TIME-DEPENDENT OR CYCLE-DEPENDENT CRACK BRIDGING

This paper presents solutions to the problem of a Mode I crack that is shielded by bridging tractions that can decay with the passage of either load cycles or time. The problem contains two competing time- or cycle-dependent processes, namely degradation of the shielding tractions (rate constant r1) and crack advance (rate constant r2), the latter being a function of the crack tip stress intensity factor range, DELTAk(tip). For given initial conditions and load level, the development of DELTAk(tip) with crack length depends only on the ratio r1/r2, rather than on each of r1 and r2 separately. Particular emphasis is placed on the roles of thresholds for crack advance or shielding degradation. It is shown that, depending on whether or not such thresholds exist, the problem can reduce asymptotically to one or another familiar, rate-independent problem, such as elastic/perfectly plastic bridging tractions in the limit r1/r2 --> infinity (fatigue crack growth applications), or fracture in the presence of a viscous process zone when r1/r2 --> 0 (monotonic loading applications). Solutions for general values of r1/r2 are found numerically by methods valid for general bridging and crack growth laws and for specimens of various common shapes. Crack propagation is comprises a history-dependent transient regime followed by a quasi-steady state regime that is insensitive to the initial conditions. Solutions are illustrated by specific application to bridging by linear springs that soften with passing load cycles or time. The springs may to represent the action of a repairing patch bonded over a crack in an alloy plate, or of bridging fibers in a metal-matrix composite or laminate.