PSI - Issue 17

Jürgen Bär et al. / Procedia Structural Integrity 17 (2019) 308–315 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

313

6

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.0 0.1 0.2 0.3 0.4 0.5

thermoelastic Effect

E-Mode from DFT

T diss

D-Mode from DFT

R = -1

stress

R = -1

stress

200

200

temperature change D T [K]

temperature change D T [K]

100

100

0

0

-0.5 -0.4 -0.3 -0.2 -0.1

stress [MPa]

stress [MPa]

-100

-100

-0.3 -0.2 -0.1

-200

-200

cycle 1

cycle 50

cycle 1

cycle 50

200.5

201.0

249.5

250.0

200.5

201.0

249.5

250.0

time [s]

time [s]

Fig. 5. Comparison of the results of the DFT with the values of the calculated thermoelastic effect and T diss for copper under fully reversed loading conditions.

In case of the aluminum alloy 7475 T761 the differences between the E-mode and the thermoelastic effect calculated with equation (1) are very small. The amplitudes are nearly the same, only a slight phase shift especially in the 50 th cycle is visible. The differences between the D-mode and T diss are more evident. While the D-mode shows a double frequency sine wave, T shows only one oscillation with the excitation frequency f L . In addition, the amplitudes of the D-mode are also significantly lower. In the first cycle the span differs only slightly whereas in the 50 th cycle the span of T meas is about twice that of the D-mode.

0.0 0.2 0.4 0.6 0.8 1.0 1.2

-500 -400 -300 -200 -100 0 100 200 300 400 500

-500 -400 -300 -200 -100 0 100 200 300 400 500

0.2

R = -1

R = -1

thermoelastic effect

E-Mode from DFT

T diss

D-Mode from DFT

stress

stress

0.1

temperature change D T [K]

-0.1 temperature change D T [K] 0.0

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2

stress [MPa]

stress [MPa]

cycle 1

cycle 1

cycle 50

cycle 50

-0.2

200.5

201.0

249.5

250.0

250.5

200.5

201.0

249.5

250.0

250.5

time [s]

time [s]

Fig. 6. Comparison of the results of the DFT with the values of the calculated thermoelastic effect and T diss for AA7475 T761 under fully reversed loading conditions.

4. Discussion

The investigations revealed distinct differences in the values for the temperature changes of the thermoelastic effect and caused by dissipative effects obtained from the two evaluation methods. These differences arise from the assumption in the DFT evaluation that both effects can be described as sine waves. When the specimen is loaded with a sinusoidal force that assumption is only correct for the thermoelastic effect (E-Mode). The measurements showed that this assumption is violated for the D-mode. In case of copper the wave form is not sinusoidal, and in case of AA7475 T761 T meas is a sine wave but with only the loading frequency and not with the double. Due to this differences