## 2 Materials and Methods
### Residual Stresses by X-ray Diffraction  
Residual stress is defined as the stress remaining in a solid material after an applied force or plastic deformation has taken place. UIT imposes a high plastic strain at the surface of the treated surface, which results in compressive residual stresses. X-ray diffraction (XRD) is a non-destructive method for analyzing the residual stress in a material and is the method of choice for this paper.  
Chemical etching of the surface was applied to remove suspected amorphous or oxide material layers, potentially caused by initial stress relaxation treatment. The effect of etching the surface and XRD quality of the scans is illustrated in Figure 5. Peak shapes become much clearer and better defined. It is also important to note that mechanical polishing or grinding will cause lattice strains to be formed at the surface and are not recommended for cleaning samples for residual stress measurements [74]. To conserve and reveal the surface stress layer, a chemical etchant--Kroll's Reagent--was used to remove small amounts of material from the top of the treated and untreated titanium specimens [75; 76]. The amount of material removed from the surface was measured to be on average \(\sim 8\) um.  
Figure 4: Orientation of line scans for surface roughness.  
It is suggested by [PERSON] et al. [40] that the surface porosity of DMLS manufactured parts poses difficulties for measuring residual stresses due to the presence of zero-stress porosity borders. Stress discontinuities on the surface result in lower residual stresses to be measured than in reality. Hence, cleaning the surface of the samples through etching would also help to reduce the effects of roughness and porosity that may negatively affect the XRD measurements.  
The XRD measurements were taken using a Malvern Panalytical Emperyean [77], shown in Figure 6b. The machines power was set to 40 kV with a current of 40 mA for a strong signal response--particularly at higher rocking angles. A half degree diffraction slit was used with a mask size of 2 mm and an anti-scatter slit of 2\({}^{\circ}\). The diffraction arm was a Branson Bragg attachment with a 0.04 mm slit. The incident arm was equipped with a 0.04 mm slit and a 9.1 mm opening.  
Figure 5: XRD Comparison between etching and without etching.  
Figure 6: XRD System. (**a**) Drawing of diffraction directions along the surface and at angles \(\phi\) and \(\psi\). Both \(\sigma_{1}\) and \(\sigma_{2}\) are perpendicular and reside in the plane of the specimen surface; (**b**) sample oriented at 0\({}^{\circ}\) on multi-purpose stage of Emperyean system.  
The analysis method for computing the stress tensor was the Winholtz-Cohen Least squares Analysis [78]. A total of 36 measurements per sample were used for the analysis, each representing a unique tilt and azimuth angles. The chosen x-ray elastic constants of the DMLS Ti-6 Al-4V specimens where \(2.355\times 10^{-5}\) MPa\({}^{-1}\) as the S\({}_{2}\) constant and \(-2.9877\times 10^{-6}\) MPa\({}^{-1}\) for the S\({}_{1}\) constant [65; 79]. These constants are the interplanar properties for the bulk alpha phase of the metal alloy. The X-ray wavelength was set to 1.519 A.  
The specimen coordinate system had the azimuth or phi (\(\phi\)) of value zero lined up with the horizontal direction (X) as illustrated by the cross seen in Figure 6a. The tilt angles or psi (\(\psi\)) is shown in Figure 6a where the 0\({}^{\circ}\) begins at 90\({}^{\circ}\) from the samples surface.