Issue 47

A. Spagnoli et alii, Frattura ed Integrità Strutturale, 47 (2019) 401-407; DOI: 10.3221/IGF-ESIS.47.30 405 2 2 2 ( 1), 2 ( 1) ( 1) ( 1) I n II t K c K c                 (10) R ESULTS n this Section we summarise the results that we have obtained, applying the method to a simple geometry, consisting of an edge crack in a half-plane. The material is linear elastic and a state of plain strain is assumed. Compressive and tangential stresses are applied remotely, such that uniform normal and shear stresses, p and q respectively, act along the crack line (see Fig. 1b). In order to explore the influence of the roughness ratio, we have performed several analyses, varying the ratio c/L and computed the mode II SIF at the crack tip. All the results presented in this Section are normalised with respect to the crack length c and the mean normal pressure p . In Fig.2 we show the variation of the normalised SIF during the increment of external loads, considering two different values of the asperity angle . We observe that K II is null until the stress ratio q/p reaches 0.5, which is the value of the coefficient of friction f chosen in the simulation: this was expected, since the stress distribution due to the external loads is constant. For q/p >0.5, we notice an increase, which is more pronounced for shorter cracks, i.e. for c/L tending to 1. In Fig.3 we show the variation of the SIF, evaluated at q/p =1, with the angle of roughness, for three different values of c/L . We can appreciate the effect of the roughness angle, which causes a decrease of the mode II SIF: as already noticed in [12],the reason for this is that the surface roughness generates a resistance to sliding, which is added to the one due to friction. However, while the decrease is almost linear for short cracks, for bigger c/L ratios we observe a greater reduction, although it appears to attenuate at bigger roughness angles. Figure 2: The normalised stress intensity factor K II versus the applied load ratio q/p . Different relative crack lengths c/L are considered. f =0.5. (a) Angle of the surface asperity  =2° and (b) angle of the surface asperity  =5°. The inset shows the loading history. Finally, we explore the effect of the ratio c/L , considering two different cases: in Fig.4a, we keep the angle constant, while in Fig.4b we keep constant the height h of the asperities. Indeed, throughout the other simulations, we have always kept the asperity angle constant: as a consequence, a change in the ratio c/L implies also a change in the height h of the saw-tooth. C ONCLUSIONS he crack tip stress fields in brittle and quasi-brittle material can be highly influenced by the surface interaction due to microscopic asperities. As a result, the stress intensity factor might differ from the theoretical values computed according to the relationships of LEFM, which assumes a crack with flat and smooth surfaces. I T