PSI - Issue 54

Jürgen Bär et al. / Procedia Structural Integrity 54 (2024) 188–195 Author name / Structural Integrity Procedia 00 (2019) 000–000 From the three relative potentials P 1 , P 2 and P 3 and the positions of the potential probes on the circumference of the specimen ( P 1 at 0°, P 2 at 120° and P 3 at 240°) the normal vector � can be calculated using equation 4, where d represents the specimen diameter in the notch root. The angle  ` gives the opposite angle of the crack initiation site in relation to the position of potential probe 1. The radius coordinate n will be used in the following to determine the crack depth a . The z-coordinate is independent of the measured potentials and therefore no additional information can be gathered from this value. � � � ` �� ⎝ ⎜ ⎜⎜⎛ �� √ � � ∙ ∙ � � � � � 2 ∙ � � � �� � � ∙ � � � � �� � ����� � √�∙�� � �� � � �� � �� � ��∙� � � � � 3 ∙ √ � � ∙ � � ⎟ ⎠ ⎟⎟⎞ (4) In figure 6a the radius coordinate n determined from the measurement of the specimen shown in figure 3 is plotted against the cycle number. Compared to the relative potential P mean the radius coordinate n shows a significantly wider range. In addition, compared to the relative potentials (figure 3b), the radius component does not show an increase at the beginning of the experiment (figure 6b). The change of temperature at the beginning of the experiment caused by dissipative effects leads to an equal increase of all 3 potentials and thus the radius coordinate remains unaffected. A first increase is visible after about 30,000 cycles indicating the formation of a crack which is also visible in figure 3a. At this point the crack has a depth of 0.48 mm, indicating that cracks can be determined very early using this method. 193 6

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Fig. 6. Plot of the radius component n against the cycle number of the specimen shown in figure 3. (a) Compared to the relative potentials the radius component shows a greater span; (b) no increase of the radius component due to temperature change of the specimen at the beginning of the experiment is visible. As shown in Figure 3, the relative potentials have a start value of 1 while the radius coordinate has a value of 0 at the beginning of the experiment (figure 6). Therefore, the equations of Johnson and Tiedemann have to be slightly modified to calculate the crack depth. In case of the Johnson equation P mean is replaced by (n+1) (equation 5). � � � � � ∙ ������� ����� � � ∙� ∙� � � ����������∙�������� � ����� ���∙ �� � � � ∙ � � ∙� �∙� � � � � � � �� � (5)