PSI - Issue 39

3

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

141

= · √ · · = · √ · · = · √ · ·

(1)

(2)

(3) In practice, mixed-mode loading crack problems appear, for example, when a structure is subjected to superimposed stresses, which is usually the case with a clinch joint. In this paper a plane mixed-mode loading condition is examined, which corresponds to a superposition of Mode I and Mode II, see Fig. 1.

Fig. 1. Basic fracture modes and principal orientation of the fracture surfaces according to Richard and Sander (2016).

The right column of Fig. 1 presents the principle orientation of the fracture surfaces for Mode I and Mode II. Mode I results in a straight crack propagation, whereas Mode II leads to a kinking angle φ 0 of 70°. A superposition of a Mode I and Mode II load leads to a mixed-mode situation and a kinking angle φ 0 between 0 and 70°. There exist many different concepts to predict the kinking angle under plane mixed-mode loading, for example: • the criterion by Sih, Sih (1974), • the criterion by Erdogan and Sih, Erdogan and Sih (1963), • the criterion by Nuismer, Nuismer (1975),

• the criterion by Amestoy et al., Amestoy et al. (1980) and • the criterion by Richard, Richard (1985) and Richard (1987).

These criteria as well as the predicted kinking angles as a function of the mixed-mode ratio are discussed and illustrated graphically in detail in Richard (1985). In addition, a comparison was made with experimental results. As a result, it can be emphasized that the experimental results could be described very well with the K -concept by Richard and the MTS-criterion by Erdogan and Sih which is why they are considered in this paper.