# (Bio)Tribocorrosion in Dental Implants: Principles and Techniques of Investigation
## 3 Synergistic Approach  
Since tribocorrosion involves numerous variables with a not yet well-understood behavior, much research was conducted to provide theoretical models [40; 41; 42; 43; 44; 45; 46; 47; 48; 49] capable of predicting the total wear for precise input conditions to be used at the occurrence. In this manuscript, only the synergistic approach was discussed (since it is one of the simplest) as an example of tribocorrosion evaluation, but the references inserted can be used by the readers for further detailed studies. Hence, [PERSON] in 1995 [50] introduced a simple model, in which is observable the absence of chemical and mechanical valuations as follows:  
\[W_{tot}=A+B+C \tag{12}\]  
where \(W_{tot}\) is the total loss volume of material, \(A\) is the loss induced by mechanical wear, \(B\) is induced by corrosion and \(C\) is the synergy contributes. Equation (12) can be further explored by better specifying the last term (C), being the most crucial factor in the formula. [PERSON] et al. [34], followed by [PERSON] et al. [35], proposed the (13), according to the standard ASTM G 119-04 (Guide for Determining Synergism Between Wear and Corrosion) as follows:  
\[W_{tr}=W_{act}^{m}+W_{act}^{c}+W_{repass}^{m}+W_{repass}^{c} \tag{13}\]  
with \(W_{tr}\) material loss in the sliding track equals to the sum of 4 components respectively due to the following two zones: one named active and the other one re-passivated, the former obtained after the rupture of passive layer, that, as explained before, protects the sample from tribocorrosion and the latter where the film is not completely destroyed, or it had time to restore. More precisely, the synergistic effect is provided by \(W_{act}^{c}\) and \(W_{repass}^{m}\) which represent, respectively, the loss of corrosion after the removal of the passive layer caused by mechanical interaction and loss of mechanical wear of the re-passivated material. The last two are \(W_{act}^{m}\) and \(W_{repass}^{c}\), i.e., respectively, the contribution for mechanical wear  
Figure 4: Equivalent circuit model: [PERSON]’s circuit. of active layer and corrosion of re-passivated sample. After calculating the four factors, it could be useful to use the parameter \(K\) defined as followings:  
\[K=\frac{W_{act}^{c}+W_{repass}^{c}}{W_{act}^{m}+W_{repass}^{m}} \tag{14}\]  
That can be rewritten in the following way [51]:  
\[K=\frac{K_{c}}{K_{m}} \tag{15}\]  
Depending on the value assumed by \(K\), the mechanism of degradation can be established as follows (Table 1):  
When \(K\) is greater than 1, the prevalent mechanism is corrosion, whereas when it is lower than 1, wear dominates. Obviously, the remaining parameters can be compared as shown below as follows:  
\[K_{m}=\frac{W_{act}^{m}}{W_{repass}^{m}} \tag{16}\]  
In this case, the expression underlines the strength of the passive layer for corrosion protection as follows: if it is >1, the film is efficient, otherwise not. [PERSON] et al. [27], instead, proposed a different relationship from the following Equation (12):  
\[W_{tot}=C_{o}+W_{o}+S \tag{17}\]  
That becomes the following:  
\[W_{tot}=C_{o}+W_{o}+\Delta C_{w}+\Delta W_{c} \tag{18}\]  
with \(\Delta C_{w}\) and \(\Delta W_{c}\), the volume of corrosion aggravated by wear and the volume of wear aggravated by corrosion, respectively. Consequently, the factor T is, by grouping the following common terms:  
\[W_{tot}=(C_{o}+\Delta C_{w})+(W_{o}+\Delta W_{c}) \tag{19}\]  
That can be rewritten as follows:  
\[W_{tot}=C_{w}+W_{c} \tag{20}\]  
* \(C_{w}=\) total loss for corrosion;
* \(W_{c}=\) total loss for wear.