Issue34

N.R. Gates et alii, Frattura ed Integrità Strutturale, 34 (2015) 27-41; DOI: 10.3221/IGF-ESIS.34.03 39 2 III 2 II 2 I q K 1 K K K     ) (  (4) According to this equation, mode I and mode II SIFs have the same contribution to the equivalent SIF value. Therefore, for this analysis, whichever loading mode produced the highest SIF was considered the preferred crack growth mode. Mode I SIF values were based on the normal stress component, as calculated from the nominally applied stresses, acting on the maximum principal stress plane at the location of the crack. To account for differences in effective crack length due to plane orientation, the overall crack length was projected onto the maximum principal plane prior to calculating the mode I SIF. Only the tensile portion of the normal stress cycle was considered for the calculation of SIF range, as the crack is assumed to be closed under compression. The mode I geometry factor function was obtained using the same crack geometry and procedures described for mode II. Although there is likely some degree of error in these calculations due to the difference in profile between the projected crack and an ideal mode I crack, this effect has not yet been evaluated. Fig. 8 shows analysis results for the four different LEFM applicable pure torsion loading levels applied in the experimental program. Each plot shows the effective mode II SIF range, computed using the proposed model, along with the mode I potential SIF range versus half crack length. The effective asperity angle is also plotted for reference. The vertical dotted lines on each plot enclose the regions of experimentally observed mode I growth for each loading level and experimental mode II growth regions are highlighted in red. By studying this figure, it can be seen that this type of analysis is able to reflect the trend observed in Fig. 3 of an increase in initial mode II crack length before branching with increasing loading level. Additionally, the predicted crack length at this transition is within a factor of 2.5 of the experimentally measured value for all loadings cases considered. It is also worth noting that a further increase in applied loading would have resulted in the correct prediction of a non-branching crack condition and that a transition back to shear-mode growth after a period of mode I growth, which was observed in experiments, was predicted by the analysis. Although in the latter case, quantitative results can vary due to the potential for a mode I branch to cause significant deviation from the idealized mode II path assumed by the model. Fig. 9 shows a fairly reasonable agreement between the experimental and predicted crack paths for the fatigue tests represented in Fig. 8(a) and 8(c). Figure 8 : Effective mode II SIF, local mode I SIF, and effective coefficient of friction vs. crack length for fully-reversed pure torsion loadings of (a) 140 MPa, (b) 150 MPa, (c) 168 MPa, and (d) 188 MPa. All results represent LEFM applicable regions of crack growth. Mode I Mode I (b) (a) τ a = 140 MPa τ a = 150 MPa τ a = 168 MPa τ a = 188 MPa Mode I Mode I (c) (d)