A Variational Method for Analysis of Fiber Stress Profiles in Unidirectional Composites with Matrix Creep

In this paper, a variational method is developed for analyzing the matrix creep induced change of fiber stress profiles in unidirectional composites. A functional of admissible profiles of fiber stress is first presented by supposing a broken fiber in matrix as well as a fiber pulled out from matrix. The functional is shown to have the stationary function satisfying a rate-type differential equation based on a shear lag theory. Then, the stationary function is determined approximately at every moment by assuming bilinear profiles of fiber stress and a power law of matrix creep, leading to an analytical solution for the time-dependent increase of a stress transfer length. The analytical solution is compared with finite difference computations based on the shear lag model and with an experiment performed by the present authors using a single carbon fiber/acryl model composite. Thus, the effects of matrix creep, matrix shear rigidity, and interfacial slip on the stress transfer length are discussed, and it is shown that the solution has a good agreement with the experiment if interfacial slip is taken into account.