Anisotropic tensile probabilistic failure criterion for composites

Abstract

A probabilistic failure criterion is needed to quantitatively predict reliability in critical applications, such as man-safe, deep-sea and air structures, and as an objective function for use in optimum design. Composites are multi-phased and anisotropic, which gives rise to failure in different modes with different probabilistic occurrences that are dependent on the applied stress tensor. Statistical representation of combines stress failure is practically impossible. Probabilistic modeling must be based on the failure modes. This investigation examines the underlying features required in a probabilistic failure criterion for unidirectional fiber-composite structures via Monte Carlo simulations. The interdependencies of the intrinsic strengths (associated with uniaxial loadings) and of the failure modes in a composite structure under combined tensile loadings are elucidated. The joint distribution function for composite failure due to a proportional loading regime is derived starting from the representation of the physical failure process in Boolean operations which, in turn, is represented by probability functions.