Residual Stresses in a Composite with Continuously Varying Young's Modulus in the Fiber/Matrix Interphase

The incorporation of a realistic interphasial region into the micromechanical analyses of composite systems is critical to the understanding of composite behavior. The interphase is usually modeled as a homogeneous region, despite the fact that it may have spatial property variations. A representative volume element with three cylinders (concentric cylinder assemblage)is considered here for the determination of local thermal stresses in a composite. Three different expressions are used to simulate the Young's modulus variations in the interphase, while the Poisson's ratio and coefficient of thermal expansion of the interphase region are chosen to be constant. The governing field equations in terms of displacements are solved in closed form. It is found that, though the solution is "dilute," the Young's modulus variations have a distinct effect on the local thermal stresses.