PSI - Issue 77

L.M. Sauer et al. / Procedia Structural Integrity 77 (2026) 34–40 Author name / Structural Integrity Procedia 00 (2026) 000–000

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Fig. 4 . Electrical resistance R S , total mean strain ε m,t , length of the electrical resistance measurement L DCPD , diameter d and resistivity ρ versus the number of cycles N .

For the compensation of geometrical influences on the electrical resistance R S , the electrical resistivity ρ was calculated according to Eq. 1 through the diameter d and the length of the electrical resistance measurement L DCPD . The combined measurement of strain and electrical resistance through the edges of the extensometer enables the calculation of the length of the electrical resistance measurement L DCPD from the measured total mean strain ε m,t . Since length and diameter changes were considered, the electrical resistivity ρ is independent of the geometrical changes. In contrast to the electrical resistance R S , the electrical resistivity ρ remains approx. constant for the first 75% of the lifetime. Therefore, it can be assumed, that the decrease of the electrical resistance R S is caused by geometrical changes. After 75% of the lifetime the electrical resistivity shows an increase that indicates microstructural changes. The influence of temperature on the electrical resistance was compensated by using the Matthiesen law, which divided the electrical resistivity in a temperature-dependent and a temperature-independent part (Matthiesen 1865). Since the temperature-independent electrical resistivity depends on the microstructure, it was used for the following analysis. For temperatures near the room temperature ( T R = 20 °C), the temperature-independent part was calculated through a linear relation according to Eq. 2 , with the specimen temperature T S , the linear temperature coefficient α , the reference temperature T 0, and the electrical resistivity at the reference temperature ρ 0 . The specimen temperature T S was measured through the thermocouples. Since the temperature changes during fatigue were comparably low, the calculated temperature independent electrical resistivity ρ D does not show a significant difference from the electrical resistivity ρ , see Fig. 5 .

Fig. 5 . Measured temperature T and calculated electrical resistivity and temperature independent electrical resistivity versus the number of cycles N .