Inertial effects in the pullout mechanism during dynamic loading of a bridged crack

Abstract Inertial effects in the mechanism of fibre pullout during the dynamic propagation of a bridged crack are examined by reposing simple shear lag models of pullout as problems of dynamic wave propagation. The only coupling considered between the fibres and the matrix is uniform, rate independent friction—no debond energy is included. Analytical solutions are found for the coupled waves propagating in the fibres and the matrix away from the fracture plane of the bridged crack as the bridging tractions increase with time. These solutions yield the time-dependent relationship between the crack opening displacement and the bridging traction. Engineering criteria for inertial effects being significant are deduced by comparing the dynamic bridging traction law with its counterpart for static loading, which is recovered as a limit of the dynamic case. The criteria are evaluated for two crack cases: the asymptotic limit of a long, fully bridged matrix crack propagating unstably through a fibrous composite under remote tension; and a finite crack partially bridged by stitches or rods that delaminates a double cantilever beam under the impetus of a flying wedge. In both cases, the rate of increase of the crack opening displacement appears to be sufficient for inertial effects to be pronounced in the bridging (pullout) mechanism. Expected trends of the significance of inertial effects with material and geometrical parameters are identified.