2023 Volume 64 Issue 6 Pages 1217-1224
To clarify the effects of vanadium additions on the strengthening mechanisms of tempered martensitic steel, the microstructures, precipitates, dislocation densities, and tensile properties of water-quenched and tempered Fe–0.2C–0.5Si–2.5Mn–xV (mass%; x = 0–0.82) steels were analyzed. The vanadium carbide precipitates were plate-shaped and had a Baker–Nutting orientation relationship with the ferrite matrix. The size and shape of the vanadium carbide precipitates on the slip plane were considered when evaluating the contribution of precipitation strengthening. The increase in yield strength upon adding 0.82 mass% vanadium to the tempered steel was mainly caused by precipitation strengthening owing to the vanadium carbide precipitates and dislocation strengthening owing to the high dislocation density. This study demonstrates that the contribution of precipitation strengthening might be overestimated if it is assumed that the precipitates all hinder dislocation motion by the Orowan mechanism.
This Paper was Originally Published in Japanese in J. Jpn. Soc. Heat Treatment 61 (2021) 5–12. Abstract was modified and Ref. 8) was added.
Fig. 10 Schematic illustration showing the shape of VC on a slip plane {110} in ferrite matrix.
Tempered martensitic steels produced by quenching and tempering are commonly used high-strength steels. The addition of vanadium to tempered martensitic steel retards temper softening and causes secondary hardening.1) Klemm-Toole et al.2) evaluated the strengthening mechanisms that contributed to this secondary hardening effect and claimed that it was caused by precipitation strengthening owing to the precipitation of vanadium carbide (VC) particles, as well as dislocation strengthening owing to the higher dislocation density in alloys with higher vanadium contents. They concluded that this higher dislocation density resulted from the higher volume fraction of MX precipitates, which slowed the recovery of dislocations during tempering. Although the strengthening mechanisms have been extensively analyzed, there are two aspects that require further analysis. First, hardness measurements are conducted in a region beyond the yield point, indicating that dislocations would have already been generated and would be increasing during the measurement. Therefore, the effect of vanadium on the strengthening mechanism of tempered martensite should be investigated in the yield strength region in which dislocation nucleation commences. Second point, the shape of of fine VC precipitates should be carefully considered when calculating the contribution of precipitation strengthening. VC precipitates exhibit a Baker–Nutting (B-N) orientation relationship with the ferrite matrix.3) It has been suggested that fine VC precipitates with a B-N orientation relationship with the ferrite matrix are plate-shaped;4) however, a previous study2) employed the Orowan model when determining the contribution of precipitation strengthening, which assumes that the precipitates are spherical.
Estimations of the contribution of precipitation strengthening differs depending on whether the Orowan mechanism or cutting mechanism is assumed. In addition, the way in which the size of the precipitates on the slip plane is estimated may affect the results. For example, in one study, the researchers used the volume of the precipitates, as obtained by observations, to calculate the spherical diameter of particles, and used this value to estimate the size of the precipitates on the slip plane.5) However, in another study, the researchers calculated the size of the intersection between plate-shaped particles and the slip plane.6) The magnitude of the precipitation strengthening contribution was closer to the experimentally obtained result when using the intersection size of plate-shaped particles rather than the spherical diameter. Thus, the way in which the shape and size of the precipitates is handled affects estimations of the contribution of precipitation strengthening.
In this study, we aimed to investigate the effect of vanadium on the strengthening mechanism in tempered martensitic steel with 0 to 0.82 mass% vanadium. Tensile tests were performed to determine the yield strength, and the strengthening mechanisms were evaluated based on dislocation density analysis and observations of the microstructure and precipitates. Furthermore, the shape of the precipitates on the slip plane was considered when estimating the contribution of precipitation strengthening.
The compositions of the steel used in this study was Fe–0.20C–0.50Si–2.5Mn–xV (mass%), where the vanadium content (x) was varied from 0 to 0.82 mass%. Table 1 lists the chemical compositions of the specimens.
Steel ingots (50 kg) with the compositions in Table 1 were obtained by vacuum melting. The ingots were heated to 1250°C and hot-rolled to a thickness of 2.6 mm with a finish rolling temperature of 900°C, after which they were water-quenched in water. Some of the water-quenched steel plates were then heat-treated at 600°C for 1 h in an Ar atmosphere and air-cooled to fabricate tempered steel plates.
The mechanical properties of the specimens were evaluated using room-temperature tensile tests. JIS No. 5 specimens with a parallel length of 60 mm, width of 25 mm, and thickness of 2.6 mm were cut from the water-quenched and tempered steel plates. The tensile direction was parallel to the width of the hot-rolled plate. Room-temperature tensile tests were conducted at a gauge distance of 50 mm and constant crosshead speed of 3.0 mm/min. The nominal stress and strain were used to determine the true stress and strain. For each test, the slope (Δss) of the true stress–true strain curve was obtained, and Δss was plotted against the true stress at 0.2 s intervals. The yield strength was defined as the true stress at which Δss suddenly decreased from a constant value of approximately 200 GPa.
X-ray diffraction (XRD) specimens were prepared by mechanical polishing followed by chemical polishing to remove the damaged layer. XRD was performed using a Cu Kα X-ray source without a monochromator. The plotted XRD line profile was analyzed using the method reported by Takebayashi et al.7) to determine the dislocation density.
The crystal orientation of the water-quenched steels was analyzed using electron backscatter diffraction (EBSD). The microstructures and precipitates of both the water-quenched and tempered steels were observed using scanning electron microscopy (SEM) and transmission electron microscopy (TEM), respectively. A JEOL JSM-7200F field-emission scanning electron microscope was used for the microstructural observations and EBSD measurements. The specimens were cut from the plates such that the observation plane was the cross-section of the rolling direction, followed by mechanical and electrolytic polishing. TEM observations were conducted using a JEOL JEM 2100F microscope for thin-film specimens and a JEOL JEM2100 microscope for replica specimens. The specimens for TEM observations were cut out such that the observation planes were the horizontal plane. For the thin-film specimens, electrolytic polishing was conducted using the twin-jet method until a hole formed in the center of the specimen. The replica specimen was prepared by the extraction replica method.8) During TEM examinations of the replica specimens, energy-dispersive X-ray spectrometry (EDX) was used to analyze the chemical composition of the precipitates. The thickness of each thin-film specimen was measured using a Keyence VK-X100 laser microscope.
Figure 1 shows the nominal stress–nominal strain curve for the tempered steels with various vanadium contents. The yield and tensile strengths increased with increasing vanadium content. Each nominal stress–nominal strain curve was used to calculate a true stress and the true stress–true strain curve, from which the slope of the curve, Δss was plotted against the true strain. Figure 2 shows the Δss-true stress curve for the tempered steel with 0.82 mass% vanadium (denoted as 0.82 V). In the low true stress region (below approximately 1200 MPa), Δss was approximately constant at 200 GPa, whereas when the true stress reached approximately 1200 MPa, Δss sharply decreased. The yield strength was defined as the true stress at which Δss sharply decreased. Figure 3 shows the yield strengths of the water-quenched and tempered steels with different amounts of vanadium. The yield strength of the water-quenched steels were approximately constant for all vanadium content, whereas those of the tempered steels sharply increased with increasing vanadium content, and began to plateau as the vanadium content approached 1.0 mass%. The yield strengths of the 0.82 V and 0 V tempered steels (which contained the largest amount of vanadium and no vanadium, respectively) were 1200 and 586 MPa, respectively, indicating that the vanadium addition increased the yield strength of the tempered steel 614 MPa. To analyze this difference in yield strength, these steels were analyzed by microstructural observations, dislocation density measurements, and precipitate observations.
Nominal stress-nominal strain curves of the tempered steels.
Slope Δss as a function of true stress in tempered 0.82 V.
Changes in yield stress as a function of V content in the water-quenched steels and tempered steels.
The microstructure of the water-quenched samples were obsereved by SEM. Figure 4 shows the microstructures of the 0 V and 0.82 V. The overall microstructure of the 0.82 V steel was slightly finer, but the vanadium addition did not seem to change the microstructural morphology. TEM observations confirmed that the 0 V steel did not contain residual austenite and that it had a fully martensitic structure. SEM observations of the 0 V tempered steel showed that it contained a large amount of dispersed cementite. The average diameter of the cementite particles, assuming they were spherical, was 85 nm. The prior austenite grain size distributions in the 0 V and 0.82 V water-quenched steels were evaluated by crystal orientation analysis based on the EBSD results of the martensitic microstructures. To reconstruct the prior austenite grains and determine the grain size distribution, the crystal orientation information was input into an automatic variant analysis program for bainitic and martensitic microstructures.9) Figure 5 shows the prior austenite grain size distributions. No significant differences were observed between the prior austenite grain size distributions for 0 and 0.82 V samples.
SEM images of water-quenched 0 V (a) and water-quenched 0.82 V (b).
Prior austenite grain size distribution in water-quenched 0 V (a) and water-quenched 0.82 V (b).
Fine carbides were expected to precipitate during tempering of the 0.82 V steel. In martensitic steels, fine carbides can suppress the recovery of dislocations during tempering, resulting in a high dislocation density, even after tempering. To determine whether this occurred here, the 0 V and 0.82 V tempered steels were investigated by XRD to compare the dislocation densities. The dislocation density of the 0 V tempered steel was 3.0 × 1013/m2. The XRD profile of the 0.82 V tempered steel had a wider tail, which was attributed to elastic strain between the VC particles and the substrate, and the maximum measured dislocation density was 3.9 × 1014/m2.
3.4 Precipitate observation resultsTo evaluate the effect of precipitation strengthening, the precipitates in the 0.82 V tempered steel were observed by TEM using a thin-film specimen. Figure 6 shows a bright field TEM in which the incident electron beam direction was along the [001] crystallographic axis of the ferrite grain. Multiple linear precipitates were observed, which each had a length of approximately 5–20 nm and were observed to intersect at right angles and were oriented along two perpendicular directions. The electron diffraction patterns confirmed that these precipitates comprised VC. Figures 6(a) and (b) show typical electron diffraction patterns. VC typically has a NaCl-type face-centered cubic structure and a B–N orientation relationship with the ferrite (α) matrix in which it precipitates, as expressed by eq. (1).3)
| \begin{equation} \begin{split} & (100)_{\text{VC}}//(100)_{\alpha} \\ & [010]_{\text{VC}}//[011]_{\alpha} \end{split} \end{equation} | (1) |
TEM bright field image showing contrasts caused by precipitates in a 0.82 V specimen tempered at 600°C for 1 h; incident electron beam direction is parallel to the 001 direction of the ferrite matrix. The selected area electron diffraction (SAED) patterns are indicated for precipitates (b) and (c).
We aimed to verify whether the VC in this steel specimen satisfied this orientation relationship. Two of the three variants of the B–N orientation relationship can be excited when the incident beam is parallel to the [001]α axis, resulting in a dark-field image. Figure 7 shows the dark-field images under the two excitation conditions corresponding to the electron diffraction patterns in Figs. 6(b) and (c). This visual field includes the area shown in Fig. 6. Linear precipitates with both variants were observed in the ferrite matrix. Linear precipitates were observed in the ferrite matrix. Therefore, a B-N orientation relationship, as expressed by eq. (1), exists between VC precipitates and the ferrite matrix in these steel specimens. The average lengths and widths of the precipitates, as determined using image analysis, were 10 and 0.80 nm, respectively.
TEM dark field images of tempered 0.82 V; the incident electron beam direction is parallel to the 001 direction of the ferrite matrix. The images were taken under a condition of g*VC = 200 and g*VC = 020 using diffraction spots indicated by the arrows in Fig. 6(b), (c).
VC precipitates that show a B–N orientation relationship with the ferrite matrix tend to be plate-shaped, with the {100} planes as the habit planes.10,11) Although the precipitates in the bright-field (Fig. 6) and dark-field images (Fig. 7) appeared to be linear, these may be cross-sections of plate-shaped VC particles, where the linear width corresponds to the thickness of the plates.
Figure 8 shows the TEM observation results of specimens prepared using the replica method. A circular precipitate with a diameter of 10 nm was observed in the center of the observation field. Chemical composition analysis using EDX showed that this precipitate contained vanadium as the main component. Because the sizes of the VC precipitates in Figs. 6 and 7 were consistent with the diameter of this circular precipitate, it was inferred that the circular precipitate was a plate-shaped VC precipitate like those in Figs. 6 and 7, but observed in the perpendicular direction. Therefore, when calculating the precipitate volume fraction and analyzing the increase in yield strength of the 0.82 V tempered steel, the VC precipitates were assumed to be disk-shaped, with average diameters and thicknesses of 10 and 0.80 nm, respectively.
TEM image of the carbon extraction replica in a 0.82 V specimen tempered at 600°C for 1 h; precipitates are indicated by arrows.
The precipitate volume fraction is required to calculate the contribution of precipitation strengthening to the increase in yield strength. To estimate the precipitate volume fraction, the total precipitate volume was calculated from the image analysis results of Fig. 7 and divided by the volume of the specimen in the observation field, which was calculated based on the measured thickness (34 nm). Thus, the precipitate volume fraction was estimated to be 1.7 vol%. The precipitate volume fraction in the equilibrium state at 600°C, as calculated using Thermo-Calc 2019a (data Base TCFE8) and the chemical composition of the 0.82 V steel, was 1.6 vol%. Assuming there was no significant change in the precipitate volume fraction between 600°C and room temperature, 1.6 vol% was used as the precipitate volume fraction in the equilibrium state. Because the estimated precipitate volume fraction for the thin-film specimen was almost the same as the volume fraction in the equilibrium state, approximately the equilibrium amount of plate-shaped VC precipitated.
In this section, the yield strengths of the 0 V and 0.82 V tempered steels are discussed to clarify the effect of vanadium on the strengthening mechanisms of tempered martensite. Based on the results in Section 3, the yield strengths of the 0 V and 0.82 V tempered steels can be described as follows:
| \begin{equation} \sigma_{\text{0V}} = \sigma_{0} + \sigma_{\text{ss,0V}} + \sigma_{\text{gb,0V}} + \sigma_{\rho,\text{0V}} + \sigma_{\text{prec},\theta} \end{equation} | (2a) |
| \begin{equation} \begin{split} \sigma_{\text{0.82V}} & = \sigma_{0} + \sigma_{\text{ss,0.82V}} + \sigma_{\text{gb,0.82V}} + \sigma_{\rho,\text{0.82V}} \\ & \quad + \sigma_{\text{prec,VC}} \end{split} \end{equation} | (2b) |
By subtracting eq. (2a) from eq. (2b) and summarizing for each term, the difference in yield strength can be written as
| \begin{equation} \begin{split} \sigma_{\text{0.82V}} - \sigma_{\text{0V}} & = (\sigma_{\text{ss,0.82V}} - \sigma_{\text{ss,0V}}) + (\sigma_{\text{gb,0.82V}} - \sigma_{\text{gb,0V}}) \\ &\quad + (\sigma_{\rho,\text{0.82V}} - \sigma_{\rho,\text{0V}}) + \sigma_{\text{prec,VC}} - \sigma_{\text{prec},\theta} \end{split} \end{equation} | (3) |
When considering the impact of solid solution strengthening, all alloying elements were assumed to be in solid solution in the water-quenched steel. The yield strength of the 0.82 V water-quenched material was the same value as that of the 0 V water-quenched steel (Fig. 3). Furthermore, as described in Section 3.4, the 0.82 V tempered steel exhibited similar VC precipitation volume to that of the equilibrium state at 600°C. The amount of solute vanadium in the equilibrium state at 600°C was minimal, at 0.84% of the total vanadium addition. Therefore, the contribution of the solid solution strengthening by solute vanadium to yield strength of the 0.82 V tempered steel was negligible.
The results in Section 3.2 demonstrate that there were no significant differences between the prior austenite grain size distributions of the 0 V and 0.82 V water-quenched steels. Therefore, the difference between the crystal grain refinement strengthening contributions of the 0 V and 0.82 V materials (σgb,0.82V − σgb,0V) was assumed to be minimal.
The results in Section 3.3 show that the 0.82 V tempered steel had a maximum dislocation density of 3.9 × 1014 m−2, which is significantly higher than that of the 0 V tempered steel (3.0 × 1013 m−2). This is consistent with reports that the presence of fine carbides suppresses the recovery of martensitic steels during tempering, resulting in a high dislocation density, even after tempering.12,13) The relationship between the dislocation density ρ and dislocation strengthening contribution σρ is expressed by the Bailey–Hirsh relation:
| \begin{equation} \sigma_{\rho} = \sigma_{0} + \alpha Gb\sqrt{\rho} \end{equation} | (4) |
Regarding the contribution of precipitation strengthening, there are two mechanisms by which precipitates may strengthen a material, depending on the size of the precipitates on the slip plane. The first is the cutting mechanism, whereby the strength increase comes from dislocations shearing precipitates, and the second is the Orowan mechanism, whereby dislocations cannot shear the precipitates and must instead bypass them, leaving dislocation loops.
In the pinning model, which considers the pinning effect of particles on dislocations,16,17) dislocation shearing of a particle (i.e., cutting) occurs when the linear tension T of the dislocation overcomes the resistance force Fm of the particle at the critical dislocation overhang angle θc. The corresponding shear stress τ can be approximately expressed by eq. (5), where λ is the average interparticle spacing and b is the magnitude of the Burgers vector of the matrix.
| \begin{equation} \begin{split} \tau & = \frac{2T}{\lambda b}\left(\frac{F_{\text{m}}}{2T} \right)^{3/2}\quad \text{when $\theta_{\text{c}} \geq 100{}^{\circ}$} \\ \tau & = \frac{0.8}{\lambda b}F_{\text{m}}\qquad\quad \text{when $\theta_{\text{c}} \leq 100{}^{\circ}$} \end{split} \end{equation} | (5) |
Because cementite and VC are hard particles, their frictional force constitutes a significant resistance force against dislocation motion.18) For a spherical particle with diameter ds, Fm can be defined using the shear strength τc of the particle:
| \begin{equation} F_{\text{m}} = d_{\text{s}}b\tau_{\text{c}} \end{equation} | (6) |
Therefore, from eq. (5), the strengthening contribution by the cutting mechanism σcutting can be determined using the Taylor factor M, by employing the expression T = βGb2, where β is the linear tension coefficient, G is the matrix rigidity, and b is the magnitude of the Burgers vector of the matrix.
| \begin{equation} \begin{split} \sigma_{\text{cutting}} & = M\tau = \frac{M(d_{\text{s}}\tau_{\text{c}})^{3/2}}{\lambda(2\beta Gb)^{1/2}}\quad \text{when $0 \leq d_{\text{s}} \leq 0.64\frac{2\beta Gb}{\tau_{\text{c}}}$} \\ \sigma_{\text{cutting}} & = M\tau = \frac{0.8}{\lambda}Md_{\text{s}}\tau_{\text{c}}\quad \text{when $0.64\frac{2\beta Gb}{\tau_{\text{c}}} \leq d_{\text{s}} \leq \frac{2\beta Gb}{\tau_{\text{c}}}$} \end{split} \end{equation} | (5′) |
Using eq. (5′), the maximum diameter dc of particles that can be sheared by dislocations can be expressed as
| \begin{equation} d_{\text{c}} = 2\beta Gb/\tau_{\text{c}} \end{equation} | (7) |
Regarding τc, a relational expression σy ≅ 0.3 × Hv between the tensile yield strength σy [GPa] and Vickers hardness Hv [GPa] has been reported,19) which was applied in the previous study.20) Using this relation, the σy values for cementite (Fe3C) and VC (V4C3) with room-temperature hardness values of 13.1 and 27.4 GPa, respectively,21) are 3.9 and 8.2 GPa, respectively. The shear strength τc can be expressed as τc = σy/M using the Taylor factor M. Thus, taking M as 2.75,22) the τc values of cementite and VC are 1.4 and 3.0 GPa, respectively. The linear tension coefficient β is defined as β = {ln(r/2b)}/(4πk), where r is the dislocation stress field radius and k is a constant that depends on the properties of the dislocation. Here, a value of 0.86 was used for k for mixed dislocations.23) For r, because the dislocation density ρ of the 0.82 V tempered steel was high, a value of β = 0.375 was obtained by estimating for $r = (1/\pi )^{1/2}/\sqrt{\rho } $. The maximum diameters dc for cementite and VC particles that can be sheared by dislocations, as calculated by substituting τc, β, G = 83100 MPa, and b = 0.248 nm into eq. (7), are therefore 10.8 and 5.2 nm, respectively.
The Orowan mechanism occurs when the linear tension T of a dislocation cannot overcome the resistance force Fm of a particle with a size exceeding the critical value dc. The dislocation then passes around the particle, leaving a dislocation loop around it. The required shear stress for Orowan looping can be expressed as follows:24)
| \begin{equation} \tau_{\text{Orowan}} = \frac{1.6\beta Gb}{\lambda} \end{equation} | (8) |
Therefore, the strengthening contribution by the Orowan mechanism is expressed as
| \begin{equation} \sigma_{\text{Orowan}} = M\tau_{\text{Orowan}} = \frac{1.6M\beta Gb}{\lambda} \end{equation} | (8′) |
From Section 3.2, the average diameter of the cementite particles in the 0 V tempered steel was 85 nm, which is significantly larger than the maximum shearable particle size dc of 10.8 nm; hence, the strengthening mechanism of cementite was assumed to be the Orowan mechanism. λ in eq. (8′) can be expressed using the precipitate volume fraction f and average particle size d:24)
| \begin{equation} \lambda = \sqrt{\frac{2}{3}} \left\{\left(\frac{\pi}{f}\right)^{1/2}{} - 2 \right\}\frac{d}{2} \end{equation} | (9) |
Next, the contribution of VC particles to the total precipitation strengthening contribution was evaluated using the observation results. Because the VC precipitates were disk-shaped, the shape of the intersection between a VC particle and the slip plane of the body-centered cubic (BCC) matrix can vary significantly depending on the particle orientation. Thus, the shape of the VC particle on the slip plane was considered when estimating the precipitation strengthening contribution by adopting the approach used by Kusumi et al.6)
As confirmed in Section 3.4, the VC precipitates had a B–N orientation relationship with the ferrite matrix, as expressed by eq. (1). Because the {100} planes of VC are largely consistent with the {100} planes of the ferrite matrix, VC tends to grow in the ferrite phase in a plate-shaped manner with the {100} planes as the habit planes.9,10) Figure 9 shows a schematic of the habit planes of VC. The BCC slip planes were the tightest-packed {110} and {112}.25) For simplicity, only the {110} slip planes were considered in this study. The VC precipitates have a 2/3 chance of intersecting these slip planes at a 45° angle, and a 1/3 chance of intersecting them at a 90° angle. Figure 10 shows the shape of the VC precipitates on the slip planes in both cases. The intersection between the disk-shaped VC precipitates and slip plane is rectangular. Assuming a particle diameter D and thickness t, then according to Kusumi et al.,6) as the average sizes of the intersection between VC particle and slip plane, the major axis of the particle is πD/4 at both 45° and 90° and the minor axis of the particle are t/cos(π/4) at 45° and t at 90°. For D = 10 nm and t = 0.80 nm, πD/4 is 7.9 nm and t/cos(π/4) is 1.1 nm.
Schematic illustration of VC habit planes in a ferrite matrix α under the condition of a Baker-Nutting orientation relationship.
Schematic illustration showing the shape of VC on a slip plane {110} in ferrite matrix.
When considering the number of each type of VC precipitate per unit area, the numbers of VC precipitates that intersect the slip plane at 45° and 90° are denoted as $n_{s_{45}}$ and $n_{s_{90}}$, respectively. The overall precipitate volume fraction was set to f, and the number of particles per unit volume was set to nv:
| \begin{equation} n_{v} = f\Bigg/\left\{\pi \left(\frac{D}{2} \right)^{2}t \right\} \end{equation} | (10) |
Therefore, ns45 and ns90 can be expressed as
| \begin{equation} n_{s_{45}} = D\sin \frac{\pi}{4}\times \frac{2}{3}n_{v} = \frac{4}{3}\frac{\sqrt{2} f}{\pi Dt} \end{equation} | (11) |
| \begin{equation} n_{s_{90}} = D\sin \frac{\pi}{2}\times \frac{1}{3}n_{v} = \frac{4}{3}\frac{f}{\pi Dt} \end{equation} | (12) |
Regarding the direction of dislocation motion, given that the easy slip directions in BCC crystals are the ⟨111⟩ directions, and that mixed dislocations have a helical component of approximately 0.5, a model in which the dislocations move in the ⟨100⟩ and ⟨110⟩ directions was considered. For dislocations moving in the ⟨110⟩ and ⟨100⟩ directions, the major axes πD/4 of VC particles intersecting with the slip plane at 45° and 90° each constitute a large resistance (Fig. 10). Various models can be used to estimate the contribution of precipitation strengthening. However, minimum possible precipitation strengthening is assumed in this study. Only VC intersecting with the slip plane at 90° was assumed, which has the lowest number density, and the magnitude of precipitation strengthening was calculated considering dislocation moving in the ⟨100⟩ direction.
The major axis πD/4 (= 7.9 nm) of the VC particles that resist dislocations is larger than the maximum particle diameter (5.2 nm) of the VC particles sheared by dislocations. If we assumed that all the particles hindered dislocation motion by the Orowan mechanism, we could calculate the average interparticle spacing λ using $n_{s_{90}}$, as expressed by eq. (12), and the resistance size πD/4, as follows:
| \begin{equation} \lambda = \frac{1}{\sqrt{n_{s_{90}}}} - \pi D/4 \end{equation} | (13) |
By substituting the values calculated using eq. (13) into eq. (8′), σOrowan was determined to be 1290 MPa. Equation (3) was transformed to confirm the validity of this value, which yields eq. (14).
| \begin{align} \sigma_{\text{0.82V}} - \sigma_{\text{0V}}& = (\sigma_{\rho,\text{0.82V}} - \sigma_{\rho,\text{0V}}) + (\sigma_{\text{prec,VC}} - \sigma_{\text{prec},\theta})\\ 614(\text{MPa}) &= 264(\text{MPa}) + \sigma_{\text{prec,VC}} - 158(\text{MPa})\\ \sigma_{\text{prec,VC}} &= 508(\text{MPa}) \end{align} | (14) |
Regardless of the method of calculating the precipitation strengthening contribution, the increase in yield strength upon adding vanadium to tempered steel can be mainly explained by dislocation strengthening owing to the delayed recovery and precipitation strengthening by VC instead of that by cementite. To clarify how the precipitates resist dislocation motion, it is necessary to observe the dislocations after tensile tests and confirm the presence (or absence) of dislocation loops.
In this study, the effects of vanadium on the strengthening mechanisms of tempered martensite were elucidated using water-quenched and tempered Fe–0.2C–0.5Si–2.5Mn–xV (mass%, x = 0–0.82) steels. The yield strength was determined from the stress–strain curves obtained by tensile tests, and the strengthening mechanisms were evaluated from dislocation density analysis and observations of the microstructures and precipitates. The main results obtained were as follows:
