Stochastic micromechanical damage modeling of progressive fiber breakage for longitudinal fiber-reinforced composites

A computational stochastic micromechanics-based framework is proposed to investigate the overall mechanical behavior of longitudinal continuous fiber-reinforced composites considering progressive fiber breaking evolution. An effective eigenstrain is newly introduced to quantify the effect of multiple breaks in a single fiber based on linear elastic fracture mechanics and the ensemble-volume averaging technique. In particular, the cumulative nature of fiber breaking evolution is characterized by a two-parameter Weibull distribution function. Taking advantage of the newly proposed eigenstrain, a damage evolution model is developed to simulate the material behavior of multiple fiber-reinforced composite materials. Further, two stochastic risk-competing models are proposed to simulate the fiber breaking evolution in an inhomogeneous fashion considering the local load sharing mechanisms. The first riskcompeting model states that the neighboring fiber of the damaged fiber with dominant weakness fractures with some probability, while the second model assumes that all surrounding fibers associated with the damaged ones have an equal chance to fracture with certain probability. Finally, the overall stress-strain responses and the fiber breaking evolution are satisfactorily predicted, and validations are performed and compared with available experimental data.