Evaluation of creep compliance of carbon-fiber-reinforced composites by homogenization theory

Effective creep compliance of carbon-fiber-reinforced composites is evaluated for applications of composites at elevated temperatures. A homogenization theory with two-scale asymptotic expansion in the Laplace domain is used to solve viscoelastic problems of composites. Effective constitutive equations and microscopic disturbed displacements are derived from the homogenization theory. A hexagonal array of fibers is employed for the microstructure of the composite and a hexagonal unit cell is placed in the microscopic field to represent a boundary value problem. In numerical calculations, a carbon-fiber-reinforced composite with thermoplastic matrix is considered at the glass transition temperature of the matrix. The matrix is viscoelastic and is represented using the generalized Maxwell model at the glass transition temperature, and fibers are considered as a transversely isotropic elastic medium. The effective creep compliance of the composite is determined by numerically solving a set of equations for macro-and microscopic fields.