Continuum modelling of damage in ceramic matrix composites

A continuum model for determining mechanical response of ceramic matrix composites with damage is presented. The mechanisms of damage considered are those observed in unidirectionally fiber-reinforced ceramic matrix composites, viz. matrix cracking, fiber/matrix interfacial slip and fiber/matrix debonding. Four basic configurations of distributed damage at the microscopic level are treated: matrix cracks only, matrix cracks in conjunction with interfacial slip, debonds only and matrix cracks in conjunction with debonds. The elementary damage entities, i.e. cracks, debonds and slipped surfaces, are represented by second-order tensors which are regarded as internal variables. Using a thermodynamics based formulation of constitutive relationships with internal variables, the stress-strain-damage relationships are derived. Specific expressions are given for changes in the engineering elastic moduli in terms of the densities of damage entities for sparsely distributed damage.