13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- [ ] ( ) ( ) ( ) 2 1 III ij III II ij II I ij I ij ϕ ϕ ϕ π σ f K f K f K r ⋅ + ⋅ ⋅ + ⋅ ⋅ = (1) 2 III 2 II 2 I I V 4 5,336 2 1 2 K K K K K ⋅ + ⋅ = + ⋅ + (2) In this regard the fatigue crack growth then is governed by the cyclic stress intensity factors ∆KI, ∆KII and ∆KIII respectively the cyclic comparative stress intensity factor ∆KV, which can be derived from Eq. 2: 2 III 2 II 2 I I V 4 5,336 2 1 2 K K K K K + ⋅ ∆ + ⋅∆ + ⋅∆ ∆ ∆ = (3) The K-concept for spatial Mixed-Mode-loading is based on the fact that unstable crack growth occurs, if the comparative stress intensity factor KV reaches the fracture toughness value KIC for Mode I. In case of fatigue crack growth the crack is propagable, if the cyclic comparative stress intensity factor ∆KV for spatial Mixed-Mode-loading reaches or exceeds the threshold value ∆Kth. Both contexts can be illustrated clearly in a KI-KII-KIII-diagram, Fig. 2. Unstable crack growth will occur, if a local loading condition along the crack front reaches a point on the fracture limit surface. Fatigue crack growth or stable crack growth develops, if points characterizing the local crack front loading conditions are lying between the threshold and the fracture limit surfaces. KII KIC KI fracture limit surface KIC KIII KIC threshold value surface ∆KII,th ∆KI,th ∆KIII,th ∆KI,th ∆KI,th ∆KI,th Figure 2. Fatigue crack growth limits at spatial Mixed-Mode-loading Precisely because the fracture mechanical treatment of such three dimensional Mixed-Mode-loaded cracks is very complicated compared to pure Mode I-loaded cracks, the prediction of the above mentioned 3D-fracture-process is not yet well understood. In addition there is a shortage of experimental investigations and findings regarding general spatial Mixed-Mode-fracture in order to compare the correlation between the experimental results and
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