PSI - Issue 19

Jan Papuga et al. / Procedia Structural Integrity 19 (2019) 405–414 Author name / Structural Integrity Procedia 00 (2019) 000–000

409

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Parameters A and B can be derived from L CD defined at N FL cycles and critical distance L CD,S related to a static problem similar with Eq. (8) but using stress intensity factor  K Ic and tensile strength S u : ��,� = � � � � �� �� �� � � � (10) where the   S is linked with the mentioned tensile strength S u corrected for the used stress ratio R . The value of the critical distance is assumed to lower while increasing the number of cycles till failure. Even Susmel and Taylor (2007) admit this way of L CD definition need not be the adequate solution due to the number of issues that may arise. The alternative way to define the critical distance is the critical distance calibration using the S-N curves of the material and of one notched component. For a given number of cycles, the stress relevant to the fatigue strength of the notched component is applied to its FE-model. The distance is looked for in the FE model along the critical cross-section, at which local stress reaches the fatigue strength of the material S-N curve. In that way, the complete description of the critical distance dependency on the number of cycles can be set. 3. FAD experiments The experimental data evaluated here are derived from tests performed on 2124-T851 aluminum alloy within the FADOFF project, Papuga et al. (2014). Its material data are summarized in Tab. 2, and the fatigue experiments on unnotched specimens are available in Fig. 2, left. The crack growth data were not measured within the FADOFF experimental campaign, so the information from Logsdon and Liaw (1986) had to be used. Only typical (quite broad) ranges of  K th values at R =0.1 and R =0.5 are provided there. The formula provided by Kunz (2005): �� ( ) = (1 − ) � �� ( = 0) (11) was used first to tune the exponent r from values at both stress ratios, and then to extrapolate to the value at R= -1 necessary in this paper. Quite varying resulting minimum and maximum values of  K th shown in Tab. 2 were obtained. The values of K Ic provided in Tab. 2 were retrieved directly from Logsdon and Liaw (1986). All specimens were manufactured from a single plate of 38.1 mm thickness delivered from Alcoa. Experiments were force-controlled with R =-1 using Amsler resonant testing machine of 100 kN capacity. The series on notched specimens was originally proposed having very similar K t factors of approximately 2.0 and the bi-notch configuration was defined and manufactured a bit later, but from the same plate.

Table 2. Material data of 2124-T851 aluminum alloy in axial loading

Static

Crack growth at R= -1

Push-pull  w · N = C

Plane bending  w · N = C

 K th [MPa·m 0.5 ]

 K Ic [MPa·m 0.5 ]

S y [MPa]

S u [MPa]

w [-]

C [-]

w [-]

C [-]

Min 1.31

Max 8.54

min 26.6

max 38.4

439.8

477.1

5.553

6.48·10 17

4.575

5.98·10 15

Table 3. Summary of experimental data of 2124-T851 aluminum alloy tested in fully reversed push-pull.

Major diameter Minor diameter

Notch root radius

S-N curve parameters  w · N = C

Notch type

w [-]

C [-]

s logN [-]

D [mm]

d [mm]

N max [-]

N min [-]

 [mm]

U-notch

20 20 20 28

16.5 17.7

1.6 0.4 1.6

8.935 4.742 5.857 7.533 3.799

5.73·10 23 6.32·10 14 1.74·10 17 6.78·10 20 6.07·10 12

0.267 18871 6792444 0.068 43303 1810458 0.178 27167 3861340 0.268 44749 1448277

Fillet

V-notch

23.4

16 20 18

Hole

2

Bi-notch (U-notch + hole)

5 (U-notch), 2 (hole)

0.121 27121

544395