Introduction

Aluminum heat exchangers have been used extensively in automotive applications such as radiators, heater cores, oil coolers, intercoolers, evaporators and condensers (Ref 1, 2). The condenser of the automotive air-conditioning unit is an aluminum heat exchanger generally manufactured by brazing extruded micro-multiport tubes (in which refrigerant flows) and corrugated fins (which exchange heat with the air side) (Ref 3, 4). Aluminum brazing involves joining the components with a brazing alloy, which is an aluminum-silicon alloy whose melting point is appreciably lower than that of the components; this filler metal is supplied in the fins as a thin clad on both sides of a core alloy. During the brazing process at around 600 °C, the low melting point Al-Si cladding alloy melts and flows, to provide upon cooling a metallic bond between the fins and micro-multiport tubes. The quality of the joints made by brazing depends not only on the proper selection of the filler material, but on many other conditions which need to be kept under control, for instance, a precisely defined temperature range, a rigorously controlled gas atmosphere (high-purity nitrogen, with very low oxygen and water vapor content) and the use of a non-corrosive flux to remove surface oxide films (Ref 5-7). All of these conditions are well specified in a state-of-the-art brazing process under the trade name Nocolok® (Ref 8).

A comprehensive analysis of the joint quality must involve several aspects, such as: (a) appearance, (b) mechanical integrity, (c) microstructure of the joint, and (d) corrosion resistance. The main focus of this work is on the aspect of corrosion resistance. The condenser is normally installed in the neighborhood of the front grill of the automobile, so it is exposed to the environment and consequently suffers external corrosion. Of main concern is the possibility of tube perforation, leading to coolant leaking (Ref 9). Conventionally, the tube is protected by sacrificing the fins, choosing the right alloy composition to reduce its corrosion potential (Ref 10, 11). Another method consists in forming a Zn diffusion layer on the surface of the tube material (Ref 12-15). Zinc has a much lower galvanic potential than aluminum and basically acts as a sacrificial material, so that in the case of an eventual corrosion attack on the micro-channel tube it will spread over the surface rather than create a cavity (i.e., deep pitting is prevented).

The most common accelerated testing to measure the corrosion resistance of heat exchanger materials is the seawater acetic acid test (SWAAT) (Ref 16). It is often used as a quality control and the test criteria are the days till perforation of the material occurs. A SWAAT performance of minimum 20 days is commonly requested by the automotive industry. Although such a test is generally accepted as a good simulation of service life, there are several drawbacks such as its long duration and the low reproducibility. Thus, some authors have used laboratory-based studies under well-controlled conditions to evaluate the corrosion performance of heat exchanger components immersed in SWAAT solution (Ref 11, 17-22). Meijers et al. (Ref 11) showed that using polarization curves as a first screening for materials selection in fin-tube systems can be a powerful tool. Afshar et al. (Ref 17-19) performed a thorough investigation on the relationship between microstructure and electrochemical reactivity for aluminum brazing sheet.

It is very important to consider that the corrosion behavior of the condensers does not depend only on the material selection (e.g., careful selection of alloys for the different components), but also on the metallurgical changes that they experience during the brazing process. Tierce et al. (Ref 23, 24) and Tu et al. (Ref 25) have discussed the changes in microstructure as well as Si-diffusion characteristics for brazing sheets. Furthermore, Laferrere et al. (Ref 20) studied the effect of microstructure on the corrosion behavior of extruded heat exchanger aluminum alloys. Similarly, Klyszewsky et al. (Ref 26) investigated the effect of chemical composition and structure on the corrosion resistance of plated aluminum alloy strips, while Wang and Jiao (Ref 21) reported the microstructural effects in corrosion of aluminum tube alloys. According to Birol et al. (Ref 27) micro-galvanic effects between the intermetallic phases and the aluminum matrix significantly affect the corrosion behavior of aluminum fin stock. As pointed out by Afshar et al. (Ref 17), there are various material-related parameters that can affect the SWAAT performance, including those directly related to the initial condition and others (e.g., brazing temperature and flux load) related to the secondary metallurgical changes during the brazing process.

So, the object of this work is to optimize the process parameters for brazing the tube-fins system of an automotive condenser, in order to achieve excellent corrosion performance together with a good joint size. Optimization was carried out by means of the Taguchi method. This method uses a special design of orthogonal arrays to evaluate the effect of processing variables with a minimum of experiment trials at a relatively low cost (Ref 28). In this work, a standard Taguchi L8 orthogonal array was chosen to analyze the effect of the following factors and interactions: type of micro-channel tube, flux type, peak temperature, dwell time, heating rate, (micro-channel tube) × (peak temperature) and (micro-channel tube) × (dwell time). Analysis of variance of means and analysis of signal-to-noise ratio to 95% confidence level were performed to know the significant factors and interactions on the response variable (corrosion current density).

Experimental Procedure

Materials and Processing

The materials for the tube-fin system were supplied by Airtemp de México as pre-assembled mini-cores, ready for brazing, as shown in Fig. 1(a). The corrugated fins consisted of a brazing sheet (temper: H14) which was 16 mm wide and 80 μm thick; modified AA3003 was used as core material, and it was clad on both surfaces with AA4343 (using a clad ratio of 10% on both sides). Table 1 shows the compositions of core and filler alloys. For the extruded micro-multiport tubes, two candidate aluminum alloys with similar compositions were evaluated (see Table 2), both with H112 temper. In the as-received condition, they had an amount of thermally sprayed Zn which during the brazing process (around 600 °C) diffuses inwards, forming a zinc diffusion layer (the sacrificial layer). The main difference between the two alloys is the amount of sprayed zinc.

Fig. 1
figure 1

(a) Condenser mini-core before brazing, (b) tube-fin joint showing with red line the fillet size, (c) tube-fin mini-assembly for electrochemical measurements

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Table 1 Compositions (wt.%) of the core and filler alloys in the brazing sheet fin, Temper H14
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Table 2 Composition of candidate tube alloys, Temper H112
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The flux was applied to the mini-cores by the dry electrostatic method. Two types of commercial fluxes were evaluated: the standard Nocolok® flux (potassium fluoroaluminate) and an improved formula containing lithium (Nocolok® Li flux) which reduces the solubility of post-braze flux residue (Ref 29).

The controlled atmosphere furnace was a THERMOLYNE 59300 horizontal furnace provided with an alumina tube (92 cm long × 6.9 cm in diameter) sealed at both ends with aluminum caps and with the aid of O-rings. For each test, the mini-core sample was placed in a region of uniform temperature at the center of the alumina tube (the temperature profile in the furnace was previously characterized). Ultra-high-purity nitrogen (UHP 99.999%) was supplied at a constant flow rate of 450 cm3/min. The dew-point was measured with an Extech psychrometer model RH360.

Design of Experiments

The five processing parameters were selected, and their corresponding levels are shown in Table 3. Factor A relates to the micro-channel tube, and the two levels correspond mainly to different amounts of sprayed zinc (which as a consequence might result in different concentration profiles of zinc during the brazing process). Factor B corresponds to the type of flux (with or without lithium), which might have an influence on corrosion performance due to the presence of the post-braze flux residue (Ref 8). Factors C, D and E are more directly related to furnace operating parameters (peak temperature, heating rate and dwell time, respectively). The levels for factors C and E were chosen so as to cover a possible range where optimal conditions to obtain a good joint could potentially exist. Concerning factor D, heating rates of 20 °C/min or higher are generally recommended; however, we used lower values in order to maintain a region of uniform temperature at the center of the furnace. The Taguchi L8 orthogonal array is presented in Table 4 and includes the following interactions: A × C (micro-channel tube × peak temperature) and A × E (micro-channel tube × dwell time). The design consists of eight experimental tests which were carried out randomly. For each experiment, three trials were performed to achieve high accuracy in the data. The samples corresponding to the eight experiments were labeled as TA1, TA2, TA3 and so on. The response variable to be optimized is the corrosion current density i corr (μA/cm2).

Table 3 L8 orthogonal array factors and levels
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Table 4 Experimental layout of Taguchi L8 orthogonal array
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In order to determine the percent contribution of factors and the processing parameters that have influence in the mean and the variability on the relevant response, analysis of variance of means (ANOVA) and signal-to-noise ratio analysis (S/N ANOVA) were conducted. The signal-to-noise ratio was computed according to Eq 1,

$$\frac{S}{N} = - 10{\text{Log}}_{10} \left( {\text{MSD}} \right)$$
(1)

where MSD is the mean squared deviation. Of the three possible categories of S/N ratios (lower is best, larger is best, or nominal is best), we selected the “nominal is best” criterion for the corrosion current density. The reason for not selecting “lower is best” (corresponding to a minimization of the corrosion rate) is because we observed that a low corrosion rate does not necessarily correspond to a joint with good fillet size. So, our approach was to select as target value of corrosion current density the one that corresponds to the experiment with best fillet size. The MSD was calculated according to,

$${\text{MSD}} = \frac{1}{N}*\mathop \sum \limits_{i = 1}^{N} \left( {Y_{i} - Y_{0} } \right)^{2}$$
(2)

where \(Y_{i}\) and \(Y_{0 }\)represent, respective, the observation\(i\) and the target value. N denotes the total number of the observations.

Finally, the prediction of the response variable was performed and a confirmation test was carried out in triplicate for the validation of the results.

Microstructure Characterization

Samples of post-brazed mini-cores were mounted in slow setting Epofix resin, and the cross section was ground with abrasive paper of grit size up to 1200, followed by polishing with Alpha alumina of 1, 0.3 and 0.05 μm. In the final step, the samples were polished with colloidal silica of 0.04 μm. The microstructure at a section of the tube-fin joint was examined for selected samples with a PHILLIPS XL30 ESEM scanning electron microscope coupled with an energy-dispersive x-ray (EDX) detector. Elemental mapping using quantitative x-ray mapping was conducted on the fin and the joint area to identify the nature of main constituent particles.

Zinc concentration profiles in the sacrificial layer of post-brazed micro-channel tube samples were obtained by x-ray energy-dispersive line scans.

Optical images were also acquired with an Olympus VANOX AHMT3 Metallographic microscope with Qimaging MicroPublisher 3.3 RTV camera. The Image Pro-Plus software was used to analyze the images and to perform measurements of fillet size (as shown in Fig. 1b) in triplicate for each sample.

Electrochemical Characterization

In order to evaluate the overall corrosion behavior of the fins and external surface of the micro-channel tubes (mimicking external corrosion of the condenser under complete wetting conditions), tube-fin mini-assemblies were immersed at ambient temperature in SWAAT solution prepared according to ASTM G85-09 A3 (Ref 16). Two of these mini-assemblies were cut out from each brazed mini-core. A copper wire was attached to the sample for electrical connection, and the ends of the tubes were sealed with epoxy resin to avoid penetration of solution to the micro-channels (Fig. 1c).

The electrochemical measurements were carried out in a three-electrode cell configuration using a Gamry series G300 potentiostat/galvanostat. An Ag/AgCl reference electrode and a counter electrode consisting of a large area Pt foil were used in the cell. The corrosion potential under open circuit conditions (E oc) for each mini-assembly sample was recorded during 1 h, and an electrochemical impedance spectroscopy (EIS) measurement was carried out immediately, using a sine wave perturbation signal with 10 mV amplitude in the frequency range of 10 KHz-250 mHz with five points per decade. Finally, a potentiodynamic polarization curve was obtained at a scan rate of 1 mV/s in the range of ±300 mV versus E oc, starting at a potential 300 mV more negative than E oc.

As indicated above, each trial of the Taguchi design was performed in triplicate. This means that three mini-cores were brazed for TA1, three for TA2 and so on. Since two mini-assemblies like the one shown in Fig. 1(c) were prepared from each mini-core, a total of six repetitions of electrochemical measurement were obtained.

Results and Discussion

Electrochemical Behavior of Tube-Fin Mini-assemblies

In Table 5, the first column shows the sample ID for the eight Taguchi experiments, and columns 2-6 show the corresponding values of each factor. The post-brazed mini-cores for the whole set are expected to exhibit significant differences in electrochemical behavior when immersed in the SWAAT solution; however, it is not the intention to discuss the results of electrochemical measurements for all of them. Only four representative Taguchi experiments were chosen (TA1, TA3, TA4 and TA8). Figure 2 shows typical corrosion potential curves over time for the selected samples. They all exhibit a shift of E oc toward less negative values during the 1-h immersion period. This behavior has been ascribed to dissolution of the oxide film and a gradual consumption of the sacrificial zinc diffusion layer (Ref 30). Furthermore, the four samples have different initial values of E oc. This feature can be related to the fact that the corresponding mini-cores were brazed using different levels for the five factors. For instance, the samples TA1, TA3 and TA4 were brazed using the same type of micro-channel tube (tube I), but due to variations in the other factors they exhibit different initial values of E oc (with a maximum difference of ~42 mV). As the surface of the tube in each sample changes due to gradual dissolution of the zinc sacrificial layer, E oc evolves to less negative values and, at the end, their corrosion potentials get very close to each other. It is interesting to compare the behavior of samples TA4 and TA1 because they differ only in the peak temperature and dwell time. The sample brazed at the lower temperature and lower dwell time (TA1) exhibits more negative values of corrosion potential during the whole immersion period. A comparison between samples TA1 and TA8 is also useful because they differ only in the type of tube and the heating rate. Sample TA8 was fabricated with tube type II. Its initial value of E oc is very similar to that of sample TA1, but exhibits only a slight shift in potential during the same immersion period. This suggests that the type of micro-channel tube may play an important role in corrosion behavior.

Table 5 Experimental design, response and S/N ratio
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Fig. 2
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Variation of the open circuit potential as a function of time for selected samples (TA1, TA3, TA4 and TA8) immersed in SWAAT solution

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Figure 3 shows the comparison of typical polarization curves for the selected experiments. The corrosion potentials determined from the polarization behavior (indicated by small arrows on the x-axis) follow the same trend observed for E oc in Fig. 2 (e.g., the corrosion potential for sample TA8 is the most negative). An important observation is that, although the corrosion potential values for samples TA1, TA3 and TA4 are very close to each other, their i corr values (determined with a Tafel extrapolation procedure) have quite different values, following the trend\(i_{\text{corr}}^{\text{TA3}} > i_{\text{corr}}^{\text{TA4}} > i_{\text{corr}}^{\text{TA1}}\). This can be explained as follows, according to the mixed potential theory: the anodic branches of the three polarization curves have very little separation between them, thus suggesting that they have a nearly constant anodic Tafel slope. On the other hand, the cathodic branches are well separated, with magnitudes of cathodic current density in the order TA3 > TA4 > TA1. This suggests that the differences in i corr (and therefore in corrosion rate) for samples TA1, TA3 and TA4 are mainly due to differences in the kinetics of the cathodic reaction (hydrogen evolution). It appears that these samples have different values of exchange current density (and possibly of cathodic Tafel slopes). As discussed in a previous publication (Ref 30), the electrochemical behavior of the tube-fin system results from the galvanic coupling of the two components. For the combination of materials used in the fabrication of the mini-cores, it can be anticipated that the tube material exhibits anodic behavior (due to sacrificial action of the zinc diffusion layer), while the fins exhibit a cathodic behavior. Variations in the furnace parameters during the brazing process (heating rate, peak temperature and dwell time) are expected to yield different zinc concentration profiles in the tube (and therefore a different concentration of zinc at the surface). It appears that for the samples TA1, TA3 and TA4 such changes in the surface condition did not significantly affect the kinetics of the anodic reaction. On the other hand, the fins are made from a brazing sheet. So, the variations in furnace parameters are clearly expected to produce significant metallurgical changes in the fins. Since the surface in contact with the electrolyte is the residual clad, the differences in its microstructure are more likely responsible for differences in the kinetics of the hydrogen evolution reaction for samples TA1, TA3 and TA4. In Ref 30, it was shown that when the Zn-coated tube and the fins are uncoupled, the tube has a more negative corrosion potential (and also a lower i corr) compared to the fins. According to the mixed potential theory for bimetallic systems, the tube-fin mini-assembly adopts a common potential in between the corrosion potential of individual elements. It is evident in Fig. 3 that sample TA8 exhibits a lower i corr compared to the other three samples. This can be explained assuming that for this system i corr decreases because the corrosion potential of the couple gets very close to the uncoupled potential of the tube.

Fig. 3
figure 3

Typical polarization curves for selected samples (TA1, TA3, TA4 and TA8), obtained after 1-h immersion in SWAAT solution. Scan rate = 1 mV/s

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The results of EIS measurements obtained for samples TA1, TA3, TA4 and TA8 after 1-h immersion in the SWAAT solution are presented as Nyquist plots in Fig. 4. Each diagram exhibits the typical impedance response for aluminum in acidic chloride solutions (Ref 31-34), which consists of a capacitive loop at high frequencies (HF) followed by an inductive loop in the low frequency(LF) range. The HF capacitive loop can be correlated to the dielectric properties of the oxide film, present even in acidic solutions (Ref 33). For the inductive loop, various interpretations have been given in the literature. In this work, it was attributed to the coverage relaxation of the adsorbed intermediate Hads in the reduction of H+ (Ref 30, 34, 35). The equivalent circuit most commonly used to fit the experimental impedance data is shown in Fig. 5(a). R s is the solution resistance, Q and α are parameters associated with a constant phase element (CPE), R p is the polarization resistance, L and R ind are the elements related to the inductive loop. As shown in the schematic diagram in Fig. 5(b), the charge transfer resistance R ct is obtained from the addition of R p and R ind. The CPE is usually introduced to account for non-ideal capacitive behavior of the interfacial charge storage mechanism. The non-ideal behavior is related to a frequency dispersion phenomenon which may have different origins (Ref 36, 37); in this case, it can be attributed to roughness and possibly a non-uniform potential and current distribution associated with electrode geometry. The admittance for this circuit element is given by \(Y_{\text{CPE}} = Q\left( {j\omega } \right)^{\alpha }\), where ω is the sine wave modulation angular frequency, Q is the CPE coefficient (with dimensions Ω−1 sα cm−2), and α is an empirical exponent (0 ≤ α ≤ 1) which measures the deviation from the ideal capacitive behavior. A sufficiently good fit of the experimental impedance data in Fig. 4 with the equivalent circuit in Fig. 5(a) was obtained (see comparison of experimental and fitted data in the Bode plots in Fig. 6). The optimum fit parameters are presented in Table 6. A column with the values of the effective interfacial capacitance (C eff) calculated from the fit parameters related to the HF loop is included. They were calculated with the following relationship for a surface time-constant distribution (Ref 37):

$$C_{\text{eff}} = Q^{1/\alpha } \left( {\frac{{R_{\text{s}} R_{\text{p}} }}{{R_{\text{s}} + R_{\text{p}} }}} \right)^{{\left( {1 - \alpha } \right)/\alpha }}$$
(3)

It can be observed that these values are lower than the typical value of the double layer capacitance C dl (50 μF cm−2). This means that the HF interfacial capacitance represents a series connection between C dl and the oxide film capacitance C ox \(\left( {\frac{1}{{C_{\text{eff}} }} = \frac{1}{{C_{\text{dl}} }} + \frac{1}{{C_{\text{ox}} }}} \right)\). The estimated values of C ox, assuming C dl = 50 μF cm−2, are around 3 μF cm−2, in good agreement with reported values of this capacitance for a thin barrier oxide film on aluminum (Ref 38, 39). In Table 6, a column for the charge transfer resistance (R ct = R p + R ind) is also included. According to the Stern-Geary equation, i corr is proportional to the reciprocal of R ct \(\left( {i_{\text{corr}} = {\raise0.7ex\hbox{$B$} \!\mathord{\left/ {\vphantom {B {R_{\text{ct}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${R_{\text{ct}} }$}}} \right)\). The proportionality constant B depends on the anodic and cathodic Tafel slopes. Assuming that B is roughly constant for the four samples, the increasing values of R ct in Table 6 would correspond to decreasing values of i corr. This trend is in good agreement with the results obtained with the polarization curves: \(i_{\text{corr}}^{\text{TA3}} > i_{\text{corr}}^{\text{TA4}} > i_{\text{corr}}^{\text{TA1}} > i_{\text{corr}}^{\text{TA8}}\).

Fig. 4
figure 4

Nyquist diagrams obtained for selected samples (TA1, TA3, TA4 and TA8) after 1-h immersion in SWAAT solution

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Fig. 5
figure 5

(a) Equivalent circuit model used to analyze the experimental data in Fig. 4, (b) schematic Nyquist diagram corresponding to the circuit in (a)

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Fig. 6
figure 6

Bode plots comparing experimental impedance data (symbols) and fitted data (lines) for the selected samples (TA1, TA3, TA4 and TA8). (a) Modulus, (b) phase angle

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Table 6 Parameters from equivalent circuit analysis of impedance spectra in Fig. 4
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Distributions of Corrosion Current Density and Fillet Size

As indicated above, the response variable to be optimized is i corr. This can be calculated by two methods: by Tafel extrapolation using the polarization curves or from the Stern-Geary equation using the R ct values determined from EIS measurements. As shown in the previous section, both methods give consistent results. So, for the statistical analysis it was decided to use the values calculated from polarization curves. Average values of i corr and S/N ratios for all the Taguchi experiments are presented in Table 5 (columns 7-11). The maximum average value is 190 μA/cm2 for TA3, and the minimum is 32.2 μA/cm2 for TA8. Additionally, the data are presented as a bar diagram in Fig. 7(a). The variability in values of the corrosion current density gives evidence that there is clearly an influence of brazing parameters on the corrosion performance.

Fig. 7
figure 7

Bar diagrams for: (a) corrosion current density and (b) fillet size

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In principle, the optimization procedure would be oriented to the minimization of i corr to ensure a low corrosion rate of the automotive condenser in the SWAAT solution. However, the results in this study show that there is another aspect of joint quality that needs to be taken into account: the joint size. Figure 7(b) shows the distribution of fillet sizes that were obtained for the brazed mini-cores. It is clear that the lowest corrosion current density value (that for TA8) does not correspond to the best fillet size (in fact it corresponds to the smallest). Based on this observation, it was decided to perform the optimization under the criterion of “nominal is best,” choosing as target value of corrosion current density the one that corresponds to the experiment with best fillet size (TA4). This is indicated schematically with an arrow in Fig. 7.

Microstructural Characterization

Figure 8 shows typical SEM micrographs of the tube-fin joints corresponding to post-brazed mini-cores TA4 and TA1. Figure 8(a), corresponding to sample TA4, resembles a typical very good fin-to-tube joint (Ref 6, 40). The joint for sample TA1 (Fig. 8b) exhibits a lower quality. According to Table 5, the only difference between these two samples is in the thermal treatment. TA4 was brazed at 610 °C during 4 min, while TA1 was brazed at 600 °C during 2 min. Apart from the evident effect on fillet length, this is expected to yield different microstructural features which in consequence affect the corrosion performance. The results of i corr in Table 5 actually show that the corrosion rate of TA4 is about twice that of TA1. So, it is interesting to analyze the microstructural features around the joint for these two samples. In Fig. 9(a), a SEM backscattered electron image of the fillet in sample TA4 is presented. The characteristic Al-Si network with Si present as a needle-like structure is clearly observed, along with some block-like precipitates appearing in bright contrast (like the one circled in red). A similar type of particle was observed by Lacaze et. al. (Ref 23, 24) in the joint zone of two brazed multilayer sheets (modified AA3003 core, clad on both faces with AA4343) and was identified as the Al-Fe-Mn-Si phase. In this work, the results of EDS mapping of alloying elements Fe, Mn and Si (Fig. 9c, d and e) suggest that these precipitates correspond rather to the Al-Mn-Fe phase. Silicon is present only in the needle-like structure. Figure 10(a) shows the SEM backscattered electron image of a small section of the fins in the joint zone of the same sample TA4. Several elongated bright particles (like the ones circled in red) can be observed. It has been extensively discussed in the literature (Ref 18-20, 41, 42) that during brazing Si diffuses from the melted cladding to the core material leading to the transformation of Al6(Mn, Fe) precipitates to phases containing Al, Mn, Fe and Si. The results of EDS mapping of the main alloying elements (Fig. 10c, d and e) confirm that these particles correspond to the Al-Fe-Mn-Si phase. It has been proposed that the presence of these particles helps in corrosion protection of the core (Ref 41).

Fig. 8
figure 8

SEM micrographs of typical tube-fin joints: (a) for sample TA4, (b) for sample TA1

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Fig. 9
figure 9

(a) SEM image for a region in the brazed joint of sample TA4. EDS mapping of: (b) Al, (c) Fe, (d) Mn and (e) Si

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Fig. 10
figure 10

(a) SEM image for a section of the fin in sample TA4. EDS mapping of: (b) Al, (c) Fe, (d) Mn and (e) Si

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As described earlier, the anodic reaction takes place mainly on the micro-channel tube, while the cathodic reaction takes place mainly on the fins. The results of electrochemical measurements showed that the difference in corrosion rate between samples TA4 and TA1 is mainly due to variations in the kinetics of the hydrogen evolution reaction. So, it is interesting to compare the microstructure in the fins for these two samples. Figure 11(a) shows the SEM backscattered electron image of a small section of the fins in the joint zone of sample TA1. Again, some bright particles corresponding to the Al-Fe-Mn-Si phase can be observed (confirmed by the EDS mappings in Fig. 11c, d and e). The Si map in Fig. 11(e) shows the presence of large silicon particles in the re-solidified clad. Apparently not enough diffusion of Si occurred from the melted cladding to the core material due to the lower temperature and dwell time of sample TA1 (as compared to sample TA4). Some of the Al6(Mn, Fe) precipitates in the core that did not transform to AlFeMnSi are shown in Fig. 11(c). These results give an indication that the fins in samples TA4 and TA1 have different Si concentrations at the surface (higher in the case of sample TA1), and this may be the reason for the variations in the kinetics of the hydrogen evolution reaction.

Fig. 11
figure 11

(a) SEM image for a section of the fin in sample TA1. EDS mapping of: (b) Al, (c) Fe, (d) Mn and (e) Si

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In the case of the micro-channel tubes, the difference in thermal treatment for samples TA4 and TA1 is expected to affect the diffusion of zinc during the brazing process. Figure 12 shows a comparison of Zn concentration profiles obtained with EDS line profile analysis, starting from the external surface. It is evident that for depths below the surface of 5-60 μm, the Zn concentration is higher in sample TA1. Due to higher temperature and dwell time for sample TA4, the amount of zinc near the surface decreased because it penetrated more into the tube material (e.g., at a depth of 140μm, the concentration is higher for sample TA4). The greater Zn concentration near the surface for sample TA1 explains the more negative values of corrosion potential shown in Fig. 2. Apparently, this difference in surface concentration of Zn in the tubes of samples TA4 and TA1 did not have any significant influence on the kinetics of the anodic reaction (as discussed with the analysis of polarization curves).

Fig. 12
figure 12

Zn concentration profiles for micro-channel tubes of samples TA4 and TA1

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The results presented in this section provide evidence that the modifications in microstructure can be correlated to the electrochemical behavior of Taguchi samples TA4 and TA1. A detailed discussion of this correlation for all the other samples is beyond the scope of this work.

Statistical Analysis

The analysis of effects for means and S/N ratio for the corrosion current density is presented in Table 7. It includes ranks based on delta statistics, which compare the relative magnitude of effects. The delta statistics are the highest minus the lowest average for each factor (or interaction). The ranks indicate the relative importance of each factor (or interaction) to the response (rank 1 corresponds to the highest delta values, rank 2 to the second highest, and so on). It is clear that the factors with major effects for the i corr means were (in decreasing order): B (the type of flux), C (the peak temperature) and D (the heating rate). On the other hand, the analysis for S/N ratio effect suggests that the higher effects on the variability correspond (in decreasing order) to factors D (heating rate), E (dwell time) and A (the type of micro-channel tube).

Table 7 Response table for mean and S/N ratio
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In order to determine the statistical significance of factors (or interactions) on the mean and the variability in the response variable, an analysis of variance was carried out. The ANOVA of means and S/N ratio for corrosion current density is presented in Table 8. Both analyses were performed at 95% confidence level. The F table for ANOVA of means was F (0.05, 1,1) = 161.45 and for ANOVA S/N ratio was F (0.05, 1,2) = 18.513. If F > F table, the factor is significant at the confidence level used. The results of ANOVA of means show that the most significant factors were B (type of flux) and C (peak temperature). These factors had the highest percentage of contribution on the mean, with values of 44 and 35%, respectively.

Table 8 Results of ANOVA for mean and S/N ratio of corrosion current density
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The ANOVA of S/N ratio shows that at the established confidence level, the most significant factors were D (heating rate), E (dwell time), A (micro-channel tube), A × C (micro-channel tube × peak temperature) and A × E (micro-channel tube × dwell time). Their percentage contributions were: 37, 31, 18, 8 and 4%, respectively. The interactions had the lowest contributions to the variability in the current density response, so it can be considered that highest contributions are mainly from factors A, D and E. The experimental error of both ANOVAs was 2%.

The factors and levels that adjust the mean to the target value and maximize the S/N ratio for the response variable (i corr) were chosen taking into account the description of factors/levels in Table 4 and the results of Tables 7 and 8. Accordingly, the factors and levels selected to adjust the mean to the target value were B1 (standard flux) and C2 (610 °C, peak temperature). The factors and levels with the highest S/N ratio that decrease the variability were A2 (micro-channel tube II), D1 (5 °C/min heating rate) and E2 (4 min dwell time). Therefore, the conditions A2B1C2D1E2 were the most suitable for obtaining the optimal response of i corr.

Optimal Conditions

The prediction of corrosion current density (nominal is the best) is computed using the optimal conditions A2B1C2D1E2 and significant interactions A × C and A × E. Since the response i corr involves a target value, the predicted optimal performance \((Y_{{i_{{{\text{corr}} }} }}^{{\prime }} )\) is given by the following equation (Ref 28):

$$Y_{{i_{\text{corr}} }}^{{\prime }} = \sqrt {Y_{{i_{\text{corr}} }} } + Y_{{{\text{target}}\,{\text{value}}}}$$
(4)

with \(Y_{{{\text{target}}\,{\text{value}}}}\) = the fixed value of corrosion current density (97  μA/cm2. \(Y_{{i_{\text{corr}} }}\)is the mean square deviation (MSD) from the target value, which is computed with the following equation

$$Y_{{i_{\text{corr}} }} = \bar{Y} + \left( {\bar{A}2 - \bar{Y}} \right) + \left( {\bar{B}1 - \bar{Y}} \right) + \left( {\bar{C}2 - \bar{Y}} \right) + \left( {\bar{D}1 - \bar{Y}} \right) + \left( {\bar{E}2 - \bar{Y}} \right) + \left( {\overline{A2} \overline{C2} - \bar{Y}} \right) + \left( {\overline{A2} \overline{E2} - \bar{Y}} \right)$$
(5)

where \(\bar{Y}\) is the grand average of the S/N ratios of the current density and \(\bar{A}2,\,\bar{B}1,\, \bar{C}2,\, \bar{D}1,\, \bar{E}2,\, \overline{A2} \overline{C2} \; {\text{and}}\; \overline{A2} \overline{E2}\) are the average effects of the S/N ratios with parameters at their respective optimum levels (Table 7). The result (\(Y_{{i_{\text{corr}} }} = - 29.79 \pm 1.24\,{\text{Db}}\)) was converted back to the units of the original observations: 30.87±4.44 μA/cm2. Thus, the predicted response is \(Y_{{i_{\text{corr}} }}^{{\prime }} = 97 \pm 30.87\) μA/cm2.

Verification Tests

Figure 13 shows the representative polarization curve of the confirmation test results evaluated under optimum conditions A2B1C2D1E2 (micro-channel tube type II, standard flux, 610 °C peak temperature, 5 °C/min heating rate and 4 min dwell time). The average of results for three samples obtained by Tafel analysis is 102.07 ± 6.68 μA/cm2 and agrees very well with the predicted value. Moreover, in Fig. 14 an optical micrograph of this sample in the as-brazed condition (not corroded) is presented. It shows a typical well-brazed tube-fin joint with a joint size (147.84 ± 9.22 μm) in excellent agreement with the selected target value.

Fig. 13
figure 13

Typical polarization curve for the confirmation test

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Fig. 14
figure 14

Optical micrograph of tube-fin joint corresponding to confirmation test

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Conclusions

A Taguchi orthogonal array was employed to optimize the brazing parameters with respect to corrosion performance of tube-fin mini-assemblies in SWAAT solution.

  • It was shown that the brazing conditions had an effect not only in the response variable to be optimized (i corr), but also on the fillet size. Thus, the nominal is the best criterion for the S/N ratio was selected, choosing as target value of i corr that corresponding to the experiment with the maximum fillet size.

  • The parameters that most significantly affect the corrosion rate are the type of flux (44%) and the peak temperature (35%). The optimal conditions to adjust the i corr to the target value were: micro-channel tube type II, standard flux, 610 °C peak temperature, 5 °C/min heating rate and 4 min dwell time. The i corr value of the confirmatory experiment is in excellent agreement with the predicted value.

  • The results of electrochemical measurements for selected samples immersed during 1 h in SWAAT solution showed that variations in i corr are mainly due to changes in the kinetics of the cathodic reaction.

  • The microstructural features in the joint zone for two samples brazed under two different peak temperatures and dwell times were analyzed and correlated with their electrochemical behavior. Variation in kinetics of the hydrogen evolution reaction on the fins was attributed to a different surface concentration of silicon.