An analytical model for elastic stress field distribution in fibre composite with partially debonded interface

An analytical model has been developed for determining the elastic stress field distribution in a fibre composite that has a partially debonded interface following the Coulomb friction law and is subjected to an axial load on the fibre and thermal residual stresses. The expressions for the matrix three-dimensional stress field and the fibre axial stress field in the bonded and debonded regions were derived based on the exact solution of the matrix displacement field from the equilibrium equations expressed in terms of displacements, which are, respectively, a superposition of a far-field solution and a transient solution. The expressions for the matrix three-dimensional stress field satisfy exactly the equilibrium and compatibility equations in the theory of elasticity, the expressions for the fibre axial stress field satisfy rigorously the equilibrium requirements between the fibre and the matrix and both satisfy well the overall boundary conditions. The finite element numerical calculations were conducted to examine validity of the model. Considerable good agreements between the analytical and numerical predictions have been obtained for all the stress, strain and displacement components.