Stress profiles around broken fibers in unidirectional composites using influence superimposition technique

Abstract The stress transfer from broken to its unbroken adjacent neighboring fibers in unidirectional fibrous composites under a tensile loading applied in the fiber axis is analyzed using a two‐dimensional (2D) shear lag model. The numerical solutions to the governing equations is greatly simplified by the assumptions that the displacements perpendicular to the fiber direction can be ignored, and the axial displacements are uniform over the cross section of any fiber. Using an influence function superimposition technique, closed‐form analytical expressions are used to predict stress profiles in both the fiber and matrix because of any number and arbitrary array of fiber breaks in the presence of matrix shear failure. These are compared to stress concentrations predicted using the finite element analysis (FEA). It is shown that the 2D modeling presented here does generalize the governing equations to include interactions with multiple damage events. The micromechanical model is vital to develop the basic mechanics that are necessary to understand failure behavior of the composite produced by the failure of one or more of its components. POLYM. COMPOS., 2013 © 2013 Society of Plastics Engineers