Multiple Flaw Fracture Mechanics Model for Ceramics

Abstract

A multiple flaw fracture mechanics model applicable to ceramic materials is formulated which includes the interaction between a distribution of flaws located on a critical fracture plane. The opening mode stress intensity factor K of this system of flaws, modeled as an array of circular cracks, is determined in terms of the area fraction, the remote uniaxial stress field and the flaw characteristic size. The resulting mixed boundary value problem is formulated in terms of the Papkovich-Neuber functions represented by appropriate series expansions which satisfy the Laplace equations. By imposing the boundary conditions, the problem is reduced to a set of dual series equations which can be rewritten as a Fredholm integral equation of the second kind. This integral equation is then simply solved using known numerical techniques. Finally, the stress intensity factor K is obtained as the strength of the singularity of the near tip stress field by a limiting process. When this solution, expressed in terms of the local defect area fraction, is compared to the known plane strain solution for the stress intensity factor of collinear cracks, it can be shown that the simpler 2 dimensional plane strain solution is valid over a range of defect area fractions of interest in ceramics. Accordingly, a simpler engineering solution based on Koiter’s solution modified by an appropriate constant is proposed for estimating the strength of ceramics.