PSI - Issue 13

Katharina Dibblee et al. / Procedia Structural Integrity 13 (2018) 322–327 Katharina Dibblee et al./ Structural Integrity Procedia 00 (2018) 000 – 000

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1. Introduction

Functionally graded materials are increasingly used in lightweight structures because they offer a decisive advantage over homogeneous materials and the use of hybrid construction methods. By using different manufacturing processes, different local material properties can be specifically set using only one material in a structure or component, see Fig. 1 (a). This allows the material properties to be optimally adapted to the expected stresses and at the same time reduces the costs for subsequent recycling. With functionally graded materials, it is possible to distinguish between two basic grading types. Elastic grading characterizes a change in all elastic properties. These concern local changes such as the modulus of elasticity E and the transverse contraction coefficient ν . The material grading pursued in this article shows a change in the fracture mechanical material properties as shown in Fig. 1 (b). These include the limits of fatigue crack propagation, the threshold Δ K I,th as well as crack toughness K C and crack propagation rate da / dN . The material area called M2 shows more favourable fracture mechanical material properties compared with area M1. The crack propagation behaviour in homogeneous structures depends on the stress intensity prevailing at the crack front. There are three basic crack loading types with which it is possible to describe any spatial crack propagation processes. With regard to fracture mechanically graded materials however, the locally different material properties must also be taken into account in crack prediction. Already known and established fracture mechanical concepts for 2- or 3-dimensional crack problems (MTS-criterion; σ 1 '-criterion) were developed for homogeneous, isotropic structures but cannot be used for crack propagation prediction in graded materials. Therefore new fracture criteria have to be developed. Taking into account a plane mixed-mode loading, it is already possible to predict the crack propagation behaviour in fracture-mechanically graded structures.

Fig. 1. Fracture mechanic material grading in any structure: (a) possible different material ranges, (b) Range dependent fracture mechanical material properties

This article deals with crack growth simulations in 3-dimensional fracture-mechanically graded. Therefore, a new 3D concept was developed to describe the crack propagation behaviour in any spatial structures, taking into account an existing material grading. 2. New 3D-Concept for fracture mechanically graded materials The influence of fracture mechanical material grading on crack propagation behaviour has already been confirmed in various experimental studies, Schramm et al. (2016). In addition, the influence of such grading only becomes apparent when the crack front has reached the material grading. This new concept is based on the σ 1 '-criterion, Schöllmann et al. (2002), and follows the approach of the 2-dimensional TSSR-concept, Schramm et al. (2014), for fracture mechanically graded materials. Under the condition that the crack propagates depending on the maximal principle stress σ 1 ' prevailing, a corresponding maximal principle stress function is determined and compared with the locally available material function. The first contact front of these two functions then provides a statement about the expected crack kinking angle. This concept is applied as soon as the crack front of the crack grows from a homogeneous material property area M1 into the material grading transition to material property area M2, see Fig. 2 (a).