The effect of a graded interphase on the mechanism of stress transfer in a fiber-reinforced composite

Based on an improved shear-lag model, the effect of an inhomogeneous interphase on the mechanism of stress transfer in fiber-reinforced composites is investigated. The inhomogeneity of the interphase is represented by the graded feature of the Young's modulus varying according to a power law or a linear one in the radius direction, while the Poisson's ratio and thermal expansion coefficient are assumed to be constants. Considering the effects of the inhomogeneous interphase as well as the Poisson's contraction and thermal residual stress, closed-form solutions to the axial fiber stress and interfacial shear stress are obtained analytically. Comparing the case with a power law to that with a linear one, we find that the fiber stress increases significantly in the former case, while it decreases slightly in the latter one with an increasing interphase thickness. With the same external tensile load and interphase thickness, it is found that the fiber in the power law case is subjected to a larger tensile stress than that in the linear variation one. However, the interfacial shear stress is not sensitive to the interphase thickness in both cases, except that near the two ends of fiber. Under the same external load, the maximum shear stress in the interphase is much smaller in the latter than that in the former. All the phenomena can be characterized by one parameter, i.e., the average Young's modulus of interphase, and denote that an interphase with a power variation law is more effective for stress transfer while the linearly graded one is more advantageous to avoid shear failure. The results should be helpful for engineers to properly design the interphase in novel composites, e.g. a carbon-fiber reinforced epoxy one.