metals Article
Using the Multi-Response Method with Desirability Functions to Optimize the Zinc Electroplating of Steel Screws Ruben Lostado Lorza 1, * , María Ángeles Martínez Calvo 1 , Carlos Berlanga Labari 2 and Pedro J. Rivero Fuente 2 1 2
*
Department of Mechanical Engineering, University of La Rioja, 26004 Logroño, La Rioja, Spain;
[email protected] Institute for Advanced Materials (INAMAT), Department of Mechanical Engineering, Public University of Navarre—UPNA, Campus Arrosadía S/N, 31006 Pamplona, Navarre, Spain;
[email protected] (C.B.L.);
[email protected] (P.J.R.F.) Correspondence:
[email protected]; Tel.: +34-941-299-527
Received: 24 August 2018; Accepted: 5 September 2018; Published: 11 September 2018
Abstract: Zinc electroplating is a coating process controlled by several input process parameters. However, the commonly used input parameters for setting the process of zinc deposition are current density, temperature of the coating solution, zinc concentration, deposition time, and concentration of additives (conditioner and brightener). The power consumed in the zinc plating process, coating thickness, increase in coating mass, and corrosion resistance are considered to be outputs or zinc coating parameters. They are widely used when the zinc coating requirements are based on the coating process cost, coating process speed, corrosion resistance, and coating thickness. This paper seeks to determine regression models by the response surface method (RSM) that relate the zinc coating parameters to the input parameters in steel screws. When considering the coating requirements of cost, coating process speed, corrosion resistance, and coating thickness, the optimal input parameters were found by using a multi-response surface (MRS). Input parameters of 0.3 amps/dm2 , 20.0 ◦ C, 13.9 g/L, 45 min, 28.5 mL/L, and 2.8 mL/L, respectively (relative to the commonly used input parameters detailed above), were obtained when considering the cost. Considering minimization of the deposition time, the input parameters obtained were 0.5 amps/dm2 , 24.6 ◦ C, 13.9 g/L, 45 min, 26.9 mL/L, and 1.1 mL/L, respectively. The optimal inputs to maximize the corrosion resistance were 0.6 amps/dm2 , 32.4 ◦ C, 14.0 g/L, 45 min, 28.7 mL/L, and 2.5 mL/L, respectively. Finally, when maximizing the coating thickness, the inputs were 0.7 amps/dm2 , 38.4 ◦ C, 12.2 g/L, 45 min, 26.5 mL/L, and 1.5 mL/L, respectively. Keywords: modeling and optimizing zinc electroplating in steel screws; experimental design; multi-response surface method (MRS); desirability functions
1. Introduction Zinc electroplating is one of the most commonly used methods to protect steel from the corrosion process. The reason for this is that it is a low-cost fabrication process in comparison to other deposition technologies. Thus, it is the preferred choice for many companies that keep a close eye on expenditures. The main way of using zinc to protect steel from corrosion is by sacrificial protection of the steel. This means that the zinc coating will be first to be corroded, instead of the metallic substrate, in order to increase the latter’s corrosion resistance [1–3]. One of the most important industrial applications of zinc electroplating is found in the automotive sector where it provides corrosion protection to brake pipes, brake calipers, and power steering components. It also can be employed in the military Metals 2018, 8, 711; doi:10.3390/met8090711
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sector (tanks and armored personnel carriers) or as a protective coating prior to painting for better adhesion of paint to steel surfaces [4,5]. However, considerable efforts are continuously given to the development and implementation of new surface finishing processes for zinc plating due to the unending requirements of industry (especially in the automotive sector) for longer service life and better corrosion resistance in harsher environments [6–8]. Several strategies have been used to improve the corrosion resistance of zinc electroplating, such as using zinc alloy coatings [9,10]. As an example, Short et al. [9] demonstrated that the use of zinc-nickel electrodeposits that contain about 12–13% Ni promoted an increase in corrosion resistance compared with pure zinc electrodeposits. However, the effect of different factors, such as temperature, current density, time, zinc concentration, and additive concentration, on the corrosion rate has not been proven yet. This process involves the electrolytic deposition of a thin coating of zinc onto the surface of the metal to be protected, which is known as a substrate. This process is governed by several factors. However, current density (ρ), temperature (T), and concentration of the zinc deposit (C) have the most significant influence on zinc deposition [11]. The current density (ρ) has a significant impact on the thickness of the zinc coating (Th). As a general rule, the thickness of the zinc coating obtained rises as the current density increases [12]. However, if the current density (ρ) exceeds a threshold value, a rough surface of the zinc substrate is generated, leading it to have a lower corrosion resistance (R) than if the surface was smooth [13]. At a higher temperature (T), there is an increase in the diffusion of hydrogen at the cathode. In addition, the absorption of hydrogen in metals is a serious problem during zinc electroplating. In fact, it is often said that a zinc layer acts as a barrier against hydrogen absorption. This greatly improves the mechanical and anticorrosive characteristics of the zinc coating. In addition, when the temperature (T) and the current density (ρ) increase at the same time, the deposited zinc is much brighter. On the other hand, when the temperature (T) increases and the current density (ρ) remains constant, the zinc coating is irregular, because the zinc crystals that are deposited on the substrate are very large [14]. Also, the concentration of zinc (C) in the coating solution affects the brightness and surface finish of the zinc deposit. Higher concentrations (C) will produce a rougher surface with large zinc crystals, whereas lower concentrations will provide a brighter finish with finer and more corrosion-resistant crystals [15]. In recent decades, some scientific studies have been conducted to determine which factors are most important in improving the performance of the zinc plating process [16,17]. However, these scientific studies have not been supported by multivariate statistical techniques that investigate how one factor influences the other factors. One of the most frequently used techniques used to study the influence of a factor or input on the others and then optimize the combination of factors to obtain the best output is response surface methodology (RSM) [18,19]. When there is more than one output, several response surfaces should be optimized using the multi-response surface method (MRS) [20]. In this paper, a group of regression models that are based on the RSM were used to relate the zinc coating requirements (outputs) to the zinc coating process parameters (inputs). The latter were current density (ρ), temperature of the coating solution (T), zinc concentration (C), deposition time (t), concentration of Additive 1 (Envirozin Conditioner (CA1)), and concentration of Additive 2 (Envirozin 100 Initial Brightener (CA2)). The response surface method (RSM) for steel screws was used. Then, while considering zinc coating requirements based on cost, manufacturing speed, corrosion resistance, and coating thickness, the optimal input process parameters were found by using the multi-response surface (MRS) with the desirability functions. The power consumed in the zinc plating process (W) and the increase in coating mass (∆M) are the zinc coating process parameters that are used when the zinc coating requirements are based on cost. However, the deposition time (t) is the parameter that is used when the zinc coating process parameters requirements are based on the electroplating process speed. Corrosion resistance (R) is the parameter used when the zinc coating process parameter requirements are based on the corrosion resistance. Finally, zinc coating (Th) is the parameter used when the zinc coating process parameters requirements are based on the coating thickness. This paper concentrates on a study of the zinc electroplating process in steel screws for
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the following ranges: current densities (ρ), 2–3 amps/dm2 ; temperature (T), 30–40 ◦ C; concentration 6, x of 20 of Metals zinc 2018 deposit (C), 8–14 (g/L); time (t), 30–60 min.; Concentration Additive 1 (CA1), 8–10 3(mL/L); and Concentration Additive 2 (CA2), 1–3 (mL/L). Figure 1 shows a scheme in which all inputs and Concentration Additive 1 (CA1), 8–10 (mL/L); and Concentration Additive 2 (CA2), 1–3 (mL/L). outputs wereaconsidered in this all work are and usedoutputs for modeling andconsidered optimizinginthe electroplating Figurethat 1 shows scheme in which inputs that were thiszinc work are used process of screws. for modeling and optimizing the zinc electroplating process of screws.
Figure Inputsand andoutputs outputsthat that were were considered considered in and optimizing of of Figure 1. 1.Inputs inthis thiswork workfor forthe themodelling modelling and optimizing the zinc electroplating process of screws. the zinc electroplating process of screws.
2. 2. Modeling with Desirability DesirabilityFunctions Functions Modelingand andOptimizing OptimizingUsing Using the the RSM with The RSM seeks to determine relationships of input variables (independent variables) to The RSM seeks to determine thethe relationships of input variables (independent variables) to output output variables variables). It was developed as a to means to model experimental responses. variables (response(response variables). It was developed as a means model experimental responses. Box and Box and Wilson introduced the in method 1951 to create a model for optimal response with Wilson introduced the method 1951 in [18] to [18] create a model for optimal response with thethe data data provided by experiments. It has been used recently along with other techniques for the of provided by experiments. It has been used recently along with other techniques for the optimization optimization of products and industrial [21–24]. In is essence, the RSM is a collection of products and industrial processes [21–24]. processes In essence, the RSM a collection of statistical techniques statistical techniques that uses a regression model based on a low-degree polynomial function that uses a regression model based on a low-degree polynomial function (Equation (1)): (Equation (1)):
Y= . . .X, X)k+) e+ e 2 ,2X Y f=( X f (1X, 1X,X ,X33, ,..., k
(1) (1)
where experimentalresponse, response, (X (X11, X input vector, e is an term,term, and fand is f where YY is is ananexperimental X22,,XX3,3…, , . . .X,k)Xisk )the is the input vector, e iserror an error a function of cross-products of the polynomial’s terms. The quadratic model (second-order) is a is is a function of cross-products of the polynomial’s terms. The quadratic model (second-order) widely-used polynomial function. It appears in Equation (2): a widely-used polynomial function. It appears in Equation (2): n
n
n −1
n
n−1 b n ij ⋅ Xi ⋅ Xj + e Y = bn0 + bi ⋅ Xi +n bii ⋅ X i2 +
1 j = i +1 Y = b0 + ∑ bii =·1Xi + ∑i =b1 ii · Xi2 + i =∑ ∑ bij · Xi · Xj + e
i =1
i =1
i =1 j = i +1
(2)
(2)
where the linear part is the first summation, the quadratic part is the second, and the product of the , bi, bii, andpart bij are determined using pairs the of variables is is thethe third. coefficients where linear part firstThe summation, theb0quadratic is the second, and theregression product of analysis. However, satisfactory results are not always obtained from these functions for complex the pairs of variables is the third. The coefficients b0 , bi , bii , and bij are determined using regression problems that havesatisfactory many inputsresults and nonlinearities. The obtained reason forfrom this isthese that continuous functions analysis. However, are not always functions for complex are defined by polynomials. Thus, if data are insufficient, the functions cannot be adjusted.are problems that have many inputs and nonlinearities. The reason for this is that continuous functions The p-value (or Prob. > F) is the probability of receiving a result that equals or exceeds what was defined by polynomials. Thus, if data are insufficient, the functions cannot be adjusted. The p-value observed. This assumes that the model is accurate. It can be determined by analysis of variance (or Prob. > F) is the probability of receiving a result that equals or exceeds what was observed. (ANOVA). If the Prob. is greater than the F value of the model and the model has no term with a level This assumes that the model is accurate. It can be determined by analysis of variance (ANOVA). If the of significance that exceeds, for example, α = 0.05, the model will be acceptable at a confidence interval Prob. is greater than the F value of the model and the model has no term with a level of significance of (1 − α). Some researchers have employed ANOVA to determine the inputs’ or process parameters’ influence on the zinc plating process outputs [25,26]. If there is more than one output, the problem is
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that exceeds, for example, α = 0.05, the model will be acceptable at a confidence interval of (1 − α). Some researchers have employed ANOVA to determine the inputs’ or process parameters’ influence on the zinc plating process outputs [25,26]. If there is more than one output, the problem is termed an MRS. This implies that the outputs are in disagreement. There can be a great difference between the optimal configurations for different outputs. Harrington [27] proposed a compromise between outputs, comprising desirability functions for each output, as shown in Equations (3) and (4), and an overall desirability measure, namely, the geometric mean D of each output’s desirability (Equation (5)).
dmax = r
dmin = r
0 fr (X) − A S B−A 1 1 fr ( X ) − B S A−B 0 R
D=
∏ dr
if fr (X) < A if A ≤ fr (X) ≤ B
(3)
if fr (X) > B if fr (X) < A if A ≤ fr (X) ≤ B
(4)
if fr (X) > B !1/R (5)
r=1
In the equations above, A and B are limit values and the exponent s determines the importance of achieving the target value; X is the input vector and fr is the model used in the prediction. To optimize one or more responses, one should use a higher-degree polynomial [28]. The desirability approach requires that each estimated response be transformed into a unitless utility whose boundaries are 0 < dr < 1, where higher values of dr indicate more desirable response values. The optimization portion of the R package v.1.6 looks for a combination of factors (or weights in the range 1–3) that simultaneously satisfy the optimization criteria of all responses and inputs. 3. Electroplating Process Factors Examined by Use of RSM Researchers have previously employed RSM to identify an optimal combination of process parameters or inputs for the electroplating process. However, most of their works have been based on modelling and optimizing the electroplating process and have involved relatively few input and output parameters. For example, Oraon et al. [29] used multi-response optimization of the nickel electroplating process to model the deposited mass per unit area (g/cm2 ) considering the concentration of NiCl2 ·6H2 O, the concentration of NaBH4 , and the temperature (◦ C) as the nickel coating process input parameters. In this case, they observed that reducing the concentration of NiCl2 ·6H2 O, the concentration of NaBH4 , and the temperature significantly influenced the deposition of the nickel coating. Santana et al. [30] studied the optimization of the electrolytic bath for electro-deposition of corrosion-resistant Fe–W–B alloys using multi-response optimization. In their case, a full factorial design was considered for the design of the experiments. Other authors, such as Poroch et al. [31], used multi-response optimization combined with a genetic algorithm to optimize the nickel electroplating process in order to improve the cathode efficiency, coating thickness, brightness, and hardness of the metallic layer. They used the nickel coating process input parameters of current density (amps/dm2 ), temperature T (◦ C), and pH. More recently, Poroch et al. [32] studied the modelling and optimization of nickel-iron electroplating process variables to maximize the surface hardness while considering current density (amps/dm2 ), temperature (◦ C), and pH as input factors. Also, Poroch et al. [33] used the design of experiments and response surface methodology to model and optimize an Fe-Ni electroplating process from a chloride-sulphate bath. They optimized the Fe-Ni electroplating process by using the desirability function approach.
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4. Experimental Experimental Setup Setup and and Results Results 4. Before undertaking undertaking the the zinc zinc electroplating electroplating process, process, all all steel steel screws screws were were subjected subjected to to aa standard standard Before zinc phosphating process. This was done to provide a foundation for improvement of the adhesion of zinc phosphating process. This was done to provide a foundation for improvement of the adhesion thethe coating to be to steel parts.parts. Then,Then, each ofeach the phosphate screws was weighed on a precision of coating toapplied be applied to steel of the phosphate screws was weighed on a balance to determine its initial mass prior to application of the zinc coating. The zinc electroplating precision balance to determine its initial mass prior to application of the zinc coating. The zinc process was then carried an isothermal that was connected an adjustable electroplating process was out thenincarried out in ancontainer isothermal container that was to connected to an heater, into which each proposed solution was poured. These solutions were proposed based on adjustable heater, into which each proposed solution was poured. These solutions were proposed zinc concentration (C), sodium hydroxide concentration, additive concentration 1 (CA1; Envirozin based on zinc concentration (C), sodium hydroxide concentration, additive concentration 1 (CA1; Conditioner), and additive concentration 2 (CA2, Envirozin 100Envirozin Initial Brightener). The positive pole of Envirozin Conditioner), and additive concentration 2 (CA2, 100 Initial Brightener). The the power supply was connected a pure zinc plate served a cathode. The negative pole was positive pole of the power supplytowas connected to that a pure zinc as plate that served as a cathode. The connected to the already phosphated steel screws, which served as the anode. Once the temperature of negative pole was connected to the already phosphated steel screws, which served as the anode. Once the previously proposed solution had been reached, each of the screws was each completely in the temperature of the previously proposed solution had been reached, of the immersed screws was this specific solution. Next, the power supply was connected and the values of intensity and voltage completely immersed in this specific solution. Next, the power supply was connected and the values forintensity the deposition of the proposed zinc coatings adjusted until valueswere of theadjusted proposed current of and voltage for the deposition of were the proposed zinc the coatings until the densities (ρ) were reached. The current density values were obtained from the current provided by the values of the proposed current densities (ρ) were reached. The current density values were obtained power source and from the surface of the screw. The current was measured using the power supply’s from the current provided by the power source and from the surface of the screw. The current was ammeter, whereas the power surfacesupply’s of the screws was obtained Catia v5 R18 (Woodlands measured using the ammeter, whereastheoretically the surfaceusing of the screws was obtained Hills, CA, USA) [34]. However, for the purpose of always keeping the exposed surface of the screws theoretically using Catia v5 R18 (Woodlands Hills, CA, USA) [34]. However, for the purpose of unchanged, the position of the screws inside the isothermal container was also left unchanged, as always keeping the exposed surface of the screws unchanged, the position of the screws insidewell the as the distance between cathode and the anode. Figure 2 shows thebetween proposed of the the isothermal container wasthe also left unchanged, as well as the distance theinstallation cathode and zinc electroplating of the phosphate screws. anode. Figure 2 shows the proposed installation of the zinc electroplating of the phosphate screws.
Figure Figure 2. 2. Details Details of of the the isothermal isothermal container container and and the the power power supply supply used used in in electroplating electroplating of of the the phosphate phosphate screws. screws.
(t) (t) for the of the coating elapsed, power supply was disconnected, After the thetime time for deposition the deposition of the had coating had the elapsed, the power supply was and the zinc-plated screw was withdrawn from the solution submerged in submerged pure water in to disconnected, and the zinc-plated screw was withdrawn fromand thethen solution and then remove the to dissolution residues from its surface. Then, the zinc-plated screw was immersed for pure water remove the dissolution residues from its surface. Then, the zinc-plated screw was 30 s in a passivating (TRIPASS 3) andECO subsequently immersed immersed for 60 s infor a sealant immersed for 30 s in aproduct passivating productECO (TRIPASS 3) and subsequently 60 s in 30). After the screws that had been treated passivant aproduct sealant(Hydroklad product (Hydroklad 30).zinc-plated After the zinc-plated screws that had with been the treated with and the sealant were completely dry, they were weighed again on weighed the precision scale. Theprecision differencescale. in masses passivant and sealant were completely dry, they were again on the The between the phosphate and galvanized screws the coating mass (∆M). Theincrease coating difference in masses between the phosphate andwas galvanized screws wasincrease the coating mass thickness (Th) was conducted by(Th) means a nondestructive technique is based on (ΔM). Themeasurement coating thickness measurement wasofconducted by means of a that nondestructive the magnetic phenomenon andinduction is in accordance with ASTM [35]. Awith measuring technique thatinduction is based on the magnetic phenomenon and is B499-09 in accordance ASTM device Minitest (Model 1100, Elektrophysik, Cologne, Germany) thatCologne, was equipped with anwas FN B499-09 [35]. A measuring device Minitest (Model 1100, Elektrophysik, Germany) that equipped with an FN 1.6-typeinprobe wasfor selected in this case for use zinc when dealingon with zinc coatings 1.6-type probe was selected this case use when dealing with coatings steel substrates. on steel substrates. The measurement of the coatings was made at four different points on each of the galvanized screws and an average value of the coatings was subsequently calculated. In order to
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6 of 20 Metals 2018 6, x Metals 2018 6, x The measurement ofthe thethickness, coatings was at four different points on each method of measuring the made thickness of the coatings of several
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6 of 20 of the galvanized screws and adjust this and an average value of the coatings was subsequently calculated. In order to validate and adjust this validate and adjustby this method of measuring thebased thickness, the thickness of the coatings of several nc-plated steel screws was measured means of destructive tests on metallographic validate and adjust this method of measuring the thickness, the thickness of the coatings of several method of measuring the thickness, the resistance thickness of all theof coatings of several of the steel of the E3-95 zinc-plated steel screws was measured by means destructive tests based onzinc-plated metallographic according to the ASTM standard [36]. The corrosion of samples obtained of the zinc-plated steelbyscrews was measured by means ofondestructive tests based on according metallographic screws was measured means of destructive tests based metallographic methods to the according to the standard [36]. The corrosionusing resistance of all samples obtained nc electroplating methods process was evaluated byASTM takingE3-95 electrochemical measurements a methods according to the ASTM E3-95 standard [36].ofThe corrosion resistance ofthe allzinc samples obtained ASTM E3-95 standard [36]. The corrosion resistance all samples obtained by electroplating by the zinc electroplating process was evaluated by taking electrochemical measurements using a dynamic polarization technique [37]. Open-circuit potential (OCP) measurement and linear by the zinc electroplating process was evaluated by taking electrochemical measurements using a process was evaluated by taking electrochemical measurements using a potentiodynamic potentiodynamic technique [37]. Open-circuit methods. potential (OCP) and linear scan experiments were chosen polarization as the electrochemical measurement The measurementpolarization potentiodynamic polarization potential technique(OCP) [37]. Open-circuit potential (OCP) measurement and linear technique [37].anexperiments Open-circuit and linear potential scan experiments potential scan were chosen asmeasurement the electrochemical measurement methods. The ments were conducted using AUTOLAB-PGSTAT computer-controlled potentiostat potential scan experiments were chosen as the electrochemical measurement methods. The were chosen aswere the aerated electrochemical methods. Thecomputer-controlled measurements werepotentiostat conducted measurements conducted using an solution AUTOLAB-PGSTAT m, Herisau, Switzerland) in a naturally 3.5 wt. %measurement NaCl at room temperature. measurements were conducted using an AUTOLAB-PGSTAT computer-controlled potentiostat using an three-electrode AUTOLAB-PGSTAT computer-controlled potentiostat Herisau, Switzerland) in (Metrohm, Herisau, Switzerland) inused a naturally 3.5 bar wt. % NaCl solution at room temperature. purpose, a conventional cell was with aaerated graphite as(Metrohm, counter (Metrohm, Herisau, Switzerland) in asolution naturally aerated 3.5 wt. % NaCl solution at room temperature. a naturally aerated 3.5 wt. % NaCl at room temperature. For this purpose, a conventional purpose, a conventional three-electrode cell was with , an Ag/AgCl/3 MFor KClthis electrode as reference electrode, and the specimen (steelused screw) as aa graphite bar as counter For this purpose, a conventional three-electrode cell was used with a graphite M bar aselectrode counter three-electrode cell was used with a graphite bar as counter electrode, an Ag/AgCl/3 KCl electrode, an Ag/AgCl/3 M KCl electrode as reference electrode, and the specimen (steel screw) as a electrode [38–42]. A glass cell containing 150 mL of 3.5 wt. % NaCl solution (corrosive electrode, an Ag/AgCl/3 M KCl electrode as reference electrode, and the specimen (steel screw) as a as reference electrode, and the specimen (steel screw) as a working electrode [38–42]. A glass cell working electrode [38–42]. A glass cell3acontaining mL of 3.5 wt. to % NaCl solution (corrosive te) was used for each electrochemical experiment. Figure shows the 150 connections made working electrode [38–42]. A glass cell containing 150electrolyte) mL of 3.5was wt. used % NaCl solution (corrosive containing mL of wt. %electrochemical NaCl solution (corrosive forconnections each electrochemical electrolyte) was used for each experiment. Figurethe 3a glass shows the made to he electrodes while Figure 3b150 shows the3.5 placement of each of the electrodes inside electrolyte) was used for each electrochemical experiment. Figure 3a shows the connections madethe to experiment. Figure 3a shows the connections made to each of the electrodes while Figure 3b shows each of the electrodes while Figure 3b shows the placement of each of the electrodes inside the glass each of the of electrodes while Figure 3b shows placement of each of the electrodes inside the glass placement each of the electrodes inside the the glass cell. cell. cell.
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validate and adjust validate this method and adjust of measuring this method theofthickness, measuringthe thethickness thickness, of the the thickness coatings of ofseveral the coatings of several of the zinc-plated of steel the zinc-plated screws wassteel measured screwsby was means measured of destructive by meanstests of destructive based on metallographic tests based on metallographic methods according methods to the according ASTM E3-95 to the standard ASTM[36]. E3-95 The standard corrosion [36]. resistance The corrosion of all samples resistance obtained of all samples obtained by the zinc electroplating by the zincprocess electroplating was evaluated process by was taking evaluated electrochemical by taking electrochemical measurements using measurements a using a potentiodynamicpotentiodynamic polarization technique polarization [37]. Open-circuit technique [37]. potential Open-circuit (OCP) potential measurement (OCP) and measurement linear and linear potential scan potential experiments scanwere experiments chosen aswere the chosen electrochemical as the electrochemical measurement methods. measurement The methods. The measurements were measurements conductedwere using conducted an AUTOLAB-PGSTAT using an AUTOLAB-PGSTAT computer-controlled computer-controlled potentiostat potentiostat (Metrohm, Herisau, (Metrohm, Switzerland) Herisau, in aSwitzerland) naturally aerated in a naturally 3.5 wt. %aerated NaCl solution 3.5 wt. % atNaCl roomsolution temperature. at room temperature. For this purpose, Fora this conventional purpose, athree-electrode conventional three-electrode cell was used with cell was a graphite used with bar aasgraphite counter bar as counter electrode, an Ag/AgCl/3 electrode,Man KCl Ag/AgCl/3 electrodeM asKCl reference electrode electrode, as reference and the electrode, specimen and (steel the screw) specimen as a(steel screw) as a working electrode working [38–42]. electrode A glass[38–42]. cell containing A glass 150 cell mL containing of 3.5 wt. 150%mL NaCl of 3.5 solution wt. % (corrosive NaCl solution (corrosive electrolyte) was electrolyte) used for each was electrochemical used for each electrochemical experiment. Figure experiment. 3a showsFigure the connections 3a shows the made connections to made to each of the electrodes each ofwhile the electrodes Figure 3b while showsFigure the placement 3b showsofthe each placement of the electrodes of each ofinside the electrodes the glass inside the glass cell. cell.
re 3. Conventional three-electrode cell used for the electrochemical corrosion tests and the glass hat contained the corrosive electrolyte (NaCl): (a) Connections cell made to each of electrochemical the electrodes; corrosion Figure 3. three-electrode for Figure 3. Conventional Conventional three-electrode cell used used for the the electrochemical corrosion tests tests and and the the glass glass Figure 3. Conventional three-electrode cell used for the electrochemical corrosion tests and the glass lacement of each of the electrodes inside the glass cell. cell that contained the corrosive electrolyte (NaCl): (a) Connections made to each of the electrodes; cell that contained the corrosive electrolyte (NaCl): (a) Connections made to each of the electrodes; cell that contained the corrosive electrolyte (NaCl): (a) Connections made to each of the electrodes; (b) of each each of of the the electrodes electrodes inside inside the the glass glass cell. cell. (b) Placement Placement of (b) each Placement of each the electrodes the glass cell. open-circuit potential for sample was of measured untilinside a steady-state value was reached.
each sample was measured until steady-state valuewas wasreached. reached. potential for each sample was until steady-state value linear potential sweepThe in open-circuit the anodic Figure direction was conducted at scan rate ofglass1testsaamV/s, 3. Conventional Figure three-electrode 3. Conventional cell three-electrode used for the electrochemical cell useda formeasured the corrosion electrochemical tests andcorrosion the and the glass that containedcell thethat corrosive contained electrolyte the corrosive (NaCl):electrolyte (a) Connections (NaCl):measured made (a) Connections to each of the made electrodes; to each of a thesteady-state electrodes; The open-circuitcellpotential for each sample was until value was reached. the anodic direction was conducted at a scan rate of 1 mV/s, Then, a linear potential sweep in 1 mV/s, nning at 0.1 V below OCP and terminating at 0.1 V above the OCP. The output from these (b) Placement of each (b) Placement of the electrodes of eachinside of thethe electrodes glass cell. inside the glass cell. Then, a linear potential sweep OCP in theand anodic directionatwas conducted at OCP. a scanThe rateoutput of 1 mV/s, but beginning at 0.1 V below terminating 0.1 V above the from beginning at 0.1 Vthe below OCP and terminating at 0.1 V above thewasOCP. open-circuit The potential open-circuit for each potential sample was forversus each measured sampleuntil was ameasured steady-state until value a steady-state was reached. value reached. The output from these ents yielded a polarization curve of The current density the applied potential. Then,V a linear potential Then, aOCP linear sweeppotential inand the anodic sweep direction in the anodic was conducted direction was at a conducted scan rate ofat 1a mV/s, scanthe rate ofOCP. 1 mV/s, The output from these but beginning at 0.1 below terminating at 0.1 V above thesecan experiments yielded abeginning curve of where the current density versus theapplied applied potential. potential. experiments yielded abypolarization curve current versus but beginning atbut 0.1 Vpolarization below OCP at 0.1and V below terminating OCP and atof 0.1 terminating Vthe above the at 0.1 OCP. V above The output thedensity OCP. from The these output from these the ting corrosion current be calculated using Tafel slope analysis the relationship experiments yielded experiments a polarization yielded curve a curve polarization of the current curvethe of density the current current versus density the applied versus potential. the applied potential. the applied potential. experiments yielded a polarization of density versus using Tafel where the relationship relationship Theand resulting corrosion current can calculated by Tafel slope analysis where The resulting corrosion The resulting current corrosion canbe be calculated current by be using calculated Tafel slope byusing using analysis Tafel slope the analysis relationship where the relationship the current density the electrode potential during the can polarization is where obtained by the between the current between density the current and the electrode and potential the electrode during potential theusing polarization duringTafel the is obtained polarization by the is obtained by the where the relationship The resulting corrosion current can bedensity calculated by slope analysis between polarization between density and the(Equation electrode potential during the polarization is obtained by the following equation following (Equation equation (6)): (6)): g equation (Equation (6)): the current between the current density and the𝐼 =electrode potential during the polarization is obtained by the (6) (6) 𝐼𝑐𝑜𝑟𝑟 𝑒 𝐼 =𝑒𝐼𝑐𝑜𝑟𝑟 𝑒 𝑒 (6)): following equation (Equation . ŋ . ŋ (7) (6) (7) following equation (6)): ŋ = 𝐸 𝐸𝑐𝑜𝑟𝑟 ŋ = 𝐸 𝐸𝑐𝑜𝑟𝑟 𝐼 = 𝐼𝑐𝑜𝑟𝑟(Equation 𝑒 𝑒 . ŋ . ŋthe difference where E is the electrode where E potential, is the electrode I is thepotential, measured I is current the measured density, ŋ is the density, difference the between the 2.303current 2.303ŋ isbetween (6) . potential, ŋ− .bc ŋcorrosion 𝐼corrosion 𝐼𝑐𝑜𝑟𝑟 applied electrode applied potential electrode and the potential potential, the corrosion is the corrosion Ecorr ispotential the] of thepotential of the ba I ==and Icorr [𝑒Ecorr eTafel e𝑒ofTafel (6) (6) ŋ corroding = 𝐸 metal,𝐸𝑐𝑜𝑟𝑟 corroding Icorr is themetal, corrosion Icorrcurrent, and ba, bc current, are the ba,constants bc are the𝑒 anodic constants and cathodic of anodic (7) and cathodic 𝐼is the=corrosion 𝐼𝑐𝑜𝑟𝑟 𝑒and half-cell reactions, half-cell respectively. reactions, Values respectively. for TafelValues plots are for derived Tafel plots from arethe derived logarithm fromofthe current logarithm of current (7) ŋ = 𝐸details 𝐸𝑐𝑜𝑟𝑟 density values asdensity a function values of voltage. as a function Moreof details voltage. the More fitting method of thefor fitting obtaining method thefor corrosion obtaining the corrosion is the electrode potential, I is the measured current density, ŋ ofis= the between the (7) 𝐸 𝐸𝑐𝑜𝑟𝑟 =[43]. Edata −difference Ecorr (7) parameters canparameters be found elsewhere can be found [43]. elsewhere The corrosion The corrosion that were data obtained that were from obtained Tafel from Tafel polarization curves polarization were obtained curves by were superimposing obtained by asuperimposing straight line on a straight the linear lineportions on the of linear the portions of the where is the electrode potential, I is the current density, is the difference between the electrode potential and Ethe corrosion potential, Ecorr isIt measured the corrosion potential of ŋthe cathodic and anodic cathodic curves. and Itanodic is important curves. to is note important that thetoTafel notepolarization that the Tafel curve polarization is the most curve is the most where E is the electrode potential, Iforanticorrosion isdetecting the the measured current ŋ is the method for detecting methodthe performance anticorrosion of performance metal surfaces. of metal Indensity, thissurfaces. sense, anIn this an difference between the electrode potential and the corrosion potential, Ecorr is thetosense, corrosion potential of the g metal, Icorr is theapplied corrosion current,efficient and ba, efficient bc are the Tafel constants of anodic and cathodic excellent corrosion excellent resistance corrosion is associated resistance with is aassociated lower corrosion with a lower rate, which corrosion corresponds rate, which to acorresponds higher a higher applied electrode electrodepotential potential and the corrosion potential, Ecorr is the corrosion potential of the and the corrosion potential, Ecorr is the corrosion potential of the corroding metal, is the corrosion current, andthe ba,logarithm bc are the Tafel constants of anodic andcorroding cathodic reactions, respectively. Values forIcorr Tafel plots are derived from of current corroding metal, Icorr is the corrosion current, and ba, bc are the Tafel constants of anodic and cathodic metal, Icorr isMore the corrosion and ba, are Tafel of anodic cathodic half-cell reactions, respectively. Values forbcTafel plots areconstants derived from the and logarithm of half-cell current alues as a function of voltage. details ofcurrent, the fitting method forthe obtaining the corrosion half-cell reactions, respectively. Values for are Tafel plots from are derived from the logarithm of current reactions, respectively. Values for Tafel plots derived the logarithm of current density values values[43]. as a The function of voltage. of the fitting method ers can be founddensity elsewhere corrosion dataMore that details were obtained from Tafelfor obtaining the corrosion density valuesofas a function ofdetails voltage. More details of the for fitting method forcorrosion obtaining the corrosion as a function voltage. More of the fitting method obtaining the parameters can parameters be found elsewhere [43].on The data that were obtained from Tafel ion curves were obtained by can superimposing a straight line thecorrosion linear portions of the parameters can be [43]. found elsewhere [43]. The were corrosion data that were obtained curves from Tafel be found elsewhere The corrosion data that obtained Tafel polarization polarization curvestowere obtained superimposing acurve straight linemost on the linear portions ofwere the and anodic curves. It is important note that the by Tafel polarization is from the polarization curves were obtained by superimposing a straight line on the linear portions of the cathodic and anodic curves. It is important note that polarization curve is the most method for detecting the anticorrosion performance of metaltosurfaces. In the thisTafel sense, an cathodic and anodic curves. It is important to note that the Tafel polarization curve is the most efficient methodwith for adetecting the anticorrosion ofa metal corrosion resistance is associated lower corrosion rate, which performance corresponds to highersurfaces. In this sense, an efficient method for detecting the anticorrosion performance of metal surfaces. In this sense, an excellent corrosion resistance is associated with a lower corrosion rate, which corresponds to a higher excellent corrosion resistance is associated with a lower corrosion rate, which corresponds to a higher .
ŋ
.
ŋ
.
ŋ
.
ŋ
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obtained by superimposing a straight line on the linear portions of the cathodic and anodic curves. It is important to note that the Tafel polarization curve is the most efficient method for detecting the anticorrosion performance of metal surfaces. In this sense, an excellent corrosion resistance is associated with a lower corrosion rate, which corresponds to a higher corrosion potential (Ecorr) or a lower corrosion current density (Icorr), respectively [44,45]. Finally, other corrosion parameters, such as equivalent weight of the metal, density, or exposed surface, are required as input parameters. With this information, the AUTOLAB software (Model 30, PalmSens, Houten, The Netherlands) generates the complete set of corrosion parameters. Thus, the corrosion rate is calculated according to Equation (8): Icorr × M (8) Corrosion rate = 327 × V × D × A where 327 = 1 year (in seconds)/96,500, and 96,500 = 1 F in coulombs. Icorr is the corrosion current and is determined by an intersection of the linear portions of the anodic and cathodic sections of the Tafel curves, M is the atomic mass, V is the valence (number of electrons that are lost during the oxidation reaction), D is the density, and A is the exposed area of the sample [44]. 5. Design of Experiments To provide accurate models without a great deal of data to support the original hypotheses, the RSM must establish a Design of Experiments (DoE) [46]. There are several methods to develop a DoE. However, they require that a design matrix (inputs) be constructed for the measurement of the outputs or experiment responses. In this case, we used a Box-Behnken design (BBD) [47] that had three factors, as well as three levels, to develop the experiment. The input process parameters that were used to develop the DoE were current density (ρ), temperature (T), time (t), concentration of zinc (C), concentration of Additive 1 (Envirozin Conditioner (CA1)), and concentration of Additive 2 (Envirozin 100 Initial Brightener (CA2)). The outputs were the power consumed in the zinc plating process (W), coating thickness (Th), the increase in the coating mass (∆M), and corrosion resistance (R). The range of study considered in this case for each of the input process parameters was based on a preliminary group of phosphate screws to which a zinc coating was applied. The coating was applied to ensure that the galvanized screws had no defects or imperfections. Coatings were rejected if they presented a very irregular and/or rough coating, a reduced coating thickness (Th), a high temperature (T), or even an excessive deposition time (t). For example, Figure 4 shows some of the metallographic analyses that were obtained from the preliminary zinc coating and examined with a 50× microscope. Figure 4a shows a zinc coating with a thickness of 20 to 25 µm. The coating was formed with irregular zinc crystals, which create a very rough surface finish. In this case, and according to [11], the current density value considered was high (1.3 amps/dm2 ), whereas the considered solution temperature was low (20 ◦ C). Figure 4b shows a coating that has a thickness of 25 to 30 µm. In this case, the temperature was excessive (48 ◦ C), whereas the current density value considered was 0.5 amps/dm2 . In this case, and according to [14], the coating surface was very rough and contained large zinc crystals. Figure 4c shows a homogeneous coating that was formed by small crystals and had a thickness of 7 to 8 µm. In this case, the values of current density, temperature, and deposition time were 0.32 amps/dm2 , 30 ◦ C, and 20 min, respectively. The crystals that formed had a reduced size. According to [15], the coating provides a brighter finish with finer crystals and is more corrosion resistant. In contrast, the coating had a reduced thickness, which was due mainly to the deposition time, which was reduced. Finally, Figure 4d shows a homogeneous coating that was formed by small crystals and a thickness of 24 to 25 µm. The values of current density, temperature, and deposition time considered in this case were 0.3 amps/dm2 , 25 ◦ C, and 90 min, respectively. The homogeneous coating was formed by small crystals with a brighter finish and higher corrosion resistance [17]. The search process to fix the parameters that did not generate effects or imperfections on the galvanized screws was carried out successively. It included other parameters, such as concentration of zinc (C), concentration of Additive 1 (CA1), and concentration of Additive 2 (CA2). After these were discarded, the ranges of all input
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process parameters were set. The input process parameters and their limits, as well as the notation, all appear in Table 1. Metals 2018 6, x 8 of 20
Figure 4. 4. Metallographic analyses of of the the preliminary zinc coating: coating: (a) (a) surface surface finish finish of of the the coating with Figure Metallographic analyses preliminary zinc coating with very rough rough surface surface finish; finish; (b) (b) very very rough rough surface surface with with large large zinc zinc crystals; crystals; (c) (c) reduced reduced homogeneous homogeneous aa very coating formed formedby bysmall small crystals a very smooth surface; and (d) homogeneous coating crystals andand withwith a very smooth surface; and (d) homogeneous coating coating formed formed by small crystals and with a very smooth surface. by small crystals and with a very smooth surface. Table The experimental experimental design design levels levels of of the the Box-Behnken Box-Behnken design design (BBD) (BBD) method Table 1.1. The method and and the the independent variables. independent variables. InputInput
Magnitude Notation Notation Magnitude
Current Density ρ Current Density ρ Temperature T Temperature T ZincZinc Concentration C Concentration C Deposition Time t Deposition Time t Concentration Additive 1 CA2 Concentration Additive 1 CA2 Concentration Additive 2 CA1 Concentration Additive 2
CA1
2 amps/dm² amps/dm
◦C
°C g/L g/L min min mL/L mL/L mL/L mL/L
−1 −1
0.300.30 20.00 20.00 8.008.00 45.00 45.00 25.00 25.00 1.00
1.00
Levels Levels 00 0.50 0.50 30.00 30.00 11.00 11.00 67.50 67.50 27.00 27.00 2.00 2.00
1 1 0.70 0.70 40.00 40.00 14.00 14.00 90 9030.00 30.00 3.00 3.00
Use of the statistical open source software R (r-project) [48] and the input parameters and levels that appear in Table 1 led to the manufacture of 54 zinc-electroplated steel screws with the corresponding inputs and outputs obtained experimentally (Table 2).
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Use of the statistical open source software R (r-project) [48] and the input parameters and levels that appear in Table 1 led to the manufacture of 54 zinc-electroplated steel screws with the corresponding inputs and outputs obtained experimentally (Table 2). Table 2. Design matrix and experiments obtained by BBD. ρ, current density; T, temperature; C, concentration; t, time; CA1, concentration Additive 1; and CA2, concentration Additive 2. Inputs Exp.No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 44 48 49 50 51 52 53 54
Outputs
P (amps/dm2 )
T (◦ C)
C (g/L)
t (min)
CA1 (mL/L)
CA2 (mL/L)
W (Watts)
Th (µm)
∆M (gr)
R (mm/year)
0.5 0.5 0.5 0.7 0.5 0.3 0.7 0.5 0.3 0.5 0.5 0.5 0.5 0.5 0.7 0.5 0.3 0.5 0.3 0.7 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.3 0.7 0.7 0.5 0.5 0.7 0.7 0.7 0.5 0.3 0.5 0.3 0.7 0.5
20.0 40.0 30.0 30.0 30.0 30.0 30.0 30.0 30.0 30.0 40.0 20.0 20.0 40.0 30.0 30.0 30.0 30.0 30.0 30.0 30.0 30.0 20.0 40.0 20.0 40.0 30.0 30.0 30.0 20.0 30.0 40.0 20.0 40.0 30.0 40.0 30.0 20.0 30.0 30.0 40.0
14.0 14.0 14.0 14.0 14.0 14.0 14.0 14.0 14.0 14.0 14.0 14.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0 11.0
135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135 135
60.0 60.0 90.0 60.0 45.0 60.0 60.0 45.0 60.0 90.0 60.0 60.0 60.0 60.0 60.0 45.0 60.0 90.0 60.0 60.0 45.0 90.0 60.0 60.0 60.0 60.0 90.0 45.0 45.0 60.0 90.0 60.0 90.0 90.0 90.0 60.0 45.0 60.0 90.0 45.0 60.0
25.0 25.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 30.0 30.0 25.0 25.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 27.0 30.0 30.0 25.0 25.0 25.0 25.0 25.0 25.0 25.0 25.0 27.0 27.0 30.0 30.0 30.0 30.0 30.0 30.0 30.0
1.31 1.97 1.35 1.93 1.33 0.71 1.96 1.35 0.74 1.38 1.38 1.35 1.35 1.28 2.03 1.35 0.74 1.40 0.74 2.07 1.33 1.38 1.40 1.35 1.35 1.25 0.74 0.74 2.00 2.03 1.30 1.35 2.14 2.00 0.69 2.03 1.45 1.96 1.33 0.69 1.50
0.68 1.13 1.32 0.97 0.61 0.56 0.75 0.78 0.53 0.96 0.75 0.46 0.66 0.98 0.86 0.59 0.74 1.06 0.56 0.69 0.51 0.84 0.46 0.74 0.77 1.05 1.16 0.43 0.77 0.61 1.14 0.85 0.80 1.07 0.72 0.57 0.39 0.70 0.47 0.27 0.51
21.34 43.49 43.96 35.96 27.73 18.60 21.70 25.19 27.84 30.68 24.05 13.54 21.49 33.04 27.91 26.10 24.50 40.79 28.75 22.94 20.25 32.51 27.69 29.14 33.06 40.59 38.04 26.55 28.09 24.30 41.60 38.15 41.85 39.83 34.99 23.04 25.11 31.24 29.29 19.55 24.19
0.034 0.021 0.104 0.015 0.143 0.166 0.111 0.041 0.011 0.046 0.13 0.044 0.049 0.081 0.078 0.096 0.05 0.046 0.009 0.009 0.03 0.066 0.087 0.089 0.031 0.034 0.022 0.133 0.05 0.059 0.17 0.104 0.033 0.046 0.136 0.055 0.13 0.102 0.124 0.121 0.008
6. Results and Discussion 6.1. Modelling the W, Th, ∆M, and R Using RSM The data in Table 2 were used to fit Equations (9)–(12) to provide regression equations for all responses. The RMS “R” package [28] was employed for this. Second-order polynomial models were constructed for each response. Selection of the most accurate model involved several criteria. These were R2 , p-value, Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE). The second-degree polynomial functions that modeled the power consumption of the zinc plating process (W), the increase in coating mass (∆M), the zinc coating (Th), and the corrosion resistance (R) are shown in the equations. These equations show that each output is provided by a combination of second-order polynomials. The latter are formed, in turn, by combinations of input variables.
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W = −5.626 + 3.660 × ρ + 0.129 × C − 0.087 × ρ × C+0.0015 × T × C − 0.0066 × C2 + 0.0031 × ρ × t + 0.0004 × C × t + 0.348 × CA1 − 0.00082 × T × CA1 − 0.00023 × t × CA1 − 0.0057 × CA12 − 0.323 × CA2 + 0.192 × ρ × CA2 + 0.0091 × CA1 × CA2
(9)
∆M = 0.894 − 1.170 × ρ2 − 0.170 × ρ + 0.0027 × T × C + 0.029 × ρ × t − 0.00074 × T × t + 0.0016 × C × t − 0.00011 × t2 + 0.0023 × T × CA1 + 0.990 × CA2 − 0.0182 × T × CA2 − 0.049 × CA1 × CA2 + 0.185 × CA22
(10)
Th = −77.0078 − 79.377 × ρ2 + 9.251 × ρ + 0.190 × T × C − 0.702 × C2 − 0.0167 × T × t + 0.069 × C × t − 0.00293 × t2 + 4.754 × ρ × CA1 + 55.864 × CA2 − 20.573 × ρ × CA2 − 0.413 × T × CA2 − 0.858 × C × CA2 − 1.460 × CA1 × CA2 + 3.095 × CA22
(11)
R = −0.860 + 0.0419 × T − 0.00031 × T2 + 0.0687 × ρ × C + 0.00125 × C2 + 0.0078 × t − 0.00708 × ρ × t − 0.00085 × C × t − 1.835 × 10−5 × t2 − 0.0171 × ρ × CA1 − 0.000903 × T × CA1 + 0.00035 × t × CA1 + 0.00247 × T × CA2 − 0.0045 × C × CA2 − 0.00099 × t × CA2 + 0.0102 × CA1 × CA2 − 0.0638 × CA22
(12)
The results of ANOVA for all final quadratic models appear in Tables 3–6. The p-value of most variables is less than 0.01. Thus, the inputs that the reduced quadratic models used are statistically significant. Similarly, it can be seen in these tables that ρ is the most influential input for “W” (Table 3), since the p-value is
