## 2 Materials and Methods
### Crack Growth Curve Determination Procedure  
The value representing the crack propagation threshold, which determines whether a crack formed under cyclic loading will continue to propagate until final fracture, is called the threshold stress intensity factor range, and can be calculated according to the expression  
\[\Delta K_{th}=K_{max}-K_{min}=\Delta\sigma Y\sqrt{\pi a_{0}}, \tag{1}\]  
where \(K_{\text{max}}\) and \(K_{\text{min}}\) are maximal and minimal stress intensity factors, respectively, \(Y\) is a dimensionless constant that depends on geometry and mode of loading, \(a_{0}\) is the initial crack length, and  
\[\Delta\sigma=\sigma_{max}-\sigma_{min}=2\sigma_{a}. \tag{2}\]  
In Expression (2), \(\sigma_{\text{max}}\) and \(\sigma_{\text{min}}\) are the maximal and minimal stress, respectively, and \(\sigma_{\text{a}}\) is the stress amplitude. If the value of \(\Delta K\) exceeds \(\Delta K_{\text{th}}\), crack propagation will begin. Experimental determination of \(\Delta K_{\text{th}}\) involves measuring crack growth rate per cycle \(\text{d}a/\text{d}N\) as a function of \(\Delta K\), typically plotted in logarithmic coordinates as shown on schematic plot in Figure 4.  
Crack propagation is initially accelerated, which is visible in region I, and then it transitions into a phase of stable growth (region II) and finally enters the phase of critical crack propagation leading to accelerated fracture (region III). The initial value of region I corresponds to the threshold stress intensity factor range \(\Delta K_{\text{th}}\). The critical value of the stress intensity factor range \(\Delta K_{c}\), at which final fracture occurs (\(\text{d}a/\text{d}N\rightarrow\infty\)), represents the critical value calculated according to Equation (3):  
\[\Delta K_{c}=K_{c}-K_{min}=\Delta\sigma Y\sqrt{\pi a_{c}}, \tag{3}\]  
Figure 3: Cylindrical test specimen dimensions. where \(K_{\rm c}\) is the critical value of the stress intensity factor, known as fracture toughness. This value represents one of the most important constants in fracture mechanics. From the above relation, the critical crack length \(a_{\rm c}\) at the moment of fracture can be calculated for a known fracture toughness, and vice versa. In region II, the crack growth rate increases linearly and can be described by the equation  
\[\frac{da}{dN}=C\Delta K^{m}, \tag{4}\]  
which, in logarithmic coordinates, represents a straight line with a slope coefficient \(m\). This relationship is known as [PERSON] law, in which \(C\) and \(m\) are material constants determined experimentally. This is the law most used in engineering practice to determine the remaining service life of machine and structural elements, based on the measured crack length or the allowable crack length for the predicted service life. By integrating Paris' law, the service life until fracture can be expressed in terms of the number of cycles to failure, as described in the standard fracture mechanics literature [19; 20; 21; 22]. The stress intensity factor threshold values and the crack growth curve was determined experimentally for the Ti-6 Al-7 Nb alloy produced by both production processes. The devices used for this experiment were Rumul Cracktronic (Russenberger Prufmaschinen AG, Neuhausen am Rheinfall, Switzerland), a resonant testing machine for dynamic bending load applications with testing frequences range from 40 to 300 Hz, and Rumul Fractomat, a crack length measuring device for tests in fatigue and fracture mechanics, which enable monitoring of the crack growth. For this type of testing, rectangular test specimens described above were used. Crack growth was monitored on one side of the specimen where the measuring tape was positioned as presented in Figure 5.  
Using the Rumul Cracktronic device, the range of stress intensity factors (\(\Delta K\)) for dynamic loading of the test specimen was defined. This range was software-controlled via the bending moment range (\(\Delta M\)) and the mean bending moment (\(M_{\rm m}\)).