Issue 41

M. Vormwald et alii, Frattura ed Integrità Strutturale, 41 (2017) 314-322; DOI: 10.3221/IGF-ESIS.41.42 321 should provide a  K eqv,eff  45 MPa  m for the case under consideration. It seems that the COD-based hypothesis, Eq. (5), currently is better able to uniquely describe fatigue crack growth under non-proportional mixed mode. Moreover, it provides a growth direction which the energy release rate based approach is currently still lacking. Figure 9: Force-Moment Diagram from the simulation (left) and from experiment (right) of R-031 (axial and torsional non- proportional mixed load), a=4 mm. C ONCLUSION his paper presented a consistent way to determine opening mode SIFs I, II and II from relative crack flank displacements that were measured using the 3D DIC technique. Use of a 3D technique is important because the 2D DIC technique is only applicable to plane problems where out-of-plane displacements are negligible in order not to jeopardize the in-plane measurements. Moreover, the use of 3D DIC allows the measurement of out-of-plane and consequently determinations of mode III crack openings and associated K III values. Calculations of mode III SIF values were useful to show that, in some cases, as for example in the present paper, they may be higher than the mode I and II SIFs and therefore influence the calculation of equivalent static SIFs and cyclic SIF ranges. This paper also presented a way to calculate equivalent SIF ranges for non-proportional loading problems using formulations already presented in literature for proportional loading. In addition, crack tangent directions were calculated from the angles where the maximum equivalent SIF range was found. Finally, it was shown that mix-mode I, II and III were present in four of the tested specimens, and that the ratio between SIFs II and I varied considerably during one cycle and from cycle to cycle for the non-proportional loaded specimens. A CKNOWLEDGEMENT he German Research Foundation (Deutsche Forschungsgemeinschaft) is greatly acknowledged by the authors for financial support under grant Vo729/13-1. R EFERENCES [1] Mróz, K.P., Mróz, Z., On crack evolution rules, Engineering Fracture Mechanics, 77 (2010) 1781-1807. [2] Zerres, P., Vormwald, M., Review of fatigue crack growth under non-proportional mixed-mode loading, International Journal of Fatigue, 58 (2014) 75–83. DOI: 10.1016/j.engfracmech.2010.02.008. [3] Schöllmann, M., Richard, H.A., Kullmer, G., Fulland, M., A new criterion for the prediction of crack development in multiaxially loaded structures, International Journal of Fracture, 117 (2002) 129-141. DOI: 10.1023/A:1020980311611. T T