Issue 48

A.C. de Oliveria Miranda et alii, Frattura ed Integrità Strutturale, 48 (2019) 611-629; DOI: 10.3221/IGF-ESIS.48.59 627 stress intensity ranges, and if da/dN = F(  K, R,  K th , K C ,...) is the crack growth rule of the material, then the crack increment in this i -th 1/2 cycle (obtained e.g. from the output of a sequential rainflow counter) is given by   max 1 2 ( ( , , ), ( , ), , ,...) i i i i a i th C a F K a f R K K           (42)   max 1 2 ( ( , , ), ( , ), , ,...) i i i i c i th C c F K a f R K K           (43) The crack growth history is then calculated by the simultaneous solution of  a i and  c i . As the crack increments  a i and  c i depend on both semi-axes a i and c i , the coupled 2D growth is well characterized. Contrary to the  K rms method, which as any statistics loses sequence effects, the cycle-by-cycle method can deal with load order effects, as long as appropriate crack retardation (or acceleration) models are introduced in Eqs. (42-43), see [10] for details. Comparison between Experimental and Numerical Results Figs. 15 and 16 compare experimental data and numerical predictions for the FCG behavior of the 4340 alloy steel specimens S10 and S11, respectively. Experimental data points plotted in these figures are listed in Tabs. 1 and 2, while the numerical results are represented as continuous lines. The numerical simulations are obtained by the cycle-by-cycle fatigue life prediction method outlined above, considering the load applied on each specimen using the proposed corner crack transition equations, the actual da/dN  K curve measured for the material as well as its other properties, and the specific geometry of the specimens. The initial values of c adopted in these simulations are equal to the measured ones in the beginning of the transition phase, for a fair comparison neglecting possible previous accumulated errors in the 2D FCG predictions, since only the 2D/1D transition equations are evaluated here. Moreover, since all load decrease steps are very small during the tests, no FCG retardation models are needed in these simulations either. Figure 15 : Measured and numerically predicted values for the crack lengths c and c’ at the front and the back face surfaces for the 4340 steel specimen S10, as a function of the number of cycles N since the beginning of the 2D/1D transition phase. Figure 16 : Measured and numerically predicted values for the crack lengths c and c’ at the front and the back face surfaces for 4340 steel specimen S11, as a function of the number of cycles N since the beginning of the transition phase. The S11 4340 steel specimen is tested until failure, which happened 453,594 cycles after the beginning of the 2D/1D transition. The simulated front and back face crack sizes after such applied cycles are c   16.0 mm and c’  14.40 mm, respectively a difference of 1.23% and 10.0% with respect to the experimental results, see Fig. 16. For the S10 specimen, the final simulated front and back face crack sizes are c  12.71 mm and c’  8,06 mm, respectively a difference of 12.41% and 38.0% with respect to the experimental results, see Fig. 15.