13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Cracks under Mixed Mode loading: Questions and solutions for isotropic and graded materials Hans. A. Richard1, Britta Schramm1,*, Alexander Eberlein1, Gunter Kullmer1 1 Institute of Applied Mechanics, University of Paderborn, 33098 Paderborn, Germany * Corresponding author: schramm@fam.upb.de Abstract In reality cracks often initiate and grow due to mixed mode loading. This paper deals with questions about stable and unstable crack growth and the crack growth direction under multi-axial loading conditions. For homogeneous materials many criteria and experimental confirmations exist. This paper shows a selection of these solutions and some experimental investigations. In practice innovative manufacturing and application-oriented products considering lightweight construction gain increasingly in importance. In this context structures with graded material properties are produced. However there does not exist many concepts for these graded materials. Within this paper fracture and fatigue criteria and experimental findings are presented. In particular the TSSRB-concept is used for the determination of crack growth in fracture mechanical graded materials. Keywords Mixed Mode, fracture criteria, isotropic materials, graded materials, TSSR-concept 1. Introduction If the two basic fracture modes (Mode I and Mode II) temporarily or permanently occur in combination, as indicated in Fig. 1, local plane Mixed Mode loading conditions at cracks can be observed. Figure 1. Mixed Mode loaded crack in a welded structure For a fail-safe dimensioning it is important to know among other things if such a crack is able to grow, how fast and whereto does the crack grow and when unstable crack growth occurs. Answers can be found using crack propagation concepts which will be briefly described in the following chapter. An extensive description can be found in [1, 2]. 2. Crack growth in isotropic and homogeneous materials An isotropic and homogeneous structure is defined by fracture mechanical and elastic material properties which are independent of place and direction, i.e. they are the same for the whole structure. With regard to the subsequent consideration of fracture criteria for graded materials and their complexity only 2D-concepts will be regarded within this paper. 2.1. Concepts for two-dimensional Mixed Mode crack growth In the following two theoretical concepts are presented which enable the determination of unstable crack growth. Information about further crack propagation concepts for 2D and 3D Mixed Mode situations can be found in [1-5].
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