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 eit her load cycles or time. The problem contains two competing time- or c ycle-dependent processes, namely degradation of the shielding traction s (rate constant r1) and crack advance (rate constant r2), the latter being a function of the crack tip stress intensity factor range, DELTA k(tip). For given initial conditions and load level, the development o f DELTAk(tip) with crack length depends only on the ratio r1/r2, rathe r 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 tract ions in the limit r1/r2 --> infinity (fatigue crack growth application s), 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 pr opagation is comprises a history-dependent transient regime followed b y a quasi-steady state regime that is insensitive to the initial condi tions. Solutions are illustrated by specific application to bridging b y linear springs that soften with passing load cycles or time. The spr ings may to represent the action of a repairing patch bonded over a cr ack in an alloy plate, or of bridging fibers in a metal-matrix composi te or laminate.