- Four-Stage Fracture Model
Thus far we have concentrated on existing model approaches for the fracture of concrete. As an extension of the cohesive model developed by Barenblatt and Dugdale in the late 1950s/early 1960s, the Fictitious Crack Model was developed by Hillerborg and co-workers in 1976. The similarity was taken very loosely because the fracture process zone is very small for the metals that were considered initially, in comparison to the large (global) size of the process zone for concrete materials. By starting out from this similarity the original “local” model for the fracture of plastic metals is transformed into a “global” model where the process zone may even exceed the size of the entire structure or specimen. As a result, the softening parameters needed in the model are size-dependent (see Figures 9.5, 9.6, and 9.8) and also are heavily in¸uenced by the boundaries (see Figure 2.11). It is obvious that, even though the model is used extensively for the moment, albeit sometimes with rather debatable outcomes, eventually a better and more reliable model needs to be developed. One might think that a micro-(or rather meso-) mechanical model may be the answer to many of the questions. Yet, one must accept lengthy analyses in that case (see, e.g., Appendix 1), and also at a smaller level of observation the same uncertainty will remain about the validity of the parameters used. We return to these matters in Chapter 11.