An Analytical Model for 3-D Radial and Axial dependent Stress Distribution Field in Short Fiber Composites

A modified analytical model is developed for 3-D elastic stress field distribution in short fiber composites subjected to an applied axial load. Two sets of exact displacement solutions for the matrix and fiber derived based on the theory of elasticity. The superposition of these two solutions are then used to obtain the analytical expressions for 3-D stress field components over the entire composite system including the fiber end region with the use of imaginary fiber technique. The main difference here is that stress field is considered to be dependent on the radial and axial direction, the fact that has been ignored by previous works. The dependency of the fiber and imaginary fiber stresses and strains to r-direction was calculated. The matrix and fiber 3-D stress field components exactly satisfy the equilibrium and compatibility conditions and also the overall boundary conditions including the surface, the interface continuity, and the axial force equilibrium conditions. The analytical results were then validated by FEM. Interestingly, good agreements are found between the analytical and numerical predictions for all the stress, strain and displacement components. Another superiority of this analytical model is in solving problems with debonding.