# Experimental Analysis and Mathematical Model of FSW Parameter Effects on the Corrosion Rate of Al 6061-T6-Cu C11000 Joints

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{2}O

_{3}suspensions, and then with a 0.25 µm diamond paste to obtain a mirror finish. Finally, the samples were rinsed with water and alcohol before being tested.

^{2}area of exhibition. The scan rate was 0.167 mV/s from −150 mV to +1500 mV vs. E

_{corr}. Before the corrosion tests commenced, each sample was cathodically polarized at −1000 mV for 5 min, followed by stabilization for 60 min [41]. After the corrosion tests, the samples were observed via scanning electron microscopy (SEM; JEOL USA, Inc., Pleasanton, CA, USA). Garcia [16] performed a semiquantitative analysis via energy-dispersive X-ray spectroscopy (EDS; JEOL USA, Inc., Pleasanton, CA, USA) on the particles found in the weld zone, in order to identify the IMCs present; this analysis was, therefore, omitted from this investigation.

## 3. Results and Discussion

#### 3.1. Effect of Welding Parameters on Upper Surface of Each Sample

_{2}Cu, Al

_{4}Cu

_{9}, AlCu

_{3}and AlCu, as an inevitability.

#### 3.2. Potentiodynamic Test

_{2}O

_{3}(boehmite), a few nanometers thick. This layer will form at any temperature as soon as the solid metal touches an oxidizing medium. Covering the barrier layer is a thicker, less compacted and more porous outer layer of hydrated oxide. This second layer grows on the first following a reaction with the external environment (probably due to hydration), and its final thickness depends on the presence of physicochemical conditions (relative humidity and temperature) that favor the growth of the film [44,45].

^{+3}+ 3OH

^{−}→ AlOOH + H

_{2}O

_{2}O

_{3}+ H

_{2}O → 2AlOOH

_{2}O → Al(OH)

_{3}

_{2}O

_{3}and hydrated Al

_{2}O

_{3}, mainly in the form of amorphous Al(OH)

_{3}or α-Al(OH)

_{3}(bayerite). This AlOOH-Al(OH)

_{3}outer coating is colloidal and porous, with poor corrosion resistance and cohesive properties. On the other hand, the inner layer is composed mainly of Al

_{2}O

_{3}and small amounts of hydrated aluminum oxide, mainly in the form of AlOOH (boehmite). This internal Al

_{2}O

_{3}-AlOOH coating is continuous and corrosion resistant [44]. Goh [46] reported that with copper, the formation of CuCl

_{2}does not allow the Cu’s self-passivation, and this will inevitably increase the rate of corrosion of Cu. Moreover, Cl

^{−}ions can act as a catalyst for copper corrosion and weaken or dissolve the stable passivation of the oxide film.

#### 3.3. Mathematical Model

- r > 0 y tends to increase when x increases;
- r < 0 y tends to decrease when x increases.

_{1}and N

_{2}are equal to 2, the normal variances ${\sigma}_{1}^{2}$ and ${\sigma}_{2}^{2}$ define the statistical factor F, as follows:

_{i,j}are the values on the table, ${\overline{X}}_{i}$ is the row average, ${\overline{X}}_{j}$ is the column average, and ${\stackrel{=}{X}}_{T}$ is the total average. The variation between the blocks is

## 4. Conclusions

- −
- Dissimilar welds of Al 6061-T6 and C11000 plates were obtained via friction stir welding in a conventional milling machine at different rotational and traverse speeds. The lowest quantity of defects was found in welds obtained at 1000 and 1150 rpm, with a traverse speed of 20 and 40 mm/min.
- −
- The lowest corrosion rate was obtained for the sample S1000-20, at 0.95924 mpy, while the sample S1300-60 obtained the highest corrosion rate of 3.45 mpy. As regards specific applications, the presented results establish the appropriate conditions for the FSW process.
- −
- The implementation of statistical tools in this work allowed the parameterization of the FSW process, incorporating better control a higher quality of the product in the manufacturing processes. In addition, it effectively simulated the effects on the corrosion rate under different welding parameters of interest.
- −
- Via ANOVA and the proposed model’s equations, it is possible to quantify the relationship between the rotational and traverse speeds. The ANOVA study establishes that the degree of relationship between the input and output variables in the FSW process is high, while the model establishes an equation for analyzing the FSW, as regards the effect of the welding parameters on corrosion resistance, without resorting to excessive experimentation.
- −
- The statistical analysis demonstrates a significant relationship between the rotational and traverse speeds and the corrosion resistance. Moreover, the mathematical analysis validates the experimentally determined effects of the processing parameters employed during the FSW process.
- −
- It is concluded that the analysis of variance assessed in each group of experiments supports the results obtained through the correlation analysis.
- −
- With the obtained results, we can conclude that the model for designing the FSW process is statistically acceptable. The correlation coefficient r shows a strong relationship between the input (welding parameters) and output (corrosion rate) variables, with 94.554% correlation achieved in each group of tests
- −
- With the obtained results, we can conclude that the model for designing the FSW process is statistically acceptable. The correlation coefficient r shows a strong relationship between the input (welding parameters) and output (corrosion rate) variables, with 94.554% correlation achieved in each group of tests
- −
- The factor r
^{2}shows the significant influence of the input variables (rotational and traverse speeds) over the model. The r^{2}value of the corrosion resistance explains a significant percentage (89.404%) of the variability in the data, and thus the uncertainty of the phenomenon - −
- The standard error is low, which means that each value estimated with the model will have an error of ±0.34201 mpy.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Scanning electron microscopy (SEM) macro-sections at 50× magnification of the upper surfaces of all the samples of Al 6061-T6–Cu C11000 under different FSW conditions.

**Figure 5.**Potentiodynamic curves of FSW Al 6061 T6-Cu C11000 joints at (

**a**) 1300 rpm and different traverse speeds, and (

**b**) 20 mm/min and different rotational speeds.

**Figure 6.**SEM micrographs of the upper surface weld zone, showing the intergranular corrosion of samples 1000-20 and 1300-60.

**Figure 8.**Effect of traverse and rotational speeds on the corrosion rates of all FSW Al 6061-T6–Cu C11000 joints.

**Figure 9.**Effect of the of rotational and traverse speeds on the microstructure of the upper surface of the weld zones the welds, (

**a**,

**c**) variation of rotational speed, (

**b**,

**d**) variation of travel speed.

**Figure 11.**Comparison between the experimental results and the estimated model concerning the effect of the welding parameters on the corrosion rate.

**Figure 12.**Surface simulation of the rotational and traverse speeds’ impacts on the corrosion rate, via the mathematical model.

Element | Al | Cu | Fe | Cr | Mg | Zn | Si |
---|---|---|---|---|---|---|---|

Al 6061-T6 | Bal. | 0.38 | 0.57 | 0.33 | 1.12 | 0.25 | 0.53 |

Cu C11000 | - | 99.9 | - | - | - | - | - |

Sample | Rotational Speed (rpm) | Traverse Speed (mm/min) |
---|---|---|

S1000-20 | 1000 | 20 |

S1000-40 | 40 | |

S1000-60 | 60 | |

S1150-20 | 1150 | 20 |

S1150-40 | 40 | |

S1150-60 | 60 | |

S1300-20 | 1300 | 20 |

S1300-40 | 40 | |

S1300-60 | 60 |

FSW Parameters | $20\text{}\frac{\mathbf{m}\mathbf{m}}{\mathbf{m}\mathbf{i}\mathbf{n}}$ | $40\text{}\frac{\mathbf{m}\mathbf{m}}{\mathbf{m}\mathbf{i}\mathbf{n}}$ | $60\text{}\frac{\mathbf{m}\mathbf{m}}{\mathbf{m}\mathbf{i}\mathbf{n}}$ |
---|---|---|---|

1000 rpm | 0.95927 | 1.68077 | 2.70767 |

1150 rpm | 1.41167 | 2.57400 | 3.01230 |

1300 rpm | 1.62900 | 3.36333 | 3.45100 |

Variables | Rotational Speed | Traverse Speed | Corrosion |
---|---|---|---|

Rotational speed | 0.95927 | 1.68077 | 2.70767 |

Traverse speed | 1.41167 | 2.57400 | 3.01230 |

Corrosion | 1.62900 | 3.36333 | 3.45100 |

Variables | Relationship | Increase |
---|---|---|

rotational speed–traverse speed | null | non-existent |

corrosion–rotational speed | weak | positive |

corrosion–traverse speed | significant | positive |

Variation Terms | dof | Quadratic Term | F |
---|---|---|---|

${V}_{R}$ | $a-1$ | ${S}_{R}^{2}$ | ${S}_{R}^{2}/{S}_{E}^{2}$ |

${V}_{C}$ | $b-1$ | ${S}_{C}^{2}$ | ${S}_{c}^{2}/{S}_{E}^{2}$ |

${V}_{E}$ | $\left(a-1\right)\left(b-1\right)$ | ${S}_{E}^{2}$ | |

$V$ | $ab-1$ |

Variable | Quadratic Sum | dof | Mean Quadratic | F | Probability | Crit. F |
---|---|---|---|---|---|---|

Rotational speed | 1.59949 | 2 | 0.79975 | 9.67707 | 0.02934 | 6.94427 |

Traverse speed | 4.69357 | 2 | 2.34678 | 28.39655 | 0.00433 | 6.94427 |

Error | 0.33057 | 4 | 0.08264 | |||

Total | 6.62365 | 8 |

Variables | Value |
---|---|

$r$ | 0.94554 |

${r}^{2}$ | 0.89404 |

${r}_{adjusted}^{2}$ | 0.85872 |

error | 0.34201 |

Observations n | 9 |

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**MDPI and ACS Style**

Montes-González, F.A.; Rodríguez-Rosales, N.A.; Ortiz-Cuellar, J.C.; Muñiz-Valdez, C.R.; Gómez-Casas, J.; Galindo-Valdés, J.S.; Gómez-Casas, O.
Experimental Analysis and Mathematical Model of FSW Parameter Effects on the Corrosion Rate of Al 6061-T6-Cu C11000 Joints. *Crystals* **2021**, *11*, 294.
https://doi.org/10.3390/cryst11030294

**AMA Style**

Montes-González FA, Rodríguez-Rosales NA, Ortiz-Cuellar JC, Muñiz-Valdez CR, Gómez-Casas J, Galindo-Valdés JS, Gómez-Casas O.
Experimental Analysis and Mathematical Model of FSW Parameter Effects on the Corrosion Rate of Al 6061-T6-Cu C11000 Joints. *Crystals*. 2021; 11(3):294.
https://doi.org/10.3390/cryst11030294

**Chicago/Turabian Style**

Montes-González, Félix Alan, Nelly Abigaíl Rodríguez-Rosales, Juan Carlos Ortiz-Cuellar, Carlos Rodrigo Muñiz-Valdez, Josué Gómez-Casas, Jesús Salvador Galindo-Valdés, and Oziel Gómez-Casas.
2021. "Experimental Analysis and Mathematical Model of FSW Parameter Effects on the Corrosion Rate of Al 6061-T6-Cu C11000 Joints" *Crystals* 11, no. 3: 294.
https://doi.org/10.3390/cryst11030294