Issue34

P. Gallo et alii, Frattura ed Integrità Strutturale, 34 (2015) 180-189; DOI: 10.3221/IGF-ESIS.34.19 187 A synthesis in terms of linear elastic SED of room and high temperature data The new high temperature data from un-notched and notched specimens made of 40CrMoV13.9 are summarized in this section by using the SED approach. On the basis of the experimental evidences of the present work, the synthesis in terms of SED has been carried out up to 500°C considering the same critical radius used in Ref. [13] for multiaxial fatigue data of the same material. In fact, as visible from Figs. 5-a, 5-b, no reduction in the fatigue strength has been detected until 500°C both for un-notched and notched specimens. In the medium and high cycle fatigue regime the critical SED range for un-notched specimens can be simply evaluated by using the following expression: 2 w n c ΔW = Δσ 2E (1) In Eq. (5) Δσ n is the nominal stress range referred to the net sectional area. The weighing parameter c W has to be applied to take into account different values of the nominal load ratio [16]. Being the actual tests referred to R=0, c w is equal to 1.0. Since Eq. (1) is applied at different temperatures, the Young’s modulus has to be updated as a function of the temperature. E is equal to 206 GPa at room temperature and 135 GPa at 650°C. In the intermediate cases a linear trend has been assumed according with Latella et al. [17]. For a temperature of 360°C the Young’s modulus E results to be 165 GPa and at 500°C it is equal to 150 GPa. For the notched specimens Eq. (2) can be directly applied up to 500°C. For the specific case of 2 α =90° and R c /ρ=0.05, parameters F and H are equal to 0.7049 and 0.5627, respectively [18]. The stress concentration factor referred to the net area is equal to 3.84. n 2 2 t,n c w K Δσ R ΔW = c F(2α)×H(2α, )× ρ E (2) Here Δσ n is the stress range, K t,n is the theoretical stress concentration factor (both referred to the net sectional area), E is the Young’s modulus. F(2 α ) depends on the notch opening angle and is equal to 0.705 for 2 α =90°. Finally H depends both on the notch angle and the critical radius-notch tip radius ratio. By using Eqs. (1, 2) the new data from the tests carried out at room temperature up to 500°C can be summarized in Fig. 9-a in a single narrow scatterband, together with room temperature data from multiaxial tests on the same material [13], characterized by an inverse slope k equal to 5.00 and a scatter index T W equal to 1.96 that becomes 1.40 if reconverted in terms of stress range. Thanks to the SED approach it has been possible to summarize in a single scatterband all the fatigue data, independently of the specimen geometry, of the loading condition, and of the temperature up to 500°C. 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. (2). Figure 9 : Synthesis by means of local SED of new fatigue data, from room temperature to 500°C (a) and at 650°C (b). (a) (b)