# Optimizing the ECAP Parameters of Biodegradable Mg-Zn-Zr Alloy Based on Experimental, Mathematical Empirical, and Response Surface Methodology

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. The Experimental Design Matrix

#### 2.2. Material and Experimental Procedure

^{−1}, and a beam energy of 2 keV [28,29].

^{−1}using the polarization technique was also used to confirm the steady-state situation. With an open circuit potential and a potential window of ±250 mV, linear potentiodynamic polarization was carried out. At open-circuit potential (E

_{corr}), electrochemical impedance spectroscopy (EIS) was used with a sinusoidal voltage of ±10 mV and a frequency range of 10 MHz to 100 kHz.

^{−3}s

^{−1}. The chosen tensile samples were cut to dimensions in accordance with the E8M/ASTM standard and taken from the middle of the ZK30 ECAPed samples. For each processing condition, three tensile samples were examined.

## 3. Response Surface Methodology-Based Experiments

#### 3.1. Regression Model

_{1,}and dummy variable x

_{2}, and identify which ones of these parameters are significantly impacting the output responses of mechanical properties and corrosion performance [62]. The obtained experimental data were thoroughly studied and analyzed using Stat-Ease Design Expert software (version 13.0.5, Stat-Ease, Inc., Minneapolis, MN, USA). It is a very powerful and efficient computer package used widely in practice for industrial and scientific purposes aiming at designing and optimizing complex systems [63,64]. Design expert provides several types of regression transformation forms, such as linear, square root, natural logarithm, power, and many others.

_{1}and x

_{2}.

_{1}= 1 and x

_{2}= 0, if route type Bc then x

_{1}= 0 and x

_{2}= 1, and if route type C then x

_{1}= 0 and x

_{2}= 0.

#### 3.2. Genetic Algorithm

## 4. Results and Discussion

#### 4.1. Experimental Results and RSM

#### 4.1.1. Microstructural Evolution

_{1}− 0.0448229 × x

_{2}+ 0.00129203 × No. of Passes × Die Angle − 0.0415678 × No. of Passes × x

_{1}+ 0.0250216 × No. of Passes × x

_{2}

^{2}) of grain size is 0.9857, and the adjusted R

^{2}is 0.9732, which is close to and within 0.2 of the predicted R

^{2}value of 0.9155. Therefore, the obtained high values of R

^{2}, adjusted R

^{2}, and predicted R

^{2}for grain size indicate that the created model is desirable. The model terms A, B, C, AB, AC, and AD all have p-values that are lower than 0.05, implying that they are significant.

_{1}and x

_{2}. The adequate precision is 29.85, which is greater than four, implying that there is an adequate signal and the model could be used for navigating the design space [69].

#### 4.1.2. Corrosion Behavior

_{1}− 40.4689 × x

_{2}+ 0.0303579 × No. of Passes × Die Angle + 16.7947 × No. of Passes × x

_{2}+ 0.333308 × Die Angle × x

_{2}+0.932053 × No. of Passes

^{2}− 0.134907 × No. of Passes × Die Angle × x

_{2}

_{1}− 2116.51 × x

_{2}− 3.14036 × No. of Passes × Die Angle + 612.013 × No. of Passes × x

_{2}+ 18.0897 × Die Angle × x

_{2}+ 210.811 × No. of Passes

^{2}− 5.19565 × No. of Passes × Die Angle × x

_{2}

^{2}, and ABD all have p-values that are lower than 0.05, implying that they are significant. In the case of pitting corrosion resistance, the model terms A, B, AB, and A

^{2}all have p-values that are lower than 0.05, implying that they are significant. Similarly, both corrosion rate and resistance models are significant with p-values less than 0.05, which designates that altering an input ECAP parameter significantly affects the corrosion rate and corrosion resistance quality criteria [67], indicating that these models are satisfactory at a 95% confidence level [68]. The number of passes of the ECAP process, factor A, has the greatest impact on corrosion rate and corrosion resistance. The adequate precision is 34.17 and 11.85 for corrosion rate and corrosion resistance, respectively, which is greater than four, implying that there is an adequate signal and the model could be used for navigating the design space [69]. The coefficient of determination (R

^{2}) values is 0.991 and 0.9456 for corrosion rate and resistance, respectively. Additionally, the adjusted R

^{2}of the corrosion rate is 0.9775, which is close to and within 0.2 of the predicted R

^{2}value of 0.9846. In addition, the adjusted R

^{2}of corrosion resistance is 0.864, which is close to and within 0.2 of the predicted R

^{2}value of 0.8798. Therefore, the obtained high values of R

^{2}, adjusted R

^{2}, and predicted R

^{2}for corrosion rate and resistance indicate that the created model is desirable. The corrosion rate’s lack of fit p-value is 0.6, which is more than 0.05, indicating an insignificant lack of fit and a good model [67].

_{corr}). Additional ECAP processing passes, 4P using the 90°-die, through different routes resulted in an additional drop of corrosion current compared to the 1P, except for the 90°_4C. In addition, increasing the die angle up to 120° using route Bc resulted in significant corrosion I

_{corr}reduction compared to 90°_4Bc. The I

_{corr}reduction could be considered a dependable indicator for decreasing the corrosion rate. However, increasing the die angle to 120° (120°_4Bc) resulted in shifting the corrosion potential E

_{corr}to more negative values.

^{2}at route A, which is attained at one pass and a 90° ECAP die angle. The corrosion resistance showed a decline with augmenting the number of passes nearly up to two passes, then it improved with augmenting the number of ECAP passes at route Bc. The ECAP die angle has a minor effect on corrosion resistance. In this context, the maximum optimum corrosion resistance 1232 Ω·cm

^{2}at route Bc, which is attained at one pass and 120° ECAP die angle. Similarly, the effect of die angle and number of passes at route C on corrosion resistance is similar to those obtained by route Bc. The maximum optimum corrosion resistance is 1114 Ω·cm

^{2}at route C, which is attained at one pass and 120° ECAP die angle.

#### 4.1.3. Mechanical Properties

#### Hardness Distribution

^{−6}× Die Angle −0.021424 × x

_{1}− 0.001141 × x

_{2}+0.000240 × Die Angle × x

_{1}+0.001192 × No. of Passes

^{2}

_{1}+ 0.000252 × x

_{2}−0.000035 × No. of Passes × Die Angle − 0.000680 × No. of Passes × x

_{2}+ 0.000180 × Die Angle × x

_{1}

^{2}that are smaller than 0.05, suggesting that these model terms are significant. Similarly, both hardness at the center and edge models are significant with p-values less than 0.05, which designates that altering an ECAP parameter significantly affects both the hardness at the center and edge quality criteria [67], indicating that these models are satisfactory at a 95% confidence level [68]. The number of passes of the ECAP process has the greatest impact on both the hardness at the center and edge, followed by the ECAP die angle. The adequate precision values are 24.5 and 26.68 for the hardness at the center and edge, respectively, which is more than four, implying that there is an adequate signal and the model could be used for navigating the design space [69]. The coefficient of determination (R

^{2}) values is 0.984 and 0.9825 for the hardness at the center and edge, respectively. Additionally, the adjusted R

^{2}of the hardness at the center is 0.9743, which is close to and within 0.2 of the predicted R

^{2}value of 0.9481. In addition, the adjusted R

^{2}of the hardness at the edge is 0.9671, which is close to and within 0.2 of the predicted R

^{2}value of 0.9245. Therefore, the obtained high values of R

^{2}, adjusted R

^{2}, and predicted R

^{2}for both the hardness at the center and edge indicate that the created model is desirable.

#### Tensile Properties

_{1}+ 3.98405 × x

_{2}+ 0.0973018 × No. of Passes × Die Angle + 0.939662 × No. of Passes

^{2}

_{1}− 4.91157 × x

_{2}+ 0.293265 × No. of Passes × Die Angle + 2.6981 × No. of Passes × x

_{2}

_{1}+ 0.894089 × x

_{2}+ 1.49867 × No. of Passes × x

_{1}− 1.51498 × No. of Passes × x

_{2}− 0.623325 × No. of Passes

^{2}

^{2}are less than 0.05, indicating that these model terms are significant. However, the other model terms with p-values greater than 0.05 are insignificant. Similarly, the YS, TS, and D% percentage models are significant with p-values less than 0.05, which designates that changing an input ECAP parameter has a significant impact on the YS, TS, and D% quality criteria [67], indicating that these models are satisfactory at a 95% confidence level [68]. The ECAP die angle has the greatest impact on YS, TS, and D percentages followed by the number of ECAP passes.

^{2}) values is 0.9321, 0.97, and 0.9848 for the YS, TS, and D%, respectively. Additionally, the adjusted R

^{2}of YS is 0.886, which is close to and within 0.2 of the predicted R

^{2}value of 0.742. In addition, the adjusted R

^{2}of TS is 0.95, which is close to and within 0.2 of the predicted R

^{2}value of 0.906. Moreover, the adjusted R

^{2}of D% is 0.97, which is close to and within 0.2 of the predicted R

^{2}value of 0.94. Therefore, the obtained high values of R

^{2}, adjusted R

^{2}, and predicted R

^{2}for the YS, TS, and D% indicate that the created model is desirable. The YS, TS, and D% lack of fit p-values is greater than 0.05, indicating an insignificant lack of fit and a good model [67].

_{,}which could be attributed to the higher plastic strain. Furthermore, the shear strain accumulation resulting from the ECAP passes of up to four passes could be assigned to the dislocation density growth, which hinders the dislocation mobility [76]. Moreover, the D% reduction after the ECAP processing could be associated with grain refinement. Additionally, better D% was observed at route Bc with a 120° die angle and four passes, compared with route Bc with a 90° die angle and four passes, which could be assigned to imposing lower strain as reported in [29]. In the same context, route Bc exhibited the highest grain refinement; therefore, it shows lower D% compared to the remaining studied route types of A and C. Consequently, route Bc could be considered the most effective route type in this perspective.

#### 4.2. Genetic Algorithm Results

#### 4.2.1. Optimization of Grain Size

_{1}, and dummy variable x

_{2}. It is presented as follows:

_{1}, x

_{2})

_{1}ϵ [0, 1];

_{2}ϵ [0, 1].

_{1}, and 1 for the dummy variable x

_{2}. The minimum optimum grain size value obtained from the hybrid RSM-GA is 1.875 µm, which was better than its counterpart response obtained by RSM at route Bc with four passes and 120° ECAP die angle, as shown in Figure 12b.

#### 4.2.2. Optimization of Corrosion Response

_{1}, and dummy variable x

_{2}. The best value of corrosion rate by GA is 0.0909 mpy, which was attained at route Bc with four passes and 90° ECAP die angle, as shown in Figure 13a. The corrosion rate values of RSM compared with the GA technique are 0.091 mpy and 0.090 mpy, respectively.

_{1}, and dummy variable x

_{2}. The best value of corrosion resistance by GA is 1144 Ω·cm

^{2}, which was attained at route Bc with one pass and 120° ECAP die angle, as shown in Figure 13c. The corrosion resistance value of RSM compared with the GA technique is 1149 Ω·cm

^{2}and 1144 Ω·cm

^{2}, respectively.

^{2}which is better than its counterpart response obtained by RSM at route Bc with one pass and 120° ECAP die angle, as shown in Figure 13d.

#### 4.2.3. Optimization of Hardness Response

_{1}, and dummy variable x

_{2}. The best values of hardness at the center and edge by GA are 88.936 HV and 96.7 HV, respectively, which were attained at route Bc with four passes and 120° ECAP die angle, as shown in Figure 14a,c.

#### 4.2.4. Optimization of Tensile Response

_{1}, and dummy variable x

_{2}. The best values of YS and TS by GA are 97.58 MPa, and 342.157 MPa, respectively, which were attained at route Bc with four passes and 90° ECAP die angle, as shown in Figure 15a,c.

#### 4.3. Validation of GA

## 5. Conclusions

- The predicted results were very close to the actual experimental results with a narrow slight deviation.
- The obtained regression models are adequate and could be useful to predict the optimization of ECAP parameters.
- Route Bc is the most effective route in grain refinement
- ECAP processing through four passes of route Bc displayed a more homogenous distribution of the ultrafine grains
- For the multiple passes, the ECAP die angle has an insignificant effect on refining the grain size compared to the effect of the ECAP route type.
- ECAP processing via 4Bc through the 90°-degree die revealed a better corrosion rate at 0.091mpy.
- The 120°-die revealed higher corrosion resistance compared to the 90°-die.
- 4Bc through the 120°-die resulted in enhancing the hardness by 86.5% relative to the AA counterpart.
- 4Bc through the 90°-die revealed the best TS, while 2C through the 120°-die showed the best ductility at fracture.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

ECAP | Equal channel angular pressing |

RSM | Response Surface Methodology |

ANOVA | Analysis of Variance |

HCP | Hexagonal close-packed |

SPD | Severe plastic deformation |

UFG | Ultra-Fine Grain |

${\epsilon}_{eq}$ | The equivalent strain |

ϕ | ECAP die angle |

Ψ | Outer corner angle |

N | Number of passes |

EBSD | Electron backscatter Diffraction |

(SCE) | Saturated calomel electrode |

(E_{corr}) | Open-circuit potential |

(EIS) | Electrochemical impedance spectroscopy |

Hv | Vicker’s microhardness test |

GA | Genetic Algorithm |

Y | Output response |

f | The ECAP process independent input factors, |

ε | The random error distributed about the response Y |

YS | Ultimate tensile strength |

TS | Tensile Strength |

D | Ductility |

x_{1} and x_{2} | Dummy variables |

R^{2} | Regression Coefficient |

## Appendix A

Source | DF | Grain Size (µm) | |||
---|---|---|---|---|---|

Sum of Squares | Mean Square | F-Value | p-Value | ||

Model | 7 | 0.1491 | 0.0213 | 78.74 | <0.0001 ^{a} |

A-No. of Passes | 1 | 0.0511 | 0.0511 | 188.98 | <0.0001 ^{a} |

B-Die Angle | 1 | 0.0029 | 0.0029 | 10.89 | 0.0109 ^{a} |

C-Dummy x_{1} | 1 | 0.0029 | 0.0029 | 10.55 | 0.0117 ^{a} |

D-Dummy x_{2} | 1 | 0.0008 | 0.0008 | 3.13 | 0.1147 |

AB | 1 | 0.0063 | 0.0063 | 23.17 | 0.0013 ^{a} |

AC | 1 | 0.0057 | 0.0057 | 21.18 | 0.0018 ^{a} |

AD | 1 | 0.0025 | 0.0025 | 9.41 | 0.0154 ^{a} |

Residual | 8 | 0.0022 | 0.0003 | ||

Lack of Fit | 5 | 0.0021 | 0.0004 | 25.92 | 0.0113 ^{a} |

Pure Error | 3 | 0.0000 | 0.0000 | ||

Cor Total | 15 | 0.1513 | |||

Fit Statistics | Std. Dev. | C.V. % | Adeq Precision | ||

0.0164 | 4.76 | 29.8545 | |||

R^{2} | Adjusted R^{2} | Predicted R^{2} | |||

0.9857 | 0.9732 | 0.9155 |

^{a}Within a 95% confidence interval, parameters referring to cells are significant.

Source | DF | Corrosion Rate (mpy) | Corrosion Resistance (Ω·cm^{2}) | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Sum of Squares | Mean Square | F-Value | p-Value | DF | Sum of Squares | Mean Square | F-Value | p-Value | ||

Model | 9 | 86.58 | 9.62 | 73.35 | <0.0001 ^{a} | 9 | 1.156 × 10^{6} | 1.284 × 10^{5} | 11.59 | 0.0037 ^{a} |

A-No. of Passes | 1 | 15.46 | 15.46 | 117.88 | <0.0001 | 1 | 1.674 × 10^{5} | 1.674 × 10^{5} | 15.11 | 0.0081 |

B-Die Angle | 1 | 0.0058 | 0.0058 | 0.0441 | 0.8405 | 1 | 88,102.62 | 88,102.62 | 7.95 | 0.0304 |

C-Dummy x1 | 1 | 0.0425 | 0.0425 | 0.3240 | 0.5898 | 1 | 1217.40 | 1217.40 | 0.1099 | 0.7516 |

D-Dummy x2 | 1 | 2.50 | 2.50 | 19.08 | 0.0047 | 1 | 5343.05 | 5343.05 | 0.4822 | 0.5134 |

AB | 1 | 5.07 | 5.07 | 38.63 | 0.0008 | 1 | 1.212 × 10^{5} | 1.212 × 10^{5} | 10.94 | 0.0163 |

AD | 1 | 26.95 | 26.95 | 205.47 | <0.0001 | 1 | 17,219.21 | 17,219.21 | 1.55 | 0.2590 |

BD | 1 | 0.0076 | 0.0076 | 0.0578 | 0.8180 | 1 | 12,575.49 | 12,575.49 | 1.13 | 0.3277 |

A^{2} | 1 | 5.31 | 5.31 | 40.45 | 0.0007 | 1 | 2.714 × 10^{5} | 2.714 × 10^{5} | 24.49 | 0.0026 |

ABD | 1 | 15.34 | 15.34 | 116.93 | <0.0001 | 1 | 22,745.80 | 22,745.80 | 2.05 | 0.2019 |

Residual | 6 | 0.7869 | 0.1311 | 6 | 66,483.81 | 11,080.64 | ||||

Lack of Fit | 3 | 0.3265 | 0.1088 | 0.7093 | 0.6078 ^{an} | 3 | 63,550.87 | 21,183.62 | 21.67 | 0.0155 ^{a} |

Pure Error | 3 | 0.4604 | 0.1535 | 3 | 2932.94 | 977.65 | ||||

Cor Total | 15 | 87.36 | 15 | 1.222 × 10^{6} | ||||||

Fit Statistics | Std. Dev. | C.V. % | Adeq Precision | Std. Dev. | C.V. % | Adeq Precision | ||||

0.3621 | 9.87 | 34.1733 | 105.26 | 17.45 | 11.8548 | |||||

R^{2} | Adjusted R^{2} | Predicted R^{2} | R^{2} | Adjusted R^{2} | Predicted R^{2} | |||||

0.9910 | 0.9775 | 0.9846 | 0.9456 | 0.8640 | 0.8798 |

^{a}Within a 95% confidence interval, parameters referring to filled cells are the significant,

^{an}are the insignificant terms.

Source | DF | Hardness at Center (HV) | Source | DF | Hardness at Edge (HV) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Sum of Squares | Mean Square | F-Value | p-Value | Sum of Squares | Mean Square | F-Value | p-Value | ||||

Model | 6 | 0.0004 | 0.0001 | 95.70 | <0.0001 ^{a} | Model | 7 | 0.0002 | 0.0000 | 63.99 | <0.0001 ^{a} |

A-No. of Passes | 1 | 0.0002 | 0.0002 | 372.73 | <0.0001 | A-No. of Passes | 1 | 0.0001 | 0.0001 | 198.13 | <0.0001 |

B-Die Angle | 1 | 0.0000 | 0.0000 | 46.84 | <0.0001 | B-Die Angle | 1 | 0.0000 | 0.0000 | 72.47 | <0.0001 |

C-Dummy X1 | 1 | 0.0000 | 0.0000 | 50.78 | <0.0001 | C-Dummy X1 | 1 | 9.004 × 10^{−6} | 9.004 × 10^{−6} | 25.34 | 0.0010 |

D-Dummy X2 | 1 | 3.150 × 10^{−6} | 3.150 × 10^{−6} | 5.03 | 0.0516 | D-Dummy X2 | 1 | 5.651 × 10^{−6} | 5.651 × 10^{−6} | 15.91 | 0.0040 |

BC | 1 | 0.0000 | 0.0000 | 49.59 | <0.0001 | AB | 1 | 5.436 × 10^{−6} | 5.436 × 10^{−6} | 15.30 | 0.0045 |

A^{2} | 1 | 0.0000 | 0.0000 | 19.34 | 0.0017 | AD | 1 | 2.090 × 10^{−6} | 2.090 × 10^{−6} | 5.88 | 0.0415 |

Residual | 9 | 5.637 × 10^{−6} | 6.263 × 10^{−7} | BC | 1 | 0.0000 | 0.0000 | 64.43 | <0.0001 | ||

Lack of Fit | 6 | 5.480 × 10^{−6} | 9.133 × 10^{−7} | 17.42 | 0.0197 ^{a} | Residual | 8 | 2.842 × 10^{−6} | 3.553 × 10^{−7} | ||

Pure Error | 3 | 1.573 × 10^{−7} | 5.243 × 10^{−8} | Lack of Fit | 5 | 1.501 × 10^{−6} | 3.001 × 10^{−7} | 0.6711 | 0.6756 ^{an} | ||

Cor Total | 15 | 0.0004 | Pure Error | 3 | 1.342 × 10^{−6} | 4.472 × 10^{−7} | |||||

Cor Total | 15 | 0.0002 | |||||||||

Fit Statistics | Std. Dev. | C.V. % | Adeq Precision | Fit Statistics | Std. Dev. | C.V. % | Adeq Precision | ||||

0.0008 | 0.7072 | 24.5495 | 0.0006 | 0.5560 | 26.6897 | ||||||

R^{2} | Adjusted R^{2} | Predicted R^{2} | R^{2} | Adjusted R^{2} | Predicted R^{2} | ||||||

0.9846 | 0.9743 | 0.9481 | 0.9825 | 0.9671 | 0.9245 |

^{a}Within a 95% confidence interval, parameters referring to filled cells are significant,

^{an}are insignificant terms.

Source | DF | YS (MPa) | Source | DF | TS (MPa) | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Sum of Squares | Mean Square | F-Value | p-Value | Sum of Squares | Mean Square | F-Value | p-Value | ||||

Model | 6 | 312.95 | 52.16 | 20.60 | <0.0001 ^{a} | Model | 6 | 2931.98 | 488.66 | 48.53 | <0.0001 ^{a} |

A-No. of Passes | 1 | 35.12 | 35.12 | 13.87 | 0.0047 | A-No. of Passes | 1 | 873.21 | 873.21 | 86.72 | <0.0001 |

B-Die Angle | 1 | 80.39 | 80.39 | 31.75 | 0.0003 | B-Die Angle | 1 | 953.57 | 953.57 | 94.70 | <0.0001 |

C-Dummy x_{1} | 1 | 4.06 | 4.06 | 1.60 | 0.2374 | C-Dummy x_{1} | 1 | 206.71 | 206.71 | 20.53 | 0.0014 |

D-Dummy x_{2} | 1 | 38.89 | 38.89 | 15.36 | 0.0035 | D-Dummy x_{2} | 1 | 9.10 | 9.10 | 0.9035 | 0.3667 |

AB | 1 | 46.53 | 46.53 | 18.38 | 0.0020 | AB | 1 | 384.40 | 384.40 | 38.18 | 0.0002 |

A^{2} | 1 | 10.25 | 10.25 | 4.05 | 0.0751 | AD | 1 | 34.03 | 34.03 | 3.38 | 0.0992 |

Residual | 9 | 22.79 | 2.53 | Residual | 9 | 90.62 | 10.07 | ||||

Lack of Fit | 6 | 20.02 | 3.34 | 3.62 | 0.1591 ^{an} | Lack of Fit | 6 | 69.12 | 11.52 | 1.61 | 0.3738 ^{an} |

Pure Error | 3 | 2.77 | 0.9217 | Pure Error | 3 | 21.50 | 7.17 | ||||

Cor Total | 15 | 335.74 | Cor Total | 15 | 3022.60 | ||||||

Fit Statistics | Std. Dev. | C.V. % | Adeq Precision | Fit Statistics | Std. Dev. | C.V. % | Adeq Precision | ||||

1.59 | 1.74 | 12.5037 | 3.17 | 0.9804 | 19.0151 | ||||||

R^{2} | Adjusted R^{2} | Predicted R^{2} | R^{2} | Adjusted R^{2} | Predicted R^{2} | ||||||

0.9321 | 0.8869 | 0.7426 | 0.97 | 0.95 | 0.9067 |

^{a}Within a 95% confidence interval, parameters referring to filled cells are significant,

^{an}are insignificant term.

Source | DF | D% (mm/mm) | |||
---|---|---|---|---|---|

Sum of Squares | Mean Square | F-Value | p-Value | ||

Model | 7 | 145.30 | 20.76 | 74.74 | <0.0001 ^{a} |

A-No. of Passes | 1 | 13.56 | 13.56 | 48.84 | 0.0001 |

B-Die Angle | 1 | 21.04 | 21.04 | 75.76 | <0.0001 |

C-Dummy x_{1} | 1 | 1.01 | 1.01 | 3.62 | 0.0934 |

D-Dummy x_{2} | 1 | 20.52 | 20.52 | 73.88 | <0.0001 |

AC | 1 | 8.76 | 8.76 | 31.55 | 0.0005 |

AD | 1 | 9.17 | 9.17 | 33.03 | 0.0004 |

A^{2} | 1 | 4.37 | 4.37 | 15.73 | 0.0041 |

Residual | 8 | 2.22 | 0.2777 | ||

Lack of Fit | 5 | 1.64 | 0.3273 | 1.68 | 0.3554 ^{an} |

Pure Error | 3 | 0.5850 | 0.1950 | ||

Cor Total | 15 | 147.52 | |||

Fit Statistics | Std. Dev. | C.V. % | Adeq Precision | ||

0.5270 | 1.57 | 29.4038 | |||

R^{2} | Adjusted R^{2} | Predicted R^{2} | |||

0.9849 | 0.9718 | 0.9410 |

^{a}Within a 95% confidence interval, parameters referring to filled cells are significant,

^{an}are insignificant terms.

## References

- Kulekci, M.K. Magnesium and its alloys applications in automotive industry. Int. J. Adv. Manuf. Technol.
**2008**, 39, 851–865. [Google Scholar] [CrossRef] - Friedrich, H.; Schumann, S. Research for a ‘new age of magnesium’ in the automotive industry. J. Mater. Process. Technol.
**2001**, 117, 276–281. [Google Scholar] [CrossRef] - Li, N.; Zheng, Y. Novel Magnesium Alloys Developed for Biomedical Application: A Review. J. Mater. Sci. Technol.
**2013**, 29, 489–502. [Google Scholar] [CrossRef] - Chen, Y.; Xu, Z.; Smith, C.; Sankar, J. Recent advances on the development of magnesium alloys for biodegradable implants. Acta Biomater.
**2014**, 10, 4561–4573. [Google Scholar] [CrossRef] [PubMed] - Gu, X.-N.; Zheng, Y.-F. A review on magnesium alloys as biodegradable materials. Front. Mater. Sci. China
**2010**, 4, 111–115. [Google Scholar] [CrossRef] - Saris, N.-E.L.; Mervaala, E.; Karppanen, H.; Khawaja, J.A.; Lewenstam, A. Magnesium: An update on physiological, clinical and analytical aspects. Clin. Chim. Acta
**2000**, 294, 1–26. [Google Scholar] [CrossRef] - Okuma, T. Magnesium and bone strength. Nutrition
**2001**, 17, 679–680. [Google Scholar] [CrossRef] - Wolf, F.I.; Cittadini, A. Chemistry and biochemistry of magnesium. Mol. Asp. Med.
**2003**, 24, 3–9. [Google Scholar] [CrossRef] - Staiger, M.P.; Pietak, A.M.; Huadmai, J.; Dias, G. Magnesium and its alloys as orthopedic biomaterials: A review. Biomaterials
**2006**, 27, 1728–1734. [Google Scholar] [CrossRef] - Yin, Y.; Huang, Q.; Liang, L.; Hu, X.; Liu, T.; Weng, Y.; Long, T.; Liu, Y.; Li, Q.; Zhou, S.; et al. In vitro degradation behaviour and cytocompatibility of ZK30/bioactive glass composites fabricated by selective laser melting for biomedical applications. J. Alloys Compd.
**2019**, 785, 38–45. [Google Scholar] [CrossRef] - Lin, X.; Tan, L.; Zhang, Q.; Yang, K.; Hu, Z.; Qiu, J.; Cai, Y. The in vitro degradation process and biocompatibility of a ZK60 magnesium alloy with a forsterite-containing micro-arc oxidation coating. Acta Biomater.
**2013**, 9, 8631–8642. [Google Scholar] [CrossRef] [PubMed] - Yamasaki, Y.; Yoshida, Y.; Okazaki, M.; Shimazu, A.; Kubo, T.; Akagawa, Y.; Uchida, T. Action of FGMgCO3Ap-collagen composite in promoting bone formation. Biomaterials
**2003**, 24, 4913–4920. [Google Scholar] [CrossRef] - Zreiqat, H.; Howlett, C.R.; Zannettino, A.; Evans, P.; Schulze-Tanzil, G.; Knabe, C.; Shakibaei, M. Mechanisms of magnesium-stimulated adhesion of osteoblastic cells to commonly used orthopaedic implants. J. Biomed. Mater. Res.
**2002**, 62, 175–184. [Google Scholar] [CrossRef] [PubMed] - Kirkland, N.T. Magnesium biomaterials: Past, present and future. Corros. Eng. Sci. Technol.
**2012**, 47, 322–328. [Google Scholar] [CrossRef] [Green Version] - Kannan, M.B.; Raman, R.K.S. In vitro degradation and mechanical integrity of calcium-containing magnesium alloys in modified-simulated body fluid. Biomaterials
**2008**, 29, 2306–2314. [Google Scholar] [CrossRef] - Li, Z.; Song, G.-L.; Song, S. Effect of bicarbonate on biodegradation behaviour of pure magnesium in a simulated body fluid. Electrochim. Acta
**2014**, 115, 56–65. [Google Scholar] [CrossRef] - Song, G. Control of biodegradation of biocompatable magnesium alloys. Corros. Sci.
**2007**, 49, 1696–1701. [Google Scholar] [CrossRef] - Song, Y.W.; Shan, D.Y.; Han, E.H. Electrodeposition of hydroxyapatite coating on AZ91D magnesium alloy for biomaterial application. Mater. Lett.
**2008**, 62, 3276–3279. [Google Scholar] [CrossRef] - El-Garaihy, W.H.; Alateyah, A.I.; Alawad, M.O.; Aljohani, T.A. Improving the Corrosion Behavior and Mechanical Properties of Biodegradable Mg-Zn-Zr Alloys Through ECAP for Usage in Biomedical Applications. In Magnesium Technology; Springer: Cham, Switzerland, 2022; pp. 259–269. Available online: https://link.springer.com/chapter/10.1007/978-3-030-92533-8_45 (accessed on 5 February 2022).
- Hornberger, H.; Virtanen, S.; Boccaccini, A.R. Biomedical coatings on magnesium alloys–A review. Acta Biomater.
**2012**, 8, 2442–2455. [Google Scholar] [CrossRef] - Sun, Y.; Zhang, B.; Wang, Y.; Geng, L.; Jiao, X. Preparation and characterization of a new biomedical Mg–Zn–Ca alloy. Mater. Des.
**2012**, 34, 58–64. [Google Scholar] [CrossRef] - Alateyah, A.I.; Aljohani, T.A.; Alawad, M.O.; Elkatatny, S.; El-Garaihy, W.H. Improving the Corrosion Behavior of Biodegradable AM60 Alloy through Plasma Electrolytic Oxidation. Metals
**2021**, 11, 953. [Google Scholar] [CrossRef] - Almenaif, O.; Alhumaydan, Y.; Alnafisah, M.; Aldhalaan, M.; Alateyah, A.I.; El-Garaihy, W.H. A Computational Investigation into the Effect of Equal Channel Angular Processing on the Mechanical Properties of Severely Deformed ZK 60 Alloy Validated by Experiments. Am. J. Eng. Appl. Sci.
**2020**, 13, 296–310. [Google Scholar] [CrossRef] - Zong, Y.; Yuan, G.; Zhang, X.; Mao, L.; Niu, J.; Ding, W. Comparison of biodegradable behaviors of AZ31 and Mg–Nd–Zn–Zr alloys in Hank’s physiological solution. Mater. Sci. Eng. B
**2012**, 177, 395–401. [Google Scholar] [CrossRef] - Ng, W.F.; Wong, M.H.; Cheng, F.T. Stearic acid coating on magnesium for enhancing corrosion resistance in Hanks’ solution. Surf. Coat. Technol.
**2010**, 204, 1823–1830. [Google Scholar] [CrossRef] - Hermawan, H.; Dubé, D.; Mantovani, D. Developments in metallic biodegradable stents. Acta Biomater.
**2010**, 6, 1693–1697. [Google Scholar] [CrossRef] - Gunde, P.; Hänzi, A.C.; Sologubenko, A.S.; Uggowitzer, P.J. High-strength magnesium alloys for degradable implant applications. Mater. Sci. Eng. A
**2011**, 528, 1047–1054. [Google Scholar] [CrossRef] - Alateyah, A.I.; Alawad, M.O.; Aljohani, T.A.; El-Garaihy, W.H. Effect of ECAP Route Type on the Microstructural Evolution, Crystallographic Texture, Electrochemical Behavior and Mechanical Properties of ZK30 Biodegradable Magnesium Alloy. Materials
**2022**, 15, 6088. [Google Scholar] [CrossRef] - Alateyah, A.I.; Alawad, M.O.; Aljohani, T.A.; El-Garaihy, W.H. Influence of Ultrafine-Grained Microstructure and Texture Evolution of ECAPed ZK30 Magnesium Alloy on the Corrosion Behavior in Different Corrosive Agents. Materials
**2022**, 15, 5515. [Google Scholar] [CrossRef] [PubMed] - Wang, Y.; Guan, S.; Zeng, X.; Ding, W. Effects of RE on the microstructure and mechanical properties of Mg–8Zn–4Al magnesium alloy. Mater. Sci. Eng. A
**2006**, 416, 109–118. [Google Scholar] [CrossRef] - Witte, F.; Hort, N.; Vogt, C.; Cohen, S.; Kainer, K.U.; Willumeit, R.; Feyerabend, F. Degradable biomaterials based on magnesium corrosion. Curr. Opin. Solid State Mater. Sci.
**2008**, 12, 63–72. [Google Scholar] [CrossRef] - Gu, X.; Zheng, Y.; Cheng, Y.; Zhong, S.; Xi, T. In vitro corrosion and biocompatibility of binary magnesium alloys. Biomaterials
**2009**, 30, 484–498. [Google Scholar] [CrossRef] [PubMed] - Goodman, S.B.; Davidson, J.A.; Fornasier, V.L.; Mishra, A.K. Histological response to cylinders of a low modulus titanium alloy (Ti-13Nb-13Zr) and a wear resistant zirconium alloy (Zr-2.5Nb) implanted in the rabbit tibia. J. Appl. Biomater.
**1993**, 4, 331–339. [Google Scholar] [CrossRef] - Alateyah, A.I.; Aljohani, T.; Alawad, M.; El-Hafez, H.; Almutairi, A.; Alharbi, E.; Alhamada, R.; El-Garaihy, B.; El-Garaihy, W. Improved Corrosion Behavior of AZ31 Alloy through ECAP Processing. Metals
**2021**, 11, 363. [Google Scholar] [CrossRef] - Alateyah, A.I.; Ahmed, M.M.; Alawad, M.O.; Elkatatny, S.; Zedan, Y.; Nassef, A.; El-Garaihy, W. Effect of ECAP die angle on the strain homogeneity, microstructural evolution, crystallographic texture and mechanical properties of pure magnesium: Numerical simulation and experimental approach. J. Mater. Res. Technol.
**2022**, 17, 1491–1511. [Google Scholar] [CrossRef] - Yamashita, A.; Horita, Z.; Langdon, T.G. Improving the mechanical properties of magnesium and a magnesium alloy through severe plastic deformation. Mater. Sci. Eng. A
**2001**, 300, 142–147. [Google Scholar] [CrossRef] - El-Garaihy, W.H.; Fouad, D.M.; Salem, H.G. Multi-channel Spiral Twist Extrusion (MCSTE): A Novel Severe Plastic Deformation Technique for Grain Refinement. Met. Mater. Trans. A
**2018**, 49, 2854–2864. [Google Scholar] [CrossRef] - Fouad, D.M.; Moataz, A.; El-Garaihy, W.H.; Salem, H.G. Numerical and experimental analysis of multi-channel spiral twist extrusion processing of AA5083. Mater. Sci. Eng. A
**2019**, 764, 138216. [Google Scholar] [CrossRef] - Fouad, D.M.; El-Garaihy, W.H.; Ahmed, M.M.Z.; Seleman, M.M.E.; Salem, H.G. Influence of multi-channel spiral twist ex-trusion (MCSTE) processing on structural evolution, crystallographic texture and mechanical properties of AA1100. Mater. Sci. Eng. A
**2018**, 737, 166–175. [Google Scholar] [CrossRef] - Fouad, D.M.; El-Garaihy, W.H.; Ahmed, M.M.Z.; Albaijan, I.; Seleman, M.M.E.; Salem, H.G. Grain Structure Evolution and Mechanical Properties of Multi-Channel Spiral Twist Extruded AA5083. Metals
**2021**, 11, 1276. [Google Scholar] [CrossRef] - Alvarez-Lopez, M.; Pereda, M.D.; Del Valle, J.A.; Fernandez-Lorenzo, M.; Garcia-Alonso, M.C.; Ruano, O.A.; Escudero, M.L. Corrosion behaviour of AZ31 magnesium alloy with different grain sizes in simulated biological fluids. Acta Biomater.
**2010**, 6, 1763–1771. [Google Scholar] [CrossRef] - El-Shenawy, M.; Ahmed, M.M.Z.; Nassef, A.; El-Hadek, M.; Alzahrani, B.; Zedan, Y.; El-Garaihy, W.H. Effect of ECAP on the Plastic Strain Homogeneity, Microstructural Evolution, Crystallographic Texture and Mechanical Properties of AA2xxx Aluminum Alloy. Metals
**2021**, 11, 938. [Google Scholar] [CrossRef] - Gao, J.H.; Guan, S.K.; Ren, Z.W.; Sun, Y.F.; Zhu, S.J.; Wang, B. Homogeneous corrosion of high-pressure torsion treated Mg–Zn–Ca alloy in simulated body fluid. Mater. Lett.
**2011**, 65, 691–693. [Google Scholar] [CrossRef] - El-Garaihy, W.H.; Rassoul, E.A.; Alateyah, A.; Alaskari, A.M.; Oraby, S. Data Manipulation Approach and Parameters Interrelationships of the High-Pressure Torsion for AA6061-15%SiCp Composite. SAE Int. J. Mater. Manuf.
**2018**, 11, 167–182. [Google Scholar] [CrossRef] - El-Garaihy, W.; Rassoul, E.S.M.; Salem, H.G. Consolidation of High Performance AA6061 and AA6061-SiCp Composite Processed by High Pressure Torsion. Mater. Sci. Forum
**2014**, 783–786, 2623–2628. [Google Scholar] [CrossRef] - Alateyah, A.I.; Alharbi, M.; El-Hafez, H.M.; El-Garaihy, W.H. The Effect of Equal-Channel Angular Pressing Processing on Microstructural Evolution, Hardness Homogeneity, and Mechanical Properties of Pure Aluminum. SAE Int. J. Mater. Manuf.
**2020**, 14, 113–125. [Google Scholar] [CrossRef] - Ge, Q.; Dellasega, D.; Demir, A.G.; Vedani, M. The processing of ultrafine-grained Mg tubes for biodegradable stents. Acta Biomater.
**2013**, 9, 8604–8610. [Google Scholar] [CrossRef] [PubMed] - Wu, W.J.; Chen, W.; Zhang, L.; Chen, X.; Wang, H.; Wang, W.; Zhang, W. Improvement of tension/compression asymmetry for high-performance ZK61 magnesium alloy rod via tailoring deformation parameters: Upsetting-extrusion temperature and upsetting ratio. Mater. Sci. Eng. A
**2021**, 823, 141767. [Google Scholar] [CrossRef] - Savaedi, Z.; Mirzadeh, H.; Aghdam, R.M.; Mahmudi, R. Effect of grain size on the mechanical properties and bio-corrosion resistance of pure magnesium. J. Mater. Res. Technol.
**2022**, 19, 3100–3109. [Google Scholar] [CrossRef] - Němec, M.; Jäger, A.; Tesař, K.; Gärtnerová, V. Influence of alloying element Zn on the microstructural, mechanical and corrosion properties of binary Mg-Zn alloys after severe plastic deformation. Mater. Charact.
**2017**, 134, 69–75. [Google Scholar] [CrossRef] - Minarik, P.; Jablonska, E.; Kral, R.; Lipov, J.; Ruml, T.; Blawert, C.; Hadzima, B.; Chmelík, F. Effect of equal channel angular pressing on in vitro degradation of LAE442 magnesium alloy. Mater. Sci. Eng. C
**2017**, 73, 736–742. [Google Scholar] [CrossRef] - Li, X.; Jiang, J.; Zhao, Y.; Ma, A.; Wen, D.; Zhu, Y. Effect of equal-channel angular pressing and aging on corrosion behaviour of ZK60 Mg alloy. Trans. Nonferrous Met. Soc. China
**2015**, 25, 3909–3920. [Google Scholar] [CrossRef] - Valiev, R.Z.; Langdon, T.G. Principles of equal channel angular pressing as a processing tool for grain refinement. Prog. Mater. Sci.
**2006**, 51, 881–981. [Google Scholar] [CrossRef] - Sankuru, A.B.; Sunkara, H.; Sethuraman, S.; Gudimetla, K.; Ravisankar, B.; Babu, S.P.K. Effect of processing route on mi-crostructure, mechanical and dry sliding wear behavior of commercially pure magnesium processed by ECAP with back pressure. Trans Indian Inst. Met.
**2021**, 74, 2659–2669. [Google Scholar] [CrossRef] - Ghaedi, M.; Azad, F.N.; Dashtian, K.; Hajati, S.; Goudarzi, A.; Soylak, M. Central composite design and genetic algorithm applied for the optimization of ultrasonic-assisted removal of malachite green by ZnO Nanorod-loaded activated carbon. Spectrochim. Acta Part A Mol. Biomol. Spectrosc.
**2016**, 167, 157–164. [Google Scholar] [CrossRef] [PubMed] - Daryadel, M. Study on Equal Channel Angular Pressing Process of AA7075 with Copper Casing by Finite Element-response Surface Couple Method. Int. J. Eng.
**2020**, 33, 2538–2548. [Google Scholar] - Alateyah, A.I.; El-Garaihy, W.H.; Alawad, M.O.; El Sanabary, S.; Elkatatny, S.; Dahish, H.A.; Kouta, H. The Effect of ECAP Processing Conditions on Microstructural Evolution and Mechanical Properties of Pure Magnesium—Experimental, Mathematical Empirical and Response Surface Approach. Materials
**2022**, 15, 5312. [Google Scholar] [CrossRef] - Saleh, B.; Jiang, J.; Xu, Q.; Fathi, R.; Ma, A.; Li, Y.; Wang, L. Statistical Analysis of Dry Sliding Wear Process Parameters for AZ91Alloy Processed by RD-ECAP Using Response Surface Methodology. Met. Mater. Int.
**2021**, 27, 2879–2897. [Google Scholar] [CrossRef] - Kilickap, E.; Huseyinoglu, M.; Yardimeden, A. Optimization of drilling parameters on surface roughness in drilling of AISI 1045 using response surface methodology and genetic algorithm. Int. J. Adv. Manuf. Technol.
**2011**, 52, 79–88. [Google Scholar] [CrossRef] - Dadrasi, A.; Fooladpanjeh, S.; Gharahbagh, A.A. Interactions between HA/GO/epoxy resin nanocomposites: Optimization, modeling and mechanical performance using central composite design and genetic algorithm. J. Braz. Soc. Mech. Sci. Eng.
**2019**, 41, 63. [Google Scholar] [CrossRef] - Hazir, E.; Ozcan, T. Response surface methodology integrated with desirability function and genetic algorithm approach for the optimization of CNC machining parameters. Arab. J. Sci. Eng.
**2019**, 44, 2795–2809. [Google Scholar] [CrossRef] - Elsanabary, S.; Kouta, H.K. Optimization of Inertia Friction Welding of Dissimilar Polymeric PA6-PVC Hollow Cylinders by Genetic Algorithm. Port-Said Eng. Res. J.
**2021**, 25, 91–100. [Google Scholar] [CrossRef] - Munusamy, T.D.; Chin, S.Y.; Khan, M.M.R. Photoreforming hydrogen production by carbon doped exfoliated g-C3N4: Optimization using design expert® software. Mater. Today Proc.
**2021**, 57, 1162–1168. [Google Scholar] [CrossRef] - Rezić, I. Prediction of the surface tension of surfactant mixtures for detergent formulation using Design Expert software. Mon. Für Chem.-Chem. Mon.
**2011**, 142, 1219–1225. [Google Scholar] [CrossRef] - Makki, A.A.; Stewart, R.A.; Panuwatwanich, K.; Beal, C. Development of a domestic water end use consumption forecasting model for South-East Queensland, Australia. In Proceedings of the 6th IWA Specialist Conference on Efficient Use and Management of Water, International Water Association, Dead Sea, Jordan, 29 Marth–2 April 2011. [Google Scholar]
- Santhosh, A.J.; Tura, A.D.; Jiregna, I.T.; Gemechu, W.F.; Ashok, N.; Ponnusamy, M. Optimization of CNC turning parameters using face centred CCD approach in RSM and ANN-genetic algorithm for AISI 4340 alloy steel. Results Eng.
**2021**, 11, 100251. [Google Scholar] [CrossRef] - Gopal, M. Optimization of Machining Parameters on Temperature Rise in CNC Turning Process of Aluminium–6061 Using RSM and Genetic Algorithm. Int. J. Mod. Manuf. Technol.
**2020**, 12, 36–43. [Google Scholar] - Dritsa, V.; Rigas, F.; Doulia, D.; Avramides, E.J.; Hatzianestis, I. Optimization of culture conditions for the biodegradation of lindane by the polypore fungus Ganoderma australe. Water Air Soil Pollut.
**2009**, 204, 19–27. [Google Scholar] [CrossRef] - Asghar, A.; Raman, A.A.A.; Daud, W.M.A.W. A comparison of central composite design and Taguchi method for optimizing Fenton process. Sci. World J.
**2014**, 2014, 1–14. [Google Scholar] [CrossRef] [Green Version] - Aljohani, T.A.; Alawad, M.O.; Elkatatny, S.; Alateyah, A.I.; Bin Rubayan, M.T.; Alhajji, M.A.; AlBeladi, M.I.; Khoshnaw, F.; El-Garaihy, W.H. Electrochemical Behavior of SiC-Coated AA2014 Alloy through Plasma Electrolytic Oxidation. Materials
**2022**, 15, 3724. [Google Scholar] [CrossRef] - Peron, M.; Skaret, P.C.; Fabrizi, A.; Varone, A.; Montanari, R.; Roven, H.J.; Ferro, P.; Berto, F.; Torgersen, J. The effect of Equal Channel Angular Pressing on the stress corrosion cracking susceptibility of AZ31 alloy in simulated body fluid. J. Mech. Behav. Biomed. Mater.
**2020**, 106, 103724. [Google Scholar] [CrossRef] - Mostaed, E.; Vedani, M.; Hashempour, M.; Bestetti, M. Influence of ECAP process on mechanical and corrosion properties of pure Mg and ZK60 magnesium alloy for biodegradable stent applications. Biomatter
**2014**, 4, e28283. [Google Scholar] [CrossRef] [Green Version] - Alateyah, A.I.; Ahmed, M.M.Z.; Zedan, Y.; El-Hafez, H.A.; Alawad, M.O.; El-Garaihy, W.H. Experimental and Numerical Investigation of the ECAP Processed Copper: Microstructural Evolution, Crystallographic Texture and Hardness Homogeneity. Metals
**2021**, 11, 607. [Google Scholar] [CrossRef] - Lei, W.; Zhang, H. Analysis of microstructural evolution and compressive properties for pure Mg after room-temperature ECAP. Mater. Lett.
**2020**, 271, 127781. [Google Scholar] [CrossRef] - Mostaed, E.; Hashempour, M.; Fabrizi, A.; Dellasega, D.; Bestetti, M.; Bonollo, F.; Vedani, M. Microstructure, texture evolution, mechanical properties and corrosion behavior of ECAP processed ZK60 magnesium alloy for biodegradable applications. J. Mech. Behav. Biomed. Mater.
**2014**, 37, 307–322. [Google Scholar] [CrossRef] [PubMed] - Tolaminejad, B.; Dehghani, K. Microstructural characterization and mechanical properties of nanostructured AA1070 aluminum after equal channel angular extrusion. Mater. Des.
**2012**, 34, 285–292. [Google Scholar] [CrossRef] - Yuan, Y.; Ma, A.; Gou, X.; Jiang, J.; Arhin, G.; Song, D.; Liu, H. Effect of heat treatment and deformation temperature on the mechanical properties of ECAP processed ZK60 magnesium alloy. Mater. Sci. Eng. A
**2016**, 677, 125–132. [Google Scholar] [CrossRef] - Huang, S.-J.; Chiu, C.; Chou, T.-Y.; Rabkin, E. Effect of equal channel angular pressing (ECAP) on hydrogen storage properties of commercial magnesium alloy AZ61. Int. J. Hydrog. Energy
**2018**, 43, 4371–4380. [Google Scholar] [CrossRef] - Minárik, P.; Zimina, M.; Čížek, J.; Stráska, J.; Krajňák, T.; Cieslar, M.; Vlasák, T.; Bohlen, J.; Kurz, G.; Letzig, D. Increased structural stability in twin-roll cast AZ31 magnesium alloy processed by equal channel angular pressing. Mater. Charact.
**2019**, 153, 199–207. [Google Scholar] [CrossRef]

**Figure 2.**EBSD orientation maps for the AA- ZK30 (

**a**) and after the ECAP processing through 1-P (

**b**), 4-A (

**c**), 4-Bc (

**d**), 4-C (

**e**) using the 90°-die and 1-P (

**f**), 4-Bc (

**g**) using the 120°-die and the inverse pole figure (IPF) coloring triangle is shown in (

**h**), red: [001]; blue: [120]; and green: [010].

**Figure 3.**Predicted versus actual values of grain size, where the blue points are for minimum output value and gradually changed to red points for maximum output value.

**Figure 4.**Three-dimensional plot of grain size with ECAP die angle and number of passes at routes A, Bc, and C.

**Figure 5.**Corrosion measurements (

**a**) potentiodynamic polarization curves, and (

**b**) Nyquist plot of AA and ECAPed billets processed via various ECAP conditions.

**Figure 6.**Predicted versus actual values of the ECAP corrosion rate (

**a**) and corrosion resistance (

**b**), where the blue points are for minimum output value and gradually changed to red points for maximum output value.

**Figure 7.**Three-dimensional plot of corrosion rate (

**a**) and corrosion resistance (

**b**) with ECAP die angle and number of passes at routes A, Bc, and C.

**Figure 8.**Predicted versus actual values of the ECAP hardness at the center (

**a**), and the edge (

**b**), where the blue points are for minimum output value and gradually changed to red points for maximum output value.

**Figure 9.**A three-dimensional plot of hardness at the center (

**a**) and edge (

**b**) with the ECAP die angle and number of passes for routes A, Bc, and C.

**Figure 10.**Predicted versus actual values of the ECAP YS (

**a**), TS (

**b**), and D% (

**c**), where the blue points are for minimum output value and gradually changed to red points for maximum output value.

**Figure 11.**Three-dimensional plot of YS (

**a**), TS, (

**b**) and D% (

**c**) with the ECAP die angle and number of passes at routes A, Bc, and C.

**Figure 13.**Optimum corrosion rate (

**a**,

**b**) and corrosion resistance (

**c**,

**d**) by GA (

**a**,

**c**) and hybrid RSM-GA (

**b**,

**d**).

**Figure 15.**Optimum tensile response YS (

**a**,

**b**), TS (

**c**,

**d**), and D% (

**e**,

**f**) by GA (

**a**,

**c**,

**e**) and hybrid RSM-GA (

**b**,

**d**,

**f**).

ECAP Parameters | Parameters Levels | ||
---|---|---|---|

−1 | 0 | 1 | |

Number of passes | 1 | 2 | 4 |

ECAP die angle | 90 | 120 | |

Processing route type | A | Bc | C |

Run | A: No. of Passes | B: Die Angle | C: Processing Route Type |
---|---|---|---|

1 | 1 | 120 | Bc |

2 | 2 | 120 | A |

3 | 4 | 90 | C |

4 | 2 | 120 | C |

5 | 2 | 90 | Bc |

6 | 2 | 120 | A |

7 | 2 | 90 | Bc |

8 | 4 | 120 | Bc |

9 | 4 | 120 | C |

10 | 2 | 120 | Bc |

11 | 1 | 120 | C |

12 | 4 | 90 | Bc |

13 | 1 | 90 | A |

14 | 4 | 90 | A |

15 | 4 | 90 | A |

16 | 1 | 90 | C |

AA | 90°-Die | 120°-Die | |||||
---|---|---|---|---|---|---|---|

1P | 4A | 4Bc | 4C | 1P | 4Bc | ||

Min | 3.39 | 1.13 | 0.23 | 0.23 | 0.28 | 2.24 | 0.76 |

Max | 76.73 | 38.10 | 14.53 | 11.76 | 12.73 | 35.22 | 17.86 |

Average | 26.69 | 3.24 | 2.89 | 1.94 | 2.25 | 5.43 | 1.92 |

St. Deviation | 14.74 | 2.42 | 1.92 | 1.54 | 1.60 | 4.22 | 1.09 |

Response | Experimental | RSM | GA | RSM-GA | |
---|---|---|---|---|---|

Grain Size (µm) | Value | 1.92 | 1.8821 | 1.8759 | 1.8759 |

Cond. | 4 passes, 120°, Route Bc | 4 passes, 117°, Route Bc | 4 passes, 120°, Route Bc | 4 passes, 120°, Route Bc | |

Corrosion rate (mpy) | Value | 0.091 | 0.09109 | 0.0909 | 0.0909 |

Cond. | 4 passes, 90°, Route Bc | 4 passes, 90°, Route Bc | 4 passes, 90°, Route Bc | 4 passes, 90°, Route Bc | |

Corrosion resistance (Ω·cm^{2}) | Value | 1232 | 1149 | 1144 | 1144 |

Cond. | 1 pass, 120°, Route Bc | 1 pass, 120°, Route Bc | 1 pass, 120°, Route Bc | 1 pass, 120°, Route Bc | |

Hardness at center (HV) | Value | 90 | 88.9517 | 88.936 | 88.936 |

Cond. | 4 passes, 120°, Route Bc | 4 passes, 120°, Route Bc | 4 passes, 120°, Route Bc | 4 passes, 120°, Route Bc | |

Hardness at edge (HV) | Value | 97 | 96.7099 | 96.7008 | 96.7008 |

Cond. | 4 passes, 120°, Route Bc | 4 passes, 120°, Route Bc | 4 passes, 120°, Route Bc | 4 passes, 120°, Route Bc | |

YS (MPa) | Value | 98 | 98.0049 | 97.5896 | 97.5909 |

Cond. | 4 passes, 120°, Route Bc | 1 pass, 90°, Route Bc | 4 pass, 90°, Route Bc | 4 pass, 90°, Route Bc | |

TS (MPa) | Value | 342.4 | 342.156 | 342.157 | 342.157 |

Cond. | 4 passes, 90°, Route Bc | 4 passes, 90°, Route Bc | 4 passes, 90°, Route Bc | 4 passes, 90°, Route Bc | |

D% (mm/mm) | Value | 37.3 | 36.19 | 36.19 | 36.19 |

Cond. | 1 pass, 120°, Route C | 1 pass, 120°, Route Bc | 1 pass, 120°, Route Bc | 1 pass, 120°, Route Bc |

Response | GA | RSM-GA | |
---|---|---|---|

Grain Size (µm) | Value | 0.6139 | 0.6139 |

Cond. | 12 passes, 135°, Route Bc | 12 passes, 135°, Route Bc | |

Corrosion rate (mpy) | Value | 0.0069 | 0.0069 |

Cond. | 12 passes, 70°, Route Bc | 12 passes, 70°, Route Bc | |

Corrosion resistance (Ω·cm^{2}) | Value | 21,019.5 | 21,019.5 |

Cond. | 12 pass, 70°, Route Bc | 12 pass, 70°, Route Bc | |

Hardness at center (HV) | Value | 89.0707 | 89.0707 |

Cond. | 4 passes, 135°, Route Bc | 4 passes, 135°, Route Bc | |

Hardness at edge (HV) | Value | 178.73 | 178.73 |

Cond. | 12 passes, 135°, Route Bc | 12 passes, 135°, Route Bc | |

YS (MPa) | Value | 213.51 | 213.509 |

Cond. | 12 passes, 135°, Route Bc | 12 passes, 135°, Route Bc | |

TS (MPa) | Value | 472.153 | 472.153 |

Cond. | 12 passes, 135°, Route Bc | 12 passes, 135°, Route Bc | |

D% (mm/mm) | Value | 37.42 | 37.42 |

Cond. | 1 pass, 135°, Route Bc | 1 pass, 135°, Route Bc |

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Alawad, M.O.; Alateyah, A.I.; El-Garaihy, W.H.; BaQais, A.; Elkatatny, S.; Kouta, H.; Kamel, M.; El-Sanabary, S.
Optimizing the ECAP Parameters of Biodegradable Mg-Zn-Zr Alloy Based on Experimental, Mathematical Empirical, and Response Surface Methodology. *Materials* **2022**, *15*, 7719.
https://doi.org/10.3390/ma15217719

**AMA Style**

Alawad MO, Alateyah AI, El-Garaihy WH, BaQais A, Elkatatny S, Kouta H, Kamel M, El-Sanabary S.
Optimizing the ECAP Parameters of Biodegradable Mg-Zn-Zr Alloy Based on Experimental, Mathematical Empirical, and Response Surface Methodology. *Materials*. 2022; 15(21):7719.
https://doi.org/10.3390/ma15217719

**Chicago/Turabian Style**

Alawad, Majed O., Abdulrahman I. Alateyah, Waleed H. El-Garaihy, Amal BaQais, Sally Elkatatny, Hanan Kouta, Mokhtar Kamel, and Samar El-Sanabary.
2022. "Optimizing the ECAP Parameters of Biodegradable Mg-Zn-Zr Alloy Based on Experimental, Mathematical Empirical, and Response Surface Methodology" *Materials* 15, no. 21: 7719.
https://doi.org/10.3390/ma15217719