Issue34

S. Henkel et alii, Frattura ed Integrità Strutturale, 34 (2015) 466-475; DOI: 10.3221/IGF-ESIS.34.52 469 For a crack oriented 45° to the loading axes (Fig. 3a), there could also be a change in the crack opening mode if a phase shift in time between the cyclic loads of both axes is applied. For a proportional load with equal amplitudes in both axes, pure mode I exists. For a phase shift of 180° it is pure mode II. Phase shifts between 0° and 180° cause changing mode I and mode II ratios during every cycle. For a phase shift of 90° and tension-tension load, Fig. 3b shows the K I and K II development during one complete cycle. Fig. 3c shows schematically the von Mises stress distribution on the crack tip during this cycle calculated by FEA for a completely elastically calculated material behavior without a hardening rule. It was found that also the principle stress axes rotate locally on the crack tip while the principle stress axes in an unnotched cruciform specimen remains fixed also for phase shifted load cases. As there are LCF conditions within the plastic zone, non proportional hardening effects have to be taken into account. Itoh et al. [16] showed only a small effect of rotating principal stress axes on LCF lifetime for the Aluminum alloy 6061. The experiments were carried out on a servo-hydraulic planar biaxial testing system Instron with a maximal force of 250 kN. The geometry function for the stress intensity factor and the level of T-stress as a function of crack length and external loads were calculated by elastic FEA using the ABAQUS program. The crack lengths were determined using the indirect potential drop method with crack gages (range 20 mm) and a FRACTOMAT of the company Russenberger. In each case, one crack gage per crack end was used. The load was applied under force control with a frequency of 20 Hz with blockwise constant load or single overloads. For the notch in load direction (Fig. 2a), the fatigue load was applied by the force F Y (perpendicular to the crack) and F X (parallel to the crack) was varied between 0 and 40 kN as a non-cyclic static load. In this case, a load of 40 kN corresponds to a stress of  Y = 118 MPa in the center of the uncracked specimen. Without a load in X-direction, a negative (compressive) cyclic T-stress is resulting, which is shifted with additional stress in X-direction into positive region. A blockwise variation of the phase between the loading axes was applied at equal load amplitude (F Xa = F Ya = 6,16 kN, R = 0.5) and frequencies in both axes for the 45° notch. The starting notch for this case was perpendicular to the rolling direction. Figure 3 : a) Crack configuration 45° to the loading axes, b) elastically calculated crack tip parameters K I and K II on a 45° crack configuration and 90° phase shifted loading for positive R-ratio, c) change in shape of the von Mises stress distribution on this crack configuration (elastic FEA). a) b) c)