# Chemical Component Optimization Based on Thermodynamic Calculation of Fe-1.93Mn-0.07Ni-1.96Cr-0.35Mo Ultra-High Strength Steel

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{s}is site fraction of chemical component a on sublattice s, P

_{IZ}is the product of the positional scores of each chemical component, L

_{IZ}is the interaction parameter, IZ is the order of the array of chemical components, and I in ${y}_{i}^{s}$ is chemical component is the lattice location score.

## 2. Thermodynamic Calculation Model

#### 2.1. Microstructure and Phase Calculation Model

_{i}and x

_{j}are the mole fractions of the i and j chemical components, respectively; the correlation of the mixed phase of the experimental material is obtained by P

_{t}performance; x

_{α}and x

_{γ}are the molar fractions of the α phase and γ phase, respectively; P

_{α}is the strength of the α phase; P

_{γ}is strength of the γ phase; and P

_{III}is the strength of phase III.

#### 2.2. Yield Strength Calculation Model

_{y}is the yield strength of the material, σ

_{0}is the grain boundary stress of the corresponding pure metal, k is the material correlation coefficient, d is the grain size, σ

_{ppt}is the second phase strength enhancement, m is the material correlation coefficient, G is the shear modulus of material, b is the Burgers vector, L is the distance of the precipitation phase, r is the size of precipitation phase, $\sigma (y,\dot{\epsilon})$ is the strength of the material after processing, $\sigma (y,{\dot{\epsilon}}_{0})$ is the strength of material at strain rate of ${\dot{\epsilon}}_{0}$, and m is the temperature state parameter.

#### 2.3. Tensile Strength Calculation Model

_{b}is the tensile strength of the mixed phase, x

_{α,}x

_{γ}, x

_{III}are the molar fractions of α, γ and precipitated phase, respectively, and σ

_{α}, σ

_{γ}, and σ

_{III}are the strength of α, γ and precipitated phase, respectively.

#### 2.4. Phase Volume and Performance Calculation Model

_{eq}is the volume under equilibrium transition, N

_{r}is the nucleation rate, G

_{r}is the grain growth rate, and t is the transition time.

## 3. Experimental Materials and Method

#### 3.1. Chemical Composition Design and Optimization

#### 3.2. Mechanical Properties Analysis

## 4. Results and Discuss

#### 4.1. Phase and Chemical Composition Optimization

#### 4.1.1. Equilibrium Phase Diagram of Original Bainitic Steel

_{1}...M

_{i}, V, Nb)

_{a}(C, N, Va

_{)c}. where M

_{1}...M

_{i}is an alloying element in steel, and Va is a vacancy. a = 1 and c = 1 are fcc phases, and a = 1 and c = 3 are bcc phases. In the (Fe, M

_{1}...M

_{i}, V, Nb)a (C, N, Va)c lattice, the first sublattice is the regular lattice position and the second sublattice is the octahedral gap [9]. Alloying elements, such as Fe, M

_{i}, V, and Nb, can be substituted for each other in the sublattice, and alloying elements, such as C and N, can be substituted for each other in the vacancy gap. According to the (Fe, M

_{1}...M

_{i}, V, Nb)a(C, N, Va)c lattice model, B

_{2}M is mainly composed of Ti and B (Figure 1); FCC_A1#2 is mainly composed of Ti, C, Cr, and Nb compound (fcc crystal structure); and M

_{6}C is mainly a compound composed of Mo, Fe, Si, C, and Cr.

#### 4.1.2. Effect of Ni and Mo Contents on Equilibrium Phase

_{6}C was minimal. When the Ni content changed from 0 to 0.3%, the solid solution temperature of M

_{6}C increased from 555 to 575 °C, but had little effect on. The alloying elements Mo and C have a strong affinity to form M

_{6}C and M

_{7}C

_{3}alloys in steel. The effects of the change in Mo content on M

_{6}C and M

_{7}C

_{3}and the solution temperature are shown in Figure 2b. With the increase in Mo content, the solid solution temperature of M

_{6}C type carbide increased, and the solution temperature of M

_{7}C

_{3}type carbide increased. The dissolution of M

_{6}C type carbide at high temperatures caused the inhibition of γ grain growth to decrease. Comparing Figure 1 with Figure 2b, it can be seen that as the temperature decreased, a large amount of Mo-rich M

_{6}C

_{-}type carbide precipitated at temperatures below 900 °C. The precipitation of M

_{6}C type carbide during the controlled cooling process enhanced the precipitation strengthening effect. In the heating process, the appropriate amount of undissolved M

_{6}C will be able to prevent the growth of γ grains, thereby increasing the hardness and tensile strength of UHSS.

#### 4.1.3. Effect of Cr and W Content on Equilibrium Precipitation Phase

_{7}C

_{3}carbide in the steel is shown in Figure 3a. The solid solution temperature of FCC_A1#1 carbide increased with Cr content, and the M

_{7}C

_{3}carbide with Cr is gradually dissolved into the matrix below 800 °C. In the controlled cooling process of the γ→α phase change, the M

_{7}C

_{3}phase act absolutely as precipitation strengthening carbide, increasing the strength of UHSS.

_{6}C and B

_{2}M. Since the content of W was relatively low, and the mass fraction of M

_{6}C was small. From Figure 1, the B

_{2}M phase began to dissolve into the γ phase at temperatures above 1250 °C during the heating process. The mass of B

_{2}M gradually decreased with temperature during the cooling process. The overall content of B

_{2}M remained stable; significant changes only occurred around 580 °C. Figure 3b shows that B

_{2}M precipitates increased with W content at 500–600 °C.

_{2}M, the temperature-chemical component equilibrium phase diagram of the W-free chemical component system was calculated and partially amplified as shown in Figure 4. Comparing Figure 1 with Figure 4, we can see the effect of W on FCC_A1#2, B

_{2}M, and M

_{2}B_TERT. It can be seen from Figure 1 that the mass of FCC_A1#2 and M2B_TETR alloy phases increased with decreasing B

_{2}M content at around 580 °C. The mass fraction of FCC_A1#2 and M2B_TETR decreased to a minimum with the increase in B

_{2}M. As can be seen from Figure 4, the content of FCC_A1#2 decreased and the content of B

_{2}M increased at about 580 °C; when the content of FCC_A1#2 decreased to a minimum, the content of B

_{2}M increased to the maximum.

_{2}M, FCC_A1#2 and M

_{2}B_TETR in the original steel and W-free steel at 580–695 °C. Through comparative analysis, we found that W determines the changes in B

_{2}M, FCC_A1#2 and M

_{2}B_TETR between 580 and 614 °C. W mainly forms M

_{2}B_TETR boride in steel, but this boride is unstable, only appearing from 580 to 614 °C, and then transforming into other types of carbides. Through the above calculation, the Ni and W contents can be minimized. However, since there was 0.13% (wt %) of Cu in the steel, in order to prevent the adverse effects of Cu, the Ni content was adjusted to a mass percent of 0.07%.

#### 4.1.4. Effect of the Optimized Chemical Component System on Balanced Phase Diagram

_{23}C

_{6}phase in steel, while the increase in Cr content inhibited the production of M

_{23}C

_{6}phase in steel [35]. After reducing Ni, Mo, and W, the chemical composition was adjusted to C 0.23, Si 1.96, Mn 1.93, Ni 0.07, Cr 1.84, Mo 0.35, Nb + V + Ti + Al + Cu + B ≤ 0.15, Fe bal. wt %), and the M

_{23}C

_{6}precision is shown in Figure 6. When the Mo content was adjusted to 0.35%, M

_{23}C

_{6}carbides appeared. M

_{23}C

_{6}caused the hardenability of B to disappear [36], and the increase in Cr content produced the effect of avoiding M

_{23}C

_{6}. By calculation and comparison, we found that when the Cr content increased to 1.94%, the generation of M

_{23}C

_{6}carbides was prevented.

_{6}C and M

_{7}C

_{3}, the equilibrium phase diagrams before and after optimization are depicted in Figure 7. When the chemical composition was adjusted to C 0.23, Si 1.96, Mn 1.93, Ni 0.07, Cr 1.96, Mo 0.35, Nb + V + Ti + Al + Cu + B ≤ 0.15, Fe bal. wt %), an equilibrium phase diagram was obtained.

#### 4.2. Effect of Alloy Content on Mechanical Properties

## 5. Conclusions

- (1).
- The equilibrium phases in steel are B
_{2}M, BCC_A2, FCC_A1#1, FCCA1#2, M_{6}C, M_{7}C_{3}, and M_{2}B_TETR. B_{2}M is a compound mainly composed of Ti and B. FCC_A1#2 is a compound mainly composed of Ti, C, Cr, and Nb. M_{6}C is a compound mainly composed of Mo, Fe, Si, C, and Cr. - (2).
- When Ni content increased from 0 to 0.3%, M
_{6}C precision temperature increased from 555 and 575 °C, and the Ni content had little effect on FCC_A1#2 and M_{6}C. Mo is a strong carbide element and forms M_{6}C and M_{7}C_{3}type carbides in UHSS. Mo content should not be too low, otherwise the strength of UHSS will decrease. M_{6}C carbide with Cr increased with increasing Cr content. Below 800 °C, M_{7}C_{3}carbide with Cr-rich gradually dissolved into the matrix. W mainly formed M_{2}B_TETR borides. M_{2}B_TETR can be converted with FCC_A1#2 and B_{2}M in the temperature zone around 580 °C. - (3).
- The chemical component system was optimized by reducing Ni, reducing Mo, removing W, and increasing Cr, then we obtained the same phase diagram as obtained with the origin content. The optimized composition is C 0.23, Si 1.96, Mn 1.93, Ni 0.07, Cr 1.96, Mo 0.35, Nb + V + Ti + Al + Cu + B ≤ 0.15, Fe bal. (wt %). With a cooling rate of 10 °C/s, the optimized alloying system fully performed its strengthening role in the steel, and the chemical components were in the optimal range. The thermodynamic models and our conclusions have the potential to be generalized for many other materials and process configurations without requiring extensive material testing. However, a lack of a real experiment is unfortunate, and the limitations and practicality of this methodology will be verified in future experiments.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Chang, L.C.; Bhadeshia, H.K.D.H. Carbon content of austenite in isothermally transformed 300 M steel. Mater. Sci. Eng. A
**1994**, 184, 17–19. [Google Scholar] [CrossRef] - Sule, Y.; Sirin, K.; Kaluc, E. Effect of the ion nitriding surface hardening process on fatigue behavior of AISI 4340 steel. Mater. Charact.
**2007**, 59, 351–358. [Google Scholar] - Wen, Z.H.; Kuang-Nian, H.E.; Hua, L.I.; Liao, W.T. Development Progress and Process Analysis of Ultra High-strength Plate. Steel Rolling
**2012**, 29, 43–45. [Google Scholar] - Matsuda, H.; Mizuno, R.; Funakawa, Y.; Seto, K.; Matsuoka, S.; Tanaka, Y. Effects of auto-tempering behaviour of martensite on mechanical properties of ultra high strength steel sheets. J. Alloys Compd.
**2013**, 577, 661–667. [Google Scholar] [CrossRef] - Abe, Y.; Kato, T.; Mori, K.I.; Nishino, S. Mechanical clinching of ultra-high strength steel sheets and strength of joints. J. Mater. Process. Technol.
**2014**, 214, 2112–2118. [Google Scholar] [CrossRef] - Little, C.D.; Machmeier, P.M. High Strength Fracture Resistant Weldable Steels. U.S. Patent 4,076,525, 28 February 1978. [Google Scholar]
- Jahazi, M.; Egbali, B. The influence of hot rolling parameters on the microstructure and mechanical properties of an ultra-high strength steel. J. Mater. Process. Technol.
**2000**, 103, 276–279. [Google Scholar] [CrossRef] - Hillert, M.; Staffansson, L.I.; Hillert, M.; Staffansson, L.I. The Regular Solution Model for Stoichiometric Phases and Ionic Melts. Acta Chem. Scand.
**1970**, 24, 3618–3626. [Google Scholar] [CrossRef] - Sundman, B.; Ågren, J. A regular solution model for phases with several components and sublattices, suitable for computer applications. J. Phys. Chem. Solids
**1981**, 42, 297–301. [Google Scholar] [CrossRef] - Porter, D.A.; Easterling, K.E. Phase Transformations In Metals and Alloys. Ann. Rev. Mater. Res.
**1992**, 1, 213–218. [Google Scholar] - Nieh, T.G.; Wadsworth, J. Hall-Petch Relation in Nanocrystalline Solids. Scr. Metall. Mater.
**1991**, 25, 955–958. [Google Scholar] [CrossRef] - Kirkaldy, J.S. Prediction of alloy hardenability from thermodynamic and kinetic data. Metall. Mater. Trans. B
**1973**, 4, 2327–2333. [Google Scholar] [CrossRef] - Doane, D.V.; Kirkaldy, J.S. Hardenability Concepts with Applications to Steel. In Proceedings of the Symposium Held at the Sheraton-Chicago Hotel, Chicago, IL, USA, 24–26 October 1977. [Google Scholar]
- International, A.; Davis, J.R.; Committee, A.I.H. Properties and Selection: Irons, Steels and High-Performance Alloys; ASM International: Materials Park, OH, USA, 2001. [Google Scholar]
- Predel, E.H.C.B.; Hoch, E.M.; Pool, E.M. Effect of Diffusion on Phase Transformations; Springer: Berlin, Germany, 2004. [Google Scholar]
- Burke, J. The Kinetics of Phase Transformations in Metals; Pergamon Press: Long Island City, NY, USA, 1965. [Google Scholar]
- Porter, D.A.; Easterling, K.E.; Sherif, M.Y. Phase Transformations In Metals and Alloys; Chapman & Hall: London, UK, 1992. [Google Scholar]
- Committee, A.I.H.; Davis, J.R.; Abel, L.A. Properties and Selection: Irons, Steels, and High-Performance Alloys; ASM International: Materials Park, OH, USA, 1995. [Google Scholar]
- Egea, A.J.S.; Rojas, H.A.G.; Celentano, D.J.; Perio, J.J.; Cao, J. Thermomechanical Analysis of an Electrically Assisted Wire Drawing Process. J. Manuf. Sci. Eng.-Trans. ASME
**2017**, 139, 7. [Google Scholar] [CrossRef] - Egea, A.J.S.; Rojas, H.A.G.; Celentano, D.J.; Peiro, J.J. Mechanical and metallurgical changes on 308L wires drawn by electropulses. Mater. Des.
**2016**, 90, 1159–1169. [Google Scholar] [CrossRef] - Allen, R.M.; Toth, L.S.; Oppedal, A.L.; El Kadiri, H. Crystal Plasticity Modeling of Anisotropic Hardening and Texture Due to Dislocation Transmutation in Twinning. Materials
**2018**, 11, 1855. [Google Scholar] [CrossRef] [PubMed] - Liu, S.; Kouadri-Henni, A.; Gavrus, A. Numerical simulation and experimental investigation on the residual stresses in a laser beam welded dual phase DP600 steel plate: Thermo-mechanical material plasticity model. Int. J. Mech. Sci.
**2017**, 122, 235–243. [Google Scholar] [CrossRef][Green Version] - Wang, Z.Q.; Denlinger, E.; Michaleris, P.; Stoica, A.D.; Ma, D.; Beese, A.M. Residual stress mapping in Inconel 625 fabricated through additive manufacturing: Method for neutron diffraction measurements to validate thermomechanical model predictions. Mater. Des.
**2017**, 113, 169–177. [Google Scholar] [CrossRef] - Porter, D.A.; Easterling, K.E.; Sherif, M. Phase Transformations in Metals and Alloys; Revised Reprint; CRC Press: Boca Raton, FL, USA, 2009. [Google Scholar]
- Hall, E.O. The Deformation and Ageing of Mild Steel: III Discussion of Results. Proc. Phys. Soc. Sect. B
**1951**, 64, 747–751. [Google Scholar] [CrossRef] - Petch, N.J. The Cleavage Strength of Polycrystals. J. Iron Steel Inst.
**1953**, 174, 25–28. [Google Scholar] - Gladman, T. On the Theory of the Effect of Precipitate Particles on Grain Growth in Metals. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci.
**1966**, 294, 298–309. [Google Scholar] - Doane, D.V. Hardenability Concepts with Applications to Steel; American Institute of Mining: Centennial, CO, USA, 1978. [Google Scholar]
- Kattner, U.R.; Boettinger, W.J.; Coriell, S.R. Application of Lukas’ phase diagram programs to solidification calculations of multicomponent alloys. Z. Metallk.
**1996**, 87, 522–528. [Google Scholar] - Predel, B.; Hoch, M.; Pool, M. Effect of diffusion on Phase Transformations. In Phase Diagrams and Heterogeneous Equilibria; Predel, B., Hoch, M., Pool, M., Eds.; Springer: Berlin, Germany, 2004. [Google Scholar]
- Christian, J.W. The Theory of Transformations in Metals and Alloys; Elsevier Science Ltd.: Kidlington, Oxford, UK, 2002. [Google Scholar]
- Caballero, F.G.; Santofimia, M.J.; Garcia-Mateo, C.; Chao, J.; de Andres, C.G. Theoretical design and advanced microstructure in super high strength steels. Mater. Des.
**2009**, 30, 2077–2083. [Google Scholar] [CrossRef][Green Version] - Aggen, G.; Allen, M. ASM Handbook Volume I Properties and Selection: Irons, Steels, and High-Performance Alloys; ASM International: Materials Park, OH, USA, 2018. [Google Scholar]
- Li, L. Precipitation of Carbonitrides Containing V and Nb in Steel and their Stability. Shanghai Met.
**2005**, 27, 1–3. [Google Scholar] - Thomson, R.C.; Miller, M.K. Carbide precipitation in martensite during the early stages of tempering Cr- andMo-containing low alloy steels. Acta Mater.
**1998**, 46, 2203–2213. [Google Scholar] [CrossRef] - Yang, S.; He, X.; Chen, M.; Dang, Z.; Jun, K. Strain Induced Precipitation at High Temperature in (Nb, B.) Microalloyed Steel. Mater. Sci. Eng.
**1994**, 12, 49–65. [Google Scholar]

**Figure 3.**Influences of (

**a**) Cr and (

**b**) W content on the equilibrium phase diagram of the bainitic steel.

**Figure 5.**Plots of B

_{2}M, FCC_A1#2, and M

_{2}B_TETR content versus temperature: (

**a**) 0.01 wt % W and (

**b**) W-free.

**Figure 7.**Plots of M

_{6}C and M

_{7}C

_{3}content (wt%) of versus temperature. (

**a**) Original; (

**b**) Optimized.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chen, Y.; Zhou, X.; Huang, J.
Chemical Component Optimization Based on Thermodynamic Calculation of Fe-1.93Mn-0.07Ni-1.96Cr-0.35Mo Ultra-High Strength Steel. *Materials* **2019**, *12*, 65.
https://doi.org/10.3390/ma12010065

**AMA Style**

Chen Y, Zhou X, Huang J.
Chemical Component Optimization Based on Thermodynamic Calculation of Fe-1.93Mn-0.07Ni-1.96Cr-0.35Mo Ultra-High Strength Steel. *Materials*. 2019; 12(1):65.
https://doi.org/10.3390/ma12010065

**Chicago/Turabian Style**

Chen, Yongli, Xuejiao Zhou, and Jianguo Huang.
2019. "Chemical Component Optimization Based on Thermodynamic Calculation of Fe-1.93Mn-0.07Ni-1.96Cr-0.35Mo Ultra-High Strength Steel" *Materials* 12, no. 1: 65.
https://doi.org/10.3390/ma12010065