Mapping complete eigensolution space for the analysis of stress transfer in and around the broken fiber: A variational principle based approach

One of the critical reasons for the failure of the Fiber Reinforced Composite (FRC) is fiber breakage. The stress transfer in and around this breakage has remained the topic of research for the last couple of decades. The two-phase composite model is generally considered standard to gain insight into the mechanics. Most of the literature simplifies the problem by considering the shear lag approximations or some other a-prior and/or ad hoc assumptions on various field variables. Moreover, the majority of the study in the literature considers both matrix and fiber to be isotropic. On the contrary, most of the fibers in FRC are transversely isotropic. In the present manuscript, an attempt has been made to provide a solution for this problem with an anisotropic fiber satisfying all the boundary conditions and continuity requirements in an exact sense. The solution strategy adopts the derivation of the solution for individual phases under axial traction and then imposes the boundary and the continuity conditions. The formulation of the problem for the individual phase is based on the variational principle and the solution is based on the method of separation of the variables and the Frobenius method. To validate the solution the numerical results for the various stresses have been compared against the results from the Finite Element Analysis (FEA). The comparison shows a good agreement between them. Further, the effect of the volume fraction and the fiber-matrix stiffness ratio on the Ineffective length, maximum shear stress at the interface, and the far-field stresses in the fiber has been studied.