Thermal stress and intensity release in ferroelectric materials by multiple cracking

Release of transient thermal stress and intensity by periodic cracking in ferroelectric materials is studied. The problem is idealized to a plate containing a row of periodic surface cracks or internal cracks. The stress and electric displacement histories in an un-cracked plate are first calculated. These stresses and the electric displacements, with opposite signs, are used as the crack surface traction and electric displacement load to formulate the mixed boundary-value problem. Then an electromechanical model is developed for the solution of the mixed boundary-value problem. Both electrically impermeable cracks and electrically contacted cracks are considered. Results for the crack tip field intensity factors as well as the stress and electric displacement are computed as functions of the normalized time, the crack size, and crack spacing. Crack initiation and growth behavior are discussed. Lower bound solutions are obtained for the maximum thermal shock that the material can sustain without failure according to the stress-based criterion and the fracture mechanics-based criterion. (In this paper, a thermal shock condition is defined as a rapid temperature change in a medium. It is not necessary for the temperature to be very high.)