Constitutive equations for densification of matrix-coated fibre composites during hot isostatic pressing

This work addresses the development of physically based constitutive equations for the consolidation of fibre-matrix-void systems typically arising in the manufacture of matrix-coated fibre metal matrix composite materials. The analyses consider square array packing of the coated fibres under symmetrical in-plane compressive load and take into account the power-law creep of the matrix. Two models have been developed. The first is based on an energy approach in which assumed velocity fields in the deforming matrix are considered and are expressed in terms of an unknown parameter. In this way, the dependence of the deformation rate on volume fraction of voids and fibres is derived through the use of Hillʹs minimum principle for velocities. The second model makes use of micro-mechanical finite element modelling in which fibre, matrix and void are modelled explicitly. The micro-mechanical finite element model is developed for validation and comparison. Theoretical predictions are examined. The constitutive equation for consolidation derived from Hillʹs minimum principle shows good agreement with results obtained from micro-mechanical finite element modelling.