*3.4. Hardness Measurement*

Measurement of hardness was carried out using Vickers microhardness. Table 4 shows the hardness value in comparison with other 21-4N heat-resistance steels manufactured through other processing routes. The hardness obtained through the powder metallurgy process was higher when compared to the hardness obtained through other processing techniques. The increase in hardness is due to the higher sintering temperature during the vacuum hot pressing technique [34]. Moreover, it can be seen that the presence of nano crystalline structures led to the formation of a fine-grained metal matrix which was evident from the microstructural analysis from Figure 9b which resulted in superior hardness for the alternate valve steel material developed using the powder metallurgy route. Similarly, the availability of precipitate strengthened metal carbides distributed heterogeneously (not as continuous structure) near the grain boundaries which had a significant effect on the increase in hardness. This acted as a strengthening mechanism in the formation of precipitates.


**Table 4.** Comparison of hardness values obtained for different valve steel made of 21-4N material.

#### *3.5. Hot Compression Measurements*

Figure 10 represents high temperature compression stress strain curves for 21-4N steel at 650 ◦C and 0.001 s<sup>−</sup>1. Superior strength of 1340 MPa was reported for the material developed using the powder metallurgy technique. The flow stress hump that can be seen within the compressive stress strain graph is due to the formation of dynamic recrystallization which accumulates during the straining [37]. Figure 11a illustrates the micrograph of hot compressed samples at a temperature 650 ◦C and strain rate of 0.001 s<sup>−</sup>1. Local bulging along with serrated irregular boundaries are indicated by arrow marks from Figure 11b. In the SEM micrograph, the serrated irregular boundaries are due to the movement of dislocations near the regions. Due to the fine microstructure, shearing of the particles is avoided, leaving behind deformations in the form of bulging. Similarly, near the serrated boundaries the structure consists of early stages of recrystallization. When compared to the compression test of the 21-4N cast product, steel developed through the powder metallurgy route showed higher compressive strength with a higher strain rate. Materials developed through cast products showed a decreasing trend in hot compressive strength. Huang et al., reported a maximum hot compressive stress value of 350 MPa with material developed through cast product [38]. Similar results of 350 MPa were reported by Li et al., and Ji et al., for 21-4N material developed through the cast process [19,20]. This can be attributed to the fact that inhomogeneous distribution of grain growth from the surface to inner layers occurred during uneven solidification rate. The development of the homogeneous and fine microstructure attained as a result of the powder metallurgy processing route showed substantial improvement in hot compressive values when compared to materials processed using the cast route.

**Figure 10.** Hot compressive strength of the sintered sample, sample before and after compression (insert).

**Figure 11.** SEM micrograph of hot compressed sample (**a**) Overview of bulged sample (**b**) indication of serrated boundaries.

#### *3.6. Corresponding Relationship between Mechanical and Microstructural Properties*

The strength of the material at room temperatures was calculated and compared with the strengthening mechanism. As stated in Equation (1), the strength of the material at room temperatures was obtained with hardness measurements, where *Hv* is the value of the obtained hardness in terms of MPa and *σ<sup>y</sup>* is the yield strength [39]. A multiplication factor of 9.8065 was used to convert the obtained hardness from Hv to MPa [40]. The value of yield stress as per Equation (1) is 1340 MPa.

$$
\sigma\_y = \frac{1}{3} H\_v \tag{1}
$$

For any alloy, the calculation of yield strength is also based on the combined contribution of the various strengthening mechanisms as stated in Equation (2) [39].

$$
\sigma\_y = \sigma\_{\rm ss} + \sigma\_{\rm \xi^s} + \sigma\_{\rm dis} \tag{2}
$$

where *σss* is strengthening due to a solid solution, *σgs* is grain size strengthening and *σdis* strengthening due to dislocations. The effect of solid solution strengthening in an alloy is mainly due to both substitutional and interstitial types of elements present in the system. In the present study, substitutional elements consisted of chromium, nickel and manganese which were the major alloying elements. Meanwhile, the presence of interstitial or minor alloying elements based on their wt% was neglected, which in this case was carbon. The solvent iron which is strengthened due to substitutional elements is given by Equation (3) [41].

$$
\sigma\_{ss} = 0.00689 K X^n \tag{3}
$$

where "*K*" is coefficient of strengthening and the corresponding values of "*K*" for the elements chromium, nickel and manganese are 1400, 6100 and 7000, respectively, "*X*" represents the elemental concentration in the present alloy in terms of atomic percentage and "*n*" is the constant valued 0.75 [42]. The effect of strengthening due of solid solution for the current study is found to be 447 MPa from Equation (3). The Hall Petch relation can be used to calculate the strengthening effect as a result of fine grain structure as per Equation (4).

$$
\sigma\_{\mathbb{S}^5} = \sigma\_0 + kd^{\frac{-1}{2}} \tag{4}
$$

where "*σo*" is taken as 30 MPa for iron alloys which is known as friction stress, "*k*" is a constant and taken as 0.4 MN/m<sup>2</sup> for austenitic stainless steel grain sizes of less than 3 μm and "d" is the grain size (in meters) for the alloy [43]. Taking the average grain size of the samples from Figure 9b as 1 μm, the yield strength due to grain boundary strengthening is 430 MPa. The increase in strength due to dislocations present in the alloy is calculated using Equation (5) [44].

$$
\sigma\_{\rm dis} = \alpha M Gb \sqrt{\rho} \tag{5}
$$

The efficiency of the hardening effect induced due to dislocation is denoted by "*α*" which as a constant ranges from 0.1 to 0.5, where the mean value is taken for calculation [42]. For a given FCC structure, "*M*" denotes Taylor's factor which is 3, "*G*" is termed as modulus of rigidity and for pure iron it is 83 GPa, "*b*" is burgers vector and for the FCC material it is 0.251 nm. Dislocation density for the vacuum hot pressed samples is expressed as "*ρ*" and is taken as 5 × 10<sup>14</sup> m−<sup>2</sup> [45]. From Equation (5), as a result of dislocation strengthening, the yield strength is 419 Mpa. From Equation (2) the overall yield strength obtained from the strengthening mechanisms, namely solid solution strengthening, grain size strengthening and dislocation strengthening can be found to be 1296 MPa. The obtained theoretical value as per Equation (1) is slightly overestimated by 3.39% which is in good agreement with the summation of all contributed strengthening mechanisms. The overestimated observation is due to either the summation or overestimation of individual strengthening contributions. Alloys consisting of solid solution strengthening lead to overestimation as a result of friction stress. The factor of friction stress is dependent on temperature, dislocation and slip system. Chauhan et al. reported that when comparing the calculated and measured values of yield stress, a small amount of overestimation for all alloys up to 53 Mpa occurs, whereas smaller values of 30 MPa were also reported by Li [42,46].

## **4. Conclusions**

The current study reported on the development and evaluation of mechanical and microstructural properties of 21-4N austenitic steel through the powder metallurgy route. Parameters used for sintering gave rise to a balanced austenitic structure when compared to cast products with a similar composition. The 21-4N austenitic valve steel developed through MA to obtain a nano-crystalline structure led to the following conclusions.

During the initial stages of milling, pre-alloyed mixtures were soft and ductile. A prolonged milling time leads to the cold welding of particles and break down due to repeated fracturing. The morphology of the milled powders revealed that the fracturing of powder particles was dominant when compared to cold welding.

MA powders were consolidated using vacuum hot pressing which had a density of 98% in comparison to the theoretical density of the samples. High dense samples were obtained due to grain boundary diffusion and volume diffusion during sintering.

SEM-EDS studies revealed the presence of carbide precipitates near the grain boundaries. XRD analysis of the hot pressed samples confirmed the precipitates as M23C6, whereas these precipitates were not present in the powder particle. The formation of M23C6 carbide particle is due to slow cooling in the sintering cycle.

The TEM analysis revealed the presence of austenitic twins as materials were subjected to cold working and annealing. Dislocations were present within the metal matrix as an outcome of severe plastic deformation which is due to hot pressing. A fine grain structure was revealed during the TEM analysis with a mean grain size is of 1 μm.

When compared to other conventional processing techniques, the hardness value of 410 ± 10 Hv obtained through the powder metallurgy route was higher. The presence of a nano crystalline structure led to an increase in the hardness value. Evaluations of the strengthening mechanism clearly reveal that strengthening due to solid solution, grain size and dislocations are the dominant forces which increase the structural rigidity of the alloy.

Substantial improvements in the hot compression value of 1340 MPa were reported for 21-4N austenitic valve steel when compared to similar material developed through the cast product technique. The development of fine microstructure throughout the material resulted in the increase in hot compression values.

With the obtained results, 21-4N austenitic valve steel developed through the powder metallurgy route was demonstrated to have better strength and structural rigidity for the metal matrix which can be used for high temperature applications.

**Author Contributions:** Conceptualization and methodology, A.P.M. and D.G.; writing—original draft preparation, A.P.M. and D.G.; writing—review and editing, S.S., E.A.N., H.M.A.H. and J.P.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research has received funding from King Saud University through Researchers Supporting Project number (RSP-2021/164), King Saud University, Riyadh, Saudi Arabia.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors extend their appreciation to King Saud University for funding this work through Researchers Supporting Project number (RSP-2021/164), King Saud University, Riyadh, Saudi Arabia. The authors would like to express their gratitude to R. Mariappan for his extended support through his valuable inputs during the course of the research work. TEM studies were carried out at PSG Institute of Advanced studies, India. We would like to extend our sincere gratitude to R. Rangarajan, Founder and Chancellor, Vel Tech Rangarajan Sagunthala R&D Institute of Science and Technology for providing facility in Metallurgical and Materials Laboratory to carry out this research work.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

