# Effect of Ti-B Grain Refiners on Wear and Corrosion of the A332 Alloy with Sr Modification
## 3 Results
### Effect of Grain Refiner Addition on Wear Behavior
The \(\mathrm{E}_{\mathrm{r}}\) is given by Equation (4):  
\[\frac{1}{\mathrm{E}_{\mathrm{r}}}=\frac{\mathrm{E}}{1-\mathrm{v}^{2}}+\frac{ \mathrm{E}_{\mathrm{i}}}{1-\mathrm{v}_{\mathrm{i}}^{2}} \tag{4}\]  
where \(\mathrm{E}\) e v are, respectively, the measured material's modulus of elasticity and its Poisson's ratio; \(\mathrm{E}_{\mathrm{i}}\) and \(\mathrm{v}_{\mathrm{i}}\) are the material's modulus of elasticity and Poisson's ratio of the tip material used in the indentation (in this case diamond). Figure 8a,b shows the hardness and elastic modulus respectively. In both cases, Fe-based intermetallic phases (\(\mathrm{Al}_{15}(\mathrm{FeMn})_{3}\mathrm{Si}_{2}\); \(\mathrm{Al}_{5}\mathrm{FeSi}\)) show higher values than the primary aluminum matrix. To determine the correlation between mechanical properties and wear, \(\frac{\mathrm{H}^{3}}{\mathrm{E}_{\mathrm{r}}^{2}}\) the index was calculated, which can be used to measure the elastic work. Generally, it is expected that higher values of \(\frac{\mathrm{H}^{3}}{\mathrm{E}_{\mathrm{r}}^{2}}\) indicate higher wear resistance [33]. In this way, by using instrumented nanoindentation with a matrix of 20 \(\times\) 20, the map of the relationship \(\frac{\mathrm{H}^{3}}{\mathrm{E}_{\mathrm{r}}^{2}}\) was obtained, which is shown in Figure 13. Considering that this relationship is inversely proportional to wear (Equation (5)). \[\frac{\mathrm{H}^{3}}{\mathrm{E}_{\mathrm{r}}^{2}}\ \propto\frac{1}{\mathrm{Material \,Wear}} \tag{5}\]  
It can be observed that the Fe-based intermetallic phase shows the higher index values, therefore, in the alloy with Al5 Ti1B grain refiner, there is more and longer \(\mathrm{Al}_{5}\mathrm{FeSi}\), matching with the lower volumetric wear loss in this condition. In addition, the friction coefficient results shown in Figure 12 are in accordance with these conclusions. Similar results were obtained with the Al5 Ti2B grain refiner. Therefore, it is possible to assert that when increasing the number of phases that satisfy a higher relation \(\frac{\mathrm{H}^{3}}{\mathrm{E}_{\mathrm{r}}^{2}}\) the wear of the part tends to decrease. Thus, there is a decrease in wear as the map colors tend to lean toward red and increase as they move towards blue (Figure 13). It can be seen that the Fe-based phase shows the highest values, which could be analyzed together with wear results and \(\mathrm{Al}_{5}\mathrm{FeSi}\) percentage in the alloy. These  
Figure 13: Map made using instrumented nanoindentation with a matrix of 20 \(\times\) 20 indentations, made with respect to \(\frac{\mathrm{H}^{3}}{\mathrm{E}_{\mathrm{r}}^{2}}\). results, apparently show that there is a link between the higher relation \(\frac{\text{H}^{3}}{\text{E}_{\text{r}}^{2}}\), hardness and percentage of Al\({}_{5}\)FeSi phase with the increase in wear resistance. Finally, it can be asserted that the use of grain refiners (Al5 Ti1B and Al5 Ti2B) caused a refinement and an increase in the length of the intermetallic particles of Al\({}_{5}\)FeSi, improving the wear resistance of the aluminum alloy A332.