Based on the principles of fracture mechanics, a crack propagates when KI >= KIC, i.e. stress intensity factor is larger than fracture toughness, where KI=σ√(πa) for a central crack. Theoretically, as crack propagates and crack length (a) becomes larger, KI increases too. Therefore, when a crack starts to grow, it never stops! However, it is not the case in many geomechanics applications in underground structures. For example, a propagating crack in a tunnel surface will stop at a distance from the tunnel wall eventually.
In numerical modeling, a stress relaxation method may be used to lower the acting stress on the crack to model crack propagation more realistically. what are other efficient ways to model this phenomenon realistically? Good references are appreciated.
Thanks.
Hi Abolfazl Abdollahipour.
The premise that the crack progressing in a brittle material will run through the body and snap it into two is based on the assumption of enough energy being available to do so. This may be true incase of statically determinate loads where the load applied continually supplies energy for deformation and crack propagation. However this is not necessarily always true for statically indeterminate loads. For example in case of a small applied displacement, the crack will cease to propogate the moment the energy from the applied displacement runs out. A simple experimental proof is that we can easily tear a slightly slit paper without necessarily tearing it into two. This is because we are limiting the displacement and thus the energy we are supplying to the paper. I guess that in your geomechanical applications something similar may be happening. Hope this helps.
The crack propagation when KI >= KIC, the stress intensity factor is larger than fracture toughness then the component will be failure.
Thanks Md. Shafiul Ferdous fro sharing the file.
Good point are mentioned by Mir Aamir Abbas . However, the question still remains. In a numerical model we need to implement a method to consider crack arrest after a period of propagation. The available energy does not increase with the crack size to provide crack propagation conditions. This is the case in many geomechanics applications. A crack in a tunnel wall may start to grow, it can nnot always continue to grow to reach another boundary and it can not break earth into two. This should be formulated in the numerical model to simulate real life crack in the model.
Hi Abolfazl,
Thanks for your interesting question. I think it might be good to consider strains rather than stresses, if you are dealing with brittle and semi-brittle materials. I would, in particular, recommend looking at the critical tensile strain criterion by Fujii and the extension strain criterion by Stacey. I hope you find this useful. Regards, Ebrahim
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