Issue 39

S. Seitl et alii, Frattura ed Integrità Strutturale, 39 (2017) 110-117; DOI: 10.3221/IGF-ESIS.39.12 114 In a next step, the stress intensity range ∆ K was computed for both geometries under the four stress ratios, using the built- in ANSYS command KCALC [1]. Fig. 3.b depicts the calculated value of ∆ K from the 3PBT geometry for the 10-70% stress ratios. Similar to the CMOD calculations, a mathematical relationship between ∆ K and α can be found through exponential curve fitting. Moreover, similar graphs for the WST can be obtained, also showing an exponential relationship between ∆ K and ⍺ . The mathematical functions, which relate the relative crack length ⍺ to the stress intensity range ∆ K where then used in further calculations. In a final step, the crack propagation rate d a/ d N is plotted against the stress intensity ratio ∆ K . As shown in Fig. 4, the data points with an according smaller value of ∆ K don’t fit the linear relationship described by the Paris-Erdogan law (grey colour). This is due to the fact that in concrete, two stages of crack growth can be observed: deceleration and acceleration [18]. Concrete fatigue fracture in the acceleration stage follows the Paris- Erdogan law [3][10]. Therefore, in order to obtain a fitting curve with a reasonably high R 2 value (index of determination), only the data points in the acceleration stage are used while the grey data points were ignored. This method was used to determine the linear fitting curves for all tested stress ratios. D ISCUSSION OF RESULTS he data points and the linear fitting curves from the correlation of the 3PBT data are depicted in Fig. 5.a. The Paris’ law parameters m and C in Eq. 1, which were obtained from the fitting curves of the d a /d N – ∆ K plots are given in Tab. 1. The last column of this table shows the number of load cycles N tot from each test. For both the 10-80% and 10-90% stress ratio tests on the 3PBT samples, no results were found due to failure of the test specimen after only one or two load cycles. Figure 4 : (a) Paris-Erdogan data points on log-log graph, showing a very poor result for the linear fitting curve; (b) data points in acceleration phase, with a reasonably accurate linear fitting curve. From these results it can be concluded that the average value m avg is greater for the 10-75% stress ratio compared to the 10- 70% stress ratio. The difference is small however. This might be a consequence of the fact that the difference between 10- 70% and 10-75% the stress ratios is rather small ( R 10-70 = 0.1429 and R 10-75 = 0.1333). Despite the aforementioned it can be stated that when the value of ∆ K increases, the crack propagation rate of for the 10-75% stress ratio increases faster compared to the 10-70% stress ratio. Based on the values of C avg , no conclusions can be drawn. Similar to the results from the 3PBT correlation, the results from the correlation of the WST data are given in Fig. 5.b and Tab. 2. From the WST’s, no results were found for the 10-70% and 10-75% stress ratio. In the data from these tests, the crack length starts to decrease after approximately 40% of the total number of load cycles, resulting in negative values for d a /d N , which cannot be plotted in a log-log graph. Therefore, no useful fitting curves were obtained for the aforementioned stress ratios. As a result, a comparison between the 3PBT and the WST based on this data is rather difficult. y = 0,1734x - 1,5271 R² = 0,0007 -2,5 -2 -1,5 -1 -0,5 -0,15 -0,05 0,05 0,15 Crack propagation rate log(da/dN) [mm/cycle] Stress intensity factor log(∆K) [MPa.√m] y = 10,686x - 1,9034 R² = 0,9191 -2,5 -2 -1,5 -1 -0,5 -0,15 -0,05 0,05 0,15 Crack propagation rate log(da/dN) [mm/cycle] Stress intensity factor log(∆K) [MPa.√m] T