Application of GPS Tensors to Fiber Reinforced Composites

In this paper we propose a pair of two new tensors called GPS tensors S and D for the concentric cylindrical inclusion problem. GPS tensor S relates the strain in the inclusion constrained by the matrix of finite radius to the uniform transformation strain (eigenstrain), whereas tensor D relates the strain in the matrix to the same eigenstrain. The tensorial form of relationship to the inclusion problem allows us to derive explicit expressions for a larger class of transformation problems, including thermal residual stress problems. Since GPS tensors take the fiber volume fraction into account explicitly, we are able to study the effect of matrix properties and fiber volume fraction on the spatial distribution of thermal residual stress. GPS tensors are also used in the evaluation of effective material properties by using the self-consistent method. Very good agreement between analytical results using GPS tensors and experimental data is observed for graphite/epoxy and glass/epoxy composites.