PSI - Issue 28

D. Weiß et al. / Procedia Structural Integrity 28 (2020) 2335–2341 D. Weiß et al. / Structural Integrity Procedia 00 (2019) 000–000

2337

3

In order to answer these questions, it is first of all important to determine the fracture mechanical parameters (like e.g. the crack growth rate curve, the threshold against crack growth) of the base material. 2. Numerical preliminary investigations To determine the fracture mechanical parameters of the base material some preliminary investigations are necessary. According to the standard ASTM E 647 a Compact tension (CT) specimen can be used for the determination of fracture mechanical parameters. Since the sheet metal to be examined is only 1.5 mm thick, the Mini CT specimen is used as the initial specimen to prevent the specimen from bulging. The ratios of the relevant distances of this Mini-CT specimen result from the scaling of the standard CT specimen, which is also standardized in the ASTM E647. Wiedemeier (2011) proofed that the scaling of the dimensions has no influence on the crack propagation curve. Furthermore, Kloster et al. (2010) and Schramm (2014) used the Mini-CT specimen as well because of its geometric size in order to be able to take specimens from almost any position of the structure and thus characterize possible gradations and the local material properties. But even the Mini-CT specimen is with 2.5 mm, 1 mm thicker than the sheets used within the clinching process. That is why the development of a specimen with a special geometry is necessary. For the measurement of the crack length within a specimen during the experiment the frequently used direct current potential drop method is applied. With this method a constant electric current I is introduced into the specimen and the potential drop U is measured. The principle is that the ohmic resistance increases with crack growth because of the reduction of the cross section of the specimen. Due to the low sheet thickness standard drill holes for the solder pins used for the measurement of the potential drop with a diameter of 0.9 mm are too large for mounting on the side face. Furthermore, the solder pins would be concealed by the clamping forks when mounted on the front face. Therefore, the thighs are extended and the drill holes for the solder pins are positioned on the front face, see Fig. 2 a.

Fig. 2. (a) Comparison of the dimensions of the Mini-CT specimen (red dotted line) and the special specimen with extended thighs; (b) numerically determined geometry factor functions for the Mini-CT specimen and the special specimen.

To be able to determine a crack growth rate curve with this new specimen, it is necessary to know the cyclic stress intensity factor Δ K . The stress intensity factor is a measure for the magnitude of the stresses and the displacements in the vicinity of the crack. It depends, among other things, on the crack location, the geometry of the specimen and the type and location of load introduction. All these dependencies are considered in the geometry factor function, Richard and Sander (2012). To examine what kind of impact the change of the specimen’s geometry has on the geometry factor function, numerical investigations are executed with the crack growth simulation program F RANC 3 D TM . The comparison of the numerically determined geometry factor function of the CT-specimen which is in accordance with ASTM E 647 and of the special specimen (Fig. 2b) illustrates that the lengthening of the thighs doesn’t have a significant influence on the geometry factor function. Therefore, the numerically determined function (in blue color) will be used with the experimental investigations. For the measurement of the crack length during the experiment, a calibration curve which describes the relationship between the potential drop and the crack length is essential, Richard and Sander (2012). The calibration curve is