# Optimization of the Continuous Galvanizing Heat Treatment Process in Ultra-High Strength Dual Phase Steels Using a Multivariate Model

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^{*}

## Abstract

**:**

_{IA}and T

_{IA}), cooling rate (CR

_{1}) after intercritical austenitizing, holding time at the galvanizing temperature (t

_{G}) and finally the cooling rate (CR

_{2}) to room temperature. In this research work, the effects of CR

_{1}, t

_{G}and CR

_{2}on the ultimate tensile strength (UTS), yield strength (YS), and elongation (EL) of cold rolled low carbon steel were investigated by applying an experimental central composite design and a multivariate regression model. A multi-objective optimization and the Pareto Front were used for the optimization of the continuous galvanizing heat treatments. Typical thermal cycles applied for the production of continuous galvanized AHSS-DP strips were simulated in a quenching dilatometer using miniature tensile specimens. The experimental results of UTS, YS and EL were used to fit the multivariate regression model for the prediction of these mechanical properties from the processing parameters (CR

_{1}, t

_{G}and CR

_{2}). In general, the results show that the proposed multivariate model correctly predicts the mechanical properties of UTS, YS and %EL for DP steels processed under continuous galvanizing conditions. Furthermore, it is demonstrated that the phase transformations that take place during the optimized t

_{G}(galvanizing time) play a dominant role in determining the values of the mechanical properties of the DP steel. The production of hot-dip galvanized DP steels with a minimum tensile strength of 1100 MPa is possible by applying the proposed methodology. The results provide important scientific and technological knowledge about the annealing/galvanizing thermal cycle effects on the microstructure and mechanical properties of DP steels.

## 1. Introduction

_{IA}) within the intercritical (ferrite + austenite) range (i.e., between Ac

_{1}and Ac

_{3}). The initial heating rate (HR

_{1}), T

_{IA}and (t

_{1}+ t

_{2}) allow conditioning of the intercritical austenite and ferrite (initial microstructure).

_{IA}, (t

_{1}+ t

_{2}), (b) grain size, and (c) chemical composition. Also, the metallurgical state of the intercritical ferrite is important (degree of recrystallization, solute content (C, N) and second particle precipitate size and distribution).

_{G}and the secondary cooling rate (CR

_{2}) is fast enough, the intercritical austenite will transform to martensite in this section and a galvanized dual phase steel strip will be produced. It is noteworthy that, in this case, the Zn coating will be formed on an (α + γ) microstructure. The effect of the volume change associated with the martensite transformation on the adherence of the Zn coating has never been investigated. On the other hand, if the metastable intercritical austenite transforms to non-martensite products (pro-eutectoid ferrite, perlite or bainite) at T > T

_{G}, due to slow CR

_{1}cooling rates, the Zn coating will be formed on a complex microstructure consisting of intercritical ferrite, pro-eutectoid ferrite, perlite, bainite and residual metastable austenite. This residual austenite may transform to martensite on further cooling to T < M

_{s}or remain in a metastable form at room temperature. Of course, this will depend on the dynamic changes in hardenability that take place during continuous cooling and the interrupted cooling of the strip at T

_{G}.

## 2. Materials and Methods

#### 2.1. Theoretical Aspects of Multivariate Model

_{1}, t

_{G}and CR

_{2}) with the response variables (UTS, YS and EL). In the regression model of Equation (1) each response variable $y$ in a sample of n observations is represented as a linear function of the process variables $x$ plus a random error ε.

_{1}, t

_{G}and CR

_{2}) on the ultimate tensile strength (UTS), yield strength (YS) and elongation (EL) of the material. It is noteworthy that, although the UTS and other mechanical properties depend on the final microstructure of the steel and the final microstructure depends strongly on the evolution of microstructure from T

_{IA}to room temperature. Therefore, the final mechanical properties depend on the phase transformation behavior of the intercritical austenite during the cooling cycle.

- a)
- Selection of the input variables according to the objective of the investigation;
- b)
- Selection of experimental design and generation of the experimental matrix;
- c)
- Perform the experiments according to the experimental matrix designed;
- d)
- Statistical analysis of the experimental data to obtain the fit of the polynomial function; i.e., obtain the ${\beta}_{i}$ coefficients in Equation (1).
- e)
- Statistical evaluation of the fitted model using multivariate variance analysis (MANOVA) and analysis of determination coefficients (R
^{2});

_{1}, t

_{G}and CR

_{2}). The multivariate model can be written in its general form as follows [38]:

_{0}) and the alternative hypothesis (H

_{1}). In this investigation the test of Wilks (Λ) was used to determine if the process variables have a significant influence on the response variables. This test is based on the calculation of Λ:

_{0}: B1 = 0, where B1 is the matrix X without the first column. The null hypothesis is rejected if Λ ≤ table value and it means that the response variables are influenced by the process variables.

^{2}. For multivariate modeling there are several measurements of association between the y’s and the x’s. One of these measurements is based on Wilks test:

_{1}, t

_{G}and CR

_{2}on the mechanical properties of the steel with chemical composition listed in Table 1.

_{1}, t

_{G}and CR

_{2}) is presented in Table 2 and the 17 conditions produced by the experimental design are shown in Table 3. The experimental matrix represents a composite center design with 3 central points for investigating the relationship of the mechanical properties with the process variables.

_{1}, t

_{G}and CR

_{2}) looking for the results of optimal mechanical properties for the manufacture of a DP steel with the desired properties. For this a genetic algorithm NSGAII (Non-Dominated Sorting Genetic Algorithm) was used, it allows to optimize several responses at the same time, that is, a multi-objective optimization.

#### 2.2. Experimental Methods

_{IA}= 800 °C. Under these conditions of intercritical austenitizing, the software predicts an initial microstructure consisting of 11.3% ferrite and 88.7% austenite, an intercritical austenite grain size of 8.5 µm and an M

_{s}of 365.6 °C.

_{IA}= 800 °C, a wide variety of microstructures, and consequently of properties can be produced depending on the actual cooling conditions during processing. In this work, the effect of introducing an interrupted cooling stage (isothermal holding) at 460 °C to simulate the thermal effects of galvanizing on the microstructure and mechanical properties after final cooling to room temperature is investigated.

^{®}, Binghamton, NY, USA) with a 500 gf load applied during 12 s. The actual initial microstructure of the steel at 800 °C for all dilatometry experiments consists of 35% intercritical ferrite and 65% intercritical austenite with an average intercritical austenite grain size of 2.8 µm. This later value is about 3 times smaller than the one predicted by JMatPro. CR

_{1}and CR

_{2}are varied between 10–110 °C/s, while T

_{G}, the galvanizing temperature, is kept constant at 460 °C. Finally, the interrupted cooling time (t

_{G}) is varied from 3 to 20 s.

## 3. Results and Discussion

#### 3.1. Effect of Thermal Cycle on Mechanical Properties

#### 3.2. Development of Statistical Model

_{0}: r = 0 versus H

_{1}: r ≠ 0 where r is the correlation between a pair of variables.

_{0}indicates that there is no correlation between the variables analyzed. Thus, the p-value is used to reject or not the null hypothesis, that is, if the p-value is less than the value of alpha (α = 0.05) the null hypothesis is rejected and therefore the variables could be correlated. The level of alpha often used is 0.05 which means that the possibility of finding an effect that does not really exist is only 5%. Then, when the alpha value is equal to 0.05, the results can be accepted with 95% confidence [41].

_{1}and CR

_{2}have a positive linear relationship with the UTS. In contrast, the cooling interruption time (t

_{G}) at 460 °C has a negative linear relationship with the UTS. The variable that has the greatest impact on UTS is t

_{G}at 460 °C, where increasing t

_{G}causes a decrease in UTS. The same behavior is noted for YS, but for EL the cooling rate CR

_{1}and the time t

_{G}have opposite effects than those presented by UTS and YS.

_{G}since smaller amounts of martensite would be present at room temperature after the final cooling.

^{2}) was calculated according to Equation (5): R

^{2}= 91%. This result indicates that the model has a good fit since the coefficient of determination is greater than 80% [41]. It can be that 91% of the variability of the process is explained. The models in Equations (6)–(8) allow optimizing the heat treatment process using the optimization algorithm NSGA II and helps to predict the behavior of the process considering input variables changes.

- a)
- The variance of the errors (residuals) must be homogeneous;
- b)
- Errors must be independent;
- c)
- Errors must have a normal distribution.

_{0}), the model can lose its efficiency and makes erroneous predictions [43]. The variance of the models (Equations (6)–(8)) is homogeneous since the p-values of the tests were greater than α = 0.05 according to the results in Table 6.

_{0}) is that the variable under analysis is not significant. According to the results in Table 7, the interactions between the input variables are not significant (p-value > α = 0.05). The results also show that CR

_{2}is not significant. However, it was assumed that this variable is significant considering that, from physical metallurgy point of view, CR

_{2}does play an important role in the transformation to martensite of any residual austenite at the end of the interruption of cooling at 460 °C. Of course, this is important when considering the thermal cycles involved in continuous galvanizing.

^{2}= 91%). Thus, Equations 6-8 were used as objective functions in the optimization of input variables, as will be shown in the next sections.

#### 3.3. Optimization

#### 3.4. Effects of Process Parameters

_{1}) must be fast enough to avoid the formation of perlite or bainite and retain carbon in solution in the metastable austenite until the transformation to martensite takes place at T < M

_{s}. With the statistical models developed in this work (Equations (6)–(8)) it is possible to predict the effect of CR

_{1}over the mechanical properties to DP steel, as shown in Figure 7. To plot this graph, the secondary cooling rate (CR

_{2}) was kept constant at 25°C/s and t

_{G}at 13 s. As can be seen, both the UTS and YS tend to decrease with slower initial cooling rates (CR

_{1}).

_{1}between 10 °C/s and 30 °C/s with the other parameters constants at: HR

_{1}= 35 °C/s; T

_{IA}= 800 °C, t

_{2}= 60 s; t

_{G}= 13s, T

_{G}= 460 °C and CR

_{2}= 25 °C/s.

_{G}at 460 °C the UTS and the YS decreases, and the elongation increases. Thus, in order to ensure the desired mechanical properties (UTS > 1100 MPa, YS between 550 and 750 MPa and elongation to fracture greater than 10%), the time of interruption of cooling must be between 13 and 17 s when the other process variables are set to: HR

_{1}= 35 °C/s; T

_{IA}= 800 °C, t

_{2}= 60 s; CR

_{1}= 13 °C/s, T

_{G}= 460 °C and CR

_{2}= 25 °C/s.

_{G}increases, the UTS decreases and this behavior is associated with the formation of lower strength microstructures. The formation of bainite and consequently the decrease in the fraction of martensite in the microstructure causes the observed decrease in tensile strength. According to the TTT and CCT diagrams (Figure 2), the transformation of metastable austenite to bainite occurs during the interruption of cooling. Fonstein [1] reported that there is little information about the effect of the presence of bainite in DP steels. However, some data indicate that the hardening generated by bainite in DP steels is weaker than that generated by the presence of martensite. Also, Fonstein et.al [44] report that a 10% replacement of martensite by bainite decreases the UTS in 40 MPa.

_{s}) of most industrial DP-steel grades are lower than 450 °C. Therefore, the formation of bainite in processes that involve interruption of cooling, such continuous galvanizing, can inhibit the formation of martensite and, consequently, the desired strength in the steel will not be obtained.

_{2}) does not significantly influence the final mechanical properties. This result is similar to that reported by other researchers [1], who suggest that this final cooling rate (CR

_{2}) does not have a significant influence on the strength of the steel. The reason for this suggestion is that the amount of martensite generated is determined by the initial cooling rate in thermal cycles to obtain DP-steels without interrupted cooling at 460 °C. However, in this work, the isothermal holding at 460 °C prior to the final cooling produces residual metastable austenite with more carbon compared to the intercritical austenite and then the final rate for the transformation of the residual austenite has a significant effect in the UTS. Furthermore, using HR

_{1}= 35 °C/s; T

_{IA}= 800 °C, t

_{2}= 60 s; CR

_{1}= 13 °C/s, T

_{G}= 460 °C and t

_{G}= 13 s, it is possible to obtain a galvanizing DP steel with minimum UTS of 1100 MPa, YS between 550 and 750 MPa and a minimum elongation of 10% with the final cooling rate (CR

_{2}) between 10 and 70 °C/s.

_{1}= 35 °C/s; T

_{IA}= 800 °C, t

_{2}= 60 s; CR

_{1}= 12–30 °C/s, T

_{G}= 460 °C, t

_{G}= 13–17 s and CR

_{2}= 15–30 °C/s, allow to obtain galvanizing DP steel with a minimum UTS of 1100 MPa, a maximum YS of 750 MPa and a minimum elongation to fracture of 10%.

_{G}is increased is related to the lower amount of martensite produced as a result of the final cooling, due to the formation of bainite during the holding period at 460 °C. These results are in accordance with those reported by Bellhouse [2] that studied the effect of the holding time at 465 °C on the mechanical properties and microstructure of TRIP steels using a thermal cycle very similar to the one used in this work.

## 4. Conclusions

_{G}has a strong impact on the UTS, due to the transformation of the metastable austenite to bainite that causes that the UTS and YS decrease as the time of interruption increases.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic representation of an idealized continuous galvanizing cycle for the production of galvanized AHSS- dual phase steel strips.

**Figure 2.**Calculated TTT (

**a**) and CCT (

**b**) diagrams for the steel investigated. The calculation was performed assuming a T

_{IA}= 800 °C.

**Figure 6.**Microstructure of TVF-3 heat treated sample: (

**a**) 2500× and (

**b**) 10,000×; B: Cainite; α: Ferrite and α’: Martensite.

**Figure 7.**Effect of CR

_{1}on mechanical properties of dual phase (DP) steel. Calculations with statistical models.

**Figure 8.**Effect of interruption of cooling (t

_{G}) on the mechanical properties of DP steel. Calculations with statistical models.

**Figure 9.**Effect of CR

_{2}on UTS mechanical properties in DP steel. Calculations with statistical models.

Element | C | Si | Mn | P | S | Cr | Mo | Ni | B |

wt. % | 0.154 | 0.260 | 1.906 | 0.013 | 0.0009 | 0.413 | 0.108 | 0.048 | 0.0010 |

Element | Al | Cu | Nb | Ti | V | Ca | N | Fe + Impurities | |

wt. % | 0.036 | 0.018 | 0.004 | 0.044 | 0.008 | 0.001 | 0.0036 | Balance |

Notation | Process Variable | Unit | Level | |
---|---|---|---|---|

Low −1 | High +1 | |||

x_{1} | Cooling rate (CR_{1}) | °C/s | 10 | 110 |

x_{2} | Hold time (t_{G}) | s | 3 | 20 |

x_{3} | Cooling rate (CR_{2}) | °C/s | 10 | 110 |

Run | Process Variables | ||
---|---|---|---|

CR_{1} | t_{G} | CR_{2} | |

°C/s | s | °C/s | |

1 | 30 | 17 | 90 |

2 | 10 | 11 | 60 |

3 | 110 | 11 | 60 |

4 | 60 | 11 | 60 |

5 | 90 | 6 | 30 |

6 | 60 | 11 | 10 |

7 | 30 | 17 | 30 |

8 | 30 | 6 | 90 |

9 | 30 | 6 | 30 |

10 | 90 | 6 | 90 |

11 | 60 | 20 | 60 |

12 | 60 | 11 | 60 |

13 | 60 | 11 | 110 |

14 | 90 | 17 | 90 |

15 | 60 | 11 | 60 |

16 | 90 | 17 | 30 |

17 | 60 | 3 | 60 |

**Table 4.**Mechanical properties for each of the experimental combination (standard deviation in brackets).

Run | Response Variables | Run | Response Variables | ||||
---|---|---|---|---|---|---|---|

UTS | YS | EL | UTS | YS | EL | ||

MPa | MPa | % | MPa | MPa | % | ||

1 | 1142 (3) | 729 (13) | 11.3 (3.3) | 10 | 1274 (13) | 959 (30) | 8.6 (0.6) |

2 | 1174 (34) | 754 (21) | 12.1 (3.1) | 11 | 1123 (4) | 730 (28) | 9.9 (1.2) |

3 | 1237 (1) | 829 (7) | 10.3 (0.5) | 12 | 1187 (9) | 828 (17) | 10.5 (1.8) |

4 | 1245 (4) | 853 (9) | 10.8 (0.6) | 13 | 1203 (20) | 781 (13) | 10.7 (0.3) |

5 | 1264 (6) | 890 (19) | 8.3 (0.7) | 14 | 1145 (13) | 779 (24) | 9.4 (1.6) |

6 | 1141 (18) | 745 (31) | 9.9 (1.6) | 15 | 1199 (8) | 844 (33) | 9.5 (1.1) |

7 | 1131 (32) | 725 (18) | 10.7 (0.9) | 16 | 1166 (12) | 777 (16) | 10.1 (0.8) |

8 | 1226 (3) | 841 (20) | 8.6 (1.3) | 17 | 1294 (31) | 1015 (11) | 8.0 (0.6) |

9 | 1196 (8) | 791 (11) | 9.8 (0.8) | - | - | - | - |

Variable | UTS | YS |
---|---|---|

YS | 0.926 0.000 | - |

EL | −0.570 0.017 | −0.717 0.001 |

Contents of the cell: Pearson Correlation p-value |

**Table 6.**Breusch-Pagan test for verification of the homogeneity of the variance of the residuals for each response variable.

Studentized Breusch-Pagan Test | |
---|---|

Model | p-Value |

(UTS ~ V1 + t2 + V2) | 0.71 |

(YS ~ V1 + t2 + V2) | 0.2588 |

(EL ~ V1 + t2 + V2) | 0.6142 |

Terms | Valor–P |
---|---|

V_{1} | 0.0432031 |

t_{2} | 0.0003479 |

V_{2} | 0.5830329 |

V_{1}t_{2} | 0.7387451 |

t_{2}V_{2} | 0.8638424 |

V_{1}V_{2} | 0.6460354 |

Test | CR_{1}(°C/s) | t_{G}(s) | CR_{2}(°C/s) | Model Results | Experimental Results | ||||
---|---|---|---|---|---|---|---|---|---|

UTS (MPa) | YS (MPa) | EL (%) | UTS (MPa) | YS (MPa) | EL (%) | ||||

TVF-1 | 10 | 15 | 26 | 1120 | 698 | 11.3 | 1140 | 749 | 10.5 |

TVF-2 | 10 | 15 | 13 | 1116 | 692 | 11.2 | 1109 | 683 | 10.7 |

TVF-3 | 13 | 13 | 25 | 1144 | 732 | 10.9 | 1116 | 734 | 11.3 |

TVF-4 | 17 | 14 | 15 | 1126 | 708 | 11.0 | 1129 | 767 | 11.6 |

TVF-5 | 15 | 15 | 24 | 1123 | 704 | 11.1 | 1162 | 757 | 10.6 |

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## Share and Cite

**MDPI and ACS Style**

Costa, P.; Altamirano, G.; Salinas, A.; González-González, D.S.; Goodwin, F.
Optimization of the Continuous Galvanizing Heat Treatment Process in Ultra-High Strength Dual Phase Steels Using a Multivariate Model. *Metals* **2019**, *9*, 703.
https://doi.org/10.3390/met9060703

**AMA Style**

Costa P, Altamirano G, Salinas A, González-González DS, Goodwin F.
Optimization of the Continuous Galvanizing Heat Treatment Process in Ultra-High Strength Dual Phase Steels Using a Multivariate Model. *Metals*. 2019; 9(6):703.
https://doi.org/10.3390/met9060703

**Chicago/Turabian Style**

Costa, Patricia, Gerardo Altamirano, Armando Salinas, David S. González-González, and Frank Goodwin.
2019. "Optimization of the Continuous Galvanizing Heat Treatment Process in Ultra-High Strength Dual Phase Steels Using a Multivariate Model" *Metals* 9, no. 6: 703.
https://doi.org/10.3390/met9060703