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.

Experimental results indicate three regimes for cracking in a ferroelectric double cantilever beam (DCB) under combined electromechanical loading. In the loading, the maximum amplitude of the applied electric field reaches almost twice the coercive field of ferroelectrics. Thus, the model of small scale domain switching is not applicable any more, which is dictated only by the singular term of the crack tip field. In the DCB test, a large or global scale domain switching takes place instead, which is driven jointly by both the singular and non-singular terms of the crack-tip electric field. Combining a full field solution with an energy based switching criterion, we obtain the switching zone by the large scale model around the tip of a stationary impermeable crack. It is observed that the switching zone by the large scale model is significantly different from that by the small scale model. According to the large scale switching zone, the switch-induced stress intensity factor (SIF) and the transverse stress (T-stress) are evaluated numerically. Via the SIF and T-stress induced by the combined loading and corresponding criteria, we address the crack initiation and crack growth stability simultaneously. The two theoretical predictions roughly coincide with the experimental observations. ferroelectric ceramics, large scale domain switching, electromechanical loading, crack initiation, crack growth stability, stress intensity factor, transverse stress

No abstract

It is widely accepted that the singular term plays a leading role in driving domain switching around the crack tip of ferroelectric ceramics. When an applied electric field approaches or even exceeds the coercive one, however, non-singular terms are no longer negligible and the switching of a large or global scale takes place. To analyze the large scale switching, one has to get a full asymptotic solution to the electric field in the vicinity of the crack tip. Take a double cantilever beam specimen as an example. The derivation of the full electric field is simplified as a mixed boundary value problem of an infinite strip containing a semi-infinite impermeable crack. The boundary value problem is solved by an analytic function and a conformal mapping to yield a full electric field solution in a closed form. Based on the full field solution, the large scale domain switching is examined. The switching zones predicted by the large and small scale switching models are illustrated and compared with each other near the tip of a stationary crack. ferroelectric ceramics, domain switching, electric field, analytic function, impermeable crack, strip

No abstract