*3.1. Roughness Measurements*

Surface roughness measurements (*Ra*—the arithmetic average of the absolute values of the profile heights over the evaluation length, and *Rz*—the average value of the absolute values of the heights of five highest-profile peaks and the depths of five deepest valleys within the evaluation length) were performed with a Surtronic 3+ contact profilometer (Taylor Hobson Ltd, Leicester, UK). Before the LSP was applied, 10 individual surface roughness measurements were carried out, with five in the rolling direction and five in the transversal direction. The number of measurements after the LSP was doubled. The characteristic surface roughness was calculated as an average of the results from longitudinal and transversal measurements.

Before the LSP, the surface roughness was at a level of *Ra* = 0.2 μm and *Rz* = 1.2 μm. After the LSP, the surface roughness increased to *Ra* = 0.6–1.2 μm and *Rz* = 3.9–7.4 μm. The minimum values of roughness were measured on the specimen treated with the smallest laser spots and the lowest PD, while the maximum values were measured on the specimen treated with the largest laser spots and the highest PD.

To obtain an overview of the e ffects of laser PD and laser spot size on the surface integrity evaluated by roughness, hardness, and RS, a general factorial design was carried out. The laser parameters were examined using the ANOVA and the response surface methodology (RSM), where the influence of individual factor was considered to be statistically significant for *P* < 0.05. According to the statistical analysis (ANOVA), we found out that interactions of PD and SD also had a significant influence on surface roughness, RS, and hardness ( *P* < 0.0001). We tested several polynomial models on statistical characteristics (*F*-value (statistical characteristics used to test the significance of adding new model terms to those terms already in the model), *R*<sup>2</sup> (reports the strength of the relationship between the set of independent variables and the dependent variable)) to fit the response to the measured values. We found out, according to the *F*-values and the *R*<sup>2</sup> values, the most suitable model for surface roughness, hardness, and RS is a quadratic model. Therefore, according to the mentioned measurements at laser SDs of 1.5, 2.0, and 2.5 mm, the results are presented as contour plots.

As can be observed in the contour plots in Figures 5 and 6, laser PD had the main influence on surface roughness. Higher PD influenced higher surface roughness, at all the diameters of the laser spot. When processing hard materials, it is di fficult to detect a clear relation between LSP processing parameters and surface roughness due to moderate increases of *Ra* and *Rz*. At a PD of 900 cm<sup>−</sup>2, the minimum roughness values were obtained when using an SD of 1.9 mm. At a PD of 1600 cm<sup>−</sup>2, the minimum roughness values were obtained when using an SD of 1.7 mm. At a PD of 2500 cm<sup>−</sup>2, the minimum roughness values were obtained when using an SD of 1.5 mm. That happened partially at the expense of decreasing the overlapping of laser spots during the LSP. At the highest PD, we can reduce surface roughness by decreasing laser spot size. At a lower PD, the optimal laser SD was between 1.8 and 2.0 mm.

**Figure 5.** Roughness (*Ra*) as a function of laser SD and PD.

**Figure 6.** Roughness (*Rz*) as a function of laser SD and PD.

The ablative nature of a laser process, because of the absence of an absorbent coating, combined with mechanical effects of laser pulse pressure, leads to profile deepening.

Profile depth (Pt) is a kind of important information for planning additional process operations after LSP, like grinding and polishing. It shows us the height difference between the untreated and LSP-treated surfaces (inserted in Figure 7). We can find out that increasing PD influences the increase of profile depth and it is more distinct at a large diameter of a laser spot. Profile depth increases linearly in conjunction with increasing PD. The line is tilt more greatly in the case of bigger SDs. Especially the trend of Pt results is very unfavorable when applying LSP with a laser SD of 2.5 mm (Figure 7). The surface profile was lowered by almost 100 μm in the case of PD = 2500 cm<sup>−</sup>2.

**Figure 7.** Profile depth (Pt) as a function of laser PD and SD.

### *3.2. Residual Stress Measurements*

RSs were measured with a standard hole-drilling method. We used a milling cutter with a diameter of 1.6 mm. Deformation of the specimen caused during the drilling was measured with 06-062-UM strain gage rosettes, which were connected to the LabVIEW software. Blind holes in the surface layer were incrementally drilled to a depth of 1 mm with a 0.1 mm increment, where the drilling process was temporarily interrupted, enabling deformations resulting from material relaxation to fully occur and stabilize. The final RS profiles were calculated with the H-Drill software, where an integral method with automatic smoothing was applied.

In the base metal, after the heat treatment, RSs were low, ranging between −13 and 49 MPa. After the LSP, at di fferent process parameters, compressive RSs arose in the surface layer. The maximum compressive RSs were at the surface in a range between −1000 and −350 MPa. At depths between 0.5 and 1.0 mm, the transition from a compressive state to a tensile state occurred. Some typical RS distributions in depth are presented in Figure 8. According to the statistical analysis (ANOVA), we found out that the interactions of PD and SD have a significant influence on the RS ( *P* < 0.0001). We fitted the measured values with the quadratic model. Therefore, according to the mentioned measurements at laser SDs of 1.5, 2.0, and 2.5 mm and at laser PDs of 900, 1600, and 2500 cm<sup>−</sup>2, the results are presented as contour plots for the whole range of laser SD from 1.5 to 2.5 mm.

**Figure 8.** Residual stress distributions in depth for di fferent PDs (i.e., 900, 1600, and 2500 cm<sup>−</sup>2) and di fferent SDs (i.e., 1.5, 2.0, and 2.5 mm).

The plots of the average RSs at specified depths, shown in Figures 9 and 10, sugges<sup>t</sup> that the maximum compressive RSs were achieved with a 2.0 mm-diameter laser spot, both at the surface and at a depth of 1.0 mm. This could not be directly connected with the pulse power density (PPD) only, which is the highest with a 1.5 mm-diameter laser spot. The interaction between laser beam size and material a ffected the propagation nature of the shock waves. Smaller-diameter shock waves probably expand like spheres with a higher attenuation rate than larger-diameter shock waves, which behave like planar fronts [15,16,24,25]. This phenomenon, together with a higher overlapping rate between laser spots, may explain our findings. The RS profiles are almost the same for di fferent PDs at a depth of 1.0 mm. The shift from big compressive RSs at the surface towards tensile RSs at a depth of 1.0 mm

is between 400 and 600 MPa. In Figure 11, we can see a comparison of the RS profiles at the surface and at a depth of 1.0 mm for PD = 1600 cm<sup>−</sup>2.

**Figure 9.** Residual stresses at the surface as a function of laser SD and PD.

**Figure 10.** Residual stresses at a depth of 1.0 mm as a function of laser SD and PD.

**Figure 11.** Residual stresses at the surface and at a depth of 1.0 mm as a function of laser SD for PD = 1600 cm<sup>−</sup>2.
