Elastic Strain Energy Change During Matrix Cracking in Unidirectional, Fiber-reinforced Ceramic Composites

Abstract

The fracture resistance of ceramics can be signi®cantly enhanched by incorporatng strong ®bers aligned with the loading direction [1±6]. The initial damage in unidirectional, ®ber-reinforced ceramic composites is often in the form of a matrix crack (or matrix cracks), which is perpendicular to the loading direction and bridged by intact ®bers. To achieve the optimum toughening effect for ceramic composites, relatively weak interfaces between ®bers and the matrix, which can debond and slide against a frictional force during matrix cracking, are required [1±6]. In the existing analyses for the matrixcracking problem, two cases have been considered: load-induced cracking [7±14] and residual stressinduced cracking [7, 9, 15]. Using the energy-balance condition during crack propagation, the critical stress for steady-state matrix cracking has been derived [7±15]. The energy terms involved are as follows: (1) Ue, the elastic strain energy in the ®ber and the matrix, (2) Us, the energy due to sliding at the debonded interface, (3) Gi, the energy due to interface debonding, (4) Gm, the energy due to matrix cracking, and (5) W, the work done by the external load, if a loading stress is applied. When the matrix crack length, c, advances a distance dc, the corresponding energy changes are dUe, dUs, dGi, dGm, and dW. The matrix-cracking criterion can be obtained from the energy balance condition, such that dUe ‡ dUs ‡ dGi ‡ dGm ˆ dW