PSI - Issue 28

Bruno Atzori et al. / Procedia Structural Integrity 28 (2020) 1329–1339 Bruno Atzori et al/ Structural Integrity Procedia 00 (2019) 000–000

1336

8

decreases, although the effect of ductility was taken into account by means of the K p coefficient. Considering the significant difference observed in terms of number of cycles between the plain material and the geometry having the smallest notch radius (r n =0.1 mm, Table 2), it can be supposed that N 0n increases, as the notch tip decreases. This hypothesis was not experimentally verified yet, but fatigue tests will be carried in the next future. By assuming that the ∆σ 0n values are correct, the fatigue curves of notched specimens were calculated, by evaluating the number of cycles N 0n , listed in Table 2. Table 2. Experimental results plotted in Fig.4 reanalysed according to the nominal stress approach

K f K p ∆σ 0n � ∆σ 0 K f,p [MPa]

N 0n N 0

r n [mm]

K f (N 0 )

K tn

q

K f

N 0n [cycles]

2  [°]

 n (N 0 ) * [MPa]

K

R n =

f,p =

45

3

222.0

1.82

4.26

0.93

4.03

2.65

152.4

1.40∙10 6

8.9

1

208.2

1.94

7.39

0.82

6.24

4.11

98.2

12.5∙10 6

78.2

0.5

209.3

1.93

8.96

0.69

6.49

4.27

94.6

16.0∙10 6

100.3

45÷9 0

0.1

181.6

2.22

26.6

0.31

8.94

5.88

68.8

28.0∙10 6

175.0

135 3

222.0

1.82

3.41

0.93

3.24

2.13

189.6

0.40∙10 6

2.5

1

208.2

1.94

4.85

0.82

4.16

2.74

147.4

1.20∙10 6

7.4

0.5

209.3

1.93

6.10

0.69

4.52

2.97

136.0

2.00∙10 6

12.2

*Experimental results

3.2. Experimental results reanalyzed according to the point stress approach Fig. 5 shows the fatigue curve of plain and cracked material (Meneghetti et al (2016)). The latter was reanalyzed in term of  K as well as  n and one can see the significant difference between N 0 and N th , supporting the hypothesis that the number of cycles corresponding to the fatigue limit increases, as the notch tip radius decreases. Therefore, from Eq.(15) different critical distances can be calculated: x 0 = x � N th � = 1 2π � ΔK th Δσ 0 � 2 = 1 2π � 8.69 404 � 2 � m � = 0.074 [mm] (18) x � N 0 � = 1 2π � ΔK � N 0 � Δσ 0 � 2 = 1 2π � 28.8 404 � 2 � m � = 0.81 [mm] (19) The linear elastic stress fields, obtained by finite element analyses by imposing  net =1 MPa, are shown in Fig.6, where for completeness of information the blunt notches obtained by the 1 st batch of material are reported. Table 3 summarises the K t,point values (see Eq.(16)), relevant to the critical distances evaluated by Eq.(18) and Eq.(19). Fig.6 shows that for the critical distance x(N 0 ), the stress field of notched geometries is comparable to that of a crack having the length equal to the notch depth, while for x(N th ) the stress field is controlled by the geometry of the notch tip.