# Rebar Shape Time-Evolution During a Reinforced Concrete Corrosion Test: An Electrochemical Model
## 4 Results  
The parameters used for elements mesh definition are shown in Table 2, where the size of the obtained mesh is also shown. The initial mesh is shown in Figure 2 (left) and a detail of the mesh obtained after one year of corrosion is shown in Figure 2 (right), where the solid line shows the initial rebar shape. In this case, a metal section reduction and a shape change can be seen. The radius decrease is higher on the bottom. This is the expected behavior because the bottom part is closer to the cathode. Level curves of \(\psi\) (20 of them are shown), i.e., current streamlines, are shown in Figure 3 for the beginning of the corrosion test (left) and after one year of corrosion (right). The dashed line shows the oxide layer. The upper part of the rebar is farther from the cathode, and a higher ohmic drop is expected, which causes a lower current density. This is confirmed by the model, which shows a higher density of current streamlines on the lower part of the rebar. It can also be seen in Figure 3 that the shape of the streamline does not change a lot during time. Nevertheless, the reduction of the metal section implies that the current streamlines are closer on the metal perimeter, which indicates a higher current density on the corroding surface. The current density on the rebar perimeter is shown as a function of the length of the perimeter of the metal \(s\) in Figure 4 for 0 days (initial), 23 days (duration of the test), and one year. Note that the curves shorten with time because the perimeter of the metal decreases, according to Equation (8). This is accompanied by a current density increase. This is expected because the experiment is carried out galvanostatically i.e., with constant current. Then a surface reduction implies a current density increase. The maximum current density occurs on the rebar bottom (\(\theta=180^{\circ}\), nearest to the cathode) and the minimum on the rebar top (\(\theta=0^{\circ}\), farthest from the cathode). Experimentally, it is observed that the first cracks appears on the sample surface at four days, when current distribution is very similar to the initial [27]. Calculated current density on the rebar bottom and the rebar top when the first cracks occur are, respectively, 154.13 \(\mu\)A/cm\({}^{2}\) and 46.14 \(\mu\)A/cm\({}^{2}\). It is worth noting that, due to  
Figure 2: Initial mesh (**left**) and a detail of the mesh after one year of corrosion (**right**). The blue line shows the initial rebar shape. the reinforced mortar specimen geometry, cracks appear first on the side where the current density is lower. Figure 4: Current density on the perimeter of the rebar at several corrosion times. Figure 3: Current streamlines (20 of them are shown) initially (**left**) and after one year of corrosion (**right**). Dashed line shows the oxide layer. The difference of radii with respect to the initial radius of the rebar for the metal \(\left(\Delta r_{m}=r_{m}-\frac{D}{2}\right)\) and for the oxide \(\left(\Delta r_{ox}=r_{ox}-\frac{D}{2}\right)\) are shown in Figure 5 for four days (appearance of the first cracks on the sample surface) and 23 days (test duration). The values for \(\theta=0^{\circ}\) (rebar top, minimum radius difference) and for \(\theta=180^{\circ}\) (rebar bottom, maximum radius difference) for several times are listed in Table 3. In this case, it can be seen that, according to the simulation, the first cracks on the sample surface appear with a decrease of rebar radius about 20 \(\upmu\)m on the bottom side of the bar, but only about 6 \(\upmu\)m on the side toward the cracked mortar surface. This estimation is in good agreement with results of experimental works, which concluded that only a few micrometers of loss in rebar radius are needed to induce visible concrete cover cracks, in experimental conditions similar to those modelized in this case [9]. Graph of \(\Delta r_{ox}\) in Figure 5 resembles a sinusoidal function of the form (12).