Stress relaxation in broken fibers in unidirectional composites: modeling and application to creep rupture analysis

This paper describes a model of stress relaxation in broken fibers in unidirectional metal matrix composites reinforced with long brittle fibers. A cylindrical cell with a broken fiber embedded in a power law creeping matrix is employed, and the broken fiber is assumed to have a bilinear distribution of axial stress. Then, on the basis of energy balance in the cell under constant overall strain, a relaxation equation of interfacial shear stress acting on stress recovery segments is derived in a simple form. The relaxation equation is approximated rationally and integrated to obtain an analytical solution, which is shown to agree fairly well with the numerical analysis of Du and McMeeking. (Du, Z.-Z., McMeeking, R.M., 1995. Creep models for metal matrix composites with long brittle fibres. J. Mech. Phys. Solids 43, 701–726.) Moreover, the relaxation equation is combined with Curtin's model (Curtin, W.A., 1991. Theory of mechanical properties of ceramic-matrix composites. J. Am. Ceram. Soc. 74, 2837–2845.), so that rupture time in long term creep is evaluated analytically and explicitly on the assumption of global load sharing. It is shown that the resulting relation represents well the dependence of creep rupture time on applied stress observed experimentally on a unidirectional metal matrix composite.