Issue 41

T. Vojtek et alii, Frattura ed Integrità Strutturale, 41 (2017) 245-251; DOI: 10.3221/IGF-ESIS.41.33 248 the asperity (see Fig. 3). The points at which the values were calculated are denoted by integers from 1 to 9 and they define the horizontal axis of Fig. 4. Only the values for points 2 to 8 are shown, since the extreme points 1 and 9 represent a discontinuity of the crack front and the corresponding SIFs are not well defined. Ratios r cal = k 2 / K III were calculated as functions of different angles α in all nodes along the half tooth and plotted in Fig. 4. In this figure each data line corresponds to one angle α. Figure 3 : The detail of roughness asperities characterized by the angle α. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1 2 3 4 5 6 7 8 9 ratio   r cal = k 2 / K III evaluated points α = 41.65° α = 38.32° α = 34.65° α = 30.61° α = 26.20° α = 21.42° α = 17.19° α = 11.80° α = 6.20° α = 3.35° Figure 4 : Results of r cal for different asperity angles α in the range from 3.35° to 41.65° in points showed in Fig. 3. Although the ratio r cal is changing along the asperity, a useful dependence of the ratio r cal on the asperity angle α can be still constructed from the computed curves in Fig. 4. Indeed, two special values of r cal can be selected: the average value r cal,av (calculated from points 2 to 8) and the maximum value r cal,max (at the point 3) that is probably relevant for the first extension of local tongues at the threshold. Both r cal,av and r cal,max as functions of α are plotted in Fig. 5. The SIF range Δ K III measured at the mode III threshold under the presumption of a smooth circumferential crack front is equal to Δ K IIIeff,th . Simultaneously, the local mode II component of the SIF range Δ k 2 at the asperities (initiation sites of mode II tongues) should be equal to the measured Δ K IIeff,th . This means that the following formula must hold at the mode III threshold:         IIeff,th 2 2 cal exp III III IIIeff,th K k k r r K K K (1) The agreement between theory and experiment could be tested by Eq. (1) since, for the ARMCO iron [10], the experimental ratio r exp was obtained as      1/2 IIeff,th exp 1/2 IIIeff,th 1.5 MPa m 0.58 2.6 MPa m K r K (2) The value r exp = 0.58 was plotted in Fig. 5 as the horizontal dashed line and its intersection with the relevant curve r cal,max vs. α indicates that the characteristic angle α of the asperities at the precrack fronts in the ARMCO iron specimens should α points in Fig. 4 shear stress maximal k 2 1 2 8 9 3 precrack