## 3 Results  
### Results of Numerical Analyses  
The results of the displacement of a non-deformable wedge (\(\mathrm{E}\rightarrow\infty\)) on an elastic/visco-plastic substrate, which has the material characteristics of 41 Cr4 steel after normalization annealing, are presented. For this steel, a Cowper-Symonds non-linear material was selected, according to Equation (35), obtaining a model dependent on the equivalent plastic strain and the equivalent rate of plastic strain according to the power law. The value of the static friction coefficient was \(\mu_{\mathrm{s}}=0.1\), and the dynamic coefficient \(\mu_{\mathrm{d}}=0.05\). Wedge rounding radius \(\mathrm{r}_{\mathrm{d}}=25\)\(\left[\mathrm{\SIUnitSymbolMicro m}\right]\), wedge internal angle \(\beta=60\)\(\left[\mathrm{\SIUnitSymbolMicro e}\right]\), wedge depth \(\mathrm{a}_{\mathrm{p}}=25\)\(\left[\mathrm{\SIUnitSymbolMicro m}\right]\) and \(\mathrm{a}_{\mathrm{p}}=250\)\(\left[\mathrm{\SIUnitSymbolMicro m}\right]\), wedge travel distance \(\mathrm{s}=0.002\)\(\left[\mathrm{m}\right]\), simulation time t = 0.0002\(\left[\mathrm{s}\right]\). The displacement speed of the wedge is \(\mathrm{v}_{\mathrm{c}}=10\)\(\left[\mathrm{m}\cdot\mathrm{s}^{-1}\right]\). The facility was divided into 60.000 PLANE162 finite elements, which were compacted in the contact zone. This number is based on multiple sensitivity analyses for different workpiece materials. For 41 Cr4 steel and given values of \(\mathrm{a}_{\mathrm{p}}\) and \(\mathrm{s}\), this number is the optimal value. The shape factor \(\mathrm{WK}=1\) was assumed, resulting from the Authors' own simulation studies and those performed by other researchers [65; 68; 79]. The Cowper-Symonds model contains a critical strain value above which the element is removed (the so-called element removal method). The value of this parameter was determined and it equals \(\varepsilon_{\mathrm{f}}=1.7\). The wedge in the contact area was discretized using 18.000 finite elements. A regular hexagonal grid with regular fields was used in the simulations. In the material machined, the mesh was refined in the contact zone and in the surface layer (the element's size being 0.1 \(\times\) 0.1 \(\mathrm{\SIUnitSymbolMicro m}\)). The influence of the inclination of the wedge relative to the ground on the type of machining (micro-cutting or sliding burnishing) as well as on the occurring strains and stresses was examined. The range of the rake angle was \(\gamma=-7010\)\(\left[\mathrm{\SIUnitSymbolMicro e}\right]\) with a step of 5\(\left[\mathrm{\SIUnitSymbolMicro e}\right]\). Selected steps from the simulation are shown in the screenshots. Some drawings have a 5 \(\times\) 5 \(\left[\mathrm{\SIUnitSymbolMicro m}\right]\) grid in order to better illustrate the size of the flash or chip created. The scale in the drawings shows the values of Huber-Mises-Hencky (HMH) stresses and is expressed in [Pa] or HMH strains expressed in a dimensionless number [-]. For each wedge inclination angle, an exemplary displacement of the node along the Y axis located just below the layer processed, located exactly 1 \(\left[\mathrm{mm}\right]\) from the beginning of the sample, is also provided. Sixteen numerical simulations were performed for wedge depressions \(\mathrm{a}_{\mathrm{p}}=25\)\(\left[\mathrm{\SIUnitSymbolMicro m}\right]\) and \(\mathrm{a}_{\mathrm{p}}=250\)\(\left[\mathrm{\SIUnitSymbolMicro m}\right]\), for different rake angles \(\gamma\). In each simulation, the displacement along the Y axis of the same node, the number and location of which is shown in Figure 11, was analyzed. A summary of the simulation results is shown in Figure 12. From the graph, one may read the limit rake angles of the wedge for a given recess at which the sliding burnishing process takes place. For depth \(\mathrm{a_{p}}=25\;[\mathrm{\upmu m}]\) and rake angles \(\gamma_{\mathrm{gr}}<-43\;[^{\circ}]\), \(\mathrm{a_{p}}=250\;[\mathrm{\upmu m}]\) and \(\gamma_{\mathrm{gr}}<-50\;[^{\circ}]\), the surface is smoothed, while rake angles are greater for micro-cutting.