Microstructural evolution and precipitation strengthening in a new 20Cr ferritic trial steel

Author’s Accepted Manuscript Microstructural Evolution and Precipitation Strengthening In a New 20Cr Ferritic Trial Steel Mujin Yang, Jiahua Zhu, Chao Wu, Shuiyuan Yang, Zhan Shi, Cuiping Wang, Xingjun Liu www.elsevier.com/locate/msea

PII: DOI: Reference:

S0921-5093(18)30674-9 https://doi.org/10.1016/j.msea.2018.05.027 MSA36465

To appear in: Materials Science & Engineering A Received date: 28 February 2018 Revised date: 7 May 2018 Accepted date: 8 May 2018 Cite this article as: Mujin Yang, Jiahua Zhu, Chao Wu, Shuiyuan Yang, Zhan Shi, Cuiping Wang and Xingjun Liu, Microstructural Evolution and Precipitation Strengthening In a New 20Cr Ferritic Trial Steel, Materials Science & Engineering A, https://doi.org/10.1016/j.msea.2018.05.027 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Microstructural Evolution and Precipitation Strengthening In a New 20Cr Ferritic Trial Steel

Mujin Yanga, Jiahua Zhua, Chao Wua, Shuiyuan Yanga, Zhan Shia, Cuiping Wanga*, Xingjun Liua,b* a

College of Materials and Fujian Provincial Key Laboratory of Materials Genome, Xiamen University, Xiamen 361005, China

b

Department of Materials Science and Engineering, Harbin Institute of Technology, Shenzhen, Guangdong 518055 P.R. China

[email protected] [email protected]

*

Corresponding author. Tel.: +86-592-2187888; fax: +86-592-2187966

Abstract Microstructural evolution and precipitation strengthening of the newly-developed 20Cr steel were investigated in present work. Three types of precipitates, including G-phase (Ni16Ti6Si7, intermetallic silicide), Laves phase (Fe2Ti, intermetallic compound) and carbide (TiC), were observed and their crystal structures were resolved with combined electrochemical phase extraction, X-ray diffraction and transmission electron microscopy analysis. G-phase particles were observed in the grains and Laves phase occurred at grain boundaries while carbides were present at both of the two sites. A temperature-dependency sketch map for these precipitates was also plotted to illustrate the characteristics of G-particles below 750oC, Laves phase at 850oC~1050oC and carbide below 1150oC. In particular, G-phase precipitated and had the cubic-cubic orientation with the ferritic matrix, thus showing a strong aging hardening characteristic. Nanodispersion of these G-particles greatly enhanced the yield strength, which was estimated to be up to ~1700 MPa. Finally, theoretical calculations for phase equilibria, critical radius and precipitation strengthening helped to understand the precipitation thermodynamics and

strengthening mechanisms for developing high-performance steel by making use of G-phase.

Keywords: microstructural evolution; nano-precipitates; high-performance steels; G-phase 1. Introduction In the past few years, great effort has been made to develop ferritic steels for combustion-type power plant applications because they have a much smaller heat expansion coefficient than austenitic steels [1-3]. Such an important characteristic offers improved thermal-shock cracking resistance in service. Moreover, ferritic steels that contain a high proportion of chromium have several excellent properties such as superior oxidation resistance, good thermal conductivity and excellent weldability, which make them more suitable for components used in harsh environments [4-7]. However, the most serious limitation in developing ferritic steels for elevated temperature components is their disappointing yield strength [6, 8-10]. For example, the yield strength of P91 steel is less than 200 MPa when the tested temperature is higher than 600oC [6, 10]. Particle precipitation, as a very effective method for strengthening, is now becoming one of the most important microstructural constituents in steels [11-14]. M23C6 or M6C as the simplest and easiest-to-implement strengthening particles, however, are known to occur selectively at grain boundaries in ferritic steel, which is the reason why all modern ferritic steels are characterized by low carbon (<0.05 wt.%) [15, 16]. The addition of a small proportion of high melting point elements, such as Mo (2622oC) and W (3410oC), has also been used widely in the development of the 600oC ferritic heat-resistant steels because of their good solid-solution strengthening and their effects on stabilization of M23C6 carbides [17-19]. Unfortunately, the development of higher temperature (>650oC) heat-resistant steels is severely hampered by their temperature stability limit [10, 20-22]. Exactly due to this limitation, it is essential that other precipitates with higher temperature stability are investigated for their potential to replace carbides. Thus, B2-NiAl and Cu-rich nano-precipitates have been gaining in popularity. Jiang et al. [23] reported that an ultra-strong steel could be made that featured minimal lattice misfit and high-density nanoprecipitation. The developed steel was strengthened by NiAl precipitate and had a strength of up to 2.2 GPa with

good ductility of up to 8%. Song et al. [24] found that a hierarchical structure was more effective in retaining a coherent interface during the growth/coarsening of precipitates in Fe-Ni-Al-Cr-Ti ferritic alloys. Jiao et al. [25] reported compelling evidence for two interesting but complex group precipitation pathways of nanoprecipitate, i.e., Cu-rich and NiAl-based precipitates. In contrast with these approaches, an intermetallic silicide, known as ‘G-phase’, has received little attention. Beattie and Versnyder [26] first identified the silicon-containing G-phase, which has the general formula A16B6Si7 in an A-286 type steel, which is a precipitation-hardening alloy, in 1956. Lai [27] found a titanium-containing G-phase in type 321 steel, which had a composition that was appreciably richer in nickel: 63.3Ni-20.9Ti-12.2Si-3.47Fe-0.13Cr (wt.%). Note that none of the reported compositions clearly showed the direct substitution of transition elements when trying to derive the stoichiometric formula. G-phase was long been believed to form only under irradiation in steels of the 300 series and in 20/25 steels. However, Powell et al. [28] showed that it formed under normal aging in 20/25 Nb-stabilized alloys in the temperature range 500~850oC and suggested that it had been identified as M6C in earlier studies of the same steel because of their similar compositions and structures. It seemed that G-phase was only observed in various austenite steels at grain boundaries and in various duplex steels in the ferrite phase [29-34]. Moreover, all these G-phase containing steels were aged for a considerably long period (>10000 hrs) and at low aging temperatures (300~500oC). However, very recent work by the present research group [15] hassled to the successful development of a new ferritic steel by utilization of G-phase as the main precipitate. As a follow-up study, systemic studies of the microstructural evolution and precipitation effects in the developed steel were carried out in the present investigation.

2. Experimental 2.1 Materials and heat treatments The studied ferritic steel, known as XD-Ti, was prepared by arc melting pure constituents under a high purity argon atmosphere. The nominal chemical composition was shown in Table 1. The experimental ingot (100 g) was melted six times in order to achieve good homogeneity. After removing the surface oxides, an ingot with dimensions of ~20 mm × ~50 mm × ~100 mm was obtained, which was solution treated at 1200oC for 1 hour, followed by quenching in ice water. Subsequently, samples cut from the ingot were annealed at 560oC for 2, 5, 8, 16 hours for the micro-hardness test and at 1100oC, 1000oC, 900oC, 800oC for 3hrs for the microstructural evolution study. Table 1 The chemical composition of the studied XD-Ti trial steel. (wt.%) XD-Ti Nominal

C *

0.016

Cr

Mn

Ni

Si

Ti

Fe

20

1

3

3

1.5

Bal.

* Carbon concentration was experimentally detected by ICP-AES in this work.

2.2 Microstructure and crystal structure To reveal the microstructure, metallographic samples were cut, ground and polished following standard procedures. The backscattered electron (BSE) microstructures were observed using a field emission-electron probe microanalyzer (FE-EPMA) (JXA-8100R, JEOL, Japan). The composition of Laves phase was determined based on the wavelength dispersive spectroscopy (WDS). Electrolytic phase extraction (EPE) was conducted using a DC power supply (1665 series) to obtain and evaluate two kinds of micro-scale precipitates. An output voltage at 18 V and an electrolyte consisting 10% HCl in ethanol were used. Extracted residues were cleaned with ethanol, followed by careful drying. To identify these extracted residues, X-ray diffraction (XRD) was carried out on a Phillips Panalytical X-pert diffractometer using Cu Kα radiation at 40 kV and 30 mA. The corresponding crystal structure evaluations, including Rietveld refinement, were conducted using Jade 6.0 software. For the TEM analysis, the specimens initially were ground to a thickness of ~50 um and were then electro-polished at room temperatures and at 28 V using jet-polish techniques in an electrolyte containing 6% HClO4, 12% CH3COOH and 12% ethylene glycol in methanol. Thin

foils were examined in a JEM-2100 (HC) TEM operating at 200 kV. 2.3 Mechanical properties A Shimadzu Micro-Hardness Tester was used with a load of 4.9 N and a holding time of 30 s to evaluate the age hardening phenomenon. Each sample was tested seven times and average values of the measured data were taken. Compression tests were carried out on all samples in both the as-quenched state as well as after aging for various times. An MTSE45.504 was used for compression tests, operating with a crosshead speed of 0.003 mm/s and using a 50 KN load cell. All of the compression samples were cylinders (5 mm in height and 3 mm in diameter). To obtain a measure of the yield strengths, each result was taken from an average of three tests. 2.4 Thermodynamic and first-principle calculations To further investigate the precipitation strengthening mechanism for the studied XD-Ti alloy steel, equilibrium fractions and compositions of several selected phases (ferrite, carbide, Laves and G-phase) and their chemical compositions as a function of the annealing temperature were calculated using Thermo-Calc® software version 3.1 with the Fe-based database (TCFE-7). As the shear modulus (G) of the intermetallic phase (G_Ni16Ti6Si7, Fm-3m) (main precipitate in the present work) was required, first-principles calculations were performed based on the density functional theory (DFT) code – Vienna ab initio simulation package (VASP) [16, 14, 15]. The projector augmented wave (PAW) method [16] and the Persew-Burke-Ernzerhof generalized gradient approximation (GGA-PBE) [17] were adopted. Brillouin zone sampling was performed using the Monkhorst-Pack scheme [18] with a 6 × 6 × 6 k-mesh. Throughout the calculation, the convergence of the total energy and the maximum force of ionic relaxation were set to less than 10-5 eV/atom and 10-2 eV/Å, respectively. The elastic constants were calculated using an efficient stress-strain method [20]. A set of strains, ε = (ε1, ε2, ε3, ε4, ε5, ε6), with ε1, ε2 and ε3 being the normal strains and ε4, ε5 and ε6 referring to the shear strains, was used to generate the small deformations of a unit cell. The corresponding set of stresses σ = (σ1, σ2, σ3, σ4, σ5, σ6), for the deformed crystal, then was obtained through first-principles calculation. Based on the Hooke’s law, the elastic stiffness constants were calculated according to the following equation:

C11 C21 C31

G = ε−1 σ =

C12 C22 C32

C13 C23 C33

C44

(

C55

C66 )

where C is a 6 × 6 elastic stiffness constant matrix with Cij (i, j = 1, 2, 3, 4, 5 and 6), and ε-1 represents the (pseudo) inverse of the sets of strains. More details are described in Ref. [21]. The shear modulus (G) was calculated by: G=

C11 −C12 +3C44 5

.

3. Results 3.1 Microstructure and crystal structure (＞700oC annealing) Microstructure and crystal structure evaluations of the studied XD-Ti alloy in both the as-cast and solution-treated states were shown in Figure 1. A sporadic distribution of two kinds of dot-type small precipitates, with different contrasts (i.e. white and black), were observed in the as-cast microstructure (Figure 1a). The two precipitates were considered to have originated during the solidification process. Their crystal structures will be further discussed in the later section. The specimen quenching from 1200oC showed a fully ferritic microstructure without any obvious precipitates, as shown in Figure 1b. Thus, 1200oC was reasonably considered as a perfect solution-treatment temperature for the subsequent aging treatments. Figure 1c showed the corresponding final X-ray Rietveld refinement result for the studied solution-treated alloy with Rp = 3.9% and Rwp = 5.8%. The result agreed with experimental data and yielded a lattice constant of a = 2.865(2) Å for the ferritic matrix (space group: Im-3m, 229). Further TEM observations (Figure 1d) found only a few dislocations, which may have come from the sample preparation process, helping to confirm that there was indeed no any precipitation in the solid-solution state.

Fig 1 Microstructures and crystal structures of the studied XD-Ti alloy: (a) BSE images of the as-cast alloy; (b) Solution-treated (1200oC/10min) alloy; (c) XRD refinement of the solution-treated alloy; (d) Corresponding TEM microstructure observation.

Figures 2 and 3 displayed two similar microstructures from the 1000oC/3hrs and 900oC/3hrs annealed samples, and their corresponding crystal structures of two precipitates also were elucidated. Electrochemical extraction and unextracted regions showed significant differences by their clear boundaries, as illustrated in Figure 3a. In the 900oC/3hrs annealed specimen (Figure 2a), many black precipitates (doped-type) were evident in the grains while the grain boundaries mainly were characterized by the white (lath-type) phase. It was observed that the content of the black phases increase further with the increasing temperature (1000oC), and even partly replaced the white phase at grain boundaries. As a result, only little of the grain boundary phase remained at intersecting grain boundaries, as shown in Figure 3b (1000oC/3hrs annealing).

Fig 2 Microstructures and structure analysis of the 1000oC/3hrs anneal-treated XD-Ti alloy: (a) BSE images of electrochemical extraction/non-extraction region; (b) Before electro-chemical extraction; (c) XRD analysis of the extraction residues; (d) and (e) TEM analysis of the metallic carbide phase.

XRD analysis data for the extraction residues in Figures 2c and 3c indicated that the two precipitates were metallic carbide with the lattice parameter (a = 4.099(3) Å, Fm-3m, 225) and Fe2Ti-Laves phase with the lattice parameters (a = 4.740(9) Å, c = 7.646(3) Å, P6mm, 194). WDS analysis further confirmed their matches: The Laves phase occurred at grain boundaries, while the doped-type phase in the grains was carbide. As shown in Figure 3c, the diffraction peaks from grain boundary Laves phase are much weak than that of the carbides, which indicated that the concentration of Laves is much lower than that of the carbides. This also was consistent with the microstructure examinations (Figure 3b). Microstructure morphologies of these extracted residues were shown in Figures 2d and 3d, respectively. Figure 2d showed a typical lath-type Laves particle ~30 × 200 nm in size. The corresponding electron diffraction pattern from the 110 incident direction was shown in Figure 2e. The carbide particles exhibited a completely hexagon-polymorphic structure (~120 nm in diameter), which was shown in Figure 3d, while the

corresponding 110 diffraction pattern was shown in Figure 3e. Thus, the microstructures and crystal structures were basically confirmed.

Fig 3 Microstructures and structure analysis of the 900oC/3hrs anneal-treated XD-Ti alloy: (a) BSE images; (b) XRD analysis of the extraction residues; (c) TEM image of the Laves particle.

Figure 4 showed another kind of microstructure that only carbides occur. Two specimens from the 800oC/3hrs annealing and 1100oC/3hrs annealing showed a similar situation. These MC carbides precipitated at both grain and grain boundary as shown in Figure 4a and b. It was worth to mention that a precipitate-free zone (PFZ, ~3 m in width) between grain boundary- and grain-precipitates occurred, as can be seen clearly in Figures 2b, 4a and 4b. It was easy to understand that theses Ti-rich precipitates (metallic carbide or Laves phase) catch a large amount of Ti, which caused the occurrence of the Ti-poor PFZ near the grain boundary.

Fig 4 BSE microstructures of the studied XD-Ti alloy: (a) 800oC/3hrs; (b) 1100oC/3hrs.

3.2 Aging treatment & mechanical properties (＜700oC aging) Two micro-hardness response curves, as a function of a serial of aging times at 560oC and 660oC, respectively were presented in Figure 5. The 660oC-result was cited from our previous work[15] for comparison. The effect of the age hardening phenomenon was very evident, as can be judged from both Figures 5a and b. For the specimen aged at 550oC, a small hardness plateau (~575 HV) was observed from 2 to 5 hrs. Subsequently, the hardness continued to increase, up to the hardness peak value (~675 HV) at 8 hrs. Then, the hardness decreased slowly. The response after aging at 660oC showed almost the same trend (i.e. two steps). The difference was that the aging response at 660oC occurred much more rapidly than at 560oC. The corresponding first and second hardness peak values occurred after 15min and 2 hrs, respectively, which should be attributed to the faster precipitation kinetics at the higher temperature (660oC).

Fig 5 Micro-hardness vs. aging time of the studied XD-Ti alloy.

Microstructural evolutions of the XD-Ti alloy aged at 660oC-aged were shown in Figure 6. In initial aging stage (0.25 hour), the BSE image as shown in Figure 6a showed only a single-phase microstructure. However, with an increase in aging time, the scattered small black carbide particles began to be evident in the matrix, as can be seen in both Figures 6b (7 hrs) and 6c (15 hrs). Thus, the origin of the second hardness peak (Figure 5b) should be interpreted as being the

effect of carbide nucleation and growth. TEM observations of the 0.25 hour-aged specimen, as shown in Figures 6d and 6e, further helped interpretation of the first hardness peak (Figure 5b). Figure 6d was a dark-field (DF) image with an inset double diffraction pattern. An extremely small particle, only a few nanometers in diameter became evident in the ferritic matrix. The high-resolution image given in Figure 6e indicated that the particles were coherent with the ferritic matrix. Both the inserted Z = 110 diffraction (Figure 6d) and Fourier transformation patterns (Figure 6e) jointly indicated that the lattice parameter of precipitate was four times of that of bcc matrix. Thus, the particle was further interpreted as G-phase, as has been reported mentioned for other steels [33, 35]. Thus, the first hardness response (Figure 5b) was considered to be associated with G-phase precipitation.

Fig 6 Microstructures evolution of the studied XD-Ti alloy at 660oC aging: (a) 660oC/0.25hr; (b) 660oC/7hrs; (c)660oC/15hrs; (d)Dark field (DF); (e) High-resolution images of the 660oC/0.25hr aged specimen.

To obtain estimates of the precipitate strengthening effect from G-phase, compression tests were performed. The results of a series of compressive stress-strain curves for different aging

times at 560oC and 660oC were shown in Figures 7 and 8, respectively. The final load strain was up to 40%, and no compression samples were broken. The yield strength of solid-solution state (1200oC/15min) alloy reached ~700 MPa, as can be seen in both Figures 7 and 8 (black curves), which were shown for comparison.

Fig 7 Compression curves from the 560oC age-treated alloys.

For samples aged at 560oC (Figure 7), the max yield strength occurred firstly with the 3hrs-aged sample (green curve) and surprisingly was as high as ~1.7 GPa. The corresponding increment of yield strength achieved through aging was ~1 GPa. Age strengthening was extremely significant. Furthermore, the yield strengths of two samples that had been aged for longer times (5 and 8 hrs) remained as high as previously, which also was illustrated in Figure 5. For the sample aged at 660oC (Figure 8), the max yield strength firstly occurred after an extremely short aging time (15 min) but it also reached a very high value (~1.4 GPa). However, the yield strength decreased quickly with increasing aging time at 660oC (i.e. 1 and 2 h). The corresponding increment of yield strength for the sample that had been aged for 2 hrs was only ~350 MPa.

Fig 8 Compression curves of the 660oC age-treated alloys.

4. Discussion The primary focus of the present investigation was the development of knowledge-driven utilization of the alloying elements in the 20Cr ferritic steel in order to optimize the use of G-phase

nano-precipitates

high-temperature

for

microstructure

strengthening. evolution

More

(>700oC)

specifically, and

the

exploitation

low-temperature

of

(<700oC)

age-strengthening effects in the developed XD-Ti trial steel alloy were carried out. The combined EPMA and TEM results provided clear insight into the precipitation microstructures and mechanical properties of the XD-Ti trial steel. In the following paragraphs, the temperature-dependency of microstructure evolution and the G-phase strengthening mechanism were discussed systematically and in detail. 4.1 Microstructural evolution Microstructures observation indicated that there were three kinds of important precipitates (G-phase, Laves phase and carbides) in the structure of the XD-Ti alloys. It was concluded that Laves phase precipitates preferentially at grain boundaries. Furthermore, this could only occur in the high-temperature range (850oC~1050oC). In contrast to the Laves phase, carbides trended to occur first inside the grains. The carbides seemed to be more stable and dissolved at ~1150oC; G-phase showed the lowest temperature stability of the three precipitates. These results were collated in a temperature-microstructural evolution schematic, as shown in Figure 9.

Fig 9 Schematic diagram of the microstructural evolution of the G, carbide and Laves (L) precipitates in the studied XD-Ti alloy.

4.2 Effect of Ni, Si and Ti on precipitation

Several theoretical phase diagrams, based on calculated data, presenting the alloying element effect were developed during the study and are presented in Figure 10. The alloying-elements involved in the thermodynamic calculations included Ni, Si and Ti and their interrelated precipitation phases, G-phase, Laves phase and carbides. The three elements (Ni, Si and Ti) were designated 'G-former' elements by the present authors because the thermodynamic nature of G-phase could be traced back to a simple ternary compound, Ni16Ti6Si7. In addition, the alloying element, Ti, also exhibited a strong relationship with the carbide (TiC) and Laves phase (Fe2Ti). The calculation results were considered as follows: Firstly, four property diagrams (mass fraction vs. temperature) for increasing Ni concentration from 2% to 5% were calculated and were mapped for comparison on the same coordinates, as shown in Figure 10a. This showed that Ni concentration affected both the G-phase and the Laves phase according to mass fraction rather than temperature stability. The mass fraction of G-phase at 200oC increased markedly from 2 wt.% (2Ni alloy) to 8 wt.% (5Ni alloy). However, the temperature at which the G-phase and Laves phases disappeared in all four alloys (2Ni to 5Ni) was essentially similar, and occurred at ~670oC and ~900oC, respectively. Secondly, the calculation results for the effect of Si differed greatly from that for Ni, as shown in Figure 10b. It was apparent that increasing Si concentration (solely) raised the temperature stability of G-phase from 600oC to 850oC (2Si to 5Si) while the max mass fraction (which occurred at 200oC) was not affected and remained at ~6.3 wt.%; By contrast, Ti hardly affected the G-phase mass fraction or temperature stability. Instead, changes in the Ti concentration only affected the mass fraction and temperature stability of the Laves phase, as shown in Figure 10c. There was a peak value for the mass fraction, which occurred at ~650oC on each calculated curve. These peak values increased from ~0.5 wt.% to 6 wt.% (0.5Ti to 2Ti alloy). Additionally, the temperature limit for Laves phase stability increased from ~750oC to 1080oC.

Fig 10 Thermodynamic calculated property diagrams of the Fe-20Cr multicomponent systems: (a) Effect of increased Ni content; (b) Effect of increased Si content; (c) Effect of increased Ti content; (d) Effect of increased (Ni+Ti+Si) content.

There is no doubt that the formation of G-phase was much favorable rather than Laves phase, due to the strong precipitation strengthening effect of G-phase. Thus, the combined alloying elements effect gave the "more-G-less-L" phase diagram, as shown in the Figure 10d. The Laves phase remained at a very low mass fraction, which was achieved by adjusting alloying element contents in the Fe-20Cr-1Mn-Ni-Ti-Si multicomponent alloy system. The calculation results indicated that there should be considerable room to develop more high-strength steels by further optimizing the alloy composition.

4.3 Coherent/semi-coherent transition The nano-scale precipitate in the studied XD-Ti trial steel was identified as G-phase by clear double diffraction patterns (Figure 6). The spherical morphology of G-phase in Figure 6d and 6e also were consistent with low misfit strain, if it is assumed that the driving force for the formation of interfacial dislocations mainly arises from the elastic energy caused by lattice misfit. Thus, the energy of the matrix with particles can be conserved when particle coherency is lost. Based on the above assumptions, Jesser [36] proposed a relationship for coherent/semi-coherent transition, as shown in the following: 𝜎𝑑is =

𝐺𝑏 2𝜋2

1

1

1

(1 + 𝛽 − (1 + 𝛽 2 )2 − 𝛽 ln (2𝛽(1 + 𝛽2 )2 − 2𝛽2 ))

(1)

where dis is the energy of interfacial dislocation network per unit area, G and b are shear modulus and Burgers vector of the matrix. Then: 𝜋𝛿

β = (1−𝜗) 𝑟𝑐2 𝜎𝑑𝑖𝑠 = 2𝑟𝑐3 𝐺𝛿 2

(2) 1+𝜗 3(1−𝜗)

(3)

where and  are lattice misfit and Poisson ratio, rc is the critical transition radius for the coherency loss, and G is shear modulus of the matrix. In the present case of -Fe matrix and G-phase particles, substitution of G = 82 GPa, b = 0.248 nm, = 0.019 (-Fe: 0.286 nm and Ni16Ti6Si7: 1.122 nm) and = 0.29 in Equations (1) and (2) produced dis = 0.155 J/m2. The critical transition radius for the coherency loss was given as rc = 4.33 nm by the combination of Equation (3) and the estimated value of dis. The practical particle size for coherency loss was expected to be larger than the above-calculated value, as sufficient activation energy was necessary for the outbreak of interfacial dislocations. The measured average radius (~3.81 nm) from the specimen aged at 660oC for 0.25 h (Figure 6d) was close to the calculated critical transition radius (rc = 4.33 nm), which implied that a coherent relationship existed during early aging. This indicated that there was a strong precipitation strengthening effect (~0.7 GPa, Figure 7). The quantitative calculation for deformation mechanisms was discussed in the following section. 4.4 Deformation mechanisms Both the micro-hardness curves (Figure 5) and compression curves (Figures 6 and 7) demonstrated that higher yield strengths (~1400 MPa, 495 HV) and ultra-high strength (~1700

MPa, 575 HV) could be achieved in the studied 20Cr ferritic alloy by G-phase precipitation. It was useful, therefore, to consider the deformation mechanisms and the corresponding effects on the yield strength in the studied precipitation-strengthened alloy. After a very short aging period, the shearing mechanism could dominate in the present instance, as with other PH steels [37, 38]. Correspondingly, the increase in yield strength contributed to coherency strengthening (Δσ1), modulus mismatch strengthening (Δσ2) and order strengthening (Δσ3) [39]. Order strengthening (Δσ3) was ignored in the present case because G-phase was known to be an intermetallic compound, unlike for B2-NiAl [23, 40] and γ́́-Ni3Al [41, 42]. Thus, the contribution to the yield strength due to coherency strengthening could be expressed as: 3

∆𝜎1 = 𝑀𝛼𝜀 (𝐺𝜀)2 (

𝑟𝑓 0.18Gb2

)

1 2

(4)

where M is the Taylor factor (= 2.9), b is the Burgers vector (= 0.248 nm) , αε = is a constant (= 2.6), G is the shear modulus (= 80 GPa) [43, 44], ε is the constrained lattice parameter mismatch (≈ (2/3)(Δa/a) = 0.0126) [45], r is the mean precipitate radius and ƒ is the volume fraction of precipitated G-phase. The strengthening by modulus mismatch was expressed as follows: ∆σ2 = 0.0055M(∆G)3/2 (

2𝑓 1/2

𝐺𝑏2

)

𝑟

3𝑚

𝑏( ) 2 −1 𝑏

(5)

where m is the constant (≈ 0.85) [39], and ΔG is the shear modulus mismatch between the matrix and precipitate. However, no any shear modulus data for the Ni16Ti6Si7 structure was found in the literature. In consequence, the first-principles calculation for shear modulus of the Ni16Ti6Si7 structure was explored. The precipitation energy of the Ni16Ti6Si7 structure was calculated according to the following equation: EG_formation = (ENi64Ti54 Si50 − 64ENi − 54ETi − 50ESi )/168

(6)

where ENi64 Ti54 Si50 is the total energy of the Ni64Ti54Si50 supercells and ENi, ETi and ESi are the chemical potentials of Ni, Ti and Si in dilute bcc Fe solid solution, respectively. Based on this calculation, the formation energy and shear modulus of the G_Ni16Ti6Si7 were determined to be -0.707 eV/atom and 40 GPa, respectively, as shown in Figure 11 on the adopted crystal structure schematic. Therefore, the shear modulus mismatch, ΔG, was estimated to be 40 GPa.

Fig 11 Atomic structures, calculated shear modulus and formation energies of the Ni16Ti6Si7-type model.

On the other hand, dislocation looping mechanism proposed by Orowan should predominate during the over-aged period. The increase in yield strength Δσor due to this mechanism was expressed by: ∆σ𝑜𝑟 =

0.4𝑀𝐺𝑏 𝜋√(1−𝜗)

∙

2𝑟 𝑏

ln( ) 𝜆

(7)

where ν is the Poisson ratio (= 0.285) [46] and λ is an effective inter-precipitate distance. For a monodispersed assembly, the parameter was given by [47]: 3𝜋

𝜆 = (√

4𝑓

− 1.64) ∙ 𝑟

(8)

By using Equations (4-8), a plot of the theoretical and measured increases in strength (both for the present work and for referenced studies [48]) as a function of the precipitate radius was presented in Figure 12. The volume fraction of G-phase particles in the studied alloy should be taken to be ~1% and ~2% at 560oC and 660oC, respectively. The result was not exactly in good agreement with the thermodynamic calculation (Figure 10), which was attributed to the imperfect database. After all, the FCFE7 database was not a goal for developing the G-phase steel. On the other hand, the shearing and dislocation loop mechanisms could be divided by a precipitate radius at ~1.6 nm by these calculations. The observed radius (3.81 nm) at peak-hardness also was not very consistent with the critical transition radius from a shearing mechanism to a dislocation loop mechanism.

Fig 12 The calculated increased yield strength as a function of the mean precipitate radius of the studied XD-Ti alloy with several experimental points from other G-phase-containing steels.

Nevertheless, the thermodynamic calculation (Figure 10) predicted the possibility of improving the volume fraction of G-phase, while the corresponding deformation mechanism could be calculated quantitatively (Figure 12). Both can help in the development of a more high-performance G-phase steel.

Conclusions The study focused on the microstructural evolution and precipitation strengthening of a recently developed 20Cr steel containing G-phase (Ni16Ti6Si7). 1. Three different precipitates, including G-phase, Laves phase and carbides, were observed. The dissolution temperature limits were estimated at 750oC for G-phase and 1050oC for carbides, while Laves phase only occurred between 850~1050oC. 2. Nano-dispersion of the G-phase particles had a strong aging hardening effect, increasing the yield strength up to 1700 MPa.

3. A series of theoretical calculations helped guide the design of ‘more G-phase fewer Laves-type’ 20Cr steels and assisted in gaining an understanding of the related deformation mechanisms.

Acknowledgements This work was financially supported by the National Key R&D Program of China (Grant No. 2017YFB0702901), the National Natural Science Foundation of China (Grant No. 51471138) and the National Natural Science of Foundation of China (Grant No. 51571168).

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