Effect of novel grain refiner and Ni alloying additions on microstructure and mechanical properties of Al-Si_9.8-Cu_3.4 HPDC castings – optimization using Multi Criteria Decision making approach

In 1982, GRA, which is part of the grey system, was introduced by Dr. Deng, as a decision-making approach for multi-criteria, i.e., it converts multi-outcomes (responses) into a single outcome problem [28]. Identification of the optimal solution is based on the grey relational grade (GRG) system because it shows the overall performance of experimental runs [29]. GRA involves the following procedural steps to change the multi-objective optimization problem into a single problem using GRG.

Step 1: Normalized output quality characteristics are computed by the following equation, which allows normalization of the “higher-the-better” quality characteristic: (4) xi*(k)=yi(k)−minyi(k)maxyi(k)−minyi(k) x_i^*\left( k \right) = {{{y_i}\left( k \right) - \min {y_i}\left( k \right)} \over {\max {y_i}\left( k \right) - \min {y_i}\left( k \right)}} where xi*(r) x_i^*\left( r \right) shows normalized data and y_i(k) shows the discerned data for ith experiment by means of the kth response.

Step 2: The following equation is used to obtain the grey relational coefficient (GRC) values to express the mutual relationship between actual and ideal normalized experimental results: (5) ξi(k)=Δmin+ξΔmaxΔi(k)+ξΔmax {\xi _i}\left( k \right) = {{{\Delta _{\min }} + \xi {\Delta _{\max }}} \over {{\Delta _i}\left( k \right) + \xi {\Delta _{\max }}}} where ξ is the distinguishing or identification coefficient, which is normally lies between 0 and 1 and is used mainly to compress or expand the range of GRC values. Normally, the value of ξ is taken as 0.5. Δ_min is the global minimum value of Δ_i(k), and Δ_max is the global maximum value of Δ_i(k), here Δi(k)=|xi*(k)−xio(k)| {\Delta _i}\left( k \right) = \left| {x_i^*\left( k \right) - x_i^o\left( k \right)} \right|

Step 3: In the third step, the GRG values are computed by the following equation: (6) γi=1n∑k=1nξi(k) {\gamma _i} = {1 \over n}\sum\limits_{k = 1}^n {{\xi _i}\left( k \right)} where γ_i is a GRG value, and n shows the number of output responses.

TOPSIS is a very easy and potent multi-objective decision analyzing method, and helps to carry out optimum single objective solutions among a large number of multi-objective alternate solutions. The basic principle of this method is to determine the optimum solution, which is the shortest distance to a positive ideal solution (PIS) and far from a negative ideal solution (NIS). TOPSIS analytical method is carried out in the following stages.

Stage I: In this stage, the primary decision matrix that has attributes and alternatives is constructed from all the collected data gathered from experimental runs. The decision matrix consists of n attributes and m alternative solutions. In the present process, the output responses are attributes (m) and the experimental trials are alternative solutions (n). (7) Dm=[b11b12b13⋯⋯b1nb21b22b23⋯⋯b2n⋮⋮⋮⋮⋮⋮bm1bm2bm3⋯⋯bmn] {D_m} = \left[ {\matrix{ {{b_{11}}} & {{b_{12}}} & {{b_{13}}} & \cdots & \cdots & {{b_{1n}}} \cr {{b_{21}}} & {{b_{22}}} & {{b_{23}}} & \cdots & \cdots & {{b_{2n}}} \cr \vdots & \vdots & \vdots & \vdots & \vdots & \vdots \cr {{b_{m1}}} & {{b_{m2}}} & {{b_{m3}}} & \cdots & \cdots & {{b_{mn}}} \cr } } \right]

Stage II: Alternative data have been normalized using the following vector normalization method: (8) Rij=bijΣi=1mbij2 {{\rm{R}}_{ij}} = {{{b_{ij}}} \over {\sqrt {\Sigma _{i = 1}^mb_{ij}^2} }} where R_ij shows a normalized value, corresponding to experiment run i with output response j.

Stage III: A decision matrix is obtained by multiplying each assigned weight of each attribute with the corresponding normalized value. For this study, three output responses were considered and all are having equal importance. So, the assigned weight value equals 1/3, and the weighted normalization for all responses are carried out by following Eq. (6). (9) Tij=RijWj∑j=1nWj=1 \matrix{ {\;\;\;\;\;\;\;\;\;{T_{ij}} = {R_{ij}}{W_j}} \hfill \cr {\sum\nolimits_{j = 1}^n {{W_j} = 1} } \hfill \cr }

Stage IV: Determination of PIS and NIS

PIS and NIS will be determined as (10) V+=(V1+,V2+…Vn+)={(maxVij/j∈B1), (minVij/j∈B2,i=1,2,…n)} \matrix{ {{V^ + }} \hfill & { = \left( {V_1^ + ,V_2^ + \ldots V_n^ + } \right)} \hfill \cr {} \hfill & { = \left\{ {\left( {\max {V_{ij}}/j \in {B_1}} \right),} \right.} \hfill \cr {} \hfill & {\left. {\;\;\;\;\left( {\min {V_{ij}}/j \in {B_2},i = 1,2, \ldots n} \right)} \right\}} \hfill \cr } (11) V−=(V1−,V2−…Vn−)={(minVij/j∈B1), (maxVij/j∈B2,i=1,2,…n)} \matrix{ {{V^ - }} \hfill & { = \left( {V_1^ - ,V_2^ - \ldots V_n^ - } \right)} \hfill \cr {} \hfill & { = \left\{ {\left( {\min {V_{ij}}/j \in {B_1}} \right),} \right.} \hfill \cr {} \hfill & {\left. {\;\;\;\;\left( {\max {V_{ij}}/j \in {B_2},i = 1,2, \ldots n} \right)} \right\}} \hfill \cr } Here, B₁ is the beneficial set of attributes and B₂ is the non-beneficial set of attributes.

Stage V: Calculation of separation measures of each alternative, i.e., positive separation measures of alternatives from PIS and negative separation measures of alternatives from NIS, are carried out using the following equations. (12) Si+=∑j=1n(Tij−V+)2 S_i^ + = \sqrt {{{\sum\limits_{j = 1}^n {\left( {{T_{ij}} - {V^ + }} \right)} }^2}} (13) Si−=∑j=1n(Tij−V−)2 S_i^ - = \sqrt {{{\sum\limits_{j = 1}^n {\left( {{T_{ij}} - {V^ - }} \right)} }^2}} where i = 1, 2, ..., m.

Stage VI: Assessment of closeness coefficient (CC)

In this stage, the CC of every alternative is assessed by Eq. (14). The CC values of every alternative to the ideal solution are computed using Eq. (11). (14) CC=Si−Si++Si− CC = {{S_i^ - } \over {S_i^ + + S_i^ - }}

Figure 2A shows the XRD results of the Al-3.5FeNb-1.5C master alloy as a grain refiner. It was observed that the Al-3.5FeNb-1.5C grain refiner primarily contains the α-Al, Al₃Nb, and NbC phases. The intermetallic particles such as Al₃Nb (characterized by a tetragonal structure with lattice parameters a = 3.848 Å and c = 8.615 Å) and NbC (characterized by a face-centered cubic structure with lattice parameter a = 4.430 Å) act as potential nucleation sites for improving the equiaxed structure. Also, the diffraction peak of Fe₂Nb, which is effective in strengthening grain boundaries and suppressing deformation, was detected in the XRD patterns. From Figure 3B, it can be observed that the intermetallic particles (Al₃Nb and NbC) are scattered uniformly and detached from each other; and the sizes of the particles are varied.

Fig. 2

Fig. 3

The microstructures of the commercial Al-Si_9.8-Cu_3.4 base alloy with and without the addition of Al-3.5FeNb-1.5C master alloy at 720°C, 750°C, and 780°C are shown in Figure 3. Figures 3A–3C show the microstructures of the Al-Si_9.8-Cu_3.4 alloy without the addition of grain refiner, and reveal the coarseness of the grain structures, because their average grain sizes are approximately 61.22 ± 3 μm, 71.93 ± 3 μm, and 64.03 ± 3 μm, respectively. From Figures 3D, 3E, and 3F, it can be observed that the coarse grains of the base alloy are refined to small equiaxed ones by the addition of the Al-3.5FeNb-1.5C grain refiner. Primarily when the base alloy is inoculated with the 0.1 wt.% of Al-3.5FeNb-1.5C grain refiner, very fine grains of the base alloy have been observed, together with uniformity in grains and more number of grains per unit area. From Figure 3D, it can be observed that the average grain size of α-Al of the base alloy was significantly decreased to 22.9 ± 3 μm particularly when the base metal was inoculated with the 0.1 wt.% of Al-3.5FeNb-1.5C grain refiner at 720°C. Also, it was noticed that these grain structures (Figure 4D) are much finer than those grain structures which were refined by the 1.0 wt.% of Al-3.5FeNb-1.5C master alloy. From observing these microstructures, it was understood that the coarse grains become the finest resultant to adding the Al-3.5FeNb-1.5C grain refiner to the base alloy up to a level of 0.1 wt.%. Nevertheless, consequent to the further increase in the addition level of Al-3.5FeNb-1.5C grain refiner from 0.1 wt.% to 1.0 wt.% to the base alloy, the fine grain structure again became coarse, and this can be attributed to the formation of β-Al₅FeSi platelets, which cause the formation of coarse grains. According to the conclusions given by Zedan and Samuel [30, 31], “these β platelets often result in the formation of large shrinkage cavities due to the inability of the liquid metal to fill the space between the branched platelets”. Samuel et al. concluded that the size of β-Al₅FeSi platelets and their distribution are greatly affected by the amount of iron. So, at 1.0 wt.% of Al-3.5FeNb-1.5C grain refiner addition to base alloy, the formation of β-Al₅FeSi platelets has taken place due to increase in the amount of iron content. Based on comparison of the grain size of the alloy with and without grain refinement, as shown in Figure 3, it was observed that the Al-3.5FeNb-1.5C master alloy has a much better grain refining performance particularly at 0.1 wt.% addition to Al-Si_9.8-Cu_3.4 alloy. Based on these results, it can be concluded that the developed Al-3.5FeNb-1.5C grain refiner can efficiently refine binary Al-Si alloys due to the formation of niobium silicides, which are more stable than titanium silicides, thus significantly limiting the so-called poisoning effect.

Fig. 4

Table 3 shows the output characteristics, such as tensile properties and Brinell and microhardness values, which are obtained from the 27 experimental high pressure die casts prepared in two sets at different weight percentages of Al-3.5FeNb-1.5C and Al-6Ni master alloys according to the experimental design. We observe significant effects of grain refinement on the mechanical properties of the commercial Al-Si_9.8-Cu_3.4 alloy, and changes are noticeable primarily in UTS and hardness values (Brinell and micro). Specifically, the UTS and hardness values of the Al-Si_9.8-Cu_3.4 alloy are improved pursuant to addition of the new grain refiner.

It also can be observed that the grain refinement of the commercial Al-Si_9.8-Cu_3.4 alloy utilizing the FeNb-C novel grain refiner leads to a significant improvement in the UTS and hardness measurements, as shown in the experimental runs R₄ and R₂₂. Moreover, these properties (UTS and hardness) of the Al-Si_9.8-Cu_3.4 alloy are further increased due to addition of Al-6Ni master alloy, particularly at 0.1 wt.% of Al-3.5FeNb-1.5C and 0.5 wt.% of Al-6Ni master alloys, as observed in the experimental runs R₅ and R₂₅.

Quantitatively, the UTS of the unrefined Al-Si_9.8-Cu_3.4 alloy is about 218.39 ± 3 MPa, and after the addition of 0.1 wt.% of Al-3.5FeNb-1.5C and 0.5 wt.% of Al-6Ni master alloys, the UTS is increased to 249.08 ± 3 MPa. That is to say, the average value of the UTS is increased by 12.3%. The hardness values (Brinell and micro) of the Al-Si_9.8-Cu_3.4 are also increased from 85 ± 3 Hv to 91 ± 3 Hv and from 113 ± 3 Hv to 136 ± 3 Hv owing to the addition of these two master alloys, respectively. The UTS and macro- and microhardness values for all experimental runs are shown in Figures 4A and 4B. It is apparent that the average hardness (Brinell and micro) and UTS values of sample R₅, having a porosity percent of less than 0.3%, are more than 90 Hv for Brinell hardness, 135 ± 3 Hv for microhardness, and 249.08 ± 3 MPa for UTS. It is worth noticing that the samples with 0.1 wt.% of Al-3.5FeNb-1.5C and 0.5 wt.% of Al-6Ni master alloys’ addition possess the highest UTS and hardness. But they have deteriorated when the addition of 1.0 wt.% of Al-3.5FeNb-1.5C compared with base metal, quantitatively the lowest UTS and hardness values at experimental run R₂₅ are 200.27 ± 3 MPa, 80 ± 3 Hv, and 107 ± 3 Hv because its microstructure is much larger than other samples such as R₄ and R₅ as shown in Figures 4C and 4D.

The investigation aims to enhance the process improvement and strength of aluminum cast alloys, and thus all the output characteristics such as macro- and microhardness and tensile strength are to be maximized. The output characteristics were normalized for “higher-the-better” using Eq. (1). Table 4 expresses the normalized value of an experimental result, GRC, and GRG calculated through Eqs (1) and (3). The GRCs and overall GRG for each combination are depicted in Table 4.

For every outcome response, the “higher-the-better” condition is chosen. It is always desirable to get the highest value of the GRG. The higher GRG grade indicates a closeness to the optimal response in the process. It is noticed that experiment run 5 has the highest GRG of 0.98. The average optimal values of GRG for each parameter at levels 1–3 are given in Table 5 and plotted in Figures 5A and 5E. The main effects of the various parameters, when changed from the lower to a higher level, are also given in Table 5.

Fig. 5

From Figure 4, we can ascertain that the parameter B is more prominent than other parameters; also, it is clear that average GRG appears to be maximum at the second level of the parameters B and C, at the first level of the parameters A and D, and then at the third level of the parameter E – i.e., A₁, B₂, C₂, D₁, and E₃ can be recognized as the best levels for enhancing the mechanical properties of the high pressure die casts of Al-Si_9.8-Cu_3.4 aluminum alloy. From GRA, the experiment run, which has the highest grey relational grade, i.e. which is very close to one is considered as an optimal solution. As per Table 5, experimental run No. 5 has the highest GRG of 0.98, and corresponding output response values are considered as optimal values would get at optimal levels (A₁, B₂, C₂, D₁, and E₃) of the process parameters.

The normalization, weighted normalization, separation, and their relative CC values, which were computed by Eqs (7) and (14), are depicted in Table 6. The experimental run that has the highest CC value, i.e., a value that is very close to 1, is considered the best experimental run. As per the values of CC, which are shown in Table 6, experimental run 5 has the highest CC value of 0.972. The ranks, which are prepared as per the grade (higher to lower) of CC values of experimental runs, are shown as: 5>4>23>6>14>22>3>20>21>12 >13>24>2>15>27>19>9>17>10 >1>21>26>7>8>16>18>25. \matrix{ {5 > 4 > 23 > 6 > 14 > 22 > 3 > 20 > 21 > 12} \hfill \cr {\;\; > 13 > 24 > 2 > 15 > 27 > 19 > 9 > 17 > 10} \hfill \cr {\;\; > 1 > 21 > 26 > 7 > 8 > 16 > 18 > 25.} \hfill \cr } Based on the ranking order of experimental runs, it could be understood that experimental run 5, which has the highest CC value of 0.972, is the best optimum solution and that experimental run 4 is the next optimum solution, being the first to follow experimental run 5. Also, it was identified that the experimental run 25 is the worst optimum solution among all alternatives. To obtain an optimized set of process parameters from the TOPSIS methodology, the average values of CC for each parameter at levels 1–3 are given in Table 7 and plotted in Figures 6A and 6E. The main effects of the various parameters, when changed from the lower to a higher level, are also given in Table 7. From Figure 6, it is known that the parameter B is more prominent than other parameters, also it is clear that average CC appears to be maximum at the second level of the parameters B and C, at the first level of parameters A and D and the at the third level of parameter E. i.e., A₁, B₂, C₂, D₁ and E₃ as the best levels for enhancing the mechanical properties of the high pressure die casts of Al-Si_9.8-Cu_3.4 aluminum alloy that are a molten metal temperature of 120°C, 0.1 wt.% of Al-3.5FeNb-1.5C grain refiner, 0.5 wt.% of Al-6Ni alloying addition, die temperature of 230°C and injection pressure of 24 MPa.

Fig. 6

The optimum results which are obtained from GRA and TOPSIS multi optimized analytical techniques are compared and noticed that both have the same set of combination of process parameters i.e A₁, B₂, C₂, D₁, E₃ as an optimum result. The comparison graph between the grade values of GRG and CC concerning the sequence of experimental runs is shown in Figure 7. From this graph, it is noticed that the same similarity has been followed in both the techniques, except for experiments 4, 14, and 20. Also, it is observed that experimental run 5 has the highest grade value and that experimental run 25 has the lowest grade value. Therefore, the confirmation test was performed to validate the predicted CC and grey grade values using the following relation: (15) γ=γm+∑i=1q(γ¯i−γm) \gamma = {\gamma _m} + \sum\limits_{i = 1}^q {\left( {{{\bar \gamma }_i} - {\gamma _m}} \right)} where γ_m is total mean of CC/GRG and γ¯i {\bar \gamma _i} is mean of CC/GRG at an optimal level of parameters.

Fig. 7

The predicted value of GRG was 0.809 and CC was 0.948, i.e., the predicted grey grade value of GRA is less than the predicted closeness value of TOPSIS. Similarly, based on the experimental confirmation, the highest values of the grey grade and CC were 0.979 and 0.972, respectively. The results of confirmation are depicted in Table 8. Mainly, a significant improvement has been observed in grey grade value from the initial set of parameters to an optimal set of parameters combination was 0.540 and CC was 0.647. Further, it was observed that optimal process parameters’ combination results yield a CC value higher than the seventh experiment for the TOPSIS approach and higher than the 10th experiment in the GRA approach, which is the highest value in the L27 orthogonal array of the set of experiments.

SEM images with EDX examination of the experimental runs R₅ at 0.1 wt.% of Al-3.5FeNb-1.5C and 0.5 wt.% of Al-6Ni with base alloy and R₂₅ at 1.0 wt.% of Al-3.5FeNb-1.5C with base alloy are shown in Figures 8A and 8D, respectively. It is observed that mainly three prominent elements (Al, Nb, and C) react to structure various types of compounds those are niobium aluminides (Al₃Nb) and niobium carbides (NbC), which act as potential heterogeneous nucleation sites i.e., inoculants which promote the effective grain refinement of Al-Si alloys through heterogeneous nucleation. Nevertheless, from Figure 8B it can be observed that the β-Al₅FeSi platelets have appeared along with Al₃Nb and NbC. These platelets often result in the formation of large shrinkage cavities due to the inability of the liquid metal to penetrate the spaces between the branched platelets. The improvement of UTS and hardness properties has been observed in experimental run R₅, as shown in Figure 8A, via effective grain refinement by Al₃Nb and NbC in the heterogeneous nucleation sites. However, the porosity has been increased in the experimental run R₂₅, as shown in Figure 8B, because of β-Al₅FeSi platelets that cause the formation of large shrinkage cavities. It was observed from the EDX pattern, as shown in Figures 8C and 8D, that presence of the elements Al, Si, Cu, Fe, Nb, C, and Ni in base Al-Si_9.8-Cu_3.4 alloy confirms the distribution of FeNb, C, and Ni materials. The fracture morphologies of the experimental runs R₅ and R₂₅, shown in Figures 9A and 9B, indicate that the specimen has the highest and lowest GRG and CC values. The effect of grain refiner content in the base materials on the fracture morphology of the tensile tested samples was examined to understand in a better way the tensile strength mechanism. It is clearly observed from Figure 9A that the fracture patterns are composed of smaller cleavage planes and a few small dimples. In the materials (experimental run R₅), the size of the voids is decreased with the addition of 0.1 wt.% of Al-3.5FeNb-1.5C and 0.5 wt.% of Al-6Ni content in the Al-Si_9.8-Cu_3.4 alloy. The grain refinement in the material causes the voids’ sizes to shrink. And it is observed from Figure 9B that uniformly distributed and bigger sized voids are present in the fracture morphology. It may be that the fracture morphology of Al-Si_9.8-Cu_3.4 alloy with the addition of 1.0 wt.% of the Al-3.5FeNb-1.5C master alloy revealed a typical ductile fracture characteristic, consisting of numerous dimples over the entire surface. The strength of Figure 9A is higher than that of Figure 9B, and this is due to grain refinement. lower size of dimples noticed in Figure 9A reveals that grain refinement and to detach the grain boundary need more load, the results of grain refinement that have more grain boundaries.

Fig. 8

Fig. 9