Reliability-analysis on damage of unidirectional composites matrix polymers

This work presents an analytical model to predict the strength of the unidirectional carbon epoxy composite using micromechanical techniques. This model supposes that a group of broken fibres surrounded by a number of intact fibres with hexagonal arrangement. The mathematical developments used are presented to justify the distribution form of the stresses around broken fibre and adjacent intact fibres. To follow the evolution of the damage in regions of debonding and local plasticity; we proceeded to a progressive increase in the fiber volume fraction and tensile external load. This, procedure enable us to evaluate the extension of the region locally plasticized, the ineffective region, the stress concentration and the longitudinal displacement of broken and intact fibres, in function of broken fibres number and specimen length. As fiber breaks are intrinsically random, the variability of input data allows us to describe the probabilistic model by using the Monte-Carlo method. The sensitivities of the mechanical response are evaluated regarding the uncertainties in design variables such as Young’s modulus of fibers and matrix, fiber reference strength, shear yield stress, fiber volume fraction and shear parameter defining the shear stress in the inelastic region