# Fatigue Crack Growth in Managing Steel Obtained by Selective Laser Melting
## 2 Fatigue Crack Growth Analysis Based on \(\Delta\)K
### Discussion  
In this Paris law regime, cyclic plastic deformation is the mechanism usually used to explain FCG. The model of striation formation by crack tip plastic blunting of Laird [9; 10] is widely accepted to generally describe the propagation mechanism of fatigue cracks in regime II of da/dN-AK curves. According to this model, plastic deformation at the crack tip is highly concentrated along the 45\({}^{\circ}\) direction, producing blunting and creation of a new fracture surface. Compression stresses at the crack tip reverse slipping, the fracture surfaces approach, but the new surface cannot be removed by re-connection of the atomic bonds, which is in accordance with the entropy law of thermodynamics.  
Figure 1: Geometry of C(T) specimen.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline R & Thickness, t [mm] & \(\mathbf{F_{min}}\) [N] & \(\mathbf{F_{max}}\) [N] & \(\mathbf{A}\) [mm] & \(\mathbf{\Delta}\)K [MPa.m\({}^{0.5}\)] \\ \hline
0.05 & 3 & 74.4 & 1488 & 7.1–27.3 & 8.1–58.1 \\
0.05 & 6 & 114 & 2284.2 & 7.2–26.6 & 7.6–47.8 \\
0.3 & 6 & 870 & 2900 & 7.1–24.0 & 7.1–27.6 \\
0.6 & 6 & 2850 & 4750 & 47.5 & 79.17 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Load parameters.  
The results for the SLM steel are very typical in terms of linearity and slope of the Paris law regime; therefore, it can be expected that FCG is controlled by cyclic plastic deformation at the crack tip. The analysis of fracture surface by Scanning Electronic Microscopy (SEM) showed that fatigue crack growth occurs mainly at the interfaces between layers of the SLM material. In some cases where the adhesion between the deposited layers is higher, the failure can occur through the grain itself, in transgranular mode. On the contrary, in many other cases, the failure occurs at the layer boundaries producing steps corresponding to the thickness of one or two grains. Please note that the layer plane is normal to the loading direction, which is expected to have a negative effect. In fact, [PERSON] and [PERSON] [11] showed that a layer plane parallel to the loading direction gives higher fatigue life. The weakness of the interfaces is responsible for a relatively tortuous crack path, and therefore for a relatively high fracture surface roughness.  
It is, therefore, questionable whether da/dN is linked to a brittle mechanism or to crack tip plastic deformation. [PERSON] et al. [12] studied FCG in WC-Co cemented carbides, which are brittle materials. They observed that da/dN strongly depends on the variation of K\({}_{\text{max}}\). A law was proposed for FCGR which was a function of K\({}_{\text{max}}\) and \(\Delta\)K (da/dN = C(\(\Delta\)K)\({}^{\text{m}}\)(K\({}_{\text{max}}\))\({}^{\text{n}}\)). The values of n were in the range 5-18, while the values of m were in the range 3-5. Intergranular crack growth is also observed in nickel base superalloys [13]. However, in this case the brittle crack growth is associated with oxidation of grain boundaries, which work as highways for the diffusion of oxygen. [PERSON] et al. [14] resorted to the progressive accumulation of tensile strains occurring near the crack tip to predict fatigue crack growth rate in RR1000 nickel base superalloy. They used vacuum in order to remove oxidation, so that viscoplastic deformation controls fatigue crack growth. Figure 3 presents da/dN versus K\({}_{\text{max}}\) for the SLM steel. The comparison with Figure 2a indicates that \(\Delta\)K is the driving force for FCG, instead of K\({}_{\text{max}}\). Therefore, cyclic plastic deformation is expected to be the controlling mechanism instead of a brittle mechanism as observed in cemented carbides and nickel base superalloys. For a better understanding of FCG mechanisms, an analysis based on crack tip plastic deformation was developed, as is described in the next section.  
Figure 2: (a) da/dN-\(\Delta\)K curves (18 Ni300 steel; t = 6 mm). (b) Effect of material on da/dN-\(\Delta\)K plots (R = 0.1; R = 0.05 for the 18 Ni300).