of transformation.

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