*3.3. Residual Stress*

The residual stress measurement was made to obtain both stress components, *σ<sup>i</sup>* and *σii*, and Equation (2) was applied in order to calculate von Mises's stress value. The results obtained are presented in Figure 7.

**Figure 7.** Residual stress results for all the combinations.

First of all, results show that compressive (negative) stress values are present in all specimens, which may prevent crack growth in fatigue regimes, confirming that positive property. In addition, no positive value of stress is reported, which is caused by the shearing suffered during the previous machining process. Therefore, the burnishing totally counteracts the effect of the machining in terms of stress, having a value near the 550 MPa of von Mises stress.

Secondly, it is also reported that the tangential direction of stress measuring, *σ<sup>i</sup>* is higher than the axial direction of stress, *σii*. This can be explained due to the fact that the burnishing input force applied in a normal direction onto the surface (X-axis in a lathe) is way higher than the dragging force applied due to the feed of the tool (Z-axis in a lathe) during the burnishing operation and, therefore, causing more deformation that relates directly to the stress.

The increase in the residual stresses is directly associated with the amount of strain induced during the plastic deformation. Several investigations pointed out that the pressure exerted on the surface was the most important parameter to induce compressive residual stresses [34,35] by means of augmenting the amount of strain and the depth of affectation. Indeed, this plastic deformation is previously described as a combined effect of static force, the number of passes exerted, and the superimposition of the dynamic component of the force (VA). The process consists of inducing this plastic deformation (after surpassing the initial elastic deformation) through the rolling ball pressure onto the surface, axial and tangential to the generatrix of the shaft. The material flow and redistribution caused by shearing provoke an increment in the stress-strain field in the surface and subsurfaces. Next, the work hardening produced is caused by the dislocation movement and rearrangement of the inner crystals, known as dislocation density evolution, and concludes at grain refinement by means of dynamic recrystallization. When the rolling ball is no longer pressurizing, the remains of the stress are relaxed and converge to residual stress. In

terms of the number of passes, some investigations declared that the parameter is not significant enough [17]. However, as was seen with roughness results previously presented, burnishing force values used seem to be quite low to heavily deform the AISI 316L texture. Residual stresses are directly dependent on the plastic deformation degree and work hardening and increase when a higher number of passes is applied [36]. Regarding the VA, Teimouri et al. [37] state that VA enhances the plastic flow stress by means of dislocation drag and thermal activation, concluding that increasing the vibration amplitude results in further strain and strain rate because of a greater value of deformation radius (augmented by the increase in the kinetic energy) and impact velocity. Furthermore, the author points out that the increased ultrasonic energy density at further vibration amplitude contributes to the reduction of activation energy and subsequent flow stress. The recrystallization is also enhanced by the softening effect during the plastic deformation, thus enhancing the strain induced [37]. This affirmation correlates with the results obtained in terms of microstructure, where the VABB specimen showed a higher amount and greater effect of deformation mechanisms than the BB specimen. Therefore, the increase in plastic deformation caused by the VA is greater and favorable for the mechanical properties and surface integrity factors [23]. In general, residual stresses are defined as a complex distribution of mechanical, thermal, and metallurgical effects simultaneously that often actuate synergistically.

When analyzing the tendency of the von Mises calculated values, it is quite clear that the effect enhances the induction of higher negative values when the combination of a high number of passes and the activation of vibration assistance is applied. The force, in this case, seems to be less significant than the other input parameters, but it has the desired effect as it increases. The best combinations are 120-5-40, 160-3-40, and 120-3-40, demonstrating that also the VABB enhances more than BB. The mean effects and the interaction plots of the model, taking the Residual stresses of both components measured and the von Mises stress as the output, are presented in Figure 8.

**Figure 8.** ANOVA results taking the: (**a**) Axial; (**b**) Tangential; (**c**) von Mises; residual stress as the output value.

The results of the tangential direction (see Figure 8b), corresponding to *σi*, determine that the number of passes, burnishing force, and the addition of the vibration assistance, in that order, are significant. When the number of passes increases, the value of the residual stress increases, and the same is applied to the vibration assistance. In the case of the force, it is appreciated that the best point is 120 N instead of 160 N. This happens due to the best combination reported is 120-5-40 and is especially higher than the rest, so the mean of the 120 N force group is higher than 160 N. However, looking at the evolution of both groups, if the design of experiments considered higher levels of force (160 N or more) with a high number of passes and vibration assistance, the expected result may be higher than the 120-5-40. The results of the Axial direction (see Figure 8a), corresponding to *σii*, determine that the number of passes, the interaction of the burnishing force plus and the number of passes, and the interaction of the burnishing force plus and the number of passes, in that order, are the most important parameters but being not significant enough. All *p*-values reported are higher than 0.05. This concludes that no parameter used has a special effect on the second direction and other input parameters. This could be explained by the fact that burnishing deformation is mainly performed in the normal direction to the surface, while the forces in the perpendicular direction to the surface are lower and then provokes less deformation. This effect was also observed by Chomienne et al. [17], who observed that plastic deformation is not that intensive in both directions during a single revolution. In the circumferential direction, the work material is always deformed in the same direction, whereas in the axial direction, the work material is deformed in two different directions. Von Mises stress values (see Figure 8c) are almost completely influenced by the first component of the stress *σi*, so both plots' graph results are essentially the same, changing a bit the *p*-values rates but not the grade of significance.

In terms of residual stresses, it is reported an increase in the von Mises residual stress at the surface by increasing the burnishing force and the number of passes, also applying VABB instead of BB to enhance them, which is estimated in an 11.5% increase. These results are within the scope because increasing the burnishing force causes a larger plastic deformation and is boosted by the vibration amplitude of the assistance. The number of passes has been reported as another very influential parameter to enhance the residual stresses within a burnishing process [38]. In conclusion, the combination 120-5-40 is the best to maximize the compressive residual stresses, either tangential or axial to the specimen, thus the equivalent von Mises stress.
