Green's function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Green's function for the T-stress is obtained in a straightforward manner. Furthermore, Green's functions are derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method. Then, Green's function is used to predict the domain-switch-induced T-stress in a ferroelectric double cantilever beam (DCB) test. The T-stress induced by the electromechanical loading is used to judge the stable and unstable crack growth behaviors observed in the test. The prediction results generally agree with the experimental data.
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.
