Issue 41

M.V.C Sá et alii, Frattura ed Integrità Strutturale, 41 (2017) 90-97; DOI: 10.3221/IGF-ESIS.41.13

failure equal to 5 x 10 8 ) and the respective fatigue notch factor, K f , was evaluated considering the relationship between the endurance limits estimated for the specific specimen type.

Parameters of the S-N curve A b

Loading Conditions Push-Pull Torsional Push-Pull Torsional

Number of data

Endurance limit [MPa]

FatigueNotch Factor

Specimen type

9 17

775.80 1298.36 194.66 259.72

-0.131 -0.187 -0.133 -0.155

56 31 14 12

1 1

Plain

V-Notched 4.1 2.7 Table 2 : Synthesis of the experimental results generated under push-pull and torsion for plain and V-notched specimens 7 9

Number of Cycles to Failure

( a )/( b )

 Gross

 Gross

- N f

[MPa]

[MPa]

Experimental (L 

) (L  -

N f

)

(a)

(b)

(c)

(d)

(e)

(f)

11.0 11.0 13.0 13.0 16.0 16.0 19.0 19.0 16.0 16.0 16.0 18.4 18.4 25.6 25.6

22.0 22.0 26.0 26.0 32.0 32.0 38.0 38.0 20.0 20.0 20.0 23.0 23.0 32.0 32.0

5.84E+06 3.34E+06 3.28E+05 7.24E+05 2.32E+05 2.42E+05 3.19E+04 1.04E+05 5.74E+06 3.45E+06 4.39E+06 2.11E+06 1.76E+06 1.13E+05 9.91E+04

3.66E+05 3.66E+05 1.37E+05 1.37E+05 4.06E+04 4.06E+04 1.47E+04 1.47E+04 1.51E+05 1.51E+05 3.60E+05 3.60E+05 3.60E+05 1.90E+04 1.90E+04

4.28E+06 4.28E+06 1.27E+06 1.27E+06 2.82E+05 2.82E+05 7.90E+04 7.90E+04 1.74E+06 1.74E+06 5.22E+06 5.22E+06 5.22E+06 1.34E+05 1.34E+05

0.5

0.8

Table 3 : Loading conditions and test results for the multiaxial fatigue data generated from the V-notched specimens

Eqs. 3 and 4 below provide the L  – N f relations and were extracted using the methodology schematically shown in Fig. 2. Tab. 3 reports the loading conditions and experimental results generated for the multiaxial fatigue tests with the notched specimens. The experimental program considered two ratios between the normal and shear nominal stress amplitudes (column c, in Tab. 3), i.e, 0.5 and 0.8. Eight tests were conducted using the first ratio and seven for the latter one. The actual lives are reported in column d of Tab. 3. The estimated lives either considering eq. (3), L  – N f curve, or eq. (4), L  – N f relation, in association with the multiaxial model (eq. (1)) are presented in columns e and f, respectively. Graphically, the quality of the results of such estimates can be assessed by plotting the actual lives against the predicted ones, as shown in Fig. 5. In such graph, the continuous lines parallel to the one passing through the origin and the dashed lines represent bandwiths by factors of 2 and 4, respectively. One can see in Fig. 5 that when the L  – N f curve was used the estimated lives were excessively conservative. Note that 11 out of the 15 points plotted for this case were out of the factor of 4 bandwith, while the other 4 points fell between the factor of 2 and 4 lines. Although an improvement in the predictions was clearly obtained when the L  – N f relation was used, still 4 of the 15 points provided non-conservative life estimates by factors between 2 and 4.      0.00314 0.2041 f f L N N (3)      0.06359 0.1784 f f L N N (4) and L  – N f

95