PSI - Issue 42

Mike Nahbein et al. / Procedia Structural Integrity 42 (2022) 433–440 Author name / Structural Integrity Procedia 00 (2019) 000–000

436 4

a

b

Fig. 1. Illustration of the geometrical model by Hartweg and Bär (2019) for the determination of the crack initiation site (a) uncracked specimen; (b) specimen with a crack near potential probe 2.

Because of the rotationally symmetrical problem, a cylindrical coordinate system is used for the mathematical description in the geometrical model. By using some calculations and transformations of this cylindrical in a cartesian coordinate system and back, the crack angle φ can be determined from the angle-coordinate of the normal vector, because these two angles are equivalent to each other. Furthermore, the radius-coordinate n r of the normal vector can be used for the calculation of the crack size as will be shown later. Finally, the z-coordinate of the normal vector maybe indicating a change of the temperature of the specimen. This last relation is at the actual point of time only a theoretical deliberation and must be validated in future experiments (see equation 2). �⃑ = � � � → → → (2) In figure 3a the fracture surface of a specimen with a secondary notch direct at the position of potential probe 1 at 0° is shown. As can be seen by the overload markers, the crack propagation started also at this position. Figure 3b shows the calculated crack angle as raw data and smoothed with a moving average (MA) over 500 data points in relation to the cycle number for the specimen in figure 3a. With the model of Hartweg and Bär (2019) the position of the crack can detect safely when the scatter of the calculated crack angle is decreasing significantly. For the shown specimen this is the case at about 56,000 cycles.