Paper number 322

ANALYTICAL MODEL FOR DEBONDED INTERFACES ASSOCIATED WITH FIBRE FRACTURES OR MATRIX CRACKS

L N McCartney

Centre for Materials Measurement & Technology, National Physical Laboratory,
Teddington, Middx. UK TW11 0LW

Summary

An analytical stress transfer model is described enabling an estimate to be made of the stress and displacement fields that are associated with fibre fractures or matrix cracks in unidirectional fibre reinforced composites. This model represents a great improvement on existing shear-lag based methodologies. The model takes account of thermal residual stresses, and is based on a single assumption, namely, that the axial stress in the fibre is independent of the radial coordinate, and similarly for the matrix. A representation for both the stress AND displacement fields is derived that satisfies exactly the equilibrium equations, the required interface continuity equations for displacement and tractions, and all stress-strain equations except for the one that relates to axial deformation. In addition, the representation is such that the Reissner energy functional has a stationary value provided that averaged axial stress-strain relations for the fibre and matrix are satisfied. The improved representation is fully consistent with variational mechanics and provides BOTH the stress and displacement distributions in the fibre and the matrix. For an isolated fibre fracture or matrix crack, interface debonding is considered where two types of condition are investigated. Firstly, it is assumed that the shear stress is uniform within the debonded region. Secondly, it is assumed that stress transfer in the debonded region is controlled by Coulomb friction. Preliminary predictions are made for carbon fibre reinforced epoxy composites.

Keywords

interface, debonding, stress, displacement, friction, variational mechanics.