MATRIX CRACKING IN CERAMIC-MATRIX COMPOSITES

Matrix cracking in ceramic-matrix composites with unbonded frictional interface has been studied using fracture mechanics theory. The critic al stress for extension of a fiber-bridged crack has been analyzed usi ng the stress-intensity approach. The analysis uses a new shear-lag fo rmulation of the crack-closure traction applied by the bridging fibers based on the assumption of a constant sliding friction stress over th e sliding length of the fiber-matrix interface. The new formulation sa tisfies two required limiting conditions: (a) when the stress in the b ridging fiber approaches the far-field applied stress, the crack-openi ng displacement approaches a steady-state upper limit that is in agree ment with the previous formulations; and (b) in the limit of zero crac k opening, the stress in the bridging fiber approaches the far-field f iber stress. This lower limit of the bridging stress is distinctly dif ferent from the previous formulations. For all other conditions, the c losure traction is a function of the far-field applied stress in addit ion to the local crack-opening displacement, the interfacial sliding f riction stress, and the material properties. Numerical calculations us ing the stress-intensity approach indicate that the critical stress fo r crack extension decreases with increasing crack length and approache s a constant steady-state value for large cracks. The steady-state mat rix-cracking stress agrees with a steady-state energy balance analysis applied to the continuum model, but it is slightly less than the matr ix-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.