# Wear Effect on the Contact between a Metallic Pin and a Rotating Polymeric Specim
## 4 Discussion  
To evaluate the polymeric debris volume and the percentage of material subject to plastic deformation, the circular wear track and the corresponding section along the radial direction were considered for each specimen. The adopted procedure starts from the polymeric sheet after the wear test (Figure 8a); a radial section is individuated, as shown in Figure 8b, obtaining the wear groove profile in Figure 8c. The wear profiles are characterized by grooves with respect to the reference line corresponding to the sheet surface, whose depth is affected by the test conditions (Figure 9). Moreover, the lateral pile-ups due to the plastic flow of the polymer are evident. It can be assumed that the material that leaves the empty area (yellow area) of the groove below the reference dashed red line partly contributes to the formation of debris  
Figure 8: Procedure for tracing the wear grove profile: (**a**) UHMWPE sheet with circular wear track and indication of the mean diameter (\(\Phi\)), (**b**) radial section of the wear track, (**c**) wear profile. Figure 9: Example of wear profiles obtained after trials lasting 180 min: (**a**) dry conditions, (**b**) lubrication with SSF. and partly to the lateral corrugations (green areas). Therefore, the volume of debris can be obtained by multiplying the difference between the yellow area (A(yellow)) and the green area (A(green)) by the length of the mean circumference (corresponding to the diameter indicated in Figure 8a). Four different sections (\(i=1\)-4) were considered for each specimen. Therefore, the volume of debris (\(V_{debris}\)) and the volume of material contributing to plastic deformation (\(V_{plastic}\)) are obtained by applying the following relationships:  
\[V_{debris}=\frac{\pi\Phi}{4}\cdot\sum_{i=1}^{4}[A(yellow)_{i}-A(green)_{i}] \tag{2}\]  
\[V_{plastic}=\frac{\pi\Phi}{4}\cdot\sum_{i=1}^{4}A(green)_{i} \tag{3}\]  
The absolute error (\(\epsilon_{a}\)) of the volumetric measurements can be calculated as follows:  
\[\epsilon_{a}=\epsilon_{r}\cdot V_{debris} \tag{4}\]  
Figure 9 shows that the ratio of \(V_{plastic}/V_{debris}\) is significantly higher in SSF than in dry conditions (1.32 in the former case, 0.42 in the latter). It can be ascribed to the plasticizing effect of the hyaluronic acid present in SSF, which lowers the wearing effects of the metallic tip on the polymer surface. The volume of debris \(V_{debris}\) (mm\({}^{3}\)) is usefully reported vs. the sliding length \(L\) (m) during each wear test:  
\[L=2\pi r\cdot n\cdot t \tag{5}\]  
being \(r\) (m) the radius of the circular track that the metallic tip leaves on the polymeric surface after the duration \(t\) (min) of a single trial. These curves are characterized by an initial transient stage in which the \(V_{debris}\) rates reduce progressively until a stationary linear stage is reached [20]. This was also documented in the literature by [30] for the same tribological couple under the higher relative speed. The specific wear rate \(W_{s}\) (mm\({}^{3}\)/Nm) can be calculated as the slope of the linear stage (\(dV_{debris}/dL\)) divided by the applied load (\(P=30\) N):  
\[W_{s}=\frac{(dV_{debris}/dL)}{P} \tag{6}\]  
In Figure 10a, the experimental points of volume loss, obtained with weight measurements, are shown; in Figure 10b, the curve \(V_{debris}\) vs. \(L\) that interpolates the experimental data obtained with direct volume measurements is compared with that deduced from weight measurements. Some considerations can be drawn as follows. First, a positive consequence of direct volumetric measurements is their better accuracy. In fact, considering the relative volumetric error \(\varepsilon_{r}=1.1\)\(\times\)\(10^{-3}\), the absolute one varies from about 0.7 \(\times\)\(10^{-3}\) to 2.1 \(\times\)\(10^{-3}\) mm\({}^{3}\) in dry conditions and from about 0.2 \(\times\)\(10^{-3}\) to 0.8 \(\times\)\(10^{-3}\) mm\({}^{3}\) in SSF. Therefore, the respective diagrams are represented by red lines drawn with thin thicknesses.