Crack initiation transient model

The performances of the 3D CZM model were compared with a previously developed 2D model and analytical solutions on mode I, mode II and mixed-mode I/n loaded cracks in bonded aluminum or composite assemblies. The results are in an overall good agreement with each other, with the exception of the first instants of propagation of the 3D model, where the CZM process zone has to shape up. Next step should to assess this initial transient of 3D process zone formation, leading to a higher predicted number of cycles with respect to 2D simulation, by experimental evidence. 

When the applied stress a is less than Su, creep of the matrix will commence after application of the load. During this creep, the matrix will relax and the stress on the fibers will increase. Therefore, further fiber failure will occur. In addition, the process of matrix creep will depend on the extent of prior fiber failure and, as mentioned previously, on the amount of matrix cracking. The details will be rather complicated. However, the question of whether steady-state creep or, perhaps, rupture will occur, or whether sufficient fibers will survive to provide an intact elastic specimen, can be answered by consideration of the stress in the fibers after the matrix has been assumed to relax completely. Clearly, when the matrix carries no stress, the fibers will at least fail to the extent that they do in a dry bundle. It is possible that a greater degree of fiber failure will be caused by the transient stresses during creep relaxation, but this effect has not yet been modeled. Instead, the dry bundle behavior will be used to provide an initial estimate of fiber failure in these circumstances. 

Fig. 10.5 (a-f) Normalized crack growth velocity A a/K] l versus normalized crack extension A = ball for transient SSC crack growth under constant / loading based on a model for crack growth by grain boundary cavitation (taken from Ref. 45). The parameters K, r A0, and Ass are normalized values of, respectively, the stress intensity factor (which is held constant), the crack growth initiation time, the initial crack velocity, and the steady-state crack velocity. 

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