13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- 4. Discussion 4.1. Estimation of the crack propagation threshold To tentatively derive a crack propagation rate from experimental data, ground KB bearing specimens tested at higher stresses were selected because (i) crack initiation was thought to occur during the first cycle, so that the number of cycles corresponding to crack propagation could be easily estimated, and (ii) because crack initiation occurred all along the KB, so that to a first approximation, the crack could be considered to affect the whole width of the specimens. Under these assumptions, a very simple estimate of the stress intensity factor was made by considering a crack of length a, propagating in pure Mode I from one side of an infinite plate, leading to the following equation [19]: + − + − = = 4 3 2 30.39 21.72 10.55 1.12 0.231 W a W a W a W a a W a a Y KI π σ π σ (2) In Eq. (2), W is the length of the ligament, here nearly equal to the plate thickness (3 mm). Eq. (2) was applied to all KB bearing specimens showing crack initiation from the KB, by using the minimum length over which KB opening was observed. This yielded a lower bound value for the stress intensity factor after opening of the KB defect. Fig. 9a shows a threshold for crack propagation in KB bearing welds of about 1 MPa√m, close to that reported for 2198-T8 base metal with the same load ratio (Fig. 9b). As-welded specimens exhibited only slight opening of the (tilted) KB, leading to Mode I stress intensity factors close to the threshold value (data points 1 to 3 in Fig. 5). This could explain why their fatigue lifetime was not correlated with the fracture initiation locus. Figure 9. (a) Initial value of ΔKI for KB bearing welds with either ground or as-welded lower surfaces, showing an apparent threshold value of about 1 MPa√m. (b) Comparison of estimated crack propagation rates during interrupted tests on KB bearing specimens (black box) with literature data 4.2. Estimation of the crack propagation rate in ground KB bearing specimens To tentatively derive a value of the average crack propagation rate over a small distance, Eq. (2) was used (i) after opening of the KB, and (ii) after interrupted crack propagation. As the length of the fatigue crack varied from place to place, minimum and maximum values were used, leading to upper and lower bounds listed in Table 3. These values are consistent with literature data obtained using the same load ratio (Fig. 9b). ground as-welded Fatigue lifetime (103 cycles) Initial value of ΔK (MPa√m) (b) Initial value of ΔK (MPa√m) Crack growth rate (m/cycle) [20] [15] [21]
RkJQdWJsaXNoZXIy MjM0NDE=