Issue 35

G. Meneghetti et alii, Frattura ed Integrità Strutturale, 35 (2016) 172-181; DOI: 10.3221/IGF-ESIS.35.20 176 test according to Eq. (8a). By using Eq. (10), being typically f L =37 Hz, n max =1000, f acq =200Hz and 0< t s < 0.5/f L , it is obtained  10 -3 ; such a reduced error was considered acceptable from an engineering point of view. After having determined the distribution of the mean temperature T m (r,  ), the heat power dissipated by conduction was calculated by solving Eq. (6) numerically on the basis of a finite number of radial temperature profiles: in particular, 7 radial paths were considered emanating from the crack tip at different  angles (see Fig. 1), namely 0°, 45°, 90°, 135°, -45°,-90° and-135°. In the present paper, the radius R of the volume surrounding the crack tip was assumed equal to 3 · 10 -4 m. Even though such a radius may be on the order of the Neuber’s structural volume size of a construction steel, it has been assumed as a pure reference example in the present paper, in order to demonstrate the applicability of the proposed approach. 150 8 90 90° Machine grip Machine grip 46 Figure 2 : Specimens’ geometry (thickness 6 mm). F ATIGUE TEST RESULTS AND TEMPERATURE PROFILES CLOSE TO THE CRACK TIP hree specimens were tested and the relevant crack growth data are shown in Fig. 3. Linear elastic, two- dimensional, plane stress finite element analyses were performed to evaluate the Mode I stress intensity factor range,  K=K max -K min , for different crack lengths. To account for the machine grip effect, displacements were applied in the numerical model to the lines shown in Fig. 2. The Paris curve relating the crack growth rate to  K was evaluated and plotted in Fig. 3b. 0 5 10 15 20 25 30 35 40 45 0 50000 100000 150000 N, number of cycles a [mm] V_3 V_4 V_5 1.E-08 1.E-07 1.E-06 1.E-05 10 100  K [MPa m 0.5 ] da/dN [m/cycle] V_3 V_4 V_5 14.2 11 K 10 37.9 dN da     Figure 3 : Tension-compression a) crack propagation curves and b) Paris curve of AISI 304 L stainless steel specimens. The crack length and the temperature field at different  K values were measured at several times t=t s , regularly distributed during each fatigue test. As stated above, 1000 infrared images were acquired at each time t s and then processed according to Eq. (8a). Some typical radial temperature profiles evaluated at  =0° are shown in Fig. 4a and 4b, in the case of  K=26 MPa·m 0.5 (i.e. K max =13 MPa·m 0.5 ) and  K=60 MPa·m 0.5 (i.e. K max =30 MPa·m 0.5 ), respectively. In the former case a temperature drop equal to about 0.8 K within a distance of 2.5 mm from the crack tip can be observed; conversely, in the latter case, the temperature decreases much more, being the drop about 3 K. Therefore, the signal-to-noise ratio is T