Toughening under non-uniform ferro-elastic domain switching

Abstract

The existing models of switch-toughening seldom consider the effect of non-uniform ferro-elastic domain switching in the vicinity of a crack. To explore this issue, an evolution law for the volume fraction of the switched portion under applied electromechanical loading is established from the minimum energy principle. Based on this law, a switching model capable of dealing with the non-uniform distribution of switching strain is developed. The domain switching zone is divided into a saturated inner core and an active surrounding annulus. Mono-domain solution of ferro-elastic toughening is obtained under the model of small scale domain switching. Toughening for ferroelectrics with different poling states is estimated via Reuss type approximation. Two sets of solutions are obtained according to spherical and cylindrical inclusions. The interval of toughening defined by these two models covers the range of experimental data. The same conclusion is reached for the size of the switching zone.

Fracture Mechanics of Piezoelectric and Ferroelectric Solids

“…The domain switching strain of the domain switching tail region would cause additive volume force i T existing on a small thin layer of the boundary of the domain switching zone model (Reece and Guiu, 2001;Reece and Guiu, 2002;Cui and Yang, 2006): The domain switching strain of the domain switching tail region would cause additive volume force i T existing on a small thin layer of the boundary of the domain switching zone model (Reece and Guiu, 2001;Reece and Guiu, 2002;Cui and Yang, 2006):…”

“…The stress intensity factor shielded by domain switching can be obtained by weight function calculation Cui and Yang, 2006):…”

A COD fracture model of ferroelectric ceramics with applications in electric field induced fatigue crack growth

“…Note that at any region only certain proportion of the domains switches in the experiments, therefore, the toughness variation related to domain switching is usually modified by multiplying a factor V 90 , which denotes the volume fraction of switched domains (Glazounov et al 2001;Jiang et al 2007Jiang et al , 2009Cui and Yang 2006). According to the experimental result of Jiang et al (2007), the observed proportion of the switched domains is about V ds ≈ 20%, which is adopted in the subsequent calculation.…”

Temperature-dependent R-curve behavior of Pb(Zr1−xTix)O3

“…According to various models [26,[44][45][46] the shielding toughness of ferroelastic materials is defined by the coercive stress, achievable strain from domain switching, and elastic modulus of the unpoled material. The magnitude of the crack closure stress is influenced by the size and shape of the process zone, the level of strain mismatch between the process zone and the surrounding material, and the material stiffness.…”

“…There have been several numerical models proposed to predict the shielding toughness due to ferroelastic domain switching [26,[44][45][46][47]. In these works ferroelasticity was assumed to be a constant volume phase transformation resulting in remanent strain perpendicular to the crack face.…”