Tensile Strength of Unidirectionally Reinforced Composites — I

Abstract

Between 1964 and 1980 most micromechanical analyses of composite strength have been based on the chain-of-bundles model. The present in vestigation abandons this model and concentrates instead on the formation and growth of multiple fiber fractures (cracks). This permits treating interac tion of cracks in different bundles and assignment of different ineffective lengths to fiber breaks of different multiplicity. Weakest link theory is used to determine the number of isolated fiber frac tures (singlets), double fractures (doublets), and multiplets of arbitrary order as a function of stress. It turns out that if the fracture of individual fibers obeys Weibull's equation, a plot of nQ i vs lnσ is a straight line of slome im. Here o is applied stress, Q i is the number if i-plets formed during loading to stress σ, and m is the Weibull modulus. The envelope of the Q i curves serves as a failure line. Use of the failure line leads directly to a rational failure criterion based on a Griffith-type instability and shows directly the inverse relationship between crack size and failure stress.