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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