PSI - Issue 54

Jürgen Bär et al. / Procedia Structural Integrity 54 (2024) 188–195 Author name / Structural Integrity Procedia 00 (2019) 000–000

191

4

potential 1. As the number of cycles increases, the deviation between potential 1 on the one hand and potentials 2 and 3 on the other increases further and further.

a

b

3.5

2.0 P 1 P 2 P 3 relative Potential P i 2.5 3.0

1.014

1.012

1.004 relative Potential P i 1.006 1.008 1.010

1.002

1.000

0

50,000

100,000

Cycle Number

1.5

1.0

0

50,000

100,000

150,000

200,000

Cycle Number

Fig. 3. (a) Fracture surface of a specimen with crack initiation directly at the position of potential 1 (0°). The colored lines on the fracture service show the crack geometries marked by overloads; (b) Plot of the three potentials. The overload cycles are marked by dashed colored lines. The colors correspond to the marked overload lines on the crack surface. These differences in the potential curves clearly show that the results of the potential measurement depend on the location of the potential probe relative to the crack initiation site. Depending on the distance between potential probe and crack initiation site for the same crack size different potentials were measured. Thus, in round specimens, a measurement of the crack depth by means of a single potential measurement without knowledge of the incipient crack location is not possible. The only way to solve this problem is to calibrate the system afterwards, considering the geometrical conditions, i.e. the position of the incipient crack in relation to the position of the potential measurement. 3.2. Functions for crack depth measurement A simple way to overcome the problem of crack depth measurement on round specimens described above is to use an average value P mean calculated as arithmetic mean from the 3 relative potentials P 1 , P 2 and P 3 . For the calculation of the crack depth a from the mean Potential two different formulas were used: the well-known Johnson equation (Johnson 1965) and a formula suggested by Tiedemann (Tiedemann 2016). The Johnson formula (equation 1) is normally used for calculating the crack length in flat specimen and was adapted to round specimen in this work by simple modifications. � � � � � � ������� ����� � � �� �� � � ������ ���� ��������� � ����� ���� �� � � � � � � �� ��� � � � � � � �� � (2) In equation 2 the specimen diameter in the notch root is denoted as d , y 0 represents the half distance between the welding points of the wires for the potential measurement and a notch is the depth of the notch. In the simple equation suggested by Tiedemann (equation 3) the parameter q describes the inclination and the parameter r the curvature of the fitted curve. � � �� � � ���� � 1 � � � � ����� � (3)