PSI - Issue 42

Jürgen Bär et al. / Procedia Structural Integrity 42 (2022) 1061–1068 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 2. Results of the DFT analysis according to equation 2. The E-Mode represents the thermoelastic effect coupled with the loading frequency and the D-Mode the dissipative effects coupled with twice the loading frequency.

The DFT dissection of the temperature signal delivers images with only qualitatively correct information. Due to the problems mentioned above a dissection into thermoelastic and dissipative temperature changes by frequency is more than questionable. It can be assumed that the E-mode image also reflects temperature changes from dissipative effects and the D-Mode parts due to the thermoelastic effect. In addition, a basic assumption of the evaluation is that all effects can be described as a single sinusoidal functions. This assumption is correct for the thermoelastic part of an excitation with a sinusoidal load, but it is not correct for the dissipative part, as the above cited works have shown. Therefore, the D-Mode amplitude and phase images are only an indication for dissipative effects, but do not allow any quantitative statements about the magnitude of the temperature changes and their temporal occurrence. 3.2. Position-Time Diagram To overcome the above discussed problems a new method was developed to investigate the temperature changes in the vicinity of a crack. Therefore, measurements with a loading frequency of 5 Hz and a camera frequency of 1000 Hz were undertaken. Since the acquisition frequency is an integer multiple of the load frequency, the thermography images are always acquired at the same time within a loading cycle. To minimize noise, the temperature values of the individual pixels in the images were reduced by averaging over several loading cycles. To visualize the temperature changes within a cycle in the vicinity of the crack, the temperature in the ligament, were plotted as a function of time within the cycle in figure 3. The ligament is defined as a horizontal line with the width of three pixels through the position of the crack tip, whereby the temperature values of the pixels with the same x-coordinate are averaged. In the PT-diagram in figure 3 the crack propagation direction is from the right to the left; the position of the crack tip is displayed as a vertical black line at the position 351px. The corresponding force-time diagram is shown on the right-hand side. Under tension loading (cycle time 0.25) a decrease of the temperature due to the thermoelastic effect near the crack tip can be observed. This effect leads to a temperature increase at the crack tip under compression loading (cycle time 0.75).