Issue 37

H.A. Richard et alii, Frattura ed Integrità Strutturale, 37 (2016) 80-86; DOI: 10.3221/IGF-ESIS.37.11 81 mode I mode II mode III Figure 1 : Stress components and fracture modes Nevertheless, cracks in real structures often experience complex loading conditions, which are to a superposition of the three basic fracture modes. For plane crack problems in the case of 2D-mixed-mode the stress distribution can be described with the help of the near field solution and the polar coordinates r and φ (see Fig. 1) by the following equation as [1]:             II ij II I ij I ij 2 1 f K f K ,r       rπ (1) with i , j = x , y . The calculation of the stress distribution spatially crack problems loaded under 3D-mixed-mode is completed by a third term to:                III ij III II ij II I ij I ij 2 1 f K f K f K ,r         rπ (2) with i , j = x , y , z . K I , K II and K III are from Irwin established stress intensity factors. They are assigned to the basic fracture modes of a crack and defined by Eq. 3. The stress intensity factor depends on the stress ( σ y , τ xy or τ yz ), the crack length a and on the boundary correction factor ( Y I , Y II or Y III ). If the loading of a structure creates a non-symmetrical, singular stress field in the vicinity of the crack front, then the crack front deforms in a way that not only an opening, but also a planar and non- planar displacement of the two crack flanks can be found. Consequently, the stress field in the vicinity of the crack is superimposed by all of three stress intensity factors K I , K II and K III . I y I Y K     aπ  II xy II Y K     aπ  III yz III Y K     aπ  (3) U NSTABLE C RACK G ROWTH UNDER 2D- UND 3D-M IXED -M ODE - LOADING f enormous interest concerning the part dimensioning is the beginning of unstable crack growth, because the consequence often is a high material and immaterial damage. To predict unstable crack growth under 2D- and 3D-mixed-mode-loading many criteria exist, which compare the occurred stress or stress intensity factor with a critical stress σ C or the fracture toughness K IC . Some of them are listed below. O