*3.3. Apparent Shear Strength*

outliers.

The distribution of shear strength by groups is presented in Figure 9. There was a significant decrease in adhesion strength for the PL group (*p* < 0.05). Shear strength in group AB90 was significantly higher than in group AB50 (*p* < 0.05) and insignificant higher than in group AB125. Groups AB50, AB125, and MC did not differ significantly. In plasma-electrolyte groups the shear strength of PZ2 was significantly higher than in PZ1 and PZ3. Ra and shear strength results in groups are presented in Table 2.

**Figure 9.** Shear strength distribution by groups, where are shown: the median (red line), the lower and upper quartiles (blue lines), and the minimum and maximum values (black lines) that are not

(**m**) (**n**) (**o**)

(**p**) (**q**) (**r**)

**Figure 8.** SEM images of the surface for various processing methods: (**a**–**c**)—surface after polishing (PL group); (**d**–**f**)—surface after milling (MC group); (**g**–**i**)—surface after sandblasting with an abrasive size of 50 μm (AB50 group); (**j**–**l**)—surface after sandblasting with an abrasive size of 90 microns (AB90 group); (**m**–**o**)—surface after sandblasting using with an abrasive size of 125 mi-

The distribution of shear strength by groups is presented in Figure 9. There was a significant decrease in adhesion strength for the PL group (*p* < 0.05). Shear strength in group AB90 was significantly higher than in group AB50 (*p* < 0.05) and insignificant higher than in group AB125. Groups AB50, AB125, and MC did not differ significantly. In plasma-electrolyte groups the shear strength of PZ2 was significantly higher than in PZ1

crons (AB125 group); (**p**–**r**)—surface after plasma-electrolyte treatment (PZ groups).

and PZ3. Ra and shear strength results in groups are presented in Table 2.

*3.3. Apparent Shear Strength* 

**Figure 9.** Shear strength distribution by groups, where are shown: the median (red line), the lower and upper quartiles (blue lines), and the minimum and maximum values (black lines) that are not outliers. **Figure 9.** Shear strength distribution by groups, where are shown: the median (red line), the lower and upper quartiles (blue lines), and the minimum and maximum values (black lines) that are not outliers. *Materials* **2022**, *15*, x FOR PEER REVIEW 15 of 20

**Table 2.** Ra and shear strength results in groups. **Table 2.** Ra and shear strength results in groups.


Thus, when considering the relationship between the roughness parameter Ra and the shear strength for the PZ group a nonlinear relationship was noted. Due to the nonlinear dependence of shear strength on Ra for the PZ group, their averaging over the full data set is incorrect. So the data from the PZ group were divided according to the Ra values into three groups (see Figure 7). For the PZ1 group from PZ roughness Ra value was equal to 1.136 ± 0.15 µm and the shear strength was 1.93 ± 0.10 MPa, for the PZ2 group Ra was 1.45 ± 0.16 µm and the shear strength was 8.35 ± 0.21 MPa, for the PZ3 group Ra was 1.91 ± 0.21 µm and shear strength was 1.38 ± 0.07 MPa. Figure 10 shows the average values of shear strength and Ra value for all groups. Thus, when considering the relationship between the roughness parameter Ra and the shear strength for the PZ group a nonlinear relationship was noted. Due to the nonlinear dependence of shear strength on Ra for the PZ group, their averaging over the full data set is incorrect. So the data from the PZ group were divided according to the Ra values into three groups (see Figure 7). For the PZ1 group from PZ roughness Ra value was equal to 1.136 ± 0.15 μm and the shear strength was 1.93 ± 0.10 MPa, for the PZ2 group Ra was 1.45 ± 0.16 μm and the shear strength was 8.35 ± 0.21 MPa, for the PZ3 group Ra was 1.91 ± 0.21 μm and shear strength was 1.38 ± 0.07 MPa. Figure 10 shows the average values of shear strength and Ra value for all groups.

**Figure 10.** Distribution of average shear strength depending on Ra value, rectangle—PL, cross—MC, circle—AB (from left to right 50, 90, 125), stars—PZ (from left to right PZ1, PZ2, PZ3) and interpolation result—red line. **Figure 10.** Distribution of average shear strength depending on Ra value, rectangle—PL, cross—MC, circle—AB (from left to right 50, 90, 125), stars—PZ (from left to right PZ1, PZ2, PZ3) and interpolation result—red line.

ሺ − ሻଶ

2ଶ <sup>ቇ</sup> (2)

Assuming the homogeneity of all data, thereby excluding the influence of the

ቆ

The parameters of interpolation (2) were as follows: *a* = 0.984 MPa, *b* = 3.271 MPa∙μm, *μ* = 1.514 μm, *σ* = 0.165 μm, error of interpolation was calculated as a squared

Due to the form of interpolation, the curve reaches a plateau in intervals of Ra values up to 1 μm and over 2 μm. In a strict sense, this fact illustrates a bad interpolation, but values of shear strength in these intervals are too small and these intervals are of no practical interest. Interpolation describes the results obtained quite qualitatively in the range of Ra values from 1 μm and up to 2 μm. Summarizing, the received interpolation

1 √

ሺሻ =+∙

norm of the residual (r2) and was equal to 0.7564.

tion (red line in Figure 10) of the form:

Assuming the homogeneity of all data, thereby excluding the influence of the chemical component and microrelief, it is possible to construct an exponential interpolation (red line in Figure 10) of the form:

$$\tau(Ra) = a + b \cdot \frac{1}{\sigma \sqrt{\pi}} \text{Exp}\left(\frac{(Ra - \mu)^2}{2\sigma^2}\right) \tag{2}$$

The parameters of interpolation (2) were as follows: *a* = 0.984 MPa, *b* = 3.271 MPa·µm, *µ* = 1.514 µm, *σ* = 0.165 µm, error of interpolation was calculated as a squared norm of the residual (r<sup>2</sup> ) and was equal to 0.7564.

Due to the form of interpolation, the curve reaches a plateau in intervals of Ra values up to 1 µm and over 2 µm. In a strict sense, this fact illustrates a bad interpolation, but values of shear strength in these intervals are too small and these intervals are of no practical interest. Interpolation describes the results obtained quite qualitatively in the range of Ra values from 1 µm and up to 2 µm. Summarizing, the received interpolation and previous interpolation of roughness distribution depending on voltage and temperature of the electrode (see Figure 5) it is possible to select the appropriate mode of plasma-electrolyte treatment to obtain the required shear strength.
