PSI - Issue 39

Deborah Weiß et al. / Procedia Structural Integrity 39 (2022) 139–147 Author name / Structural Integrity Procedia 00 (2019) 000–000

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The K-concept by Richard is an empirically developed criterion, Richard (1985) and Richard (1987). The equation for the determination of the kinking angle φ 0 according to the K -concept is as follows: 0 = ∓ � 140° | | | | + | | − 70° � | | | | + | | � 2 � (4) The MTS-criterion by Erdogan and Sih is based on the maximum of the tangential stress σ φ . It assumes that the crack grows perpendicular to the maximum tangential stress σ φ ,max . The formula below shows the calculation of the kinking angle φ 0 according to the MTS-criterion, Erdogan and Sih (1963). 0 = − arccos ⎣ ⎢ ⎢ ⎢ ⎢ ⎡ 3 � � 2 + � 1 + 8 � � 2 1 + 9 � � 2 ⎦ ⎥ ⎥ ⎥ ⎥ ⎤ (5) Both mentioned criteria depend on the stress intensity factors for Mode I and Mode II. The determination of the kinking angle φ 0 according to the K -concept and the MTS-criterion at specific K II /K I -ratios provide almost the same values. Since the K -concept is purely empirical in nature, it is appropriate to continue using the physically based MTS criterion in the following, because it can easily be adapted to other circumstances. 3. Experimental investigations and results In the recent years, several types of specimens have been developed for plane mixed-mode problems, Richard (1985) and Richard (1989). For example, the CTS specimen with a thickness of 10 mm combined with its loading device has proven its usability, Richard and Benitz (1983) and Richard (1984). Nevertheless, the undeformed sheet metal used within the clinching process has a thickness of only 1.5 mm. Thus, it has to be verified whether the existing test setup and criteria for predicting the kinking angle can be applied to these thin sheet metals. In this section, the experimental investigations and results of a modified CTS specimen adapted to the thin sheet metal are presented in detail.