Balancing phases for obtaining the same hardness in Al-Cu-Zn alloys with different compositions

1. INTRODUCTION

The Al-Cu-Zn alloy system is important for several reasons. In the region of the ternary diagram, it has a shape memory (Lovely and Torra, 1999Lovey, F.C., Torra, V. (1999). Shape memory in Cu-based alloys: phenomenological behavior at the mesoscale level and interaction of martensitic transformation with structural defects in Cu-Zn-Al. Prog. Mater. Sci. 44 (3), 189-289. https://doi.org/10.1016/S0079-6425(99)00004-3.; Iacovello et al., 2018Iacoviello, F., Di Cocco, V., Natali, S., Brotzu, A. (2018). Grain size and loading conditions influence on fatigue crack propagation in a Cu-Zn-Al shape memory alloy. Int. J. Fatigue 115, 27-34. https://doi.org/10.1016/j.ijfatigue.2018.06.039.), in another section, they present superplasticity (Hsu and Wang, 1996Hsu, C.-C., Wang, W.-H. (1996). Superplastic forming characteristics of a Cu-Zn-Al-Zr shape memory alloy. Mater. Sci. Eng. A 205 (1-2), 247-253. https://doi.org/10.1016/0921-5093(95)09884-4.) and in another, the transformation of the four phases that causes a contraction of 4% of its volume (Kovachera et al., 1993Kovacheva, R., Dobrev, R., Zadgorski, S., Lilova, A. (1993). Phase transformations in Zn- Al- Cu alloys. Mater. Charact. 31 (4), 217-224. https://doi.org/10.1016/1044-5803(93)90065-4.; Klopotov et al., 2016Klopotov, A., Ivanov, Y., Vlasov, V., Dedov, N., Loskutov, O. (2016). Phase transformations in the system Cu-Zn-Al under conditions far from equilibrium. AIP Conf. Proc. 1698 (1), 030004. https://doi.org/10.1063/1.4937826.).

We have developed a series of investigations in which we have determined the mechanical properties of an Al-Cu-Zn alloy modifying the percentage of Zn, Al or Cu in order to determine the increase or decrease of one of the mechanical properties, for example hardness (Adeosun et al., 2011Adeosun, S.O., Balogun, S. A., Osoba, L.O., Ayoola, W.A., Oladoye, A.M. (2011). Effect of Cu and Zn addition on the mechanical properties of structural aluminum alloy. Journal of modern manufacturing technology 3 (1), 103-110.; Yan et al., 2014Yan, L., Zhang, Y., Li, X., Li, Z., Wang, F., Liu, H., Xiong, B. (2014). Effect of Zn addition on microstructure and mechanical properties of an Al-Mg-Si alloy. Prog. Nat. Sci-Mater. 24 (2), 97-100. https://doi.org/10.1016/j.pnsc.2014.03.003.; Saravanan and Sellamuthu, 2014Saravanan, R., Sellamuthu, R. (2014). Determination of the Effect of Si Content on Microstructure, Hardness and Wear Rate of Surface-refined Al-Si Alloys. Procedia Eng. 97, 1348-1354. https://doi.org/10.1016/j.proeng.2014.12.415.). These investigations are important because deducing or predicting what will happen when one of the elements is varied will allow for the design of alloys that fulfill required needs.

Therefore, many of the questions that researchers have proposed in material investigation have to do with which proportion of elements should be mixed in order to obtain materials with the desired mechanical, physical and chemical properties (Suárez et al., 2011Suárez, M.A., Esquivel, R., Alcántara, J., Dorantes, H., Chávez, J.F. (2011). Effect of chemical composition on the microstructure and hardness of Al-Cu-Fe alloy. Mater. Charact. 62 (9), 917-923. https://doi.org/10.1016/j.matchar.2011.06.009.; Tiryakioğlu, 2015Tiryakioğlu, M. (2015). On the relationship between Vickers hardness and yield stress in Al-Zn-Mg-Cu Alloys. Mater. Sci. Eng. A 633, 17-19. https://doi.org/10.1016/j.msea.2015.02.073.; Guler et al., 2018Guler, M., Aldırmaz, E., Gül, S., Koyuncuoglu, E., Kulucan, F.F., Güngüneş, H., Guler, E. (2018). The effect of alloying element Zn on magnetic properties of martensite phase in FeNiMn alloy. J. Mol. Struct. 1174, 103-106, https://doi.org/10.1016/j.molstruc.2018.05.028.).

Many studies have been performed on the phases in Al-Cu-Zn alloys in which the changes in mechanical properties, related to the presence of certain phases or the absence of the same have been explained, as shown in various investigations (Saravanan and Sellamuthu, 2014Saravanan, R., Sellamuthu, R. (2014). Determination of the Effect of Si Content on Microstructure, Hardness and Wear Rate of Surface-refined Al-Si Alloys. Procedia Eng. 97, 1348-1354. https://doi.org/10.1016/j.proeng.2014.12.415.; Alaneme et al., 2017Alaneme, K.K., Okotete, E.A., Maledi, N. (2017). Phase characterisation and mechanical behaviour of Fe-B modified Cu-Zn-Al shape memory alloys. J. Mater. Res. Technol. 6 (2), 136-146. https://doi.org/10.1016/j.jmrt.2016.10.003.).

In previous works it has been theorized, but not shown, that there can be different alloys with the same hardness that have chemical percentages and phases that are very different from Al-Cu-Zn ternary alloys (Villegas-Cárdenas et al., 2011Villegas-Cardenas, J.D., Lopez-Hirata, V.M., De Ita-De la Torre, A., Saucedo-Muñoz, M.L. (2011). Assessment of Hardness in As-Cast and Homogenized Zn-Al-Cu Alloys. Mater. Trans. 52 (8), 1581-1584. https://doi.org/10.2320/matertrans.M2011084.: Villegas-Cárdenas et al., 2014Villegas-Cárdenas, J.D., Saucedo-Muñoz, M.L., López Hirata, V.M., Dorantes Rosales, H.J. (2014). Predicción de la dureza de aleaciones Al-Cu-Zn en estado de colada y templado. Rev. Metal. 50 (2), e015. http://dx.doi.org/10.3989/revmetalm.015.).

Understanding that the type of interaction between phases affects the mechanical properties of an alloy has been an important topic for many years. In other words, a key question in material investigation has been how elements can be combined in such a way as to produce a solid with specific properties (Rohrer, 2014Rohrer, G.S. (2014). Structure and Bonding in Crystalline Materials. Cambridge University Press, United States.). The objective of this work is to obtain a series of different alloys with different chemical compositions but with the same hardness, only by manipulating the percentages of the phases.

2. MATERIALS AND METHODS

2.1. Obtaining the percentages of alloys

 ⌅

According to the article “Prediction of the Hardness of Al-Cu-Zn Alloys in Casting and Cooling” (Villegas-Cárdenas et al., 2014Villegas-Cárdenas, J.D., Saucedo-Muñoz, M.L., López Hirata, V.M., Dorantes Rosales, H.J. (2014). Predicción de la dureza de aleaciones Al-Cu-Zn en estado de colada y templado. Rev. Metal. 50 (2), e015. http://dx.doi.org/10.3989/revmetalm.015.), it is possible to determine the hardness of the Al-Cu-Zn alloys when they are within a zone made up by phases α, η and τ. In Fig. 1, in isothermal range 25°C, we can see two series of dotted lines, in which the first goes from M1 to M8 and the second from M9 to M16. Each of these is an Al-Cu-Zn alloy with a different chemical percentage.

Figure 1.  Ternary balance diagram at 25 °C in which two series of alloys are shown.

From each line shown in Fig. 1 we obtain an equation that represents a chemical percentage; Eqs. (1) and (2).

$X_{zn}\mathrm{ }=\mathrm{ }-1.9438X_{cu}\mathrm{ }+\mathrm{ }0.50334$  (1)

$X_{zn}\mathrm{ }=\mathrm{ }-2.9823X_{cu}\mathrm{ }+\mathrm{ }0.97337$  (2)

The Eq. (1) is the straight line that represents the points that go from M1 to M8 in Fig. 1. The Eq. (2) represents points M9 to M16. Each of the points shown in Fig. 1 represents an alloy, when the hardness of these alloys is obtained after the homogenizing process, the hardness of these alloys shows a lineal tendency as observed in Fig. 2. The graph of equations 3 and 4 are shown in Fig. 2,

The equations from this lineal regression are:

$HB\mathrm{ }=\mathrm{ }18.617ln{X}_{cu}\mathrm{ }+\mathrm{ }122.12$  (3)

$HB\mathrm{ }=\mathrm{ }33.326ln{X}_{cu}\mathrm{ }+\mathrm{ }146.05$  (4)

In Fig. 2 we show the samples used in this work. As can be seen, there is a horizontal line set at 74RB so that all samples present this same hardness. Each of these alloys has a certain percentage of Cu, but the percentages of Zn and Al are unknown. Therefore, the slope formed between each of the alloys proposed with respect to the point of intersection of equation 3 and 4 must be known. The point of intersection of the two lines is 19.65% Cu with a hardness of 91.83 RB, with the previous point and the points of each of the samples, the slope of the hardness of each alloy as shown in Table 1 is obtained.

Figure 2.  Representation of equations 3 and 4 and of the test samples used to obtain a hardness of 74 RB in all samples.

Table 1.  Obtaining the slope of hardness as per the hardness of each alloy classified from S1 to S5

Sample	%Cu	Teórica Hardness (RB)	Slope of Hardness
S1	0.074274	74	18.3249
S2	0.084512	74	21.1290
S3	0.094751	74	24.4408
S4	0.104990	74	28.4406
S5	0.115229	74	33.3973

The slope of hardness have a direct relationship with the slopes of atomic percentages therefore we used an interpolation between the slopes of Eqs. (1-4Eqs. 1, 2, 3, 4) and the slopes of Table 1.

Table 2 shows interpolation, where P_Hd is the hardness slope obtained in Table 1 while P_at is the slope formed by the atomic fraction which is unknown and therefore is a dependent variable in interpolation, and:

$P_{at}=\left[\frac{-2.9823-(-1.9438)}{33.326-18.617}\right]\left[P_{Hd}-18.617\right]-1.9438$  (5)

Table 2.  Relationship between slopes for interpolation

Independent Variable (slope of hardness)	Dependent Variable (slope atomic fraction)
18.617	-1.943800
P Hd	P at
33.326	-2.982300

It is also necessary to determine the intercept with X_Zn for which the point of intersection of Eqs. (1) and (2) is needed, and which is a virtual point that is found at 0.452605 at. Cu and -0.376433 at. Zn. The equation of the ordinate at origin B is:

$B\mathrm{ }=\mathrm{ }-0.376433\mathrm{ }-\mathrm{ }{P}_{at}\left(0.452605\right)$  (6)

With the slopes from Table 1 and equations 5 and 6 we obtain Table 3 that shows the percentage of Zn and Al needed to obtain a hardness of 74 RB. Each of the simples in theory, as per our methodology, should have a hardness of 74 RB.

Table 3.  Obtaining percentages of Al, Cu, Zn for obtaining a hardness of 74RB in each of the samples

Sample	Pat	B	Zn (fraction at.)	Al (fraction at.)	Cu (fraction at.)
S1	-1.9232	0.4940	0.3512	0.5746	0.0743
S2	-2.1212	0.5836	0.4043	0.5111	0.0845
S3	-2.3550	0.6894	0.4663	0.4389	0.0948
S4	-2.6374	0.8173	0.5404	0.3547	0.1050
S5	-2.9873	0.9756	0.6314	0.2534	0.1152

2.3. DRX Analysis

 ⌅

The results obtained in the diffractometer are shown in Fig. 3. All samples have the phases η, ε, α and τ’, but samples S2, S3 and S4 show the phase β and samples S1 and S2 show the phase θ. Sample S2 shows a greater number of phases, 6, and as per the results shown in Table 4, we can see that this sample has greater hardness (only 2RB). Also, seen in Fig. 3 is the intensity in the phases η and α which decreases as the amounts of Zn and Cu increase. At the same time the intensity of phase ε increases in sample S2, in which there is almost no phase ε, phases β and θ are present, especially the latter, which is present in greater intensity.

Figure 3.  Diffractogram for each of the samples, in which the phases of each can be seen.

2.4. Metallography

 ⌅

Figure 4 shows the different metallographic taken for each sample using an SEM in backscatter mode for phase identification:

Figure 4.  Metallography of each sample in backscatter mode in the electronic scan microscope.

In the metallographic shown in Fig. 4, we can see that there is a considerable increase in the white zone where the greater proportion in phase η and a lower proportion in phase ε are found. As the amount of Zn is increased, this white zone increases, which is logical because phase η is rich in Zn. The issue is that this increase does not occur in lineal form as corresponds to the amount of Zn, which does increase in linear form. We can see important differences in the metallography, for example, when a perimeter analysis, shown in the metallographic, has a white zone, compared to the rest of the phases, the graph shown in Fig. 5 is obtained. Analysis of the graph in Fig. 5 shows that all the samples behave in the same way, meaning that they all have a greater number of repetitions within the range of 25.09 to 35.61 micrometers. We must point out that the graph only shows 52% of all information obtained, however, the graph shows the densest part of the statistics for each sample used.

Figure 5.  Bar chart of the perimeter of phase η for each of the samples from S1 to S5.

Table 5 shows the maximum and minimum measurements for each sample, along with the percentage that is represented in Fig. 5.

Table 5.  Additional information from Fig. 5, in which standard deviation averages are presented, as well as the real percentages for the three main ranges shown in Fig. 1

Sample	# Measurement	Measurement		Average	Standard	# Dates by interval			Total	% Total
		Maximum	Minimum			14.58 a 25.01 (µm)	25.02 - 35.61 (µm)	35.62 - 46.12 (µm)
S1	83.00	119.71	14.58	47.36	26.47	11.00	25.00	19.00	55.00	66.27
S2	178.00	253.13	15.47	58.92	41.95	23.00	48.00	25.00	96.00	53.93
S3	659.00	923.30	15.95	99.61	116.05	37.00	148.00	101.00	286.00	43.40
S4	646.00	506.35	17.20	67.99	63.45	49.00	158.00	134.00	341.00	52.79
S5	1132.00	4097.79	15.34	111.45	262.69	61.00	247.00	240.00	548.00	48.41

3. DISCUSSION OF RESULTS

Even with the error that exists between the theoretical and real results, we must mention that the hardness remained the same, in other words all samples basically have the same hardness. The difference between the highest and lowest hardness is only 2.07 RB and the standard deviation in the samples is 0.7901l, achieving the goal of having 5 samples with the same hardness.

All samples have the phases η, ε, α and τ’ and the intensity of these changes with the chemical percentage. This change in the intensity of the phases helps to have the same hardness even when exist a dramatic change in the chemical percentage, for example the percentage of cupper between the samples S1 to S5 are 50% and the same the Aluminium and Zn. Therefore, is possible to obtain materials with the same hardness but with different percentages chemical.

On the other hand, we must remember that the perimeter shown in the metallographic is just the proportional relationship of the area that is in contact with other phases. This is important because in the surface area there is a greater number of dislocations, and more dislocations will correspond to greater hardness, showing a relationship between dislocations and hardness.

The perimeter of each of the samples with respect to the white zone increases proportionally to the increase in the percentages in Zn and Cu. According to table 5 in each sample the 50% have a perimeter within a range of 14.58 µm to 46.12 µm and this is presented in the Fig. 5.

Therefore, we can say that this methodology can obtain different samples with different chemical percentages but with the same hardness. This is possible maybe by the perimeter that have the η phase with respect another phase according to the metallographic.

4. CONCLUSIONS

According to what we have previously analyzed: