A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Abstract

Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90° and 180° is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress σ ∞ and electric field E ∞ or ( σ ∞, E ∞) is replaced by strain ϵ ∞ and electric displacement D ∞ or ( ϵ ∞, D ∞). Mixed conditions ( σ ∞, D ∞) and ( ϵ ∞, E ∞) are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with ( E y ∞, σ y ∞) for negative E y ∞ and ( D y ∞, ϵ y ∞) for positive D y ∞ while the mechanical conditions σ y ∞ or ϵ y ∞ are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth.