A new analytical model for three-dimensional elastic stress field distribution in short fibre composite

A new analytical model has been developed for three-dimensional elastic stress field distribution in short fibre composite subjected to an applied axial load and thermal residual stresses. Two sets of the matrix displacement solutions, which were called respectively as the far-field solution and the transient solution, were exactly derived based on the theory of elasticity. These two sets of the displacement solutions were then superposed to obtain simplified analytical expressions for the matrix three-dimensional stress field components and the fibre axial stress field components in the entire composite system including the fibre end region with the use of the technique of adding imaginary fibre. The matrix three-dimensional stress field components satisfy exactly the equilibrium and compatibility conditions in the theory of elasticity, the fibre axial stress field components satisfy the equilibrium requirements within the fibre and between the fibre and the matrix. The above stress field components also satisfy well the overall boundary conditions including the surface conditions, the interface continuity conditions and the axial force equilibrium conditions. The finite element numerical calculations were conducted to examine the validity of the analytical model. Considerable good agreements have been obtained between the analytical and numerical predictions for all the stress, strain and displacement components.