A Phenomenological Constitutive Law for Ferroelastic Switching and a Resulting Asymptotic Crack Tip Solution

An isothermal, multiaxial, phenomenological constitutive law for ferroelastic switching in polycrystalline ceramics is developed. The law is valid for unpoled ferroelectric ceramics loaded by mechanical stress but no electric fields or other materials in which permanent deformation accumulates by a similar volume conserving twinning mechanism. The initial switching behavior of the material is described using perfectly plastic J2 flow theory. Unlike metal plasticity in which dislocations are generated by sources, deformation as a result of twinning is limited by a finite transformation strain. Hence, special yield surfaces and associated flow rules are introduced to account for plastic deformation in the two possible "lock-up" states of the material. To demonstrate the constitutive law we have analyzed the stress and displacement fields occurring in the lock-up regime asymptotically close to a crack tip under mode I loading.