Toughening produced by crack‐tip‐stress‐induced domain reorientation in ferroelectric and/or ferroelastic materials

Abstract

A calculation is carried out of the toughening produced by the crack-tip-stress-induced reorientation of domains in a ferroelectric and/or ferroelastic material. The calculation is based on obtaining the shielding stress intensity factor produced by the shear transformation of a zone surrounding the crack tip and extending over the crack surfaces. It is argued that the effective shear strain γ_e of the transformation is not uniform inside the transformation zone but is a function of the resolved shear stress of the crack tip, τ activating the domain reorientation. It is shown that the relation between γ_e and τ can be obtained experimentally from the compressive stress-strain curve of the material. An accurate calculation of the shielding stress intensity factor produced by such an inhomogeneous transformation zone requires the solution of a difficult problem which is not attempted. However, a simple overestimate is made, showing that the toughening which can be expected from the crack-tip-stress-induced reorientation of domains in a ferroelectric and/or ferroelastic material is less than 10% even in the most favourable conditions. This result is justified on physical grounds and it is argued that the small toughening predicted by the calculations arises because the crack tip stresses needed to drive the transformation increase proportionally with the transformation strain. This case is contrasted with the much greater toughening which is expected from the crack tip-stress-induced phase transformations which are largely driven by the chemical or bulk, free-energy change of the transformation.