Uniaxial dynamic mechanical responses of ferroelastic materials under temperature cycling via phase field modeling

Abstract

The dynamic mechanical responses of the ferroelastic materials under uniaxial straining and temperature cycling are studied via the Landau‐type phase field model in two dimensions. The model may exhibit a single‐well (double‐well) energy profile when temperature is greater (less) than the critical temperature. Effective negative stiffness in the vicinity of the temperature‐induced solid–solid phase transformation is numerically demonstrated through monotonic uniaxial straining on a single‐domain ferroelastic under temperature cycling around the Curie temperature. Under sinusoidal uniaxial straining, the effective Young's modulus and damping, as indicated by the enclosed area of the stress–strain curve, may be largely increased due to the phase transition. Our calculated responses here are consistent with experimental data reported in the literature, as well as theoretical results based on the composite theory with inclusions assumed to have negative modulus. No negative stiffness values are directly assigned in our phase field model as the underlying physics of the order parameters, i.e., spontaneous strains, provides effective negative stiffness into the systems.