# Fatigue Crack Growth in Managing Steel Obtained by Selective Laser Melting
## 3 FCG Analysis Based on Plastic CTOD Range
### Numerical Results
In literature the crack closure level is usually quantified by \(\mathrm{R_{eff}}\), and values of 0.25, the maximum value obtained here for the highest crack length studied, are relatively low. This is explained by the relatively low plastic deformation obtained for this material. Values in the range of 0.2 to 0.3 are typical of plane strain state [25; 26; 27; 28; 29]. However, no crack closure was found for the SLM steel in the case of plane strain state. Figure 9 shows the plastic CTOD range, \(\mathrm{\delta_{p}}\), versus da/dN for different crack lengths and stress ratios. According to this figure, there is a progressive increase of FCGR with \(\mathrm{\delta_{p}}\), as could be expected. The increase of stress ratio, R, moves the curve up. This variation, which should not exist, is relatively small and can be explained by errors of \(\mathrm{\delta_{p}}\) and da/dN. In fact, in a previous work of the authors [21] it  
Figure 8: Crack closure level versus \(\mathrm{\Delta K}\) (18 Ni300; R = 0.05). Figure 7: Evolution of plastic CTOD range, \(\mathrm{\delta_{p}}\), with effective load range (R = 0.01). was shown that the da/dN-\(\delta_{\rm p}\) curves are invariant to the stress ratio. In other words, the approach based on plastic CTOD range is able to remove the effect of R observed when \(\Delta\)K is being used. This indicates that \(\delta_{\rm p}\) dictates fatigue crack growth. [PERSON] et al. [30] also observed independence relatively to stress ratio. In that study, \(\delta_{\rm p}\) was measured experimentally using Digital Image Correlation. A 2 nd-order polynomial was fitted to the results obtained for R = 0.05:  
\[\frac{\rm{da}}{\rm{dN}}\ =\ 95.987\times\delta_{\rm p}^{2}+1.052\times\delta_{ \rm p} \tag{7}\]  
where the units of da/dN and \(\delta_{\rm p}\) are \(\upmu\)m/cycle and \(\upmu\)m, respectively. The correlation coefficient is R\({}^{2}\) = 0.9842 and its validity is limited to \(\delta_{\rm p}\) in the range 0-0.8 \(\upmu\)m. Figure 9 also presents results for other materials. The material models for the 304L stainless steel and the 18 Ni300 steel were obtained using C(T) specimens, while the aluminum alloys were studied with M(T) specimens. For the same \(\delta_{\rm p}\), the fatigue crack growth rate is significantly higher for the laser sintered material (18 Ni300) than for the remaining materials. ASTM E647 standard defines the experimental procedure to obtain fatigue threshold, \(\Delta\)K\({}_{\rm th}\). The load range is gradually reduced until there is no crack propagation. In each loading step, some crack propagation is required to eliminate the influence of crack closure from previous load. The load range reduction can be done setting the stress ratio, R, or the maximum load. In the constant R load reduction method, the maximum and minimum loads are successively reduced such that the stress ratio (R = K\({}_{\rm min}\)/K\({}_{\rm max}\)) remains constant. However, the measured values of \(\Delta\)K\({}_{\rm th}\) are affected by stress ratio, being this effect linked to crack closure phenomenon. To overcome the effect of stress ratio, the constant K\({}_{\rm max}\) test procedure is proposed in the ASTM E647 standard. In this case, K\({}_{\rm min}\) is progressively increased in order to eliminate the effect of crack closure. The resulting effective threshold stress intensity, \(\Delta\)K\({}_{\rm th,eff}\) is often referred to as an intrinsic measurement of fatigue crack growth resistance. The experimental approach is however laborious and time consuming. Two alternatives to predict \(\Delta\)K\({}_{\rm th}\) were proposed here, based on the numerical analysis of plastic CTOD. In the first numerical approach, K\({}_{\rm max}\) was kept constant (= 23.4 MPa.m\({}^{0.5}\)), while K\({}_{\rm min}\) increased. Figure 10 presents the plastic CTOD range versus \(\Delta\)K. The decrease of \(\Delta\)K decreased \(\delta_{\rm p}\), as expected, and the extrapolation to the horizontal axis gave a threshold value \(\Delta\)K\({}_{\rm th}\) = 11.2 MPa.m\({}^{0.5}\).