3.2. Correlation between Alloy Composition and Microstructure
Alloys with different aluminum and constant copper contents were cast in a first step. Like in the simulations, an alloy that solidifies primarily in the zinc-rich η phase (ZnAl2Cu0.7), an alloy close to the ternary eutectic (ZnAl5.5Cu0.7) and an alloy with primary β-phase solidification (ZnAl20Cu0.7) were examined.
Cooling curves recorded during the casting process give information about the heat extraction rate, which can be used as a process condition for the phase-field simulations. In
Figure 4, an SEM image of the microstructure of the alloy ZnAl2Cu0.7, which primarily solidifies in the η phase, is compared with the simulation results.
The comparison shows a good agreement regarding major microstructural features. Primary η-dendrites surrounded by the eutectic are visible with comparable phase fractions and dendrite arm spacings of about 25 µm. The dendritic grain structure is close to globular, i.e., primary trunk and side arms are difficult to distinguish in the 2D section. The phase-field simulation calculates phase fractions of 92% η and 8% β in the as-solidified microstructure. An equilibrium calculation with the same database yields 6.1% β, suggesting that the solidification takes place rather close to equilibrium. The microsegregation pattern for Cu shows that Cu accumulates in areas of the microstructure that solidify last, in particular at the boundaries between eutectic cells. In larger interdendritic areas, the eutectic microstructure is rather lamellar, but due to the geometrical constraint by the primary dendritic network, fibrous or irregular eutectic patterns are present as well.
The eutectic spacing in the simulation is slightly coarser than that found in the experiment. This suggests that either the values of the diffusion coefficients and/or the interfacial energies are too large in the simulations or that there is a difference in the cooling rates between the real casting and simulation. Beside these uncertainties, the grid resolution is another limiting factor: the finest lamella thickness which can be represented by the numerical grid is twice the phase-field interface thickness, i.e., 6 × ∆x = 1.5 µm. This is larger than the experimentally observed spacing. A proper resolution of the eutectic spacing would require a higher grid resolution. Due the increasing computational effort, this would be only feasible on smaller computational domains with volumes below the average grain size. However, the primary target of the phase-field simulations presented in this paper is not to predict the eutectic spacing, but to compute the phase fractions and the Cu microsegregation in the primary phases as input for the hardness calculation. Thus, a more detailed analysis of the eutectic microstructure is a future task which offers the opportunity to derive quantitative values for the solid/liquid interfacial energies and the diffusion coefficients of Al and Cu in the melt.
The comparison between the cast and simulated microstructures of ZnAl20Cu0.7 is shown in
Figure 5. It demonstrates also for a hypereutectic alloy a good correlation between the as-cast and simulated microstructures. Both phase fractions and the shape of the phases are well represented by the simulation. Overall, the simulation calculates 82% β and 18% η. In ZnAl20Cu0.7, the β phase with local Al concentrations up to 45 wt.% in the dendrite centers is the primary phase. It decomposes into the zinc-rich η and the aluminum-rich α phases. The resulting eutectoid microstructure is not resolved in the SEM image shown in
Figure 5, but the variation in the Al concentration leads to the contrast within the dendrites. The local Al concentration decreases from the center areas of the dendrites towards the outer areas that solidify last. The same distribution is obtained in the simulations. The qualitative agreement of the concentration profiles verifies that the values for the diffusion coefficients used in the simulation are at least in the right order of magnitude.
The morphology of the interdendritic eutectic exhibits a rim of η phase around the dendrites, whereas a lamellar structure can only be formed in larger interdendritic areas. The simulation also predicts this behavior. Furthermore, Cu is mainly distributed within the eutectic regions.
The microstructure of the near-eutectic alloy ZnAl5.5cu0.7 is shown in
Figure 6. As already shown in
Figure 3b, the solidification of this alloy takes place at 382 °C starting with the formation of small η or β nuclei which are fully surrounded by the eutectic phases. The as-cast microstructure, as well as the simulated one, again shows the same overall appearance. Both microstructures are dominated by eutectic grains. The eutectic appears lamellar or fibrous in the 2D cutting plane. The lamellar appearance is partly a geometrical effect due to the cutting, but also the 3D structures exhibit lamellar regions with a higher tendency in the last stages of solidification. Moreover, here, the simulated eutectic structure is coarser than the experimental ones. The local Cu concentration is again highest at the boundaries between eutectic grains.
For the alloys investigated in this paper, the calculated phase fractions of the β phase are compiled in
Table 2 and will later be discussed for the evaluation of the hardness computation model.
The comparison between phase-field results and equilibrium calculations shows a significant difference for low and high Al contents. The deviation is most striking for the alloy with 20 wt.% Cu. According to the thermodynamic equilibrium, a single β phase is expected, however, in the experimental micrograph, a still large amount of eutectic, i.e., η phase, is present. This is also seen in the phase-field results which show 11.3% η. For lower Al contents, the equilibrium calculations underestimate the amount of β phase after solidification, also in accordance with the experimental findings.
Another advantage of quantitative phase-field simulations is evident for ZnAlCu alloys with higher copper contents. As already mentioned, ε-Zn4Cu forms at copper contents above 2 wt.%. The Zn
4Cu phase can only be identified by EDS analysis with great effort. In SE and BSE contrast, there is no visible difference between the η phase and ε phase because of the similar atomic mass of Cu and Zn. Hence, the determination of the phase fractions of these two phases in an SEM analysis is accompanied by large uncertainties. With the help of phase-field simulations, phase fractions, size and distribution can be illustrated as shown in
Figure 7. The figure shows a partially solidified microstructure with 62% solid fraction.
In ZnAl5.5Cu4, all three phases, β, η and ε, grow from the melt and form a ternary eutectic microstructure with predominantly ε but also smaller fractions of β as primary phases. In
Figure 7, the ε phase appears red, η appears green, β appears blue and black marks the liquid. β/η eutectic islands grow in between the primary ε dendrites. In the BSE image, this corresponds to the coarse eutectic areas, e.g., in the upper left quadrant.
3.3. Hardness Measurement Results
The hardness of a material is a decisive parameter for its suitability for use as a bearing material. A good adaptation to the shaft material and a good embedding capability for wear particles are basic requirements that a bearing material must fulfil in order to prevent severe damage to the shaft and bearing.
Knowledge of possible correlations between alloy composition and material hardness, both at the macroscopic and microscopic level, is therefore essential. Results from microhardness measurements of alloys that predominantly solidify in a single phase are shown in
Figure 8, i.e., the alloy compositions are in the single-phase regions of the equilibrium phase diagram. The hardness values were measured at arbitrary positions on the samples, with approximately 0.5 mm distance between two indents. In the plot, the values are sorted by size (rank sort), therefore the plot does not show any correlation of the hardness with its location in the microstructure—it is a solely statistical analysis. The solid curves are calculated values based on the Cu microsegregation as derived from the phase-field simulation. We suggest a correlation between the hardness and the local Cu concentration following the relationship HB
i = HB
0i + a
i·[Cu]
i, where HB
0i is the hardness of phase i with zero Cu. For the ε-phase CuZn
4, the dependence from the Cu concentration is attributed to the difference from the reference concentration [Cu]
0ε, thus the hardness model reads: HB
ε = HB
0ε + a
ε·([Cu]
ε − [Cu]
0ε). The experimental data for ZnAl1Cu18 show data points with low hardness values. These points can be attributed to indents, which are in microstructure regions that show residual amounts of the η phase.
Experimentally, it would be a large effort to measure the local Cu concentration, whereas it is a direct result from the simulation. The variation in the computed hardness values, again sorted from minimum to maximum, reflects the distribution of local Cu concentrations in the simulation domain. The good match of the model data with the experimental distribution is evidence that the hardness in all three phases, η, β and ε, depends on the (local) Cu concentration. For η in ZnAl1Cu0.7 and β in ZnAl20Cu0.7, the Cu concentration is below the solubility limit at solidus temperature and the samples were measured in the as-cast state, i.e., without any subsequent heat treatment. Therefore, it is likely that, at least partially, the impact of Cu on hardness is caused by solid solution strengthening, as has already been reported by Savaskan et al. [
5,
11,
23].
From the diagram and the modeling, one can infer that η is the phase with the lowest hardness, and ε is the one with clearly the highest hardness. One should keep in mind that β decomposes into η and α’ via a eutectoid reaction, thus the hardness values for β should be considered rather as an effective value for a composite structure and not as a value for a single phase.
In the following, we will discuss the measured macroscopic Brinell hardness from the as-cast samples and show that the data follow a simple mixture rule. The macroscopic hardness was determined by Brinell hardness measurement HBW10-2.5/62.5/15. The measured hardness for alloys with different aluminum contents and thus different β-phase contents is shown in
Figure 9. As was to be expected from the results of the microhardness measurements, an increase in the β-phase content leads to an increase in the macroscopic hardness. Extrapolating the hardness to a complete β-phase sample yields 117 HB. The values from the microhardness measurements are systematically below the values from a macroscopic indent. We attribute this to a different deformation behavior on the different scales.
The hardness increases monotonously with the β-phase fraction. Except from the alloy with 2% Al, the hardness follows a linear relationship: HB =
, where
is the phase fractions and
is the hardness of the individual phases, in this case with 0.7 wt.% Cu. The calculated curve in
Figure 9 is based on
and
.
The dependency of macroscopic hardness on copper content shows a nonlinear behavior, as can be seen for the macroscopic hardness of ZnAl5.5CuX shown in
Figure 10. In the range below 1.5 wt.% copper, barely any formation of the ε phase takes place, but the hardness increases from 72 to 98 HB. Again, this increase can be attributed to solid solution hardening. For Cu concentrations below 1.5 wt.%, the phase fractions of β and η only weakly change for different Cu concentrations and we can describe the hardness by the relation HB =
+ a·[Cu], where a = 21.4/wt.%. The hardness of a Cu-free ZnAl5.5 alloy with 33% β and 67% η would be less than 70 HB.
For Cu concentrations above 1.5 wt.%, the ε phase becomes stable and its amount then increases linearly with the Cu concentration. The formation of ε gives an upper limit for Cu in solid solution and therefore for the hardness of the β/η microstructure. The microhardness measurements for ZnAl1Cu18 prove that the ε phase is considerably harder than β and η with a noticeable effect on the macroscopic hardness. An even small increase in Cu from 1.4 to 3 wt.% increases the phase fraction of ε from 0 to 13% with a corresponding hardness increase from 98 to 110. Again, it can be described by a linear relationship of the form HB = + a·[Cu-1.4], where a = 6.25/wt.% and the constant offset = 102.5.
Higher phase fractions of the ε phase are not desirable in plain bearing applications due to the brittle and abrasive effect.