PSI - Issue 5

M. Dabiri et al. / Procedia Structural Integrity 5 (2017) 385–392 M. Dabir et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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3. Experiments

3.1. Specimens

Round specimens with circumferential grooves were prepared for testing, and the same geometry was used in the numerical modelling. Semi-circular notches with a radius of 0.5 mm or 1.5 mm were introduced to the specimens. The geometry and dimensions are shown in Fig. 1.

Fig. 1. Configurations of the notched specimens (dimensions in mm).

3.2. Specimens

Two load cases were applied in the experiments and all tests were performed at room temperature. The maximum load was selected to keep the net stress less than the value of general yielding (less than 0. 8 σ' y ). Tests were conducted in the fully reversed (zero mean stress) load-controlled mode at a frequency of approximately 0.5 Hz until the total rupture of the specimens. The experimental values of applied loads, net stresses, cross-section measurements and total cycles to failure are shown in Table 2.

Table 2. Load cases and nominal applied values Load case ID Target force amplitude (kN)

Notch radius (mm)

Average force amplitude (kN)

Target net diameter (mm)

Net diameter (mm)

Nominal stress (MPa)

Cycles to failure

N1 N8 N3 N4 N5 N6 N9

11.08 11.01 20.95 20.98 10.06 10.14 19.93 19.97

4.92 5.01 6.78 6.79 4.99 5.01 6.94 6.95

583 558 581 579 514 515 527 526

19042 29718 8715 9440 41402 47923 26698 29750

1.5

11

5

1

0.5

21

7

1.5

10

5

2

0.5

20

7

N11

4. Analytical Approximations

4.1. Linear, Neuber and SED rules

The simplest model to calculate the strain value at a notch is a linear rule that assumes an equal value for the strain concentration factor K ε (local strain, ε , over nominal strain, e ) and the elastic stress concentration factor, K t . The loads on notched parts are often sufficiently high that the local stress is considerably greater than the yield strength. In such cases, K t can no longer be used to relate the notch stress to the nominal stress. In addition, stresses are no longer proportional to strains. Neuber (Neuber, 1961) derived the following equation for grooved shafts experiencing shear loading K ε K σ =K t 2 (1)