Role of elastic compatibility in martensitic texture evolution

Abstract

We employ the time-dependent Ginzburg-Landau (TDGL) method to analyze the time evolution of strain fields in a model for materials with martensitic phase transformations. The free energy functional is expressed in terms of the components of the strain tensor, and its functional derivatives with respect to these components give their rate of change. However, the components of the strain tensor are not independent fields; rather, they are related by the Saint-Venant compatibility condition. This condition imposes constraints on the variations of the strain tensor components needed to obtain the equations of motion. Incorporating these constraints in the TDGL procedure introduces extra terms that effectively act as long-range, anisotropic elastic interactions. The latter govern the types of elastic textures that may emerge during a martensitic transformation. The results from the numerical solution of these evolution equations exhibit fine and coarse tweed, twinning, and tip-splitting.

Key Words:

• Compatibility
• Ginzburg-Landau
• Martensite
• Textures
• Tweed
• Twins