The theory of critical distances to predict static strength of notched brittle components subjected to mixed-mode loading

This paper summarises an attempt to use the theory of critical distances (TCD) to predict static failures in notched brittle components when the applied system of forces results in multiaxial stress states in the vicinity of the stress concentrator apex. In order to reformulate the TCD to coherently address this complex problem, the cracking behaviour of cylindrical specimens of polymethylmethacrylate (PMMA), weakened by different geometrical features and tested under combined tension and torsion, were initially investigated. The direct inspection of the cracked specimens showed that, in an incipient failure condition, the cracking mechanisms changed as the degree of multiaxiality of the stress field damaging the material process zone changed; this held true even though, from an engineering point of view, the investigated material showed a classical brittle behaviour (that is, mode I dominated). In more detail, in tension (and in plain-specimen torsion) failure occurred as soon as a small craze/crack initiated. On the contrary, for notched specimens in torsion failure was preceded by the formation and growth of many small cracks near the notch root. This complex material cracking behaviour resulted in values of the material characteristic length which changed as the degree of multiaxiality of the stress field damaging the material in the vicinity of the stress raiser apex changed. The above phenomena were incorporated into the devised reformulation of the TCD, allowing our method to perform predictions falling in an error interval of about ±20%. Finally, in order to better check the accuracy of our method in predicting static failures in notched brittle materials, it was also applied to some results taken from the literature and generated under combined mode I and II loading. Again the TCD was seen to be highly accurate allowing not only the static strength but also the crack propagation direction to be predicted. These results are very promising, especially in light of the fact that the TCD can easily be used to post-process linear-elastic finite element (FE) models, making it suitable for being successfully employed in an industrial reality