Issue 50

J.M. Vasco-Olmo et alii, Frattura ed Integrità Strutturale, 49 (2019) 658-666; DOI: 10.3221/IGF-ESIS.50.56 664 E with the same slope than that obtained for the elastic regime in the loading half cycle. As is the case for the loading half cycle, there is a change in the linearity during further unloading due to the reversed plastic deformation. The elastic and plastic ranges of CTOD during the loading half cycle were therefore obtained from Fig. 6a as 13 μm and 6 μm, respectively and the corresponding values for the unloading half cycle were 13.2 μm and 5.8 μm, respectively. The plastic CTOD is hence 31.6% (loading) and 30.5% (unloading) of the maximum CTOD. The region between points A and B in Figs. 6a and 7a is associated with crack opening and closing and additional work could be done to estimate the opening and closing loads; however, any additional information gained on the subjects of crack closure and crack tip shielding is both complex in interpretation of its true effects, and is not germane to the present study. Similar procedure can be extrapolated in the case of the specimen tested at R = 0.6 but with the difference that the loading range is between 450 N and 750 N. The elastic and plastic ranges of CTOD were 8.7 μm and 2.9 μm, respectively. It is clear the difference between these values and those obtained for R = 0.1. However, these values are coherent since the loading range for the test at high ratio is a 44% of that corresponding to the low ratio. Another important difference respect the CTOD plot at low R -ratio is that the region between A and B point was not identified. This is not surprising since at R = 0.6 any crack shielding effect was not expected. The methodology described above to obtain the CTOD range for the elastic and plastic components was applied to data recorded during crack growth for the tests conducted at the stress ratios of R = 0.1 and 0.6. Fig. 8a shows the elastic and plastic CTOD data as a function of crack length. Significant scatter is observed in the elastic CTOD values, being those at R = 0.6 about a half of those values at R = 0.1; while those representing the plastic CTOD show a more consistent increment with increase in crack length. Plastic CTOD demonstrates a faster rate of increase at R = 0.1 than at R = 0.6. However, normalising the elastic and plastic ranges of CTOD values by the total range of CTOD gives a much more uniform picture at the two stress ratio values (Fig. 8b) and the data for the elastic CTOD now shows more consistent behaviour. The trends in the CTOD curves in Fig. 8b appear sensible since, as the crack is propagating, the plastic deformation is increasing and, with it, the plastic CTOD, whilst the value of the elastic CTOD undergoes a corresponding decrease as a percentage of the total CTOD. Figure 8 : (a) Elastic and plastic CTOD ranges as a function of the crack length for both tests. (b) Elastic and plastic CTOD ranges as a percentage of the total CTOD range as a function of crack length. Fig. 9a presents data for da / dN as a function of the ranges of CTOD t , CTOD el and CTOD p for the specimen tested at R = 0.1. It is clear that only the plastic component of CTOD shows a consistent increase with crack growth rate and could therefore be used to characterise fatigue crack growth rate. Fig. 9b shows the da / dN versus ΔCTOD p curves obtained at both R = 0.1 and 0.6 that demonstrate a very good correlation of fatigue crack growth rate into a single linear relationship. It should be noted that this correlation is obtained without employing logarithmic scales as is necessary when using the Paris law. The crack growth rate is then given by linear regression as: 0.2706 p da CTOD dN    (2) 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 3 4 5 6 7 8 9 10 ΔCTOD (mm) crack length (mm) elastic [CT1 (R=0.6)] elastic [CT2 (R=0.1)] plastic [CT1 (R=0.6)] plastic [CT2 (R=0.1)] 0 20 40 60 80 100 120 3 4 5 6 7 8 9 10 ΔCTOD percentage (%) crack length (mm) elastic [CT1 (R=0.6)] elastic [CT3 (R=0.1)] plastic [CT1 (R=0.6)] plastic [CT3 (R=0.1)] (a) (b)