Issue 41

M. Vormwald et alii, Frattura ed Integrità Strutturale, 41 (2017) 314-322; DOI: 10.3221/IGF-ESIS.41.42 316                                                                                1 2 2 1 2 2 2 2 sin( ). cos ( ) sin( ). cos ( ) 2(1 ) 2 2 1 2 2 2 1 2 2 2 sin( ). cos ( ) sin( ). cos ( ) 2(1 ) 2 2 1 2 2 2 1 2 4(1 ) I A A A B B B I II A A A B B B II III A III E COD r r K E COD r r K E COD r K                   1 ' ' ' ' ' ' sin( ) sin( ) 2 2 2 2 A B B I A B II A B III A B r COD V V COD U U COD W W (1) Figure 2 : Displacements at points A, B located on the crack-flank and near to the crack tip. One advantage of using the SIF related COD formulation is the possibility of determining elastic equivalent SIFs when crack plasticity and blunting affect near field displacement or strain measurements occurring at points very close to and in front of the crack-tip. CODs are lesser influenced by particular point measurements, once they correspond to integrated displacement values of points located over the crack flanks between the measuring point (A or B) and the crack tip. The total COD measurement in such cases corresponds to an elastic component COD e plus a plastic component COD p resulting in a total SIF* or K*, [13]. The K* value therefore results from an elastic SIF e or K e plus a plastic equivalent SIF p or K p . Of course, any relation between the total K* value with near crack tip stress or strain values must be understood as an equivalent linear crack tip elastic stress or strain value. C ALCULATION OF E QUIVALENT SIF S USING DIC or a number of 2D or 3D cracked body problems, the prediction of monotonic static fracture or the prediction of crack growth by the equivalent or comparison static stress intensity factor, K v , or by the equivalent fatigue crack growth SIF range,  K v , can be made by a number of different formulations, as for example those proposed by references [1-6, 9]. The present paper addresses  K v calculations using K v equations initially developed by Erdogan and Sih [9] for opening modes I and II and by Schöllmann et al. [3] for opening modes I, II and III and the Richard et al. [4-6] concept that SIF ranges  K i can be used in place of K i to determine equivalent ranges  K v in fatigue crack growth evaluations, as given by Eqs. (2) and (3).               2 0 0 0 3 cos cos sin 2 2 2 vES I II K K K (2)                               2 2 2 2 0 0 0 3 0 0 1 3 3 cos cos sin cos sin 4 2 2 2 2 2 2 vS D I II I II III K K K K K K (3) The use of Eqs. (2) and (3) is valid if the mixed-mode ratios do not change inside a specific loading cycle. When SIF ratios change inside one cycle, the  0 angle also changes during the cycle. Therefore, it is needed to find a maximum range value F