PSI - Issue 39

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

140

2

1. Introduction Nowadays, complex manufactured structures are part of our everyday life. Sheets of different materials and thicknesses are joined to form these complex structures, Liebig (1991) and Geoffrey (2012). Particularly in the automotive industry, multi-material design is used to produce lightweight car bodies and thus to comply with political regulations on the reduction of harmful emissions, Friedrich (2017) and EC-European Commission (2019). One of the most common methods in industry for joining different and coated materials is clinching due to its simplicity as well as cost and weight reduction. Clinching needs no consumables or pre-drilled holes and is executed in a one-step process. The main area of application is sheet metals with a maximum total thickness of 4 mm, Eshtayeh et al. (2015) and Dietrich (2018). Furthermore, for component design mechanical parameters (e.g. static strength R m and fatigue strength σ D ) are required. At the same time, fracture mechanical parameters are necessary to design components from a fracture mechanical point of view and to evaluate cracked components with respect to crack propagation and the achievable crack growth lifetime, Richard and Sander (2016). The focus of this paper lies on the last two mentioned points – crack propagation and the achievable crack growth lifetime. Within a structure cracks may have already occurred during the joining process (e.g. clinching) or may develop as a result of operational stress and corrosion. Consequently, these cracks can propagate due to cyclic loading and finally lead to structural failure, Richard and Sander (2016). For the prevention of these damage cases knowledge about the fatigue crack growth behavior in clinched structures is essential. For this purpose, fundamental tests have to be carried out first to identify the fracture mechanically behavior of the base material. Thus, the fracture mechanical material parameters (e.g. the threshold against crack growth Δ K I,th and the fracture toughness K IC ) have already been determined using modified Mini-CT specimens, Weiß et al. (2020) and Weiß et al. (2021). Furthermore, it has to be verified whether existing concepts can be used for thin sheet metals of merely 1.5 mm used in the clinching process. Therefore, the mixed-mode behavior in the thin structures is investigated and it is examined whether the concepts that apply to standard specimens can also be used for thin structures or whether these criteria need to be adapted. This paper is explicitly about experimental investigations of the crack propagation behavior with focus on the crack propagation direction to answer the question “In which direction does a crack grow under mixed-mode loading?”. 2. Fracture mechanical fundamentals To answer the question about the direction of crack propagation, fracture mechanical fundamentals are essential. First of all, there exist three basic fracture modes, which consider the following different loading types of a crack, Richard and Sander (2016): • Mode I involves all normal stresses which cause an opening of the crack, • Mode II applies for all plane shear stresses that cause an opposite sliding of the crack surfaces and • Mode III corresponds to a non-plane stress state which causes an opposite sliding of the crack. Each fracture mode is related to a corresponding stress intensity factor K . This factor describes the intensity of the singular stress field and is simultaneously a measure of the magnitude of the displacements in the crack area. The stress intensity factors depend among other things on external loads of the component as well as on the length, depth and position of the crack. They describe the intensity, but not the distribution of stresses and displacements near the crack, Richard and Sander (2016) and Gross and Seelig (2018). Local mixed-mode loading situations at cracks can be observed when the three basic fracture modes occur in combination due to either the external loading or the orientation of the crack. This implies that the loading of the structure generates an asymmetric, singular stress field near the crack front. In this case, the crack distorts in such a manner that not only the two crack surfaces open, but also displace planar or non-planar. As a result, the stress field in the vicinity of the crack front is influenced not only by the stress intensity factor K I , but also by K II and/or K III , Richard et al. (2004). These stress intensity factors of the different crack loading modes can be described by the following equations: