Application of an experimental design to study AISI 4340 and 300M steels electropolishing in a concentrated perchloric/acetic acid solution

A typical electropolishing installation is used, comprising a direct current (DC) power source (Fontaine S30050 (300 V-50 A)), a cell fitted with a lead sheet (50 × 100 mm²) as cathode (−) and a steel part as anode (+) with an inter-electrode distance of 20 mm. The amount of metal removal depends on the electrolyte composition, the temperature, the current density and the metal being electropolished.

The electrolytes used are mixtures of concentrated analytic grade perchloric acid/acetic acid (5/95 Vol.%) [31]. To study the effect of the iron enrichment of EP electrolytes during electropolishing, an iron ion concentrate solution is preliminary prepared by dissolving iron sheet in a perchloric/acetic acid mixture. The working solution is obtained by diluting the iron -ion concentrate solution into adequate concentration. The temperature is maintained at a given level by thermostated water circulating through the jacketed electrochemical cell (250 ml).

AISI 4340 and 300M steel sheets (electrode area 3 cm²) are used in this study. Their chemical compositions (wt.%) are given in table 1. 300 alloy is similar to 4340 with the addition of vanadium and higher silicon content. 300 M steel offers a combination of toughness and ductility at high strength levels without increasing carbon content.

Before EP, the specimens are (i) degreased in an alkaline solution, (ii) mechanically polished with 600-grit SiC paper, (iii) rinsed with water then with alcohol, (iv) air-dried and then (v) weighted. After EP, the specimens are (i) rinsed with tap water, distilled water and alcohol, (ii) air-dried and (iii) weighted again. The dissolved thickness is computed using Faraday's law. Each test is repeated twice under the same conditions.

Surface morphology is observed by Contour GT-I 3D Optical Microscope and surface roughness measurements are made using a Mahr-Penthen perthometer S6R profilometer. Measurements are repeated three times for each specimen and the criteria roughness (R_a) is obtained thereby.

As the literature indicates [1–15], the factors that affect the electropolishing process are numerous including pre-treatment of the metal surface, orientation from the workpiece in the electropolishing bath, choice of cathode material, electrode spacing, bath age, electropolishing time, temperature, composition of the bath, voltage or current density imposed, ...

As many factors are involved and must be optimized in an electropolishing process, there is no one-fit-all parameter set for all electropolishing setups. So, the following four variables are selected and investigated in the FFD study: U_1: electrical charge amount Q (A min dm⁻²), U₂: anodic current density (A dm⁻²), U₃: Iron ions concentration of the EP solution, U₄: temperature of the EP solution.

In addition to the current density and the electrical charge, the choice of factors is strongly linked to industrial practices. The electropolishing bath age i.e. the iron ions concentration in the EP bath is also a big concern during the process. Indeed, it is a standard practice in industry to reuse the electrolyte to keep a low profile of cost and minimize the detrimental effect to the environment [4]. Moreover, the temperature impacts the surface brightness which decreases with the decrease of the temperature. The reaction rate in the limiting current region becomes mass transport controlled as the temperature is increased [5, 14, 15].

A two-level fractional factorial design (FFD), noted 2^4-1, is implemented to identify the most influential variables affecting the studied responses and to carry out a low number of experiments, ensuring that the results are as precise as possible and to focus on the main effects and low-order interactions. A non-dimensional coded variable X_i is associated with each natural variable U_i. The limits of the experimental domain in terms of coded variables are identical for all variables and the extreme values are equal to ±1 (table 2). To check the validity of the empirical model, three central experiments need to be added to the experimental design.

The design is constructed by using the independent generator 1234. This type of design is classified as—'resolution IV' design [33, 34] i.e. all the main effects are confounded with three-factor interactions. From the principle of effect sparsity, a system is likely to be driven primarily by main factor and low-order interaction effects. So, the effects of the high-order interactions (three or greater) are assumed to be negligible, and therefore enabling all the main effects to be determined. Two-factor interactions are confounded with each other thus making it impossible to determine all of them for all responses. The eight selected effects and their aliases are listed in table 3. Eight experiments are replicated to determine the influence of the variables on the four responses noted:

• 1.  
  Y₁, dissolved thickness (μm) and Y₂, mean roughness (arithmetic average of the absolute values (Ra)) for AISI 4340 steel,
• 2.  
  Y₃, dissolved thickness (μm) and Y₄, mean roughness (arithmetic average of the absolute values (Ra)) for 300 M steel.

Nemrod-W software is used for regression, statistical analysis and graphical analysis of the obtained data [37].

From an examination of the results in table 4, the dissolved thickness (Y₁) and Ra (Y₂) of AISI 4340 steel vary respectively from 10.2 to 24.3 μm and from 0.06 to 0.22 μm, indicating that certain factors and/or interactions should show significant effects on the measured responses (Y₁ and Y₂).

For the Y₁ response, data from table 6 reveal that only X_1, X_2, X₃ factors and two confounded interaction effects, 'l₁₂' and 'l₂₃' are significant at a confidence level greater than or equal to 95%. If we consider that interaction effects between the extra factors (X₄) and the basic factors (X₁, X₂ and X₃) are not taken into account in the theoretical analysis due to the hypothesis on the construction of the fractional design, we are able simplify the expression of the confounded effects. For the confounded interaction effect, l₁₂ = b₁₂ +b₃₄, we can assume that the factor interaction effect b₁₂ is the dominant term since electrical charge amount (X₁) and current density (X₂) have the greatest effects on the response, as emphasized in the literature. In this respect, we can conclude that the factor interaction effect b₂₃ is the dominant term for the confounded interaction effect l₂₃ = b₂₃ + b₁₄.

So, according to the empirical model obtained, the dissolved layer can be represented by the following equation:

$$\begin{eqnarray}&&{{\rm{Y}}}_{{\rm{1}}}=16.79+3.40{{\rm{X}}}_{1}+0.60{{\rm{X}}}_{2}-0.12{{\rm{X}}}_{3}+0.54{{\rm{X}}}_{1}{{\rm{X}}}_{2}-0.16{{\rm{X}}}_{2}{{\rm{X}}}_{3}\end{eqnarray} \tag{ 1 }$$

The equation (1) indicates that the positive coefficients of X₁, X₂ and X₁X₂ have a constructive contribution to the dissolved layer response. However, the negative coefficients of X₃ and of X₂X₃ indicate antagonistic effects on the response.

From the analysis of ANOVA (table 5), the results shown in table 6 and following the same analysis as above, a fitted polynomial model (2) can be generated for the roughness criteria, Y₂:

$$\begin{eqnarray}&&{{\rm{Y}}}_{2}=0.088+0.019{{\rm{X}}}_{1}+0.013{{\rm{X}}}_{2}-0.011{{\rm{X}}}_{3}+0.020{{\rm{X}}}_{1}{{\rm{X}}}_{2}-0.018{{\rm{X}}}_{2}{{\rm{X}}}_{3}\end{eqnarray} \tag{ 2 }$$

This model quantitatively elucidates the effects of the EP variables with statistical significance. The equation indicates the synergetic effects of X₁, X₂ and X₁X₂ and antagonistic effects of X₃ and X₂X₃ on the Ra response. Note that for two models (1) and (2), the temperature (X₄) shows no significant effect without any significant interactions.

All these results are confirmed by the high values of the multiple correlation coefficient squares (R²): 99%, 93% for Y₁ and Y₂ respectively. It should be noted that R² values represent the percentage variation in the responses explained by the deliberate variation of the factors in the course of the experiments.

To validate the statistical models (1)–(2), three additional central experiments are conducted. The predicted values are in fair agreement with those measured suggesting that the first order models chosen are suitable and can be used as a prediction equation (table 7).

As previously mentioned, the fractional design allows the calculation of the estimates for factors and two confounded interaction effects for the dissolved thickness Y₃ and the roughness criteria, Y₄ of the 300M steel (table 6).

Following the procedure described above, the equations of the fitted models are:

$$\begin{eqnarray}&&{{\rm{Y}}}_{3}=16.56+3.42{{\rm{X}}}_{1+}3.42{{\rm{X}}}_{2}-0.16{{\rm{X}}}_{3}+0.73{{\rm{X}}}_{1}{{\rm{X}}}_{2}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{{\rm{Y}}}_{4}=0.104+0.012{{\rm{X}}}_{1}+0.019{{\rm{X}}}_{2}-0.013{{\rm{X}}}_{3}+0.026{{\rm{X}}}_{1}{{\rm{X}}}_{2}-0.018{{\rm{X}}}_{2}{{\rm{X}}}_{3}\end{eqnarray} \tag{ 4 }$$

The equation (3) indicates that the positive coefficients of X₁, X₂ and X₁X₂ have a constructive contribution to the dissolved layer response. The negative coefficient of X₃ indicates an antagonistic effect on the response whilst factor X₄ has null effect. Accordingly, the dissolution is enhanced when factors X₁ and X₂ are respectively set as the highest level to obtain a synergistic effect and X_3, as the lowest level. For Y₄ response, X_1, X₂, X₃ factors show significant effect with significant interactions (X₁X₂ and X₂X₃) whilst factor X₄ has null effect.

The values of multiple correlation coefficients, R², equal to 99% and 94% for Y₃ and Y₄ respectively show a good fit to the experiment data.

Three additional central experiments are conducted to validate the statistical models. As shown in table 7, the measured and the predicted values are in close-agreement. For overall results, we can conclude that the first order models chosen are considered suitable for this study and can be used as a prediction equation.

At this point, it is worth noting that the influence of the factors cannot be discussed separately due to the importance of their interactions [32–36]. Indeed, data from table 6 reveal that three factors, X₁, X₂ and X_3, and their interactions are significant according the literature. However, the factor X₄ is not significant which is at odds with literature [5, 14, 15]. Several authors have shown the importance of the temperature for electropolishing on the plateau current density and so on the diffusion coefficient of the rate limiting species in the electropolishing bath. The insignificance of the temperature in the FFD is likely due to the fact that the interval of variation is small.

As indicated previously, the focus of this study is to satisfy one principal objective which is finding the EP operating conditions allowing (i) the dissolution of a sufficient thickness to eliminate the layer affected by residual compressive stresses due to the mechanical polishing and (ii) low roughness. For this purpose, we define an acceptable range for each response: (i) a dissolved thickness comprised between 15–17 μm and (ii) an arithmetic roughness criterium less than 0.06 μm. The evolution of the four considered responses Y₁ to Y₄ are plotted (figures 1–2). Note that, according to the expression of these responses, the X₃ factor (iron ion- concentration) has been kept at its high level (+1). By mere inspection of these diagrams, it is easy to accurately choose each part of the domain that is acceptable according to the criteria above. A satisfactory zone is the part of the domain for which the value of each one of the calculated responses is acceptable (table 8). Taking into account all the requirements for the two responses of each steel, looking for a compromise where all the experimental responses fulfill the specifications imposed by the researchers to achieve the aims proposed is required (table 8).

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Table 8.  Compromise domain fulfilling the requirements for AISI 4340 and 300 M steels.

	AISI 4340		300 M
Requirements	Y1 [15; 17]/μm	Y2 ≤ 0.06/μm	Y3 [15; 17]/μm	Y4 ≤ 0.06/μm
Xi combinations fulfilling each Yi	X1 [−1.00; −0.60],	X1 [−1.00; −0.40],	X1 [−1.00; −0.65],	X1 [−1.00; −0.9],
requirement (i = 1 to 4)	X2 [0.74; 1.00],	X2 [0.60; 1.00],	X2 [0.75; 1.00],	X2 [0.84; 1.00],
	X3 = 1.00	X3 = 1.00	X3 = 1.00	X3 = 1.00
Compromise domain fulfilling	X1 [−1.00; −0.60],		X1 [−1.00; −0.9],
Yi [15; 7] with i = 1;3 and	X2 [0.74; 1.00],		X2 [0.84; 1.00],
Yj ≤ 0.06 with j = i+1	X3 = 1.00		X3 = 1.00

Figure 3 depicts typical 2 and 3-dimensional micrographies of 300M steel samples after electropolishing according to experimental design runs (runs 1, 4 and 8).

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The topography of the surface has been considerably modified and surface roughness is reduced or increased according to the operating conditions. As observed in figure 3(c), peaks and valleys are clearly observed. On the contrary, for figure 3(a) with a lower Ra value, the surface is flat due to a uniform dissolution. Similar profiles are observed for 4340 steel samples.