1 Introduction

The actualization of the 4.0 industrial revolution has become a global phenomenon because of its role in reducing carbon emissions. Hence, the quest for a high-strength to lightweight material with excellent corrosion, wear, and creep resistance is increasing. The aviation, automobile, marine, and chemical processing industries demand fully dense, high-strength, tough materials for high-temperature applications and lightweight materials that can withstand stress. Metallic alloys such as aluminium, titanium, and nickel-based superalloys have been employed to meet this requirement [1, 2]. However, these alloys are characterized by high-density characteristics requiring a high mechanical load to operate. This consequently results in increased fuel consumption and carbon emission to the environment. The emergence of NiAl is a potential candidate material with the capabilities to replace these alloys. It possesses high-temperature capability to the tune of 1638 °C. The thermal and mechanical stability at elevated temperatures and low-density characteristics are added advantages. Nickel aluminide has gained attraction in developing lower-weight to high-strength structural alloys with an advantage of strengthening the second phase for extreme temperature applications. Nickel and aluminium have a strong bond at extreme temperatures. This bond has generated outstanding properties at an extreme temperature and good strength that could effectively compete with superalloys and ceramics. The NiAl-based alloy has shown superior thermomechanical properties, excellent corrosion, wear, and creep resistance compared to the conventional nickel-based superalloys [1,2,3,4,5,6]. Nickel-aluminide is an intermetallic compound containing aluminium and nickel and has been the focus of recent researchers. The two most widely known are Ni3Al and NiAl. However, for this study, we will focus on fabricating Ni–Al-Ti-Mn-Co-Fe–Cr HEA.

The intermetallic compounds are composed of two or more elemental metals in different ratios, forming new properties and crystal structures different from their constituents’ elements, such as nickel aluminides. These intermetallic materials are alloyed to obtain more desirable properties. Most importantly, the nickel aluminides; γ’ (Ni3Al: L12) and βʹ (NiAl: B2) are known for their strength and brittleness with excellent mechanical properties at an elevated temperature [7,8,9]. They also often exhibit excellent magnetic, superconducting, and chemical properties because of strong internal order and mixed (metallic and covalent/ionic) bonding [10]. As a result, they have found applications in hydrogen storage materials, turbine blades, barrier and contact layers in microelectronics, automobile industries, aerospace, etc. Due to its wide range of acceptance, a lot of research has gone into improving its mechanical properties through microalloying and production processes. [11, 12]. Hence, adopting a new approach to optimize NiAl alloy by alloying with other elements is imperative. Therefore, incorporating highly stable metals in the nanoscale rendered a super strength to NiAl alloy both at room and higher temperatures, improving the hardness and enhancing creep and corrosion resistance.

Further to the actualization of the industrial 4.0 revolution came high entropy alloys (HEA). The HEA adopted the idea of mixing different primary elements in an equal or near-equimolar ratio to produce a multi-component alloy rather than the conventional alloying of a single-based element or compound to form the matrix. The deviation from the conventional single alloying system has left a design gap to be explored to meet the industrial revolution. Given this, this research was birthed to develop Ni–Al-Ti-Mn-Co-Fe–Cr HEA. High entropy alloy is a new class of alloys with excellent mechanical properties at elevated temperatures [13]. In the past 16 years, HAE has drawn significant research because of its unique properties and by defying the principles of alloying in existence for many years. It has been established that HEA is suitable for use due to its numerous properties, ranging from high strength to thermostability and corrosion resistance, thus increasing its developmental potential [14]. In the space of 16 years, HEA has attracted so much interest from different fields. Studies have been carried out on its physical properties, such as magnetic, electrical, or thermal, by Tsai [15] and Zhang et al. [16]. Researchers have investigated the corrosive behavior and HEA’s excellent mechanical performance and deformation behavior. This has expanded its application at elevated and cryogenic temperatures [17,18,19,20,21,22,23,24,25]. Figure 1 describes HEA with different circle sizes representing the ratio in at.% of the alloying elements in the final alloy.

Fig. 1
figure 1

Schematic diagram of high entropy alloy composition in at %

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The development of Ni–Al-Ti-Mn-Co-Fe–Cr HEA will be a groundbreaking achievement in solving most of the challenges associated with NiAl. There is so much prospect in NiAl if the limitations can be addressed. To develop Ni–Al-Ti-Mn-Co-Fe–Cr HEA, careful consideration must be given to the characteristics of the continuous matrix material, the type or nature of constituent elements, the percentage weight composition of the alloys in the matrix, the particle size, the binding nature of the continuous-discontinuous material interface, and the processing technique employed to modify the microstructural evolution [26].

Process and material selection are essential factors in developing Ni–Al-Ti-Mn-Co-Fe–Cr HEA. The mechanical alloy method will produce fully pre-alloyed Ni–Al-Ti-Mn-Co-Fe–Cr HEA powders, and spark plasma sintering (SPS) will provide the ideal consolidation method. Indisputably, the SPS process has been demonstrated to be excellent powder metallurgy (PM) approach to developing nanostructured ultrafine-grained materials due to their flexibility in fabricating complex shapes. It produces highly dense consolidated solid materials with good bonding structure and barrier to the coarsening of grains [27]. This process enhanced the consolidation of solid bulk materials at a low temperature. It enabled the addition of a larger percentage of particles that are traditionally impossible to fabricate by other processing methods.

In this present research, NiAl alloyed with titanium (Ti), manganese (Mn), iron (Fe), cobalt (Co), and chromium (Cr) was fabricated using the spark plasma sintering process of powder metallurgy. The effect of these alloying elements cannot be over-emphasized. These alloying elements are employed to improve the mechanical properties of HEA developed [28, 29]. When alloying, it is worth noting that the alloying elements influence the final properties of the developed HEA, such as the melting point, density, and lattice constant. Therefore, the fabrication of a novel HEA Ni-14.29Al-14.29Ti-14.29Mn-14.29Co-14.29Fe-14.29Cr-14.29 (at.%) using the spark plasma sintering route to study the influence of sintering parameters (sintering temperature (ST), and the heating rate (HR)) on the relative density (RD), and microhardness (MH) is the focus of this study. The user-defined design of response surface methodology (UDD-RSM) was applied to optimize the process parameters (ST and HR) to improve the mechanical properties of Ni-14.29Al-14.29Ti-14.29Mn-14.29Co-14.29Fe-14.29Cr-14.29 (at.%). RSM is a statistical technique that uses experimental designs to develop mathematical models with linear, quadratic, or interaction terms for optimum performance from given factors and response variables [30, 31]. Adopting this technique reduces the number of experimental trials required to evaluate multiple parameters and their interaction. It is essential to state that the outcome of the properties is a function of the combined factorial effect of sintering parameters.

2 Materials and methods

2.1 Thermodynamic simulation

Thermodynamic simulations were performed using THERMOCALC software version 2021b with the TCHEA5 HEAs database. This was employed to determine the amount of phases and phases formed, the solidus and liquidus temperature of the developed HEAs. The alloy’s applicable solidus and liquidus temperatures were understood and used as a guide for the sintering of the alloy.

2.2 Experimental materials

Thermo Fisher Scientific supplied the powders used in this research, with details shown in Table 1.

Table 1 Details of starting powders
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2.3 Design of experiment

Design of experiment (DOE) became widely accepted due to the possibilities of minimizing the number of experimental runs and trial by error, reducing production cost. The DOE was first introduced in the 1920s by R.A Fisher for statistical modeling and to determine the effects of individual parameters and interactions between parameters on any design output [32]. This method employed both mathematical and statistical techniques. This was done using UDD-RSM to optimize the parameters required to enhance the mechanical properties of the developed HEA. However, this technique has been proven to be reliable by different researchers [30, 31, 33, 34]. Tables 2 and 3 show the model’s buildup information and the factors’ coded and actual operating conditions, respectively. In this research, ST and HR were the controlled parameters. Using Design Expert 13 software, two factors-three levels UDD was applied, and a total of 9 experimental runs were obtained, with a 95% confidence interval (Table 4). The experimental and statistical data were analyzed using analysis of variance (ANOVA). Since the number of levels is just three, the appropriate model to adopt was the second-order polynomial model given in Eq. (1) [35, 36].

$${\mathrm Y}_=\beta_0+\sum\nolimits_{j=1}^k\beta_jX_j+\sum\nolimits_{j=1}^k\beta_{jj}X^2{}_j+\sum\nolimits_i^k\sum\nolimits_{<j=2}^k\beta_{ij}X_iX_j+{\mathrm e}_i$$
(1)

where

Y:

is the predicted response

k:

is the number of studied factors

Xi and Xj:

are the variables (factors)

\({\beta }_{0}\):

is the constant coefficient

\({\beta }_{j},{{\beta }_{jj},\beta }_{ij}\):

are the interaction coefficients of linear, quadratic, and second-order terms. ei is the error

Table 2 Buildup information for RSM model
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Table 3 Coded and actual operating conditions of the factors
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Table 4 Design of experiments (DOE)
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2.4 The procedure of the spark plasma sintering process

The powders were measured based on the designed weight composition (Table 5) and placed in an air-tight container for subsequent homogenous alloy mixing using a tubular mixer at 150 rpm for 12 h. A spark plasma sintering machine, model SPS FCT Systeme GmbH, Germany, was utilized to consolidate the mixed powders of Ni–Al-Ti-Mn-Co-Fe–Cr in equal atomic percent. The measured admixed metal alloys were poured into a 20 mm graphite die with the right punches. A graphite sheet was used to create space between the powder and the inner wall of the graphite die before the powder was added. This was done to make it easier to remove the consolidated powder after sintering and to lessen the temperature difference on the workpiece. The samples were sintered according to the design in Table 4 at a constant pressure of 50 MPa and dwelling time of 5 min. Afterward, the sintered samples were taken out of the graphite die, sandblasted to eliminate the impurities, and exposed to metallographic treatment by grinding and polishing.

Table 5 Compositions of the elements of the alloys
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2.5 Characterization and analysis of the sintered samples

2.5.1 Density analysis

The density of the sintered alloys was determined using a densitometer, which functions based on Archimedes principles. The measurement was carried out five times, and the mean value was reported as the mean experimental density. The theoretical density was also determined using the mixture’s rule as expressed in Eq. (2). Using Eqs. (3) and (4), the alloys’ relative density and percentage porosity obtained from the experimental density were assessed.

$$Theoritical\; density={\left(\frac{\%Ni}{\rho Ni}+ \frac{\%Al}{\rho Al}+\frac{\%Ti}{\rho Ti}+\frac{\%Mn}{\rho Mn}+\frac{\%Fe}{\rho Fe}+\frac{\%Mn}{\rho Mn}+\frac{\%Cr}{\rho Cr}\right)}^{-1}$$
(2)
$$Relative\; density= \left(\frac{Experimental\; density}{Theoritical\; density} \times 100\right)\%$$
(3)
$$Percentage\; Porosity=100\%-Relative\; density$$
(4)

2.5.2 Microstructure and crystalline phase characterization

After being hot mounted with a Struers CitoPress-1 Machine, the prepared samples were ground and polished with a Struers TegraPol-11 550 Machine, utilizing successive disc grades of 90, 220, and 330. The samples were then washed and air-dried, followed by etching with a Keller’s etchant (190 ml distilled water, 5 ml nitric acid, 3 ml hydrochloric acid, and 2 ml of hydrofluoric acid). After this, a scanning electron microscope model JEOL JSM-7900F was used to observe how the sintered sample’s microstructure had changed. The microscope revealed each designed sample’s grain boundaries (neck formation). Additionally, the crystalline phase and chemical present in the samples were investigated using X-ray diffraction (XRD) at a wavelength of 1.5406 and K-alpha of 0.94. The Scherrer formula, as expressed in Eq. (5), was used to determine the size of the crystallites present in each sample at the nanoscale.

$$D=\frac{K\lambda }{\beta cos\theta }$$
(5)

where

D:

is the crystallites size

K:

is the Scherrer constant given as 0.9

λ:

is the wavelength of the X-ray used given as 0.154060 µm

β:

is the FWHM (Full width at half of the maximum) in radians

θ:

is the peak position in radians

2.5.3 Microhardness

Using a diamond indenter-equipped Vickers tester, model FM-800, the micro-hardness was assessed. This was done with an applied load of 100 gf for 15 s dwell time at 0.5 mm spacing. Five indentations were taken for each sintered sample, and the effective mean hardness was calculated and recorded.

3 Results and discussion

3.1 Microstructural study of the sintered samples

Figure 2 shows the SEM image of the admixed powders. The constituent elements in the admixed powder exhibited a highly homogenous state, as shown in Fig. 3. The SEM and EDS analysis reveals the powder’s morphology and ascertains the chemical constituent.

Fig. 2
figure 2

SEM of mixed Ni14.29Al14.29Ti14.29Mn14.29Co14.29Fe14.29Cr14.29

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Fig. 3
figure 3

EDS analysis of sintered Ni14.29Al14.29Ti14.29Mn14.29Co14.29Fe14.29Cr14.29

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However, Fig. 4 represents the microstructure obtained under different sintering conditions, as shown in Table 4, at a constant pressure of 50 MPa and dwelling time of 5 min. As the ST increases, the necking between particles increases, which initiates stronger inter-particle bonding and reduction of pores while the porosity reduces. The bonding between the particles increases as the ST increases, thereby improving the packing density of the powder. It could also be observed that as the ST increases, the microstructural refinement increases. The reduction in pore space and higher densification observed could be attributed to condensation and diffusion of constituent elements during the sintering process at the given ST [27]. Figure 4g, h, and i shows fully formed adhesion of particles and excellent microstructural refinement. Hence, it could be stated that to achieve excellent densification and strong material bonding, it is imperative to sinter at a high ST and HR. These parameters improve particle wettability and diffusion at grain boundaries, which in turn improve the bonding structure and properties of the developed HEA.

Fig. 4
figure 4

SEM of sintered Ni14.29Al14.29Ti14.29Mn14.29Co14.29Fe14.29Cr14.29 at varying sintering processing parameters

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3.2 Phase analysis

The amount of phase formed and the identification of the different phases achieved by the alloys were predicted via CALPHAD-based tools using ThermoCalc software. Figures 5 and 6 show the amount of phase and phase diagram, respectively. The master alloy shows only the presence of the BCC phase as seen from the XRD result in Fig. 7. This phase is responsible for the high brittleness of NiAl [11]. Alloying of this master alloy introduced an additional phase (FCC and sigma). This result is further established experimentally with the XRD result in Fig. 7.

Fig. 5
figure 5

Ni14.29Al14.29Ti14.29Mn14.29Co14.29Fe14.29Cr14.29 amount of phase

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Fig. 6
figure 6

The XRD phases of the sintered samples

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Fig. 7
figure 7

Ni14.29Al14.29Ti14.29Mn14.29Co14.29Fe14.29Cr14.29 phase diagram

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The XRD pattern was analyzed to examine the phase composition. The strong bonding among the alloys results from the wettability between the NiAl and the 13.48 wt.%Ti-15.47 wt.%Mn-16.59 wt.%Co-15.72 wtFe-14.64 wt.%Cr. The XRD result coincides with that of the THERMOCALC. Three dominant phases were identified (BCC, FCC, and SIGMA). The lattice parameters and the miller indices (1 1 1 and 1 1 2) indicate that the crystal structure is body-centered cubic (BCC) and face-centered cubic (FCC) [37,38,39,40,41,42,43]. It would be noticed that as the ST increases, the peak also increases. Another interesting observation is the crystallite size, as seen in Table 6, which decreases with increasing temperature. The chemical composition and thermal histories of the developed HEA affect the degree of crystallization [38, 41, 43]. The physical and mechanical properties of the developed HEA are influenced mainly by its size; these properties improve as size decreases. [37]. These phases are responsible for the changes observed in the refinement of the grain structure.

Table 6 The crystallite size of the Equal atomic nano-Ni–Al-Ti-Mn-Co-Fe–Cr HEA at different optimized conditions
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3.3 Mechanical analysis

Table 7 presents the mechanical properties of the developed HEA. It is evident that the MH increases with a corresponding increase in ST. These increases were justifiable given the crystalline size outcome. Also, from the SEM result in Fig. 3, the volume fraction of pores could be seen to reduce as the ST and HR increase, which is directly proportional to the hardenability of the material [44,45,46,47]. Figure 8 shows the MH variation. It was observed that as the ST increases, the hardness also increases. It was also observed that as the ST increases, the density also increases. This implies that as the ST increases, the diffusion rate is enhanced; hence, pores are rapidly closed, leading to porosity reduction and microstructure refinement [44,45,46,47]. Therefore, as the ST and HR increase, there is a corresponding increase in weight and improvement in strength [27].

Table 7 Design of experiments, response, and prediction table
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Fig. 8
figure 8

Variation in MH and RD of the developed HEA

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3.4 Model adequacy checking

The model’s accuracy is a crucial component of this research because it is essential for ensuring that the model fits and offers a good approximation of the real system. Figure 9 displays the normal probability plot of the studentized residuals for MH and RD to demonstrate the model's suitability. Inferring that the data is normally distributed, it was seen from the result that the points follow a straight line [48].

Fig. 9
figure 9

Normal probability plot for (a) MH and (b) RD

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3.5 Interaction of variables

To ensure the model’s fitting, the interaction between the variables (ST and RD) employed to enhance the mechanical properties of the developed HEA was verified. The perturbation plot in Fig. 10 describes the effect of all the factors at optimal when all the experimental conditions in the design space are compared. The response is more affected by the factor with a sharper curvature [30, 49]. When the impacts of all the factors were compared, it was found that MH and RD were more sensitive to ST than HR. ST is represented by the coded value A, and HR by the coded value B.

Fig. 10
figure 10

Perturbation plot for (a) MH, and (b) RD

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The residual versus run plots in Fig. 11 show if the design points are within the control limit. The red lines indicate the control limits from 4.6553 to −4.6553 for both MH and RD. The design points must lie between the control limits for the model to be valid. Figure 11 established the model’s validity, as it was clearly observed that the design points fall between the control limits.

Fig. 11
figure 11

Residual plot for (a) MH and (b) RD

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Figure 12 shows the contour plot for the interactive effects of ST and HR on the MH and RD at a design point above the predicted value. The contour pattern describes the relationship between the factors [50, 51]. The surface response graph shows the optimal process parameters that produce the response’s maximum or minimum value [52]. In this work, the optimum MH was observed as the ST and HR increased.

Fig. 12
figure 12

Contour plot of interaction between HR and ST on (a) MH and (b) RD

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3.6 Development of a regression model equation

The design matrix of the nine experimental runs alongside the coded factors for each variable was implored in determining all the constants in Eq. (1). The software used a quadratic model for the MH and RD for the responses. The parameters were coded with three coding levels for each variable, as shown in Table 4. Table 5 data were regressed by Design Expert 13.05.0 to develop a mathematical model for the coded and actual values. A second-order polynomial was used to correlate the response and variable values for MH and RD. The final equations in terms of coded and actual factors are represented in Eqs. (6–9).

$$MH=+132.34+3.40A+0.8967B$$
(6)
$$MH=+69.91889+0.067933ST+0.089667HR$$
(7)
$$RD=+97.96+1.25A+0.3016B$$
(8)
$$RD=+75.23096+0.025021ST+0.030162HR$$
(9)

where

A:

represents the coded value for Sintering Temperature

B:

represents the coded value for Heating Rate

ST:

represents Sintering Temperature, HR represents the Holding Time

MH:

represents the Microhardness Hardness

RD:

represents the Relative Density

The positive sign in the equations indicates synergy effects. This sign also implies that the response improved with an increase in the factor level [49]. The coefficients with one factor of ST and HR represent the effect of that factor. For a specific level of each factor, the equations can predict the response. By default, the high levels of the factors are coded as + 1, and the low levels are coded as − 1 in the equation in terms of coded factors. However, for the actual factor, the levels must be provided in the original units for each factor [30]. By comparing the factor coefficients, the coded equation aids in determining the relative importance of the factors. The actual equation, however, cannot be used because the coefficients have been scaled to account for each factor’s units, and the intercept is not located in the middle of the design space [30].

3.7 Model validation

The resulting standard deviation, R2, and Adjusted R2 values are used to verify the proposed model’s accuracy. The model is accurate if the Adeq Precision score is greater than four and the discrepancy between the Predicted R2 and Adjusted R2 is less than 0.2 [31, 53]. While the value of Adeq Precision represents the signal-to-noise ratio, the value of R2 shows the significance and acceptability of the developed model. The model is valid and can be used to examine the design space, according to the result in Table 8.

Table 8 Model validation for SH
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Figure 13 shows the relationship between the actual and the predicted response. The plots all follow a similar pattern; this implies that the experimental data and the model agree.

Fig. 13
figure 13

Comparison of experimental and predicted results for MH and RD

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3.8 ANOVA and statistical significance of the model

ANOVA was employed to validate the validity and importance of the model. The model term is significant if the resulting P-values are less than 0.1. In this study, MH and RD shows P-values of less than 0.0500; hence, the coded A and B for MH and RD are significant model terms. The Model F-value for MH and RD is 278.07 and 166.84, respectively, which implies that the model is also significant. The possibility that the obtained F-values result from noise is extremely low (0.01%). Table 9 shows the statistical analysis of the model, where the factor coding is coded, and the sum of squares is Type III Partial.

Table 9 ANOVA table
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3.9 Optimization studies

Optimization was carried out to maximize material strength with the selected ranges of parameters (ST and HR). The best desirability of 0.985 out of four runs was selected for MH and RD, as shown in Fig. 14. Table 10 shows that the constraints measured applied for optimization.

Fig. 14
figure 14

Optimization result for MH and RD

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Table 10 Constraints measure for optimization
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4 Conclusion

This research successfully fabricated a novel Ni14.29Al14.29Ti14.29Mn14.29Co14.29Fe14.29Cr14.29 High Entropy Alloy via a spark plasma sintering route. To improve the mechanical properties of this alloy, the process parameters (ST and HR) were optimized, and a predicting model was developed, with a minimum experimental run of 9 using RSM. The influence of each parameter on microhardness and relative density was observed, and the result indicates that temperature has more influence on its mechanical properties. At an ST of 850 °C and HR of 100 °C/min, maximum hardness (136.3 HV) and 99% densification (99.61) were attained. The results obtained from the Model; F- value, P-value, R2, Predicted R2, and Adeq Precision established the significance of the model developed. Therefore, comparing the experimental and the predicted values, the accuracy of the model developed was established.