Time-dependent failure in fiber-reinforced composites by fiber degradation
The failure of fiber-reinforced ceramic and metal matrix composites under a fixed load for extended times occurs because of strength degradation in the constituent fibers. Specifically, the ceramic fibers possess a Weibull strength distribution caused by crack-like flaws, which can grow according to a power-law growth mechanism. Failure of individual fibers causes interfacial slippage and stress redistribution to unfailed fibers, which in turn accelerates the degradation rate of the remaining fibers, and culminates in abrupt Failure of the composite after sufficient damage has accumulated. This sequence of events is modeled both analytically and numerically within the Global Load Sharing (GLS) approximation previously utilized for quasi-static loading. Analytically, a general constitutive model for the relationship between the stress on the damaged fiber bundle, the strain in the unbroken fibers, and the extent of damage, is combined with a time-dependent damage evolution equation derived from the slow-crack-growth kinetics to yield an integral equation for the strain cs time at fixed applied load. The relevant gauge length for a fixed load rupture process is found to be delta = r sigma/tau which is twice the slip length prevailing at the initial applied load sigma, where tau is the interfacial sliding resistance between fiber and matrix. The underlying time scale for rupture is the time scale for a typical fiber of gauge length delta to Fail under the applied load sigma; this time can be quite different From that measured by stress-rupture tests on single fibers at an unrelated laboratory gauge length L(0). A simple, accurate but approximate relationship between applied load, time to failure, fiber Weibull modulus, and slow crack growth exponent is presented. The numerical simulations of the same degradation process verify the general accuracy of the failure time obtained from the analytic results. The remaining tensile strength after some time at load but prior to failure is also studied, and the simulation results generally exhibited a more sudden-death failure than the analytical predictions. A specific application to the failure of a Nicalon fiber composite is presented. (C) 1997 Acta Metallurgica Inc.