Mathematical Modeling of Fiber Reinforced Composites with Linear Grading
Many materials are fabricated using fiber reinforced composite materials, which consist of a set of aligned stiff fibers embedded in a softer matrix. A common example is the automobile tire. It is becoming increasingly common for composites manufacturers to add a thin linearly graded coating to improve the bulk properties of the composite, but very little modeling of linearly graded materials has been done. The linearly graded zone can also be used to model damage and fiber-matrix separation. The goal of this project is to develop a micro-mechanical mathematical model to determine the local displacement, stress and strain fields surrounding a single fiber when there is a linearly graded transition zone between the fiber and the matrix. Both fiber and matrix are assumed to be isotropic or transversely isotropic. The composite is homogenized to determine its effective mechanical properties (elastic moduli, Poisson ratios, and bulk modulus).