The effect of a fiber loss in periodic composites

Three types of analyses are combined to investigate the effect of missing fibers in periodic continuous fiber composites that are subjected to thermomechanical loadings. The representative cell method is employed in the first analysis for the construction of Green’s functions elastic fields for the fiber–matrix interfacial jumps problem. As a result, the infinite domain problem is reduced, in conjunction with the discrete Fourier transform, to a finite domain problem on which Born–von Karman type boundary conditions are applied. In the second analysis, the transformed elastic field is determined by a second-order expansion of the displacement vector in terms of local coordinates, and by imposing the equilibrium equations, the interfacial traction and displacement conditions, and the Born–von Karman type boundary conditions. The actual non-periodic elastic field at any point is obtained from the Fourier-transformed fields by a numerical inversion. In the third one, a micromechanical analysis for periodic continuous fiber composites in which all fibers are perfectly bonded to the surrounding matrix provides the elastic field within the phases. A superposition of the thermoelastic fields obtained from the first and third analysis provides the traction-free boundary conditions at the interface of the missing fibers. The accuracy of the offered approach is verified by comparison with analytical solutions that exist in some special cases. Results show the effect of a missing fiber in boron/epoxy and glass/epoxy composites that are subjected to various types of thermomechanical loadings.