MATRIX CRACKING IN CERAMIC-MATRIX COMPOSITES

Matrix cracking in ceramic-matrix composites with unbonded frictional interface has been studied using fracture mechanics theory. The critical stress for extension of a fiber-bridged crack has been analyzed using the stress-intensity approach. The analysis uses a new shear-lag formulation of the crack-closure traction applied by the bridging fibers based on the assumption of a constant sliding friction stress over the sliding length of the fiber-matrix interface. The new formulation satisfies two required limiting conditions: (a) when the stress in the bridging fiber approaches the far-field applied stress, the crack-opening displacement approaches a steady-state upper limit that is in agreement with the previous formulations; and (b) in the limit of zero crack opening, the stress in the bridging fiber approaches the far-field fiber stress. This lower limit of the bridging stress is distinctly different from the previous formulations. For all other conditions, the closure traction is a function of the far-field applied stress in addition to the local crack-opening displacement, the interfacial sliding friction stress, and the material properties. Numerical calculations using the stress-intensity approach indicate that the critical stress for crack extension decreases with increasing crack length and approaches a constant steady-state value for large cracks. The steady-state matrix-cracking stress agrees with a steady-state energy balance analysis applied to the continuum model, but it is slightly less than the matrix-cracking stress predicted by such theories of steady-state cracking as that of Aveston, Cooper, and Kelly. The origin of this difference and a method for reconciliation of the two theoretical approaches are discussed.