13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- the structure. For static loading the occurrence of unstable crack growth can be predicted using the material function KC(ϕ). At first it is assumed that the crack is not able to grow resulting in a stress function without point of contact with the material function ΔKth(ϕ). Subsequently the cyclic load will be increased until the corresponding stress function has a contact with the material function. At this point the crack is able to grow. Furthermore the point of contact defines the kinking angle ϕTSSRB due to the loading situation and the material gradation. 3.2.1 Mode I loading in a graded material As a special case of a Mixed Mode loading at first a pure Mode I situation is considered. In Fig. 9a a single Mode I (ΔKII = 0) is considered leading to the reduced stress function Δσϕ√(2πr), see Eq. (9), derived from Eq. (5). 2 cos Δ 2 K Δσ π 3 I ϕ ϕ = r (9) The point of contact can be found at the polar coordinate ϕM = 30° resulting in the kinking angle ϕTSSRB = ϕM = 30°. First experimental investigations considering the same loading condition and the same gradation angle ϕM confirm this theoretical concept (Fig. 9b). In spite of pure Mode I the crack kinks due to the material gradation. For the further crack propagation the kinked crack evokes a Mixed Mode loading situation. a) b) Figure 9. a) Point of contact for the determination of occurrence and direction of fatigue crack growth for a Mode I loaded crack, b) experimental confirmation of the TSSRB-concept 3.2.2 Mixed Mode loading in a graded material The TSSRB-concept can also be used for a Mixed Mode loading situation. Thereby the Mixed Mode ratio V, see Eq. (10), defines the combination of the pure loading cases Mode I and Mode II. Fig. 10 shows the stress functions Δσϕ√(2πr) (Eq. 11) for a Mixed Mode ratio V = 0,23, see also Eq. (5). II I II K K K V + = . (10)
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