Deformation of adaptive materials. Part I. Constrained deformation of polydomain crystals

Abstract

Deformation of an adaptive heterophase crystal with variable microstructure is considered. Under mechanical constraint the phase transformation in single component systems result in an equilibrium two-phase mixture. A typical equilibrium microstructure of a constrained crystal is a polydomain, i.e. an alternation of the plane-parallel layers, or domains, of the parent and product phases with a special crystallographic orientation of interfaces between domains. The relative fractions of the domains are determined by the external conditions. The free energy of a polydomain is a non-convex function of constrained strain. Therefore, the stress–strain relation at displacement controlled deformation of the polydomain is characterized by a negative Young’s modulus. If deformation proceeds under stress control, a hysteretic stress–strain curve on loading and unloading should be observed instead of a negative stress–strain slope. Besides this thermodynamic hysteresis, anelastic hysteresis appears at a constant strain-rate deformation, if the microstructure relaxes more slowly than the strain changes.