Analysis of the reduction on elastic modulus due to fiber cracking in unidirectional composites

摘要

In an effort to uncover the effect of fiber cracking on the reduction of composites stiffness, the double inclusion method is carried out to examine the influence on the overall modulus of unidirectional composites containing randomly distributed penny-shaped cracks in fibers. In this paper, a fiber containing cracks is proposed to be a nested sequence of two inhomogeneous whose elastic constants are different both from that of a matrix and from each other. Using the double inclusion method, the equivalent eigenstrains in both crack and fiber can be obtained, then the overall elastic modulus of the composites can be derived according to the energy analysis. As a result, we can find how the crack density parameter and the volume fraction of the fiber effect on the overall elastic modulus of the unidirectional composites. The theory is also compared with some results by self-consistent, differential scheme and Hashin-Shtrikman bound when the unidirectional composite without cracks is regarded as one matrix phase. It suggests that the concept proposed to estimate the reduced modulus of unidirectional composites with fiber cracking is a viable one.