A 3D model for possible micro-instability patterns in a boundary layer of a fibre composite under compression

A 3D model is presented for possible micro-instability patterns in a boundary layer of a fibre composite under compression. The model accounts straightforwardly for the presence of the external boundary, for the distinct difference in the properties of the micro-components (fibres, matrix) and also for the fibre/matrix interfaces at the microlevel. Certain idealised bonding conditions between micro-components can be satisfied exactly. Behaviour of the fibres and the matrix is described by the Treloar potential with differing stiffness coefficients. Numerical results are presented for cases of perfect fibre/matrix bonding and, also, for the sliding contact without normal displacement discontinuity. It is shown that the critical loading parameters can depend significantly on the local geometrical parameters of the microstructure and on the parameters of micro-instability modes (spatial orientation, wavelengths). These latter are influenced substantially by the boundary effects and must be properly determined in order to get acceptable estimations of the critical loads.