2024 年 64 巻 10 号 p. 1599-1606
The hardness of martensitic steels with high Ms temperatures is reduced by auto-tempering after transformation, therefore the true hardness of martensite with carbon in fully solid solution is not known. In this study, we investigated a method to quantitatively evaluate the true hardness of quenched martensite unaffected by auto-tempering and the effect of auto-tempering was quantitatively evaluated by the diffusion area of carbon in bcc iron at temperatures below 400°C. As a result, it was clarified that the effect of auto-tempering is more pronounced in steels with an M50 temperature higher than 300°C and that the softening behavior of martensitic steels can be uniformly evaluated regardless of the carbon content if the activation energy of carbon diffusion is known. Furthermore, it was clarified that the degree of auto-tempering can be quantitatively evaluated by calculating the integral diffusion area S (= ∑Dt) below the M50 temperature during quenching.
Many studies have long been conducted on the tempering process of martensitic steels with increasing temperature, and it has been reported that the formation of carbon atom clusters and modulated structures occurs near room temperature, the precipitation of transition carbides such as η and χ carbides occurs at 100 to 200°C, and a transition from transition carbides to cementite θ occurs above 300°C.1,2,3,4) The rates of these reactions are thought to be determined by the lattice diffusion of carbon atoms. Above 400°C, Ostwald ripening of θ occurs, and for alloyed steels, lattice diffusion of substitutional alloying elements becomes the rate-determining process.5) However, since the auto-tempering that occurs during industrial quenching does not involve the Ostwald ripening of θ that occurs at temperatures above 400°C, the discussion can focus on carbide reactions involving lattice diffusion of carbon atoms.
Conventionally, the tempering parameter P,6) expressed by the following equation, has been widely used as an index to evaluate the strength of tempered martensitic steel:
| (1) |
where T is the tempering temperature [K], t is the tempering time [h], and A is a constant that depends on the carbon content (mass%C) and is given by the following equation:6)
| (2) |
However, this parameter is only an industrial indicator of the compatibility of tempering temperature and time to obtain the required strength; when the rates of structural changes are determined by different thermal activation processes, the characteristics cannot be organized based on the same parameter. Therefore, it is not possible to consistently evaluate the tempering behavior of steels with different types and contents of alloying elements using this parameter. To solve this problem, a new tempering parameter representing the diffusion behavior of alloying elements has been proposed for high-temperature tempered materials tempered above 400°C, and it is also known that the strength of tempered martensitic steel can be estimated for various steels using this parameter.7)
On the other hand, as mentioned above, in the tempering temperature range below 400°C, the rate of the tempering reaction is determined by the lattice diffusion of carbon atoms, and therefore, a tempering parameter based on the diffusion of carbon atoms should be adopted. For tempering at a constant temperature, the degree of tempering reaction can be evaluated by the diffusion area (Dt), which is the product of the diffusion coefficient D of carbon at that temperature and the tempering time t. However, for auto-tempering that occurs during continuous cooling, it is necessary to evaluate the degree of tempering reaction by the integral diffusion area because the temperature changes continuously with the cooling rate.8) Large members that utilize martensitic transformation are susceptible to the effect of auto-tempering because their cooling rate after martensitic transformation is slow. Especially for low-carbon martensitic steels with high Ms temperatures, auto-tempering may not be prevented even by water cooling,8) and in fact it has been confirmed that some carbides precipitate after martensitic transformation in a 0.12 mass%C low-alloy steel that has been solution treated and then water quenched.9) Since the degree of auto-tempering depends on the Ms temperature of the steel and the cooling rate, the degree of auto-tempering of the martensite formed during continuous cooling is expected to vary depending on the location of the member and the cooling method.
Auto-tempering greatly affects the strength of martensitic steels and is closely related to quench cracking and distortion of members, so there is a need to accurately evaluate the effect of auto-tempering that depends on the cooling rate from an industrial perspective. In addition, although simulation technology has advanced and the accuracy of strength and distortion prediction has improved, the effect of auto-tempering has not been taken into account, so it is necessary to quantitatively evaluate the effect of auto-tempering in order to perform simulations with higher accuracy. In this way, the industrially important phenomenon of auto-tempering of martensite has been elucidated using analytical instruments such as electron microscopes10) and atom probe tomography (APT),11) but there are no examples of quantitative evaluation.
Therefore, this study aimed to determine the true hardness of quenched martensite unaffected by auto-tempering and then to quantitatively evaluate the effect of auto-tempering that occurs after martensitic transformation by the diffusion area, which is the product of the diffusion coefficient of carbon in bcc iron and the retention time, in order to enable hardness prediction.
The specimens used were carbon steels (S25C, S35C, S45C, and S55C) with carbon contents of 0.20 to 0.55% and chromium-molybdenum steels (SCM420, SCM435, and SCM440) with approximately 1 to 1.2 mass% chromium and 0.17 mass% molybdenum as shown in Table 1. The chromium-molybdenum steel was subjected to homogenization treatment at 1200°C for 3 hours to reduce the effect of element segregation. The degree of auto-tempering varies depending on the cooling rate and Ms temperature. Therefore, to obtain the fastest possible cooling rate, the specimens were 16 mm in diameter and 3 mm thick, and the temperature was measured by drilling a hole 1.1 mm in diameter from the steel surface and fixing a sheathed thermocouple at a depth of 8 mm. Figure 1(a) shows the specimen geometry. The specimens were solution treated at 890°C for 0.5 hours and then rapidly cooled in stirred cold 5% NaCl aqueous solution to form a martensitic structure. The hardness of the as-quenched specimens was measured after holding them at room temperature for about one hour after quenching, while the others were stored at about −20°C and then tempered for one hour at temperatures ranging from 150°C to 600°C, which are the industrial low-temperature and high-temperature tempering conditions, respectively. The hardness of the specimens was evaluated by Vickers hardness test (load: 2.9 N). To reduce the effects of auto-tempering as much as possible, hardness was measured at a depth of 0.5 mm from the cut surface (3 × 16 mm) of the specimen. Measurements were taken five times, and the average value was taken as the hardness of each specimen. The transformation temperature was measured with a phase-transformation tester using high-induction heating system. Figure 1(b) shows a schematic diagram of the thermal expansion curve. The temperatures at the intersections of the tangent to the thermal contraction curve during cooling after solution treatment and the tangent to the expansion curve due to martensitic transformation were taken as the Ms and Mf temperatures. Meanwhile, many studies have been conducted on the relationship between the Ms temperature and alloy composition in martensitic steel, and the following equation has been obtained:12)
| (3) |
It was confirmed that the Ms temperature obtained experimentally was almost the same as that obtained from Eq. (3). The M50 temperature was defined as the temperature at which the thermal expansion curve overlaps the midpoint between the tangent to the thermal contraction curve during cooling after solution treatment and the tangent to the thermal contraction curve below the Mf temperature.
| C | Si | Mn | P | S | Cr | Mo | Ni | Cu | Ms (°C) | M50 (°C) | γR (%) | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| S25C | 0.271 | 0.198 | 0.472 | 0.016 | 0.015 | 0.129 | – | 0.011 | 0.001 | 410 | 372 | 0 |
| S35C | 0.363 | 0.185 | 0.746 | 0.017 | 0.017 | 0.106 | – | 0.016 | 0.011 | 338 | 301 | 0 |
| S45C | 0.450 | 0.210 | 0.720 | 0.017 | 0.012 | 0.180 | – | 0.010 | 0.010 | 282 | 254 | 0 |
| S55C | 0.520 | 0.160 | 0.730 | 0.015 | 0.014 | 0.140 | – | 0.020 | 0.010 | 262 | 232 | 2 |
| SCM420 | 0.223 | 0.305 | 0.811 | 0.010 | 0.019 | 1.194 | 0.168 | 0.026 | 0.013 | 430 | 394 | 0 |
| SCM435 | 0.370 | 0.168 | 0.739 | 0.013 | 0.020 | 1.139 | 0.171 | 0.018 | 0.014 | 345 | 310 | 0 |
| SCM440 | 0.425 | 0.301 | 0.794 | 0.014 | 0.004 | 1.041 | 0.175 | 0.014 | 0.016 | 318 | 290 | 0 |
The amount of retained austenite was quantified by saturation magnetization measurement,13) and it was confirmed that S55C steel had about 2% retained austenite, while the other steels had a single martensite structure. Table 1 lists the Ms and M50 temperatures and the amount of retained austenite in the steels used.
JIS standard round bar specimens (φ25 × 100 mm) were used as Jominy test pieces, and the temperature was measured by drilling holes with a diameter of 1.1 mm from the steel surface at multiple locations at a predetermined distance from the quench end and fixing the thermocouple in the center of each test piece. The heating conditions in the Jominy test were 845°C for 0.5 hours, and the test was conducted by one end spray quenching in accordance with JIS G 0561. Hardness was evaluated by Vickers hardness test (load: 2.9 N). Jominy test pieces were cut parallel to the axial direction and then measured in the longitudinal direction at the center of the cut surface (25 × 100 mm).
Figure 2 shows the hardness of carbon steel and chromium-molybdenum steel tempered for one hour at various temperatures after quenching, which were organized by tempering temperature. It shows that in the temperature range above 200°C, the hardness decreases monotonically as the tempering temperature increases. A particularly pronounced softening is observed in the temperature range below 350°C, and it can be assumed that carbon lattice diffusion is involved in the softening, at least in this temperature range. It should be noted that for low-carbon steels with relatively high Ms temperatures, the hardness does not decrease in the tempering temperature range below 200°C and remains almost constant. This suggests that auto-tempering may have occurred during quenching in low-carbon steels with high Ms temperatures.
Here, assuming that the tempering rate in the temperature range below 350°C is determined by carbon lattice diffusion, the data were reorganized using the diffusion area S (= ∑Dt). The diffusion coefficient D is usually expressed as a function of temperature T by the following equation:
| (4) |
where D0, Q, and R are the frequency term, the activation energy of lattice diffusion, and the gas constant (8.3145 J/(mol-K)), respectively. Regarding carbon diffusion in bcc-Fe, Kunitake summarized previously reported diffusion coefficients obtained by the decarburization method or the delay time measurement of atomic diffusion in internal friction.14) He then presented the most reliable D value available in the temperature range from room temperature to 800°C, although the reported activation energies of diffusion coefficients have been varied from approximately 70 to 100 kJ/mol, depending on researchers. The authors attempted to fit the data using Eq. (4) and derived optimal values of 91 kJ/mol and 5.7 × 10−6 m2/s for D0 and Q, respectively. As shown in Eq. (4), the value of D is given as a function of tempering temperature T, and the diffusion area S can be calculated by setting t = 3.6 ks for one hour. Figure 3 shows the calculation results of Eq. (4) and the M50 temperatures of each specimen. The diffusion coefficient D is very small below 300°C, but increases rapidly above 300°C, so it can be said that the effect of auto-tempering is more pronounced in steels with an M50 temperature above 300°C. Figure 4 shows the data from Fig. 2 as a function of the diffusion area S in the temperature range below 350°C. For the as-quenched specimens, the tempering reaction hardly progresses at room temperature, but since they were kept at room temperature for about one hour after quenching before measuring the hardness, the diffusion area S was calculated as that after tempering at 20°C for one hour. As shown in Fig. 3 above, the diffusion coefficient of carbon below 350°C is extremely small, and it is known that there is almost no effect of auto-tempering when the martensitic transformation temperature is below 350°C.8) As shown in Table 1, the Ms temperatures of S45C, S55C, and SCM440 are below 350°C. However, if the Ms temperature is too low, austenite may remain, resulting in low hardness. Therefore, the softening curves of S45C and SCM440 were taken as standard functions for both steels, and the hardness of the steels is expressed by the following equations, respectively:
| (5) |
| (6) |
Next, a proportionality factor A was introduced for the hardness of the two steels with different carbon contents, which is expressed by the following equations:
| (7) |
| (8) |
The proportionality factor A was then adjusted to the optimum value so that the above equations matched the experimental data. The resulting fitting curves are shown as solid curves in Fig. 4. The white plots in the figure show the hardness of the quenched materials as estimated from the fitting curves and are considered to represent the “true hardness” of the quenched materials that have not been affected by auto-tempering. Hereafter, the hardness of martensite unaffected by auto-tempering is referred to as the true hardness and denoted as HV*. For steels with high Ms temperatures, the HV* values estimated from the fitting curves are all higher than the experimental values. Table 2 lists the A value and HV* value corresponding to each fitting curve shown in the figure.
| Steel | Coefficient A | HV* (GPa) |
|---|---|---|
| S55C | 1.06 | 7.72 |
| S45C | 1 | 7.28 |
| S35C | 0.92 | 6.70 |
| S25C | 0.84 | 6.12 |
| SCM440 | 1 | 7.03 |
| SCM435 | 0.94 | 6.61 |
| SCM420 | 0.80 | 5.62 |
To date, to clarify the effect of solute carbon on HV*, it was first necessary to know the hardness of martensite without carbon. Industrially used martensitic steels contain small amounts of alloying elements such as Mn and Cr. In this paper, carbon-free martensite is referred to as “pure iron martensite” for convenience. The hardness of quenched low-carbon martensite has been studied in detail by Ueno et al.15) and Speich et al.16) Figure 5 shows the results reorganized in terms of the relationship between the square root of the carbon content and the Vickers hardness. There is a good linear relationship between the two, and the hardness of pure iron martensite can be estimated to be about 1.75 GPa-HV from the extrapolated values of the fitting lines. Figure 6 shows the results organized in terms of the relationship between the hardness and HV* of pure iron martensite, and the carbon content. As a result, the following equation was obtained as an approximate curve that optimally connects all the data:
| (9) |
It is generally known that the degree of solid solution strengthening is proportional to the square root of the amount of alloying elements,17) and Uranaka et al. recently reported that the hardness of quenched martensitic steel can be organized by the half power of the solute carbon content, and that the effect of microstructure-dependent strengthening factors such as dislocation strengthening and grain refinement strengthening is relatively small.18) The authors also confirmed that the effect of austenite grain size is negligible for the hardness of SCM440 with varying austenite grain size in the range of 5 to 50 μm. However, the dislocation density of martensitic steel tends to increase with carbon content,19) and the above equation shows that the hardness of martensitic steel increases in proportion to the square root of the carbon content, including the effects of the frictional force in the matrix and dislocation strengthening.
Thus, it is now possible to estimate the true hardness of the martensite, which is not affected by auto-tempering, so in this study, the hardness HV of the specimen, which is affected by tempering, divided by HV* is called the “quench hardening rate” and is denoted as Hs:
| (10) |
Figure 7 shows Hs organized as a function of the carbon diffusion area S for the steels used in this study. In Fig. 7(a), it is assumed that the activation energy of carbon diffusion is 91 kJ/mol for both carbon and chromium-molybdenum steels. The results show that although the trends are almost the same, there are variations depending on the type of steel. This is considered to be because the addition of alloying elements changes the activation energy of carbon diffusion in bcc-Fe.14) Therefore, Hs is recalculated assuming that the activation energy of carbon diffusion in chromium-molybdenum steel is 98 kJ/mol. The results are shown in Fig. 7(b). Both carbon steel and chromium-molybdenum steel are plotted almost on the same curve, which is expressed by the following equation:
| (11) |
To verify the validity of this relationship, the same calculation was also performed using the data reported for nickel-chromium and nickel-chromium-molybdenum steels with the chemical compositions given in Table 3.20) The results are shown in Fig. 8. Here, assuming that the activation energy of carbon diffusion is 98 kJ/mol for nickel-chromium steel, and 103 kJ/mol for nickel-chromium-molybdenum steel, they can be plotted almost on the same curve. Since there are no reports on the effect of alloying elements on the activation energy of carbon diffusion below 400°C, the validity of these values cannot be verified, but by using these values, the quench hardening rate can be determined uniquely of the steel type. The quoted hardness values were measured in the tempered specimens that were oil-quenched after solution-treatment, but since there are no data on the cooling curve, it is not possible to determine the S value during cooling. However, there is a noticeable effect of auto-tempering, and since it is equivalent to Hs = 0.8, the S value is estimated to be 1.59 × 10−12 m2. In the range of S values from 10−9 to 10−12 m2, the data lie on the curve expressed by Eq. (9). Thus, if the activation energy of carbon diffusion is known for each steel type, the quench hardening rate Hs is given by Eq. (11) for the steel type. That is, if the S value is known, Hs can be obtained from Eq. (11), and the hardness of tempered martensite can be estimated from Eqs. (9) and (10).
| C | Si | Mn | P | S | Cr | Mo | Ni | |
|---|---|---|---|---|---|---|---|---|
| SNC631 | 0.26–0.35 | 0.15–0.35 | 0.35–0.65 | <0.030 | <0.030 | 0.60–1.00 | – | 2.50–3.00 |
| SNC836 | 0.32–0.40 | 0.15–0.35 | 0.35–0.65 | <0.030 | <0.030 | 0.60–1.00 | – | 3.00–3.50 |
| SNCM625 | 0.20–0.30 | 0.15–0.35 | 0.35–0.60 | <0.030 | <0.030 | 0.60–1.00 | 0.15–0.30 | 3.00–3.50 |
| SNCM431 | 0.27–0.35 | 0.15–0.35 | 0.60–0.90 | <0.030 | <0.030 | 0.60–1.00 | 0.15–0.30 | 1.60–2.00 |
| SNCM439 | 0.36–0.43 | 0.15–0.35 | 0.60–0.90 | <0.030 | <0.030 | 0.60–1.00 | 0.15–0.30 | 1.60–2.00 |
| SNCM447 | 0.44–0.50 | 0.15–0.35 | 0.60–0.90 | <0.030 | <0.030 | 0.60–1.00 | 0.15–0.30 | 1.60–2.00 |
When cooling from a high temperature range, the temperature changes continuously with time, and the degree of auto-tempering varies with the cooling rate. Therefore, the degree of auto-tempering should be evaluated by the integrated diffusion area of carbon according to the cooling curve. Figure 9 shows the cooling curve during quenching and how to determine the integrated diffusion area of carbon S. Regarding the martensitic transformation of steel, there is a large difference between the Ms and Mf temperatures, and even within a single austenite grain, there are martensite formed just below the Ms temperature and that formed just above the Mf temperature.21) In other words, the degree of auto-tempering varies depending on the temperature at which martensite is formed. Therefore, in this study, in order to average the degree of auto-tempering, the M50 temperature, at which the volume fraction of martensitic transformation reaches 50%, was used as a convenient starting temperature for transformation to determine the integrated diffusion area S of carbon in the temperature range below it. Figure 10 shows the difference between the Ms and M50 temperatures obtained from the transformation curve. When the carbon content is 0.3 mass% or less, the temperature difference is about 37°C, but when it exceeds 0.3 mass%, the temperature difference tends to decrease. Since auto-tempering occurs significantly in low-carbon steels with high Ms temperatures, this study focused on data for steels with carbon content of 0.3 mass% or less, and evaluated the temperature given by Eq. (12), which shifts Eq. (3) to the lower temperature side by 37°C, as the M50 temperature (M50 = Ms − 37):
| (12) |
For the steels used in this study, the experimentally determined M50 temperature is confirmed to be almost equal to the value obtained by the above equation.
To quantitatively evaluate the effect of auto-tempering, the cooling rate must be accurately determined, but it is difficult to do so for practical members due to their size and location. In the Jominy test, however, the cooling rate corresponding to the distance from the quench end is known, so the degree of auto-tempering can be estimated for each location. Figure 11 shows the relationship between the distances from the quench end and the cooling curves of the Jominy test pieces. Naturally, the greater the distance from the quench end, the slower the cooling rate, and it is expected that the effect of auto-tempering will be more significant. Table 4 shows the quench hardening rate Hs and hardness HV obtained from Eqs. (10) and (11) using the integrated diffusion area S of carbon from the M50 temperature to 100°C based on the cooling curves shown in Fig. 11 for SCM440 (M50 temperature: 282°C) and SCM420 (M50 temperature: 364°C), as well as the experimentally obtained hardness HV and Hs obtained from the hardness. The calculated hardness of the quench end was defined as HV*. If the distance from the quench end is the same, the cooling rate is the same, but since the M50 temperature is about 100°C higher in SCM420 than in SCM440, the carbon diffusion area S is about an order of magnitude larger in SCM420. For example, for SCM420, the carbon diffusion area S at 1 mm from the quench end is about 1.0 × 10−13 m2, which corresponds to the S value when tempered at about 200°C for one hour. Figure 12 shows the hardness calculated in this way and the actual measured values. For SCM440, the calculated and experimental values are in close agreement. It should be noted here that the hardness at the quench end is the same as the hardness obtained from Eq. (9), and that pronounced auto-tempering has already occurred at a distance of only 1 mm from the quench end. On the other hand, SCM420 does not achieve hardness equivalent to the true hardness HV* at the quench end. This result suggests that for steel types with high Ms temperatures, auto-tempering cannot be suppressed even by rapid cooling. In other words, for SCM420, auto-tempering occurs even if a thin specimen is quenched in cold 5% NaCl aqueous solution. In addition, to verify the validity of the quantitative evaluation method of auto-tempering proposed in this study, a comparison was made between the measured hardness reported by Tsuya22) and the calculated values shown. In the Jominy test, the cooling curve is uniquely determined if the distance from the cooling end is the same, so the change in hardness was determined by the same calculation as in this test. The results are shown in Fig. 13. The calculated values and experimental values were in good agreement, confirming that the evaluation method proposed in this study can be applied to different steel types.
| z (mm) | Calcuratated Value | Experimental Value | |||||
|---|---|---|---|---|---|---|---|
| S (m2) | Log S | Hs | HV (GPa) | HV (GPa) | Hs | ||
| SCM440 (M50: 282°C) | 0 | 1 | 7.09 [HV*] | 7.02 | 0.990 | ||
| 1 | 7.845×10−15 | −14.11 | 0.921 | 6.54 | 6.34 | 0.894 | |
| 3 | 2.410×10−14 | −13.62 | 0.900 | 6.39 | 6.23 | 0.900 | |
| 5 | 4.258×10−14 | −13.37 | 0.889 | 6.31 | 6.13 | 0.889 | |
| SCM420 (M50: 282°C) | 0 | 1 | 5.69 [HV*] | 4.89 | 0.859 | ||
| 1 | 1.026×10−13 | −12.99 | 0.869 | 4.90 | 4.69 | 0.824 | |
| 3 | 2.410×10−14 | −12.54 | 0.845 | 4.76 | 4.44 | 0.780 | |
| 5 | 4.258×10−14 | −12.33 | 0.833 | 4.69 | 4.31 | 0.757 | |
In the introduction above, we pointed out the problem with the widely used tempering parameter, P.6) Finally, to reconfirm the problem, the Hs values obtained in this study were organized based on tempering parameters. The results are shown in Fig. 14. In Fig. 7(b), the data organized by P value shows greater variability than the data organized by S value. This may be because the P value does not take into account the factor that corrects the effect of alloying elements on carbon diffusion. The most important feature of the method proposed in this study using the diffusion area as a parameter is that it corrects the effect of alloying elements on the diffusion coefficient D by the activation energy Q, and therefore it can evaluate the temper softening behavior of all steels based on the carbon diffusion area alone.
(1) The true hardness HV* of quenched martensite not affected by auto-tempering is given by the following equation as a function of carbon content (mass%C):
(2) By adopting the quench hardening rate Hs, which is obtained by dividing the hardness HV of tempered martensitic steel by HV*, the temper softening behavior of martensitic steel can be uniformly evaluated regardless of the carbon content of the steel.
(3) For tempering in the temperature range below 400°C, the following equation is established between the diffusion area S (= Dt), which is the product of the diffusion coefficient D for carbon lattice diffusion in bcc iron and the holding time t, and Hs:
However, if the frequency term for carbon lattice diffusion is 5.7 × 10−6 m2/s, the activation energy of diffusion is 91 kJ/mol for ordinary carbon steel, 98 kJ/mol for SCM steels, and 103 kJ/mol for SNCM steels. For quenched materials, it can be considered that the smaller the Hs value obtained in the experiment, the greater the degree of auto-tempering that occurs during quenching.
(4) For continuous cooling, the degree of auto-tempering can be accurately and quantitatively evaluated by substituting the integrated diffusion area S (=∫D(T)dt) below the M50 temperature into the above equation. It was also confirmed that the experimental data obtained in the Jominy test and the hardness calculated using the above equation were in good agreement.
