Issue 43

F. Berto et alii, Frattura ed Integrità Strutturale, 43 (2018) 1-32; DOI: 10.3221/IGF-ESIS.43.01 18 0.1 1 10 1.E+04 1.E+05 1.E+06 1.E+07 Number of cycles to failure, N SED range [MJ/m 3 ] Multiaxial data, R=-1, Room temp. Plain sp, R=0, Room temp. Plain sp, R=0, T=360°C V-notched sp., R=0, Room temp. V-notched sp., R=0, T=360° V-notched sp., R=0, T=500°C T  W =1.96 k=5.0 SED range (2x10 6 , P.s. 50%)=1.50 MJ/m  Figure 23: Synthesis by means of local SED of new fatigue data up to 500°C and multiaxial fatigue data. By using Eq. (3) and Eq. (13) the new data from tests carried out at room temperature up to 500°C can be summarized in a single narrow scatterband characterized by an inverse slope k equal to 4.6 and a scatter index T ΔW , related to the two curves with probabilities of survival P S = 10% and 90%, equal to 2.1 (see Fig. 22). By converting the data from multiaxial tests on the same material carried out at R =-1, in terms of SED range and by considering c w =0.5 a single scatterband has obtained, as shown in Fig. 23. Dealing with data carried out at 650°C, the fatigue strength of un-notched and notched specimens has been found strongly lower than the corresponding data from tests carried out at T <500°C. For this specific temperature ( T =650°), which is important in practical industrial applications in particular for hot rolling of aluminum alloys, an empirical formula has been proposed for notched specimens by modifying Eq. (3). This allows us to take into account the notch sensitivity of this material at temperatures higher than 500°C [123]:          2 2 , 0 ( ) ( / ) (2 ) (2 , ) t n n c w K R W c Q T L f f F H E (14) Q (T) is the notch sensitivity function at a specific temperature T. This function has to be set (as a function of the temperature T) by equating at high cycle fatigue (10 6 cycles) the SED value from plain specimens and those from notched specimens. f is the test frequency of notched specimens at high temperature and f 0 the test frequency of unnotched specimens at the same temperature. L is a function related to the sensitivity of the material to the load frequency and depends on the ratio f/f 0 . Function L is required to be equal to 1.0 if f=f 0 , which is a condition respected in the actual tests. The critical radius R 0 is kept constant and equal to that obtained at room temperature (R c =0.05 mm). Dealing with our specific case Q (T=650°C)= 0.18. Eq. (6) can then be re-written by substituting the numerical value of each function [123]:            2 2 2 2 , , 1.0 0.18 1.0 0.7049 0.5627 0.07139 t n n t n n K K W E E (15) For the considered geometry K t,n =3.84. By considering Eq. (15) applied to notched specimens and Eq. (13) applied to plain specimens, the SED master curve for 40CrMoV13.9 at 650°C has been obtained. The fatigue data from tests at 650°C are plotted in terms of averaged strain energy density range over a control volume in Fig. 24, considering the aforementioned critical radius derived from room temperature tests. It is possible to observe that the scatter band is narrow, being the scatter index T w = 2.6, which is equal to 1.61 when reconverted to an equivalent local stress range. The inverse slope of the scatterband is equal to 1.51. Thanks to the SED approach it is possible to summarize in a single scatterband all the fatigue data at the same temperature, independent of the specimen geometry. Future developments will be devoted to set the proposed empirical equation to other geometries and