Issue 41

M. Vormwald et alii, Frattura ed Integrità Strutturale, 41 (2017) 314-322; DOI: 10.3221/IGF-ESIS.41.42 317  K vmax that would occur during one cycle by searching which angle  0 , function of the instantaneous K i occurring during the cycle, would lead to the maximum  K v =  K vmax . First, Eqs. (1) for mode I, II and III SIFs were calculated for each pair of frames (captured images) of three data acquisition cycles (300 pairs of frames). The interval between blocks of the three cycle acquired data lasted a number of cycles (500 or 1000). For example, SIFs I, II and III calculated for specimen R-031 (subjected to non-proportional (90 o ) out-of-phase alternated axial-torsional load) are presented in Fig. 3. The plot shows that SIF are out-of-phase. If SIFs were in phase, Eqs. (2) and (3) could be applied straightforward using the  K imax ranges occurring in the cycle. For the out-of-phase plot of Fig. 3, the calculation of the equivalent range for the cycle using, for example, the Schöllmann et al. Eq. (3),  K vS3D , follows the herein outlined procedure. Terms P j and Q j are defined in Eq. (4) to simplify the representation of Eq. (3). The subscript j denotes each data acquisition instant inside one cycle, for example j = 1,2, …, 100 (corresponding to one full cycle) designating each triple of SIFs I, II and III to be determined along the cycle using Eqs. (1). In Eq. (4), the angle  k takes values from -60 o to +60 o in2 o steps in order to find the maximum  K vS3Dj . For the pair (P j , Q j ), depicted in the plot of Fig. 4, the square root of Eq. (4) is given by the vector PQ j , while for the pair (P j+n , Q j+n ) is given by the vector PQ j+n . Subtraction of these vectors gives the vector range  PQ and its algebraic addition to (P j – P j+n ) results in the equivalent range  K vS3Dj,j+n depicted in Eq. (5). The representative equivalent range for the cycle will result for the maximum value of  K vS3Dj,j+n found, after all values of  k had been investigated. After this search, not only the maximum range value is found,  K vS3D , but also the crack-path tangent direction  k =  0 where it happens. Figure 3: All mode SIF variations, ranges and applied loads as calculated from the COD method after 30,000 load cycles for a crack sizing 9.28 mm for specimen R-031 under (90 o ) out-of-phase alternated axial-torsional load                   2 2 3 2 3 (cos ) cos sin 2 2 2 2 (cos ) 2 vS Dj j j j k k Ij IIj k j k j IIIj K P P Q K K P Q K (4)                  2 2 3 , vS Dj j n j j n j j n j j n K P P P P Q Q (5) Figure 4: Calculation of the range of the square root term of Eqs. (3) and (4).