Introduction

Alumina-forming austenitic (AFA) steel is an advanced high-temperature-resistant stainless steel. The steel forms Al2O3 and Cr2O3 double oxide films at high temperatures, adding 1.5–3.5 wt% Al1. AFA steel has excellent high-temperature creep strength and corrosion resistance at 500–950 °C, 50–200 °C higher when compared with standard heat-resistant steels having only the Cr2O3 layer. AFA steel has potential applications in power generation, petrochemical, and energy fields, especially as the core component of steam engines in ultra-supercritical units2. Under long-term high-temperature and high-pressure service conditions, the steel must have a stable austenitic matrix to sustain high-temperature oxidation resistance and other crucial mechanical properties.

A high Ni content is required to counteract the effect of ferrite-forming elements such as Al and Cr to obtain stable and single austenite. However, the cost and scarcity of Ni have limited the application of austenitic steels3. Replacing Ni with inexpensive elements, such as C, N, Mn, and Cu, can reduce nickel consumption while maintaining high-temperature oxidation resistance and mechanical properties. Mn is the preferred substitution element as it is a strong austenitic stabilizer and much cheaper than Ni, significantly reducing the overall production cost4,5,6. However, Mn tends to form MnS compounds, leading to a deterioration of the corrosion properties7,8,9. In addition, a high Mn content lowers the steel weldability10, so an appropriate Mn content is critical in partial substitution for Ni11.

First-principles methods based on density functional theory can be applied to predict steel's mechanical, corrosion, and interfacial properties at the atomic level12. Yang et al.13 studied the electronic structure and elastic properties of metal element-doped α-Fe (N) high-nitrogen steel through first-principles methods. They verified that Mn and Ni slightly weakened the stability of α-Fe (N), enhancing the overall elastic performance. Wang et al.14 carried out a first-principles study on the stacking fault energy of Fe–Mn alloy and found that Mn atoms have an obvious short-range effect on the stacking fault energy in the matrix. Adding Co and W to Sanicro 25 austenitic heat-resistant steel can improve structural and thermodynamic stability15. Huang et al.16 investigated the effects of alloying elements on the structural stability and segregation behavior of the γ-Fe(111)/Cr2N(0001)interface using first principles. They concluded that Mn reduced the local electrochemical corrosion behavior of the γ-Fe/Cr2N interface by reducing the voltage potential difference (VPD) between them. Dong et al.17 studied the effect of Al on the composition optimization and mechanical properties of an AFA heat-resistant steel. When Al was present as a solid solution in the Fe–Cr–Ni alloy system, the austenitic matrix was stable at high temperatures; the solid solution of Al and Al + Si improved the system's plasticity. It is essential and rare to study the influence of altering the Mn content in Mn-substituted-for Ni AFA steel on the structural stability and mechanical properties by the first-principles method at an atomic scale.

In this study, an Mn-substituted-for Ni AFA steel (Ni content reduced from 20 wt% of traditional AFA steel to 10 wt%) with high Mn content (up to 12.8 wt%) is used as a means of reducing costs. The lattice parameters, formation energy, binding energy, elastic constant, ideal stress–strain curve, and state density are calculated using the first-principles method. We explored the strength of Mn-substituted-for Ni AFA steel and assessed the influence of Mn content (3.2–12.8 wt%) on the structural stability and mechanical properties at the atomic level. The optimal mechanical properties are demonstrated experimentally, which can inform the production of high-performance heat-resistant steel for the core component of steam engines in ultra-supercritical units.

Computational method and material structure

Calculation methods

The designed high-Mn AFA steel is Fe–14Cr–10Ni–3Al– (3.2–12.8) Mn (wt%) with Cr, Ni, Al, and Mn as the main alloying elements, and other alloying elements such as Nb, Cu, Ti, and Si also be added. As austenitic steel, γ-Fe has an Fcc structure, belonging to a cubic crystal system with the space group Fm-3 m. Atomic sizes of Cr, Ni, Al, and Mn are close to Fe atoms and are mainly present in the matrix as a solid solution. The modeling idea is to add different contents of Mn into the basis alloy system Fe–14Cr–10Ni–3Al (wt%). Considering the number of atoms and the actual computational efficiency, 2 × 2 × 2 supercells containing 32 atoms were used to represent the matrix structure of the high-Mn AFA steel. We used the mcsqs (Monte Carlo special quasirandom structure) algorithm based on the special quasi-random structure model in the Disordered Alloy Theory Research Toolkit (ATAT) to construct a reasonable crystal structure model of Fe22–Cr5–Ni3–Al2. We found the closest random model by matching the cluster association function and then simulated the disordered structure of Fe22–Cr5–Ni3–Al2 (The calculated model is shown in Fig. 1). The Fe22–Cr5–Ni3–Al2 model was constructed based on Fe–14Cr–10Ni–3Al system (Fig. 1a). Considering the computational efficiency, the composition percentage of the model is close to the composition of Fe–14Cr–10Ni–3Al (wt%). Then Mn atoms were added into the Fe22–Cr5–Ni3–Al2 model (Fig. 1a) to obtain Fig. 1b–e models, where the proportions of Mn atoms (3.125, 6.25, 9.375, and 12.5 at.%) converted to weight percentages were 3.2, 6.4, 9.6, and 12.8 wt%, respectively.

Figure 1
figure 1

Schematic diagram of the calculation model: (a) Fe22–Cr5–Ni3–Al2 (b) Fe21–Cr5–Ni3–Al2–Mn (c) Fe20–Cr5–Ni3–Al2–Mn2 (d) Fe19–Cr5–Ni3–Al2–Mn3 (e) Fe18–Cr5–Ni3–Al2–Mn4.

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The first-principles calculations were based on the CASTEP (Cambridge serial total energy package) module in MS (Material Studio) software for the models given in Fig. 1. The calculation parameters were as follows: the approximation of commutative associative energy selected the PBE (Pardew–Burke–Engenho) function under the generalized gradient approximation; the Boyden–Fletcher–Goldfarb–Shannon (BFGS) method was used for self-consistent field operations; the valence electron potential field was constructed by ultrasoft pseudopotential18. Convergence tests were performed for the K-point and cut-off energy (Ecut), as shown in Fig. 2. When the Ecut and the K-point are 400.0 eV and 8 × 8 × 8, respectively, the system's energy converges. That means when the Ecut was 400.0 eV, the K point of the unit cell in the Brillouin region was taken as 8 × 8 × 8. The convergence accuracy of the self-consistent field was set to 1 × 10−5 eV/atom. After structural optimization, the force on each atom was less than 0.3 eV/nm, the tolerance offset less than 1 × 10–4 nm, and the stress deviation 0.05 GPa. In this study, austenitic heat-resistant steel contains Fe, Cr, Ni, Mn, and other atoms, and the steel exhibits weak magnetism. Considering the spin polarization approximation, the antiferromagnetic of double layers was added to the model's calculation after the convergence tests.

Figure 2
figure 2

Convergence tests of the parameters: (a) Energy cut-off (Ecut) (b) K Point.

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Materials and characterization

Table 1 shows the chemical composition of the tested steel. The steel was received as a hot-rolled plate with a 2.1 mm thickness. The hot-rolled plate was solution treatment at 1150 °C for 2.5 h, air-cooled to room temperature, and then cold-rolled to 1.0 mm thickness. The tensile specimen was designed according to GB/T 228.1-2010, as shown in Fig. 3. A one-way tensile experiment was performed at room temperature using the INSTRON-8801 testing machine with a tensile rate of 2 mm/min. A microhardness test was performed using the HVS-1000 digital microhardness tester with a loading force of 4.903 N and a loading time of 10 s. The tensile and microhardness tests took the average value of five and nine measurement results, respectively.

Table 1 The compositions of high-Mn AFA steel (wt%).
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Figure 3
figure 3

Schematic diagram of tensile specimen (mm).

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Results and discussion

Effect of Mn content on austenitic stability of low Ni AFA steel

Effect of formation energy and binding energy on austenite stability of low Ni AFA steel with different Mn contents

The structural parameters of Fe22–Cr5–Ni3–Al2, Fe21–Cr5–Ni3–Al2–Mn, Fe20–Cr5–Ni3–Al2–Mn2, Fe19–Cr5–Ni3–Al2–Mn3, and Fe18–Cr5–Ni3–Al2–Mn4 were calculated and are given in Table 2. After geometric optimization, all five belong to orthogonal crystal systems where a ≠ b ≠ c. An increase in Mn atoms solidified in the matrix accompanied by a volume expansion.

Table 2 Optimized parameters of the five structural systems.
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The formation energy and binding energy can be used to describe the stability of austenite in the five systems for high-Mn AFA steel. The formation energy measures the difficulty of forming the five systems19. The binding energy indicates that the multi-atomic systems must overcome certain attractive forces when they are joined together, reflecting the system structure's tightness20. The formation and binding energy can be calculated using Eqs. (1) and (2), respectively19,21.

$$ E_{f} = \frac{1}{{\sum N_{i} }}\left[ {E_{total} - \sum \left( {N_{i} E_{atom} } \right)} \right] $$
(1)
$$ E_{b} = \frac{1}{{\sum N_{i} }}\left[ {E_{total} - \sum \left( {N_{i} E_{iso} } \right)} \right] $$
(2)

where Etotal is the total energy after optimization, Ni is the number of atoms i (i = Fe, Cr, Ni, Al, or Mn) in the unit cell, Eatom is the single atomic energy of atom i in its elemental state (the elemental states of Fe, Cr, Ni, Al and Mn are Fcc-Fe, Bcc-Cr, Fcc-Ni, Fcc-Al and Bcc-Mn in the computational state, respectively), and Eiso is the energy of atoms i in the isolated state, placing atom i in the center of a simple cubic structure of 10 Å and calculating its relaxed energy.

The formation and binding energy of Mn elements solidified in the Fe22–Cr5–Ni3–Al2 system are shown in Fig. 4. The formation energy for Fe22–Cr5–Ni3–Al2, Fe21–Cr5–Ni3–Al2–Mn, Fe20–Cr5–Ni3–Al2–Mn2, Fe19–Cr5–Ni3–Al2–Mn3, and Fe18–Cr5–Ni3–Al2–Mn4 are all negative value, indicating that all five structures can form stably and spontaneously. Fe18–Cr5–Ni3–Al2–Mn4 is the easiest to develop with increased Mn content dissolved in the Fe22–Cr5–Ni3–Al2 system. The absolute value of the formation energy of the system increases with the rising Mn content, and the entire austenitic structure is more easily formed. The binding energy of the five systems is between − 4.95 and − 4.75 eV, indicating that the five systems are very stable. An increase in Mn content in the solid solution with Fe22–Cr5–Ni3–Al2 was accompanied by a slight decrease in the absolute value of the binding energy, reflecting a limited effect on the stability of the structure, and the austenite can be stabilized. In summary, after adding Mn, the high-Mn AFA steel structure maintained stability, retaining the austenitic structure in the matrix.

Figure 4
figure 4

The effect of the Mn content on the formation energy and binding energy.

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Effect of electronic properties on the austenite stability of low Ni AFA steel with different Mn contents

Figure 5a gives the total state density of five structural systems. The state density curves of the different systems are essentially similar, and most of the regions coincide, indicating that adding Mn did not change the energy level structure of the Fe22–Cr–Ni53–Al2 system. The electron distribution near the Fermi surface mainly determines the steel's properties. When different levels of Mn form a solid solution in the Fe22–Cr5–Ni3–Al2 system, the number of electrons at the Fermi energy level is non-zero. It exhibits metallic characteristics that increase first and then decrease. As the Mn content increased to 9.6 wt%, the electrochemical stability of the matrix increased, and when the Mn content further increased to 12.8 wt%, the electrochemical stability of the matrix decreased.

Figure 5
figure 5

Total density of states and partial density of states of the five structural systems: (a) Total density of states (b) Fe22–Cr5–Ni3–Al2 (c) Fe21–Cr5–Ni3–Al2–Mn (d) Fe20–Cr5–Ni3–Al2–Mn2 (e) Fe19–Cr5–Ni3–Al2–Mn3 (f) Fe18–Cr5–Ni3–Al2–Mn4.

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Taking the Fe22–Cr5–Ni3–Al2 system, the energy levels below the Fermi energy level are mainly due to the 3d orbital electrons of Fe, with a secondary contribution from the 2p orbital electrons of Cr, the 3d orbital electrons of Ni and the 1s and 2p orbital electrons of Al. Energy levels above the Fermi are primarily attributed to the 3d orbital electrons of Fe, the 3d orbital electrons of Ni, and 2p orbital electrons of Cr, with a lesser contribution from Al. From the fractional density diagram in Fig. 5b–f, when the Mn atom dissolved into the Fe22–Cr5–Ni3–Al2 system, the number of Mn 3d orbital electrons at the Fermi surface energy level increased; however, the number of Mn 3d orbital electrons is lower than that of Fe. Mn occupies the position of the Fe atom, and the charge density around Mn is lower than that of Fe; therefore, the hybridization effect of the Mn, Cr and Ni atoms is weakened; the binding bond between atoms also is weakened, rendering the structure slightly less stable.

Effect of Mn content on the mechanical properties of low Ni AFA steel

Calculation of elastic modulus

According to the parameters in Table 2, the Fe22–Cr5–Ni3–Al2 system belongs to the orthogonal crystal system after optimization. A total of nine independent elastic constants are calculated for C11, C12, C13, C22, C23, C33, C44, C55, and C66, as shown in Table 3.

Table 3 Elastic constants of the five structural systems.
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The bulk modulus (B), shear modulus (G), and Young's modulus (Y) of the experimental steels were determined using the Voight–Reuss–Hill (VRH) equation22 for all crystalline systems with:

$$ B = \frac{1}{9}\left( {C_{11} + C_{22} + C_{33} } \right) + \frac{2}{9}\left( {C_{12} + C_{13} + C_{23} } \right) $$
(3)
$$ G = \frac{1}{15}\left( {C_{11} + C_{22} + C_{33} - C_{12} - C_{13} - C_{23} } \right) + \frac{1}{5}\left( {C_{44} + C_{55} + C_{66} } \right) $$
(4)
$$ Y = \frac{9GB}{{G + 3B}} $$
(5)

The values of B, G, and Y for the different systems were calculated according to Eqs. (3) (4) (5) (Fig. 6). With an increase of Mn content in Fe22–Cr5–Ni3–Al2, the bulk modulus of the system increased significantly, the shear modulus decreased; Young's modulus was essentially unchanged. The incorporation of Mn in the matrix impacts the steel's ability to resist shear deformation, where stiffness and strength are reduced, but the change is insignificant. Therefore, the solid solution of Mn will reduce the strength of the Fe22–Cr5–Ni3–Al2 system, but the effect is slight.

Figure 6
figure 6

Elastic modulus of the five structural systems: (a) bulk modulus (b) shear modulus (c) Young's modulus.

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Calculation of mechanical properties

The five crystal cells in Fig. 1 were tensioned by applying strain incrementally along the (001) plane of the cell, fixing the z-axis direction of each atom but not fixing the x- and y-axis directions so that the atoms relaxed sufficiently in both the x- and y-directions to obtain the corresponding stresses. The strain was gradually applied until the stresses reached their highest point and then decreased, obtaining the ideal stress–strain curve for each system, as shown in Fig. 7. As the strain increases, the stresses of the five structural cell models increase. When the strain is between 0.26 and 0.28, the stresses reach their maximum values (45.38, 45.18, 44.91, 44.79, and 44.72 GPa, respectively). As the strain increases further, the stresses decrease. With increased Mn content, the highest points of the ideal stress–strain curves for the five systems decrease slightly. The strength of high-Mn AFA steel reduces by about 1% as the Mn content increases from 3.125 at.% (3.2 wt%) to 12.5 at.% (12.8 wt%).

Figure 7
figure 7

Ideal stress–strain curves of the five structural systems.

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Based on the bulk and shear moduli of the different systems, microhardness was calculated according to the semi-empirical Eq. (6)23, and the results are shown in Fig. 8.

$$ H_{V} = 2\left( {\frac{G}{{K^{2} }}} \right)^{0.585} - 3 $$
(6)
$$ K = G/B $$
(7)
Figure 8
figure 8

Theoretical microhardness of the five structural systems.

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The microhardness of Fe22–Cr5–Ni3–Al2 was the largest, with a value of about 19.4 GPa. When different levels of Mn were incorporated into the system to form Fe21–Cr5–Ni3–Al2–Mn, Fe20–Cr5–Ni3–Al2–Mn2, Fe19–Cr5–Ni3–Al2–Mn3, and Fe18–Cr5–Ni3–Al2–Mn4 solid solutions, the microhardness of the newly formed systems all decreased; as the Mn content increased from 0 to 12.8 wt%, the hardness decreased from 19.4 to 15.8 GPa (Fig. 8), which is consistent with Figs. 6, 7. Therefore, the hardness of Al-containing austenite, formed by Mn solid solution in the Fe22–Cr5–Ni3–Al2 system, decreases.

Figure 9 shows Poisson's ratio (ν) and Pratt's modulus ratio (B/G). When the Mn solid solution formed in Fe22–Cr5–Ni3–Al2, the Poisson's ratio of the austenite matrix increased with improved elastic properties, i.e., Mn is beneficial in enhancing the elastic properties exhibited by high-Mn AFA steel. An increase in Mn content in the matrix accompanied by the rise in Poisson's ratio from 0.171 to 0.203 with a concomitant increase in Pratt's modulus ratio; B/G for the Fe18–Cr5–Ni3–Al2–Mn4 system is 1.36, representing the best plasticity. Our findings confirm the beneficial effect of Mn in high-Mn AFA steel in terms of enhancing the elastic properties and plasticity of the austenite matrix.

Figure 9
figure 9

Poisson's ratio (ν) and Pratt's modulus ratio B/G for the five structural systems.

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Experimental analysis of mechanical properties

Figure 10 shows the mechanical properties of high-Mn AFA steel tested at room temperature with 5.91–11.82 at.% Mn contents (corresponding to 6.03–12.02 wt%, as shown in Table 1). As the Mn content increased, the tensile strength decreased from 581.75 to 565.70 MPa, representing a 2.7% decrease in tensile strength. In addition, the hardness decreased from 187.2 HV to 183.3 HV, and the elongation increased from 36.7 to 45.2%. The increase in Mn content decreased tensile strength and yield strength while increasing elongation and material plasticity but reducing hardness. The results of the elasticity and ideal stress–strain calculations (Figs. 6, 7) also show that at higher Mn content in the Fe22–Cr5–Ni3–Al2 system, the strength and hardness of the austenite matrix decrease and plasticity increases. At the Mn content of 8 wt%, the AFA steel has good strength and toughness: a tensile strength of 581.64 MPa, hardness of 186.17 HV, and elongation of 39%. Thus, after adding 8.0 wt% Mn to the high-Mn AFA steel with 10 wt% Ni content, the austenite is stable, and the mechanical properties are optimal.

Figure 10
figure 10

Test results of the mechanical properties of high-Mn AFA steel with different Mn content: (a) stress–strain curve (b) Vickers hardness and elongation.

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Conclusion

  1. 1.

    Adding Mn to low Ni-AFA steel increases the unit cell volume with an accompanying increase in the absolute value of formation energy; the austenite formed more easily. The austenitic matrix binding energy decreases and remains negative, indicating austenite stability. As the Mn content increases from 3.2 to 12.8 wt%, the system's bulk modulus (B) rises significantly, and the shear modulus (G) falls. In addition, the system's strength and hardness decrease, and the Poisson ratio of the austenite matrix increases with improved elasticity; the system has excellent plasticity with an increase in the B/G.

  2. 2.

    Addition of Mn does not change the energy level structure of the Fe22–Cr5–Ni3–Al2 system. All the systems have a non-zero number of electrons at the Fermi energy level and exhibit metallic properties. At different Mn solid solution content in Fe22–Cr5–Ni3–Al2, the number of electrons at the Fermi energy level increases first and then decreases. An appropriate amount of Mn atoms can improve the electrochemical stability of the matrix. As the content of Mn increases to 9.6 wt%, the electrochemical stability of the matrix gradually increases. However, with Mn further increasing to 12.8 wt%, the stability of the matrix decreases.

  3. 3.

    When the Mn content increases from 6.03 to 12.02 wt%, the tensile strength and microhardness decrease from 581.75 to 565.70 MPa and 187.2 to 183.3 HV, respectively. Accordingly, the elongation increases from 36.7 to 45.2%. At a Mn content of 8 wt%, the overall mechanical properties of the high-Mn AFA steel are optimal, with a tensile strength of 581.64 MPa, a hardness of 186.17 HV, and an elongation of 39%.