A deformation-theory based model of a damaged metal matrix composite

A shear-lag and deformation-theory based model for a metal matrix composite reinforced by continuous unidirectional fibres is proposed. The model accounts for fibre and matrix cracking, matrix plasticity, and fibre-matrix interfacial sliding through seven characteristic non-dimensional parameters, which combine geometric, phase and interface properties. It allows arbitrary tensile loading and unloading history along the fibre direction, and predicts the history-dependent elastoplastic displacement, strain, and stress fields in all the fibre and matrix elements. Broken elements may be present initially, or form during the imposed loading history. Non-linear one-dimensional governing differential and algebraic equations are formulated on the basis of the model. A computationally fast solution methodology based on pseudospectral collocation is implemented. The present model is employed to predict the elastic strain profiles in a Ti/SiC composite tape near pre-existing breaks. These predictions agree well with experimental measurements reported in the literature.