On the fiber-bridging of cracks in fiber-reinforced composites

Abstract

A formulation is systematically derived for a fully or partially bridged straight crack in anisotropic elastic materials such as fiber reinforced composites. Following Ting's (1988, Phys. Stat. Sol. (b) 145, 81–90) use of new sum rules for Stroh formalism, the governing equation of fiber bridging of cracks is formulated explicitly in real form. The straight crack is in terms of the superposition of dislocation density distributions and the bridging force is linearly or nonlinearly dependent on the crack opening displacement (COD). Along the crack, there may be an arbitrary variation of the stiffness of the bridging materials due to partially failed fibers or ligaments. Additionally, the crack may have any orientation with respect to the axis of the material symmetry. Finally, the solution is explicitly made in terms of Chebychev polynomials for the linear case and can be compared with that calculated by the boundary element method. In the case of a linear relation between COD and bridging traction the numerical solution is in excellent agreement with the analytic solution. This can be regarded as justification for the numerical scheme. For an oblique crack, both mode I and mode II fracture exist. In the case of a nonlinear relation between COD and bridging traction, only a numerical solution is available. By adopting Hsueh's fiber-pull-out model we know that the interfacial properties σ d , σ c and μ play important roles in the debonding, sliding and crack opening steps in fiber bridging phenomenon. The dependence of COD and K I on σ d , σ c and μ have been analyzed. Since the larger σ d , vb σ c vb and μ are, the larger bridging tractions fibers can offer, COD and K I decrease as the values of σ d , σ c and μ increase.