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

Deformation of an adaptive heterophase crystal with variable microstructure is considered. Under mechanical constraint the phase transformation in sin gle 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 plant-parallel layers, or domains, of the parent and product phases with a special crystallographic orientation of interfaces be tween domains. The relative fractions of the domains are determined by the external conditions. The free energy of a polydomain is a non-convex functi on of constrained strain. Therefore, the stress-strain relation at displace ment controlled deformation of the polydomain is characterized by a negativ e Young's modulus. If deformation proceeds under stress control, a hysteret ic stress-strain curve on loading and unloading should be observed instead of a negative stress-strain slope. Besides this thermodynamic hysteresis, a nelastic hysteresis appears at a constant strain-rate deformation, if the m icrostructure relaxes more slowly than the strain changes. (C) 1999 Elsevie r Science Ltd. All rights reserved.