Effects of Retained Austenite upon Softening during Low-temperature Tempering in Martensitic Carbon Steels

Abstract

The effects of retained austenite upon softening during low-temperature tempering at 373 K were investigated using martensitic carbon steels with and without retained austenite. To increase the amount of retained austenite, 10 mass% Ni was added to the base carbon steel (Fe-0.3C alloy). During tempering, the hardness decreased more rapidly in the Ni-added steel containing 6 vol.% retained austenite than in the base steel without retained austenite. Analyses of the microstructure and the carbon content in the solid solution (i.e., the solute carbon concentration) revealed that the retained austenite tended to suppress carbide precipitation and significantly reduced the solute carbon concentration in the martensitic matrix. We demonstrated that retained austenite acts as an effective absorption site for solute carbon in the martensitic matrix; however, the partitioned carbon is unevenly localized near the martensite/austenite interface, owing to the poor diffusivity at 373 K.

1. Introduction

Low-temperature tempering (i.e., performed at a temperature below 473 K) increases the toughness of quenched carbon steels without sacrificing their high hardness; this occurs because the residual stress introduced by quenching is significantly reduced but the fine substructures and high-density dislocations in the martensitic structure are maintained.¹⁾ However, the toughening effect of low-temperature tempering is limited; therefore, this heat treatment is generally applied to mechanical structural steels (e.g., shafts and tools) which require wear and fatigue resistance rather than toughness. On the other hand, structural steels require a higher toughness; thus, high-temperature tempering (at a temperature exceeding 673 K) is often applied to increase toughness at the cost of strength. A low-temperature tempering process that can achieve similar toughness improvements to high-temperature tempering would expand the applicability of tempered martensitic steels.

Controlling the concentration of carbon in the solid solution (hereinafter called the “solute C concentration”) is crucial for improving the mechanical properties of low-temperature-tempered martensitic steels, because the hardness of martensite is more strongly affected by the solute C concentration than the dislocation density and residual stress. However, quantitative analysis of the solute C concentration is not generally easy, because carbide precipitation always accompanies the quenching (particularly in the case of low-carbon steels). Although three-dimensional atom probes (3DAPs)^2,3,4) and field emission electron probe micro analyzers⁵⁾ have recently become popular as a means of evaluating the distribution of C in martensitic steels, these analyses cannot necessarily identify the states of carbon atoms (e.g., solid solution, segregation, and precipitation), and the obtained information is extremely local. On the other hand, electrical resistivity measurement methods (which can obtain the average solute C concentration) can effectively elucidate mechanical properties such as hardness and tensile strength. Masumura et al.⁶⁾ formulated a relationship between the solute C concentration and electrical resistivity in martensite, by using martensitic steels with different carbon contents. Moreover, they established a convenient method for evaluating the solute carbon concentration using electrical resistivity, and they demonstrated that a continuous change in solute C concentration during low-temperature tempering can be quantitatively evaluated in low-temperature-tempered martensitic C steels.⁶⁾

In this study, we apply the electrical resistivity method to the low-temperature tempering process of medium C martensitic steels containing retained austenite. It is considered that retained austenite dispersed in the martensitic matrix can influence the solute C concentration during tempering, particularly when the C content is relatively high. This is because the solute C atoms diffuse from the martensite to the retained austenite and increase the C content therein (partitioning); this reduces the solute C concentration in the martensitic matrix during low-temperature tempering. The C-partitioning alters the stability of the retained austenite and the amount of precipitated carbide. Therefore, it is important to understand the characteristics of this C partitioning when trying to control the mechanical properties of martensitic steels. However, very few reports have discussed the effects of retained austenite upon low-temperature-tempering behaviors in martensitic steels.

Quenched Fe-2Mn-0.3C alloy was used as the base steel for the experiments. To enhance the effect of C partitioning, specimens with 10 mass% Ni added to the base steel (i.e., the amount of retained austenite was intentionally increased) were also prepared. Subsequently, the effects of retained austenite upon softening behaviors during low-temperature tempering were clarified by comparing the results of both steels; then, the relationship between solute C concentration and hardness in tempered martensitic steels was discussed.

2. Experimental Procedure

2.1. Chemical Composition and Heat Treatment

Fe-2 mass% Mn-0.5 mass% Si-0.3 mass% C alloy (0.3C steel) and Fe-2 mass% Mn-0.5 mass% Si-0.3 mass% C-10 mass% Ni alloy (0.3C-10Ni steel) were used as specimens in this study. The detailed chemical compositions and martensite start temperatures (M_s temperatures) obtained via thermal expansion tests are listed in Table 1.

Table 1. Chemical compositions (mass%) and M_s temperatures of the alloys used in this study.

	C	Si	Mn	Ni	P	S	Fe	Ms [K]
0.3C	0.30	0.50	1.97	<0.003	<0.002	0.0010	Bal.	653
0.3C-10Ni	0.30	0.49	2.03	10.00	<0.002	0.0009	Bal.	488

Bar specimens of 15 mm × 15 mm × 60 mm were first austenitized at 1373 K for 1.8 ks, followed by water quenching. Thereafter, the quenched specimens were sub-zero-treated at 77 K for 600 s with liquid nitrogen, to ensure that the retained austenite was stably retained during the electrical resistivity measurements (as-quenched specimen). Some 0.3C-10Ni steel specimens were cold-rolled up to 20%, to eliminate the retained austenite via deformation-induced martensitic transformations [cold-rolled (CR) specimen]. Subsequently, tempering was performed at 373 K using a silicon oil bath (tempered specimen). In addition, all specimens were stored at a low temperature (258 K) when not in use in the experiments, to suppress room-temperature aging.

2.2. Microstructure Evaluation

The microstructures of the specimens were observed via electron backscatter diffraction (EBSD) experiments using a field-emission scanning electron microscope (SEM; acceleration voltage: 20 kV; SIGMA 500, Zeiss). The surfaces of the observed specimens were prepared by first applying wet-polishing with emery polishing papers, followed by twin-jet electropolishing (25 V-30 mA-120 s) with an electrolyte solution comprising 90 vol.% acetic acid and 10 vol.% perchloric acid. In addition, the retained austenite and precipitated carbides were observed using a transmission electron microscope (TEM) with a column-type energy filter (acceleration voltage: 300 kV; JEM-3200FSK, JEOL). The TEM observation specimens were first cut into bars of 3φ × 15 mm, which were then sliced into discs of 3φ × 1 mm. The discs were first wet-polished with emery polishing papers to a thickness of ~80 μm, followed by buff polishing with diamond slurry and then thinning via twin-jet electropolishing (15 V-20 mA-180 s) with an electrolyte solution comprising 90 vol.% acetic acid and 10 vol.% perchloric acid.

The presence of retained austenite was confirmed via X-ray diffraction (XRD; tube voltage: 40 kV; tube current: 15 mA; Aeris, Malvern Panalytical) experiments using Cu radiation. The surfaces of the XRD specimens were prepared by first applying wet-polishing with emery polishing papers and then electropolishing above 50 μm⁷⁾ to remove the effects of the strained layer due to the mechanical polishing, using an electrolyte solution comprising 67 mass% phosphoric acid and 33 mass% chromium (VI) oxide. The volume fraction of retained austenite (f_γ) was estimated by measuring the saturation magnetization (I_s) under magnetic field of 550 kA/m², via

  

$$f_{\gamma }=1-f_{\alpha \text{'}}=1-I_{\mathrm{s}}/I_{\mathrm{s}}*,$$(1)

where I_s* is the standard saturation magnetization obtained when the measured specimen consists only of martensite. Square bar specimens of 4 mm × 4 mm × 30 mm were used to assess saturation magnetization.

The neutron diffraction experiment was performed at a time-of-flight neutron diffractometer (beam size: 20 mm × 20 mm; iMATERIA) at the Japan Proton Accelerator Research Complex (J-PARC) to evaluate the C partitioning from martensite into austenite during tempering. The diffraction line profiles were obtained from the backscatter bank (145° < 2θ <175°), and the square bar specimens of 6 mm × 8 mm × 65 mm were used for the measurements.

The dislocation density (N_dis) of the specimens was estimated using the modified Williamson-Hall/Warren-Averbach method (mWH/WA method).^8,9) The X-ray diffractometry and sample preparation procedures matched those mentioned above for the retained austenite content experiments. It has been reported that N_dis is overestimated by the mWH/WA method for as-quenched martensitic C steels, owing to the high tetragonality.¹⁰⁾ However, Masumura et al.¹⁰⁾ reported that, in tempered martensitic 0.55 mass% C steel at a tempering parameter [TP = T × (logt + 20),¹¹⁾ where T: tempering temperature (K); t: tempering time (h)] of 12000–13000, the true N_dis of as-quenched specimen could be estimated. This is because, under these conditions, a decrease in N_dis does not occur, and the tetragonality of the martensite disappears. Therefore, in this study, the specimens tempered at 573 K for 600 ks (TP = 12700) were used to estimate N_dis in the as-quenched specimens.

The solute C concentration (C_sol) of the specimens was estimated from electrical resistivity measurements using the four-point method at 77 K.⁶⁾ The relevant specimens were prepared by first producing square bars of 1 mm × 1 mm × 50 mm and then wet-polishing these bars with emery polishing papers. The specimens were held in liquid nitrogen for 60 s; then, the electrical resistivities were measured twice whilst varying the current direction, and the average value was calculated. Matthiessen’s rule holds for electrical resistivity; thus, ρ = ρ_L + ρ_i, where ρ_L arises from the lattice vibration and is temperature dependent and ρ_i represents the effects of solute atoms, defects, and so on and is not temperature dependent. Therefore, by performing measurements in liquid nitrogen, the effect of ρ_L became approximately zero. We previously reported that the C_sol value in steels consisting only of martensite is expressed as⁶⁾

  

$$\begin{array}{l}{C}_{\mathrm{s}\mathrm{o}\mathrm{l}}\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\right]=\\ \left\{{\rho }_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}-({\rho }_{\mathrm{F}\mathrm{e}}+\mathrm{\Delta }{\rho }_{\mathrm{s}\mathrm{u}\mathrm{b}})-(\mathrm{\Delta }{\rho }_{\mathrm{d}\mathrm{i}\mathrm{s}}+\mathrm{\Delta }{\rho }_{\mathrm{H}\mathrm{A}\mathrm{G}\mathrm{B}})\right\}\left[\mathrm{m}\mathrm{\Omega }\mathrm{m}\mathrm{m}\right]/0.25,\end{array}$$(2)

where ρ_total is the measured electrical resistivity, ρ_Fe (0.00704 mΩmm at 77 K) is the electrical resistivity of pure iron, Δρ_sub is the effect of substitutional elements, Δρ_dis is the effect of dislocations, and Δρ_HAGB is the effect of high-angle grain boundaries. Each factor was estimated as follows:⁶⁾

  

$$\begin{array}{l}\mathrm{\Delta }{\rho }_{\mathrm{s}\mathrm{u}\mathrm{b}}\left[\mathrm{m}\mathrm{\Omega }\mathrm{m}\mathrm{m}\right]=\left(0.0504\pm 0.0008\right)\times \mathrm{M}\mathrm{n}\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\right]\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+\left(0.133\pm 0.003\right)\times \mathrm{S}\mathrm{i}\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\right],\end{array}$$(3)

  

$$\mathrm{\Delta }{\rho }_{\mathrm{d}\mathrm{i}\mathrm{s}}\left[\mathrm{m}\mathrm{\Omega }\mathrm{m}\mathrm{m}\right]=1.7\times {10}^{-18}\times N_{\mathrm{d}\mathrm{i}\mathrm{s}}\left[{\mathrm{m}}^{-2}\right],$$(4)

  

$$\mathrm{\Delta }{\rho }_{\mathrm{H}\mathrm{A}\mathrm{G}\mathrm{B}}\left[\mathrm{m}\mathrm{\Omega }\mathrm{m}\mathrm{m}\right]=1.58\times {10}^{-9}\times N_{\mathrm{H}\mathrm{A}\mathrm{G}\mathrm{B}}\left[{\mathrm{m}}^{-1}\right].$$(5)

Here, N_HAGB is the high-angle grain boundary density. The electrical resistivity of the martensite in specimens containing retained austenite was calculated from the mixture model of electrical resistivity on a multi-phase structure,¹²⁾ as

  

$${\rho }_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=\frac{{\rho }_{\alpha \text{'}}\left({\rho }_{\alpha \text{'}}+2{\rho }_{\gamma }\right)}{\left(1+3f_{\gamma }\right){\rho }_{\alpha \text{'}}+\left(2-3f_{\gamma }\right){\rho }_{\gamma }},$$(6)

where ρ_α’ and ρ_γ are electrical resistivities of martensite and retained austenite, respectively. In a previous study, the relationship between ρ_γ and C_sol in retained austenite was formulated using as-quenched Fe-2 mass% Mn-0.5 mass% Si-(0.3–0.9) mass% C-10 mass% Ni alloys, as follows:¹³⁾

  

$${\rho }_{\gamma }\left[\mathrm{m}\mathrm{\Omega }\mathrm{m}\mathrm{m}\right]=0.26\times C_{\mathrm{s}\mathrm{o}\mathrm{l}}\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\right]+\mathrm{0.21.}$$(7)

As we shall see later, auto-tempering occurs in as-quenched 0.3C-10Ni steel; this influence is neglected in Eq. (7). Therefore, the relationship between ρ_γ and C_sol in retained austenite was modified using as-quenched Fe-2 mass% Mn-0.5 mass% Si-(0.45–0.9) mass% C-10 mass% Ni alloys in which auto-tempering hardly occurred, as follows (see Supporting Information for details):

  

$${\rho }_{\gamma }\left[\mathrm{m}\mathrm{\Omega }\mathrm{m}\mathrm{m}\right]=0.28\times C_{\mathrm{s}\mathrm{o}\mathrm{l}}\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\right]+\mathrm{0.20.}$$(8)

The distribution of C atoms in several specimens was evaluated via a 3DAP (CAMECA LEAP 4000 XHR). The measurements were performed at a laser pulse frequency of 250 kHz, a pulse energy of 30 pJ, a specimen temperature of 50 K, and a base voltage of 3–7 kV. Needle specimens for 3DAP were prepared via two-step electropolishing with 25% perchloric acid in acetic acid (AC: 10 V) for the first step and 2% perchloric acid in butoxyethanol (DC: 15 kV) for the second.

The hardness of the specimens was measured using a Vickers hardness tester (load: 98 N; loading time: 10 s; AVK-A hardness tester, AKASI). The measurement was performed at 12 points in the center of each specimen. Subsequently, the average value was calculated from ten points (i.e., excluding the maximum and minimum values). In specimens containing retained austenite, the hardness of the martensite was estimated under the assumption that the measured Vickers hardness (HV_total) is expressed as a function of the relationship between the hardness of the martensite (HV_α’) and retained austenite (HV_γ) and f_γ, as follows:

  

$$H{V}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}\text{≒}H{V}_{\alpha ’}\times \left(1-f_{\gamma }\right)+H{V}_{\gamma }\times f_{\gamma }.$$(9)

HV_γ was calculated using the following equation, as reported by Cohen:¹⁴⁾

  

$$H{V}_{\gamma }\left[\mathrm{H}\mathrm{V}\right]=51\times C_{\mathrm{s}\mathrm{o}\mathrm{l}}\left[\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\%\right]+109.$$(10)

3. Results and Discussion

3.1. Hardness and Microstructure of As-quenched Martensitic Steel

Figure 1 shows the crystallographic orientation maps and phase maps of as-quenched (a, d) 0.3C, (b, e) 0.3C-10Ni, and (c, f) 20%CR 0.3C-10Ni steels obtained via SEM-EBSD experiments. In the phase maps, the red and green regions show body-centered cubic (BCC) iron and face-centered cubic (FCC) iron, respectively. Both as-quenched specimens [Figs. 1(a), 1(b)] share a similar and typical lath martensitic structure, although the average block width of 0.3C-10Ni steel is slightly finer than that of 0.3C steel (0.91 μm and 1.23 μm, respectively). The as-quenched 0.3C steel exhibits a martensitic single structure; meanwhile, the 0.3C-10Ni steel contains blocky retained austenites at the block boundaries [shown by the yellow arrows in Fig. 1(e)]. On the other hand, Fig. 1(f) indicates that most of the retained austenite disappeared in 20%CR 0.3C-10Ni steel. Figure 2 shows (a) a bright-field (BF) image of the as-quenched 0.3C-10Ni steel, (b) the selected area electron diffraction pattern (SAEDP) and (c) key diagram for that region of the BF image, and (d) the dark-field (DF) image obtained from the spot shown by the gray circle in the SAEDP. Film-like retained austenites were observed between laths of martensite, as shown in Fig. 2(d). The average width of the retained austenite films was measured at ~50 nm using eight observation fields of the TEM. These retained austenites exhibited the Kurdjumov-Sacks crystallographic orientation relationship, as described by the following equation with the surrounding martensites:

  

$${\left(\overline{1}11\right)}_{\gamma }//\mathrm{\hspace{0.17em} }{\left(01\overline{1}\right)}_{\alpha \text{'}},\mathrm{\hspace{0.17em} } {\left[110\right]}_{\gamma }//\mathrm{\hspace{0.17em} }{\left[111\right]}_{\alpha \text{'}}.$$(11)

Fig. 1. Crystallographic orientation maps of (a) as-quenched 0.3C, (b) 0.3C-10Ni, and (c) 20%CR 0.3C-10Ni steels, and phase maps of (d) as-quenched 0.3C, (e) 0.3C-10Ni, and (f) 20%CR 0.3C-10Ni steels. In the phase maps, red and green regions indicate BCC and FCC iron, respectively. In Fig. 1(e), retained austenites are denoted by yellow arrows. (Online version in color.)

Fig. 2. (a) TEM BF image of as-quenched 0.3C-10Ni steel, (b) selected area electron diffraction pattern, (c) key diagram, and (d) TEM DF image of the region in Fig. 2(a), where diffraction vector Z = 110_γ.

The XRD line profiles of Fig. 3 show that the retained austenite observed in as-quenched specimens is no longer present in the 20%CR specimen, suggesting that the retained austenite has fully transformed into martensite after 20% cold rolling. Figure 4 shows the change in the volume fraction of retained austenite (f_γ) after cold rolling, as estimated from the saturation magnetization measurement under the assumption that the 20%CR 0.3C-10Ni steel consists only of martensite; thus, the standard saturation magnetization in Eq. (1) (I_s^*) corresponds to the value for 20%CR 0.3C-10Ni steel. The initial f_γ was calculated at 6 vol.% in an as-quenched specimen. A further reduction in cold rolling causes f_γ to gradually decrease until it fully disappears at 20% cold rolling.

Fig. 3. X-ray line profiles of as-quenched 0.3C-10Ni steel and 20%CR 0.3C-10Ni steel.

Fig. 4. Change in volume fraction of retained austenite as a function of rolling rate in 0.3C-10Ni steel.

It should be noted that C is not necessarily distributed homogeneously (even in the as-quenched specimens), owing to auto-tempering during quenching. The M_s temperature in 0.3C steel is 653 K, sufficiently high to cause diffusion of C atoms; thus, C segregation or precipitation might occur in the martensite transformed just below M_s temperature.¹⁵⁾ Masumura et al.⁶⁾ examined the C distribution in as-quenched 0.3C steel using 3DAP, and they reported that approximately half of the C content (C_total) had already segregated or precipitated via auto-tempering during quenching. The specimens used in this study might undergo a similar auto-tempering; hence, the C distribution was examined by 3DAP in as-quenched 0.3C-10Ni steel. Figure 5 shows (a) an image quality map (IQ map), (b) an inverse pole figure map (IPF map), (c) a phase map of the as-quenched 0.3C-10Ni steel obtained via EBSD, (d) a C atom map for the region enclosed by the black square in the phase map [Fig. 5(c)], and (e) the C concentration and Ni concenotration profiles obtained for the region enclosed by the black square in Fig. 5(d) along the direction of the gray arrow. C was remarkably enriched over 6 mass% at the interface of martensite and retained austenite (martensite/austenite interface); meanwhile, the solute C concentration in martensite fell to less than half of C_total. On the other hand, Ni concentration agreed with the bulk content in either phase. Moreover, several C-enriched regions (of several nanometers in size) were present; these were assumed to be carbide particles, as shown by the black arrows in Fig. 5(d). Via 3DAP analysis, it was clarified that some carbon atoms had already been eliminated from the martensitic lattice by precipitation or partitioning into retained austenite in as-quenched 0.3C-10Ni steel.

Fig. 5. (a) IQ map, (b) IPF map, (c) phase map, (d) carbon atom map at the region enclosed by the black square in the phase map, and (e) C concentration and Ni concentration profiles analyzed along the gray arrow in the region enclosed by the black square and belonging to the gray arrow in the carbon atom map of the 3DAP specimen for as-quenched 0.3C-10Ni steel. In Fig. 5(c), red and green regions show BCC and FCC iron, respectively. (Online version in color.)

The carbides appeared to have precipitated in the martensite in the as-quenched 0.3C-10Ni steel [as indicated by the black arrows in Fig. 5(d)]; hence, the microstructure was observed using TEM to confirm the presence of these precipitated carbides. Figure 6 shows (a) the BF image of the as-quenched 0.3C-10Ni steel, (b) the SAEDP and (c) key diagram for the same region of the BF image, and (d) the DF image obtained from the spot indicated by the gray circle in the SAEDP. Figure 6(d) shows that nanometer-sized particles are dispersed in the martensitic matrix. By analyzing the diffraction pattern in Fig. 6(b), we found that metastable η carbide (Fe₂C: orthorhombic) precipitated with an orientation relationship of (110)_α’//(020)_η. Lu et al.¹⁶⁾ investigated the crystallographic orientation relationship between η carbides and the martensitic matrix in an Fe-15 mass% Ni-1 mass% C alloy aged at room temperature: an orientation relationship of (110)_α’//(020)_η for the incident direction of [001]_α’ was observed, which accords with the results of this study. Moreover, martensite possesses a significantly heterogeneous microstructure, and the measured quantities of precipitated carbides can differ for each martensite block, depending on the transformation temperature. Therefore, the average volume fraction of carbide was quantitatively evaluated by taking ~50 TEM images for multiple specimens and observation fields. The calculated average volume fraction of carbides (f_η) in the as-quenched 0.3C steel (white circle) and 0.3C-10Ni steel (white square) are plotted in Fig. 7 as a function of the number of observations. When the number of observations is small, the averages are widely scattered from one measurement to the next. However, the average value tends to converge when more than 30 observations are taken. As a result, f_η was estimated at ~3 × 10⁻³ and ~1 × 10⁻³ in the as-quenched 0.3C steel and 0.3C-10Ni steel, respectively. This suggests that the f_η of 0.3C-10Ni steel is only one third that of 0.3C steel. The foregoing discussion suggests that the lower M_s temperature suppresses auto-tempering and reduces the amount of carbide precipitation in 0.3C-10Ni steel; alternatively, the solute C concentration in martensite may decrease via C partitioning from martensite to retained austenite, as shown in Fig. 5(e).

Fig. 6. (a) TEM BF image of as-quenched 0.3C-10Ni steel, (b) selected area electron diffraction pattern, (c) key diagram, and (d) TEM DF image of the region in Fig. 6(a), where diffraction vector Z = 001_η.

Fig. 7. Average volume fraction of η carbide (as calculated from TEM results) as a function of the number of observations.

To evaluate solute C concentration (C_sol) quantitatively, the as-quenched specimens were first subjected to electrical resistivity measurements. As listed in Table 2, 0.3C and 0.3C-10Ni steels exhibit C_sol values of 0.13 mass% and 0.15 mass%, respectively; meanwhile, the ratios of C_sol to C_total (X_sol = C_sol/C_total) for 0.3C and 0.3C-10Ni steels were 0.44 and 0.50, respectively. The decrease in C_sol attributable to auto-tempering was found to be more suppressed in 0.3C-10Ni steel than in 0.3C steel. The Vickers hardness (HV_total) of the as-quenched 0.3C and 0.3C-10Ni steels were 569 HV and 607 HV, respectively; furthermore, the hardness of martensite (HV_α’) in as-quenched 0.3C-10Ni steel was estimated as 631 HV, by calibrating the influence of retained austenite using Eqs. (9) and (10); this value is ~60 HV higher than that of 0.3C steel. Table 2 lists the high-angle grain boundary density, block width, dislocation density, volume fraction of η carbide, volume fraction of retained austenite, electrical resistivity, solute C concentration, ratio of C_sol to C_total (X_sol = C_sol/C_total), Vickers hardness of specimens, and Vickers hardness of martensite (HV_α’).

Table 2. Summary of as-quenched 0.3C and 0.3C-10Ni steels.

Steels	High-angle grain boundary density (/m)	Block width (μm)	Dislocation density (/m2)	Volume fraction of η carbide.	Volume fraction of retained γ	Electrical resistivity (mΩmm)	Solute C concentration (mass%)	Xsol	Vickers hardness (HV)	HVα’ (HV)
0.3C	1.73 × 106	1.23	4.24 × 1015	3 × 10−3	–	0.234	0.13	0.44	569	569
0.3C‑10Ni	3.94 × 106	0.91	4.45 × 1015	1 × 10−3	0.06	0.404	0.15	0.50	607	631

3.2. Change in Hardness and Microstructure during Tempering

Figure 8 shows the change in electrical resistivity during tempering at 373 K. Under the tempering conditions applied in this study, the change in electrical resistivity can be primarily attributed to the decrease in C_sol, because the diffusion of substitutional elements, the annihilation of dislocations, and the migration of grain boundaries during recovery hardly occur.¹⁾ Notably, no decomposition of the retained austenite was observed in saturation magnetization measurements during tempering. In 0.3C steel and 20%CR 0.3C-10Ni steel without retained austenite, the electrical resistivity decreased gradually and monotonically. On the other hand, in 0.3C-10Ni steel with retained austenite, the electrical resistivity decreased more rapidly; thus, the reduction rate of C_sol in martensite seems to be more significant.

Fig. 8. Variation in electrical resistivity as a function of tempering time.

Figure 9 shows (a) the Vickers hardness of specimens tempered at 373 K and (b) the change in Vickers hardness of as-quenched specimens as a function of tempering time. The 0.3C and 20%CR 0.3C-10Ni steels without retained austenite exhibited a slight hardening after short-term (~1 ks) tempering and subsequent softening. We previously reported upon the hardening produced in 0.3C steel by the precipitation of fine metastable carbides.¹⁷⁾ The similar hardening observed in 20%CR 0.3C-10Ni steel may also have been produced by the same cause. On the other hand, in the 0.3C-10Ni steel with retained austenite, the hardness decreased rapidly and monotonically without producing hardening.

Fig. 9. (a) Vickers hardness (HV_total) and (b) change in HV_total as a function of tempering times.

The carbide precipitation under tempering was investigated via TEM, to clarify the cause of the monotonic softening in 0.3C-10Ni steel. In the above-mentioned Fig. 7, the volume fraction of η carbide (f_η) in 0.3C and 0.3C-10Ni steels tempered for 3 ks are denoted by the black circles and squares, respectively. In the tempered 0.3C steel, f_η is ~1.7 times larger than in the as-quenched specimens, which produces hardening; meanwhile, in the 0.3C-10Ni steel, f_η remains almost unchanged after tempering; thus, it is natural that precipitation hardening does not arise under tempering. However, electrical resistivity (i.e., C_sol) decreased more rapidly in 0.3C-10Ni steel than in 0.3C steel during tempering; thus, it is reasonable to assume that the decrease in C_sol was significantly influenced by C partitioning from the martensitic matrix to retained austenite, and that this contributed to the acceleration of softening during tempering in 0.3C-10Ni steel.

3.3. Effect of Retained Austenite on Behavior of Solute C during Tempering

To investigate the change in C_sol in the retained austenite during tempering for 0.3C-10Ni steel, the diffraction line profile changes after tempering for martensite and retained austenite were examined via neutron diffraction. Figure 10 shows the neutron diffraction line profiles of 200 peaks for the (a) martensite and (b) retained austenite in as-quenched and 600 ks-tempered 0.3C-10Ni steels, as obtained by neutron diffraction. Broadening of the peak at the high lattice-spacing side (attributable to the tetragonality of martensite) decreased with tempering, as shown in Fig. 10(a); this suggests that the tetragonality decreased with decreasing C_sol in the martensitic matrix.¹⁰⁾ On the other hand, the profile of the 200 peak for retained austenite did not change before or after tempering, as shown in Fig. 10(b), although C partitioned from the martensitic matrix to the retained austenite under tempering; thus, it is suspected that C could not diffuse to the inside of the retained austenite and that the partitioned C was therefore unevenly localized near the martensite/austenite interface.

Fig. 10. Neutron diffraction line profiles of (a) 200_α’ and (b) 200_γ in 0.3C-10Ni steel.

To demonstrate the above hypothesis, the C distribution was examined via 3DAP in 0.3C-10Ni steel tempered at 373 K for 600 ks. Figure 11 shows (a) an IQ map, (b) an IPF map, (c) a phase map of the tempered 0.3C-10Ni steel (as obtained via EBSD), (d) a C atom map for the region enclosed by a black square in the phase map [Fig. 11(c)], and (e) the C concentration and Ni concentration profiles for the region enclosed by the black square in Fig. 11(d) along the direction of the gray arrow. Carbon concentration in the retained austenite was almost unchanged from C_total (= 1.4 at.%), although a C-enriched region of a few nanometers width was found near the martensite/austenite interface. Note that, Ni partition was not be confirmed. This situation resembles that of the as-quenched specimen, which indicates that C cannot diffuse to the center of the retained austenite, even after 600 ks of tempering.

Fig. 11. (a) IQ map, (b) IPF map, (c) phase map, (d) carbon atom map for the region shown by the black square in the phase map, and (e) C concentration and Ni concentration profiles analyzed along the gray arrow at the region shown by the black square in the carbon atom map of the 3DAP specimen for 0.3C-10Ni steel tempered at 373 K for 600 ks. In Fig. 11(c), red and green regions show BCC and FCC iron, respectively. (Online version in color.)

To show theoretically the incomplete C partitioning, the profile of solute C concentration in retained austenite for the tempered specimen was estimated via a thermodynamic model, using the diffusion equation. A model in which plate-like martensites and retained austenites were alternately assumed is shown in Fig. 12(a). The width of retained austenite was set at 50 nm, the average value obtained in the TEM observations. In addition to this, it was assumed that an interface equilibrium exists at the interface between martensite and austenite. The constrained-carbon-equilibrium (CCE) model proposed by Speer et al.¹⁸⁾ is often used to calculate the C partitioning. In the CCE model, the equilibrium shows the minimum state of free energy in the system, provided the following conditions are fulfilled:

(1) No diffusion of iron or other substitutional elements, and no migration of the martensite/austenite interface occurs.

(2) C diffusion occurs freely.

(3) Carbide precipitation is completely suppressed.

Fig. 12. (a) Schematic drawing of 0.3C-10Ni steel and (b) solute carbon concentration profiles in a film-like austenite for as-quenched and tempered 0.3C10Ni steel, as estimated using Fick’s second law.

However, in this study, the metastable η carbide precipitates (as mentioned above); therefore, the modified CCE accompanied by cementite (θ) precipitation (CCEθ) model (in which carbide precipitation is considered using the CCE model proposed by Toji et al.¹⁹⁾) was applied to calculate the equilibrium. In the CCEθ model, under a thermodynamic condition when the chemical potentials for martensite, austenite, and cementite are equal, it is assumed that (1) cementite precipitates in martensite, (2) no migration of the martensite/austenite interface occurs, and (3) only C atoms diffuse. The equilibrium solute C concentration (C^*) is calculated via

  

$$3{\mu }_{F{e}_{CCE\theta }}^{\alpha }+{\mu }_{C_{CCE\theta }}^{\alpha }=G\left(\mathrm{F}{\mathrm{e}}_3\mathrm{C}\right),$$(12)

  

$${\mu }_{C_{CCE\theta }}^{\alpha }={\mu }_{C_{CCE\theta }}^{\gamma },$$(13)

where ${\mu }_{F{e}_{CCE\theta }}^{\alpha }$ is the chemical potential of iron in martensite; ${\mu }_{C_{CCE\theta }}^{\alpha }$ and ${\mu }_{C_{CCE\theta }}^{\gamma }$ are the chemical potentials of C in martensite and austenite, respectively; and G(Fe₃C) is the free energy of cementite. It should be noted that, because the precipitated carbide is not Fe₃C but Fe₂C in this study, the following equation was applied instead of Eq. (12):

  

$$2{\mu }_{F{e}_{CCE\theta }}^{\alpha }+{\mu }_{C_{CCE\theta }}^{\alpha }=G\left(\mathrm{F}{\mathrm{e}}_2\mathrm{C}\right).$$(14)

Here, G (Fe₂C) is the free energy of the η carbide. The value of C^* at 373 K in 0.3C-10Ni steel was calculated as 1.6 mass% (7.2 at.%) using Eqs. (13) and (14), where the TCFE12 database in Thermo-Calc was used.

Therefore, the profile of the solute C concentration in retained austenite [C(x, t)] was calculated by applying the following equation obtained from Fick’s second law (under a fixed concentration of 7.2 at.% at the martensite/austenite interface):

  

$$C\left(x,t\right)\left[\mathrm{a}\mathrm{t}.\%\right]=C^{*}-\left(C^{*}-C_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}\right)\mathrm{e}\mathrm{r}\mathrm{f}\left(\frac{x}{2\sqrt{Dt}}\right).$$(15)

Here, x [m] is the distance from the martensite/austenite interface, t [s] is the tempering time, and D [m²/s] is the diffusion coefficient of carbon in austenite at 373 K [= 3.68 × 10⁻²⁴ (m²/s)²⁰⁾]. It should be noted that Eq. (15) assumes that the initial C concentration (t = 0) is equal to C_total. However, in as-quenched 0.3C-10Ni steel, C partitioning into retained austenite has already occurred, and a C-enriched region of ~5 nm is present near the martensite/austenite interface, as shown in Fig. 5(e); therefore, in the initial state, the profile of the solute C concentration must include the effects of auto-tempering. One profile of the solute C concentration (when t = 600 ks) expressed by Eq. (15) is shown by the dashed line in Fig. 12(b). The C-enriched region width is ~5 nm in this case, which nearly matches the C-enriched region shown in Fig. 5(e); thus, this profile is regarded as the initial profile for the solute C concentration in retained austenite. That is, the profile of the solute C concentration in 0.3C-10Ni steel tempered at 373 K can be predicated as

  

$$C\left(x,t\right)\left[\mathrm{a}\mathrm{t}.\%\right]=C^{*}-\left(C^{*}-C_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}\right)\mathrm{e}\mathrm{r}\mathrm{f}\left(\frac{x}{2\sqrt{D\left(t+600\times {10}^3\right)}}\right).$$(16)

The solute C concentration profile for the specimen tempered at 373 K for 600 ks, as predicted using Eq. (16), is shown by the black line in Fig. 12(b). It was confirmed that C diffusion is insufficient at 373 K, and C is unevenly localized at a region ~10 nm wide. This is similar to the 3DAP results shown in Fig. 11(e). On balance, it is reasonable to assume that the C partitioned from the martensitic matrix to the retained austenite cannot diffuse to the center and becomes unevenly localized near the martensite/austenite interfaces; therefore, the lattice spacing in 0.3C-10Ni steel barely changes after tempering.

Figure 13 shows the change in C_sol for the martensitic matrix after tempering, as estimated from electrical resistivity measurements using Eqs. (2), (3), (4), (5), (6) and (8). In the 0.3C-10Ni steel with retained austenite, the decrease in C_sol is significant compared to the 0.3C steel; furthermore, in the 0.3C-10Ni steel tempered for 600 ks, the C_sol value is less than that estimated for the 0.3C steel, although it exceeds it in the as-quenched specimen. Figure 14 shows the change in the Vickers hardness of the martensitic matrix (HV_α’) after tempering, as estimated using Eqs. (9) and (10). It was confirmed that, in the 0.3C-10Ni steel with retained austenite, HV_α’ decreases significantly compared to the 0.3C steel without retained austenite. In a previous study,¹⁷⁾ we researched the relationship between HV_α’ and C_sol in Fe-2Mn-0.5Si-C alloys and found that the hardening attributable to solute C (ΔHV_sol.C) is expressed as

  

$$\mathrm{\Delta }H{V}_{\mathrm{s}\mathrm{o}\mathrm{l}.\mathrm{C}}=773\times C_{\mathrm{s}\mathrm{o}\mathrm{l}}{}^{2/3},$$(17)

or

  

$$\mathrm{\Delta }H{V}_{\mathrm{s}\mathrm{o}\mathrm{l}.\mathrm{C}}=780\times C_{\mathrm{s}\mathrm{o}\mathrm{l}}{}^{1/2}.$$(18)

Figure 15 compares the relationship between C_sol and HV_α’ obtained in this study against the previously reported.¹⁷⁾ It is confirmed that hardness decreases along the curves of Eqs. (17) and (18) for both alloys; this suggests that the softening with tempering at 373 K is primarily caused by decreasing C_sol.

Fig. 13. Variation of solute carbon concentration in martensite as a function of tempering time.

Fig. 14. (a) Vickers hardness of martensite (HV_α’) and (b) change in HV_α’ as a function of tempering time.

Fig. 15. Relationship between solute carbon concentration and Vickers hardness of martensite.

In 0.3C-10Ni steel, the C_sol value in the martensitic matrix decreases significantly via C partitioning from the martensitic matrix to the retained austenite under tempering, and this seems to accelerate the softening. That is, we clarified that retained austenite acts as an effective absorption site for solute C in the martensitic matrix and accelerates softening during the tempering of martensite containing supersaturated solute C. Retained austenite is present in the conventional C steels with relatively high C content; this seems to affect the softening rate in martensite; thus, it was shown that the presence of retained austenite strongly influences the changes in microstructure and mechanical properties during low-temperature tempering.

4. Conclusion

(1) The rate of decrease in the solute C concentration in the martensitic matrix during low-temperature tempering is more rapid in martensitic C steels with retained austenite because C partitions from the martensitic matrix to the retained austenite; on the other hand, the precipitation of metastable carbides is suppressed compared to the case of martensitic C steels without retained austenite.

(2) The softening in the martensitic matrix during low-temperature tempering occurs more rapidly in martensitic C steels with retained austenite (compared to those without retained austenite). This occurs via the acceleration of the decrease in solute C concentration in the martensitic matrix and the suppression of carbide precipitation.

(3) C partitioned from the martensitic matrix to the retained austenite is unevenly localized near the martensite/austenite interfaces under low-temperature tempering in martensitic C steels containing retained austenite.

(4) The presence of retained austenite significantly affects the behavior of the solute C in martensitic matrixes during low-temperature-tempering; therefore, retained austenite is an important factor influencing the changes in microstructural and mechanical properties during low-temperature tempering.

Supporting Information

Modification of the relationship between electrical resistivity and solute C concentration in retained austenite.

This material is available on the Journal website at https://doi.org/10.2355/isijinternational.ISIJINT-2023-100.

Acknowledgment

Neutron experiments at the Materials and Life Science Experimental Facility of the J-PARC were performed under a user program (proposal No. 2018PM0008).

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