PSI - Issue 37

Jürgen Bär et al. / Procedia Structural Integrity 37 (2022) 336–343 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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quotients according to equation 2 temperature effects are eliminated and the crack initiation is easy detectable by separation of curves of the two quotients as it is visible in figure 7b. In this graph a small separation of the curves is visible after about 4,000 cycles and a clear separation takes place after 6,000 cycles indicating the initiation and propagation of a crack at the edge of this specimen. When a crack is propagating symmetrically as shown in figure 4a, no differences between the potentials measured on the front- and backside of the specimen can be observed. Consequently, the run of the potential quotients Q front and Q back are congruent (figure 8a). In this case there are only differences between the potential measured on the narrow side and the potentials on the front or back of the sample resulting in an increase of the two potential quotients as it is visible in figure 8a. The use of the increase of the potential quotients for crack detection has one major advantage compared to the increase of the relative potentials (figure 4c). The potentials can be influenced by temperature changes whereas this temperature induced potential changes are eliminated by dividing the potentials P front and P back by P narrow (equation 2) leading to a more reliable crack detection. In most cases a clear separation of the two runs of the quotients takes place. As it is visible in figure 8b for the specimen shown in figure 5a already a slight asymmetry in the crack front causes a clear separation of the run of the two potential quotients and, consequently, an easy and reliable detection of crack initiation is possible.

1.003

1.005

Q front Q back

Q front Q back

1.002

1.000 Potential quotient Q i 1.001

1.000 Potential quotient Q i

0.999

0.995

0

5,000

10,000

15,000

0

5,000

10,000

15,000

cycle number

cycle number

(a) (b) Fig. 8. Run of the potential quotients for a nearly perfect symmetrical crack front (a) (detail from figure 4c); and a slightly asymmetrical crack front (b) (detail from figure 5c). 4.2. Geometry of the crack front Beside the detection of crack initiation with the multiple potential drop measurements information about the geometry of long fatigue cracks can be obtained. As shown in figure 4 for a nearly perfect symmetrical crack front the run of both potentials P front and P back and hence the potential quotients Q front an Q back are identical. Even minor deviations in the crack length on the front- and backside of the specimen lead to a clear separation of the associated potentials and quotients. With the simple calculation of quotients, it is possible to assess the inclination of the crack front, but a quantification is currently not possible due to the non-linear relationship between potential and crack length (Johnson, 1965; Bär, 2020). Statements about the curvature of the crack front are even more difficult. The decisive problem here is the geometrically determined difference in the sensitivity of the potential probe on the front side compared to the potential probes on the two sample flat sides. In order to solve this problem, extensive experimental investigations and FEM calculations have to be undertaken. 5. Conclusions The investigations presented in this work clearly show that a multiple potential drop measurement enables easy and reliable determination of the time and place of crack initiation. Based on the results, the following conclusion can be drawn: