Stochastic modeling of fracture processes in fiber reinforced composites

Abstract

The longitudinal strength of unidirectional continuous and short fiber reinforced composites is predicted by the stochastic modeling of the fracture process. The model captures the kinetics of damage evolution starting from the nucleation site to the final failure. The damage evolution is modeled by a multidimensional Markovian pure birth process. Fiber breaking, matrix cracking, and fiber/matrix interface debonding are included as interacting micromechanisms for fracture development. The probability of having a nucleation site at a particular state is calculated by the forward Kolmogorov differential equations. The transition rates of failure modes are obtained by utilizing the micromechanics based models of stress distribution. The final failure of the composite is considered to be precipitated in one of the two ways. It may be a result of a single nucleation site developing into an unstable macrocrack or may result from coalescence of arrested or stably growing damage states. The effect of the interfacial shear strength and short fiber length are studied. The analytical results show satisfactory agreement with the experimental results. Analytical predictions suggest an optimum value of the interfacial shear strength for obtaining the maximum longitudinal composite strength.