Crack bridging time-dependent

The mathematical approaches pertaining to the full-shielded case (Keff = 0) for time-dependent bridging are very similar. In this case, Eqn. (19) still holds, but for a particular p(u) relation holding over a portion of the crack, the extent of that zone is determined by the Keff = 0 condition. For example, if, as in Eqn. (19), the cohesive tractions act over the entire crack, then the crack length itself is determined by that condition. 

If the crack is considered to be a wake zone and p = p(u, t) in Eqns. (19) and (21) then, for a stationary crack, both the crack shape and Keff are time dependent, given respectively by u(x,t) and KejAt) from Eqns. (19) and (21) for the case of partial shielding. Cox and Rose35 recently considered an elastic time-dependent bridging law of the form... 

For a fully shielded crack tip (Keff = 0) time-dependent bridging is modeled in close conjunction with the crack growth rate itself, since daldt... 

Fig. 10.8 Results of the development of K with crack size, A, from the model of Cox and Rose33 for the case of time-dependent elastic bridging of matrix cracks.

B. N. Cox and L. R. F. Rose, Time or Cycle Dependent Crack Bridging, Mechanics of Material, submitted. 

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