Twinning-induced stress and electric field concentrations in ferroelectric ceramics

Experimental investigations suggest that microcracking may be the major cause for the commonly encountered degradation of ferroelectric actuators, namely electric fatigue, It is commonly believed that stress concentration is responsible for the onset of cracking although the quantitative relation between these two events has not been understood completely, It is expected that formation of ferroelectric twins, i.e., 90 degrees domains, can cause severe stress concentration at intersections of domain walls with grain boundaries because of the incompatibility of lattice distortions with grain boundary constraints. This article presents an analysis upon the asymptotic behavior of stress and electric fields near these intersections, The asymptotic analysis is carried out within a framework of electrostatics for deformable continua, assuming that the electromechanical state in each of the ferroelectric domains is slightly distorted from one of the natural states of the crystal, the authors developed a piecewise linearized model for which concentrations of stress and electric fields correspond to singularities of these fields, The analysis concludes that both the stress and the electric fields exhibit a power-law singularity; i.e., their magnitudes are proportional to r(lambda), with r being the radial coordinate originating at the intersecting point and lambda being a constant whose value is within the range (-1,0). The examples included show that the severity of concentration depends upon the crystal orientation and the orientations of the domain walls with respect to the grain boundary which they intersect. Considering the microcracks may be generated during the cooling or poling process, the authors have also studied the interaction of ferroelectric twins with preexisting microcracks, both intergranular and transgranular. The analysis indicates that this interaction makes the singularity substantially stronger than the conventional root r-singularity and hence it suggests that this interaction promotes crack growth.