PSI - Issue 5

Ralf Urbanek et al. / Procedia Structural Integrity 5 (2017) 785–792 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

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3. Experimental Results

3.1. Stress amplitude calibration on unnotched specimen

The unnotched specimens were cyclically loaded with different constant stress amplitudes of 50, 100 and 150 MPa at loading frequencies of 5, 10 and 20 Hz, respectively. The stress was calculated using the values of K 0 with the values given in table 1. Due to the low yield strength the Cu specimen have been loaded with stress amplitudes of 50 and 75 MPa. For all experiments, the mean values and standard deviations of all pixels in a square box were determined. In figure 3a the stress determined with thermography and in figure 3b the deviation between applied and measured stress is plotted as a function of the loading frequency.

a

175

1.15

b

150

1.10

125

1.05

100

1.00

75

0.95

50

0.90

25

0.85

X5 - 50 MPa X5 - 100 MPa X5 - 150 MPa

Cu - 50 MPa Cu - 75 MPa

7075 - 50 MPa 7075 - 100 MPa 7075 - 150 MPa

X5 - 50 MPa X5 - 100 MPa X5 - 150 MPa

Cu - 50 MPa Cu - 75 MPa

7075 - 50 MPa 7075 - 100 MPa 7075 - 150 MPa

themograhic stress / loading stress [-]

thermographic stress amplitude [MPa]

0

0.80

5

10

15

20

5

10

15

20

loading frequency [Hz]

loading frequency [Hz]

Fig. 3.a) results of the stress measurement b) accordance between applied and measured stress.

The experiments show a linear dependence between the applied stress amplitude and the values measured by thermography. No considerable influence of the frequency is visible, thus the adiabatic conditions seem to be fulfilled for all frequencies. The results of Cu and the steel X5 specimen are 5-10% lower than expected. This can be attributed to the typical emissivity of a black coating of 0.9 to 0.95. The measured stress values of AA 7075 are in all cases 5% above the applied stress values. These deviations are probably caused by inaccurate literature values. Especially the heat capacity and the coefficient of thermal expansion are difficult to determine and deviating values are given in the literature. Moreover, the values may differ in due to different production processes or material conditions. Due to the mentioned reasons, the determination of the thermoelastic constant and the emissivity is very difficult. Therefore, a calibration with an unnotched specimen of the same material with an equal surface treatment stressed with defined loads is more appropriate than relying on the material properties itself. The slight decrease of the measured stress amplitudes in case of the high alloyed steel (X5) is still not understood, but for higher accuracy a frequency specific calibration of the K 0 is advisable. As mentioned above the loading signal is transferred from the control electronics to the camera and stored as a 14 bit signal with each recorded frame. In the dft the shift between the force and the temperature signal is determined resulting in the phase images. The temperature signal and therewith the computed stress should be in counter shift (180°) to the loading signal, when tension is attributed to a positive load due to equation 1 and 3. Figure 4a shows the phase shift between the force und the thermo-elastic response. The mean phase shift is measured within the square box mentioned in Figure 2a. The thermo-elastic stress shows for all materials and loading levels an unexpected shifting decreasing from 160° at 5 Hz linear to 100° at 20 Hz. The resulting delay raises from 20° at 5 Hz to 80° at 20 Hz. Dividing the delay by 360° and the loading frequency leads to the time shift. Figure 4b shows this time shift as a function of the loading frequency for the different stress amplitudes. The time shift is nearly constant with about 11 ms. The influence of the small decent for Cu and X5 is neglectable, because it only leads to 3.2. Calibration of phase shift via simple specimen