Issue 50

J.M. Vasco-Olmo et alii, Frattura ed Integrità Strutturale, 49 (2019) 658-666; DOI: 10.3221/IGF-ESIS.50.56 665 The constant in Eq. (2) does not have units, unlike the constants defined by Paris law, and a linear relationship between da / dN and the range of CTOD was also observed by Guo et al. [11], Tvergaard [20] and Pippan and Grosinger [32]. Those works, however, all used the total CTOD and they did not distinguish between the plastic and elastic CTOD components. A linear relationship between da / dN and ΔCTOD p has been reported by Antunes et al. [33] in work on 7050-T6 aluminium alloy that combined numerical modelling and experimental data in recently published work. They obtained da / dN data from experiments in middle-tension (MT) specimens for different stress ratios while the plastic CTOD data were numerically determined by using the methodology previously reported in [21]. They obtained the relationship da / dN = 0.5246 x ΔCTOD p . In contrast, in the experimental work presented here, da/dN data were obtained from measurements of crack length and number of cycles, with the CTOD data obtained from analysis of DIC measurements of the vertical displacement. To the knowledge of the present authors, this is the first time that plastic CTOD data, determined solely by experimentation, has been used to characterise fatigue crack growth rate at two different stress ratio values. Figure 9 : (a) Crack growth rate per cycle ( da / dN ) as a function of the range of total CTOD (ΔCTOD t ), elastic CTOD (ΔCTOD el ) and plastic CTOD (ΔCTOD p ) for the specimen tested at low stress ratio (R = 0.1). (b) Plot of da/dN versus ΔCTOD p for the two tests conducted at low ( R = 0.1) and high ( R = 0.6) stress ratio values. C ONCLUSIONS he plastic range of CTOD is clearly linked with the plastic deformation generated at the crack tip during fatigue crack propagation at constant amplitude. The range of plastic CTOD (ΔCTODp) has therefore been used to characterise and correlate fatigue crack growth data obtained at two different stress ratio values of 0.1 and 0.6. A linear relationship between da/dN and ΔCTODp, independent of stress ratio was, observed for a CP titanium alloy. The CTOD was measured from the relative vertical displacement between the crack flanks. A sensitivity analysis was performed to determine the optimum position behind the crack tip of the points where displacement was measured, and it was found that the CTOD value showed a significant dependence on their location in the plane of the crack. However, the influence of the vertical distance from the crack plane was not as restrictive, with a stable value of CTOD being obtained at a distance of 136.9 µm. This conclusion was reached using a methodology that analysed different displacement profiles plotted from the vertical displacement map. This work has demonstrated that CTOD represents a viable alternative technique to stress intensity factor in characterising fatigue crack growth rate since CTOD considers fatigue threshold and crack shielding in an intrinsic way [33]. However, further work is necessary to determine whether the linear relationship observed between da / dN and ΔCTOD p may be considered as an intrinsic material property, independent of the geometry and loading conditions. The plastic CTOD approach is, however, unlikely to shed light on the physical mechanisms underlying such phenomena as plasticity-induced crack tip shielding and a combination of approaches will be required to advance understanding, e.g. the use of plastic CTOD and the CJP model of crack tip fields. 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018 0 0.005 0.01 0.015 0.02 da/dN (mm/cycle) ΔCTOD (mm) total CTOD elastic CTOD plastic CTOD da/dN = 0.2706 ΔCTOD p R² = 0.9836 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018 0 0 .001 0.002 0.003 0.004 0.005 0.006 0.007 da/dN (mm/cycle) ΔCTOD p (mm) CT1 (R=0.6) CT2 (R=0.1) T (a) (b)