Issue34

N.R. Gates et alii, Frattura ed Integrità Strutturale, 34 (2015) 27-41; DOI: 10.3221/IGF-ESIS.34.03 35 Figure 5 : Final crack paths for selected smooth specimen tests under (a) torsion with static tensile stress, (b) torsion with static compressive stress, and (c) pure torsion loadings. M ODELING OF FRICTION EFFECTS s evidenced by the experimental results, the role of friction and roughness induced closure effects on mode II crack growth is a complex, yet significant, issue. Because of the many factors involved and their inherent variability, quantification of these effects is challenging. This section will aim to reproduce some of the crack growth trends observed in experiments by presenting a simplified model to predict and quantify crack growth attenuation due to crack face friction and roughness. The proposed model takes as its starting point the idea that friction and roughness induced crack face interaction allow a portion of the nominally applied loading to be transferred through a crack. Consider two extremes for pure torsion loading: an uncracked volume of material can transmit all of the nominal loading and creates no stress concentration effect, while a geometrically ideal mode II crack cannot transfer any load between crack faces and produces the theoretical mode II SIF value at its crack tip. Therefore, it would seem logical that an effective mode II SIF could be determined by taking into account the amount of loading transferred between crack faces in an actual cracked component. The model should be able to account for experimentally observed trends such as normal stress effect and loading level dependence and should also depend on quantities relative to crack face friction and roughness such as coefficient of friction and crack face asperity angle. For ease of implementation, it should also ideally only depend on readily available material properties and not require the use of geometry dependent functions, other than those used in SIF calculations. In order to compute the proposed effective mode II SIF, the first step is to determine the nominal stress state. Nominal, in this case, refers to the stress state that would exist in the volume of material surrounding a crack if the crack were not present. This is assumed to be a two dimensional stress state aligned with the direction of overall crack growth. Loads transferred through the crack face are considered on an averaged basis along the entire length of the crack. If significant stress gradients exist along the length and/or depth of the crack, average stress values should be considered. The nominal coordinate system ( x-y ) is shown schematically in Fig. 6 along with other expressions relevant to the following discussions. Once the appropriate stress state is known, it is transformed into a coordinate system (subsequently named x ' -y ' )  aligned with the average effective crack face asperity angle, α eff , the calculation of which will be explained later. Of the stresses in the transformed coordinate system, the crack can only directly transfer a compressive stress, σ x’ , normal to the asperity face. However, a resulting friction induced stress component allows for additional loads to be transferred as well. It should be noted that the model will not correctly predict frictional attenuation for asperity angles exceeding 45°. Above this angle, attenuation starts to become more of a function of mechanical interlocking than friction. Additionally, shielding from the alternating asperity angles will begin to have an effect on stresses at the crack interface above this angle. A (a) (b) (c)