Probabilistic crack growth model for application to composite solid propellants

Abstract

In this study a crack growth model, based on probabilistic mechanics, is developed. The developed crack growth model yields a power law relationship between the crack growth rate and the mode I stress intensity fac- tor. The sensitivity of the crack growth rate to the variation of the parameters in the crack growth model is inves- tigated and the results are discussed. The limitations and the applicability of using the developed crack growth model to predict crack growth behavior are also discussed. N past years, a considerable amount of work has been done in studying crack growth behavior in solid propellants15 based on linear viscoelastic and elastic fracture mechanics theories. The basic approach used in these studies is to relate the crack growth rate to the stress intensity factor. Experimental data indicate that a power law relationship exists between the crack growth rate and the stress intensity factor. This experimental finding supports the theory developed by Knauss 6 and Schapery7 in their studies of crack growth behavior in linear viscoelastic materials. The exist- ence of a good correlation between the crack growth rate and the stress intensity factor implies that the crack growth behavior is controlled by the local stress near the crack tip. Therefore, it is expected that the local microstructure will have a significant effect on the crack growth behavior. It is well known that a highly filled composite solid propellant, on the microscopic scale, can be considered as nonhomogeneous material. Depending on the degree of cross linking of the matrix material, filler particle size and distribution, and the bond strength at the interface of the particle and the matrix, the local stress and strength will vary in a random fashion. Therefore, it is reasonable to expect that the failure location ahead of the crack tip will also vary in a random manner. In other words, failure may not occur at the location where the local stress attains a highest value. In addi- tion, since the failure of the material is closely related to the dam- age state and since the damage process is a time-dependent pro- cess, it is expected that the failure time will also vary randomly. From the probabilistic viewpoint, the failure site and the associated failure time should be considered as random variables. Therefore, to obtain a fundamental understanding of the crack growth behav- ior in solid propellants, it is desirable to develop a crack growth model based on probabilistic mechanics. Various stochastic crack growth models have been proposed in the literature, mainly for metallic materials and super-alloys.8'2