Lattice Strain and Strength Evaluation on V Microalloyed Pearlite Steel

Abstract

The strengthening mechanism of microalloyed vanadium (V) on eutectoid pearlite steel was investigated from the perspectives of nano-precipitation and lattice strain. The 0.2% proof stress of specimens, isothermally transformed at 873 K, increased by about 160–170 MPa with the addition of 0.1% V. However, the interphase precipitation of vanadium carbide (VC), regarded as the principal strengthening factor, was detected neither by transmission electron microscopy nor by 3D atom probe microscopy (3D-AP). A lattice strain in lamellar ferrite, analyzed by broadening of the X-ray diffraction peak, has been experimentally estimated to understand the strengthening mechanisms by V-addition. The lattice strain data of 0.1% V-added pearlite specimens were plotted on the same correlation line as those of the V-free specimens with proof stress. In addition, the elemental map obtained by 3D-AP showed that V atoms concentrate in lamellar cementite rather than ferrite, which could change the cementite lattice parameters and gain ferrite/cementite misfit, causing lattice strain increment. These results revealed that microalloyed V influences not only VC precipitation in lamellar ferrite but also the lattice strain increment in pearlite lamellar. In the case of pearlite steels containing at most 0.1% V, lattice strain was considered the major factor of their yield behaviors. Furthermore, 0.1% V addition did not enhance work-hardening behavior as notably as that estimated by Ashby’s work-hardening theory of dispersion-hardened crystals. Therefore, VC precipitation is not necessary for the V strengthening effect on pearlite steel.

1. Introduction

Pearlite steels have been used in a variety of applications where high strength and wear resistance are required, including for example sliding parts and undercarriages of automobiles. Demand for weight reduction in commercial applications has provided incentive to further increase the strengthening potential in these materials. Several alloys were designed with the goal of maximizing strength by microalloying additions, taking into consideration solubility and alloying level as well as heating and cooling processes. In the eutectoid or hypo-eutectoid compositions, microalloyed pearlite steels, containing about 0.1–0.5% vanadium (V), have often been used.^1,2)

Strengthening by microalloyed V on pearlite steel is considered to be caused by interphase precipitation of vanadium carbide (VC) in proeutectoid ferrite or lamellar ferrite.³⁾ However, in the case of pearlite strengthened by addition of 0.1% V, only a few studies have clearly observed VC particles, which were expected to exert pinning effects, by transmission electron microscopy (TEM).⁴⁾ The VC particles seemed to have been clearly observed in pearlite when the V content in the steels was 0.2% or more.^1,2,5) Even when 0.2% V was added, VC precipitation is not always detected in the steels due to effects of other alloy components and transformation temperatures.⁶⁾ According to a precipitation (dispersion) strengthening theory presented by the Orowan mechanism, the effective particle size for strengthening is estimated to be several nanometers to 10 nm.⁷⁾ However, the emergence of the strengthening effect in the V microalloyed pearlite steel is not considered to be caused only by the VC particles. Clusters⁸⁾ and solid-solution of V are also considered to contribute to strengthening. Here, the problem is that the precipitation, clustering, and solid-solution strengthening have not been characterized in pearlite steels. Therefore, it is necessary to identify the strengthening mechanism by V addition of only as low as 0.1%.

Pearlite structure is characterized by a large amount of elastic strain due to the misfit between ferrite and cementite leading to high strength. Nakada et al. proposed that a significant amount of elastic strain is accumulated in the pearlite structure by means of analysis using electron backscattered diffraction and X-ray diffraction (XRD).⁹⁾ They suggested that the elastic strain is caused by misfit at the phase interface between ferrite and cementite.¹⁰⁾ In addition, the elastic strain is quantified from the full width at half maximum (FWHM) of the ferrite diffraction peak measured by XRD, and has been confirmed to be correlated with the yield strength.^9,11,12,13) However, this analysis has not yet been performed on alloys intended to be strengthened by “nano-precipitates” in lamellar ferrite, such as V-microalloyed pearlite steel.

In this study, we have evaluated the strengthening effect of 0.1% V addition on the isothermally transformed eutectoid pearlite steel.

2. Experimental Procedures

Eutectoid steels without and with 0.1% V were prepared as ingots of 25 kg each by vacuum induction melting followed by forging. Their chemical compositions are given in Table 1. The specimens were austenitized at 1223 K, followed by cooling to 873 K and 823 K and isothermal holding for from 180 s to 3600 s at the pearlite transformation temperature. The microstructures and mechanical properties were evaluated by scanning electron microscopy (SEM) and by Vickers hardness test and tensile test, respectively.

Table 1. Chemical composition of steels (mass%).

	C	Si	Mn	Cr	V
V free	0.74	0.19	0.79	0.10	<0.001
0.1 V	0.76	0.19	0.78	0.10	<0.10

Fig. 1.

Heat treatment conditions.

The specimens intended for microstructural observations were etched with 2% nital, and eight regions in each specimen were observed at magnifications that allowed clear identification of pearlite lamellae. The lamellar spacing was measured in the area where cementite lamellae plates would perpendicularly intersect the observation surface and was averaged for the eight regions in each specimen. The measurements of lamellar spacing were skipped over the area where cementite was partially spheroidized.

Precipitations, V distribution and lattice strain in the lamellar ferrite were examined by TEM observation, 3D-atom probe microscopy (3D-AP), and XRD measurement. The specimens for TEM observations were prepared by twin-jet electropolishing in a solution consisting of 10 vol.% perchloric acid and 90% methanol at about 223 K. AP measurements were performed on LEAP-4000HR (CAMECA Co.) in the voltage pulse mode under the condition that detection rate, pulse rate, pulse fraction, and specimen temperature were 1%, 200 kHz, 20%, and 50 K or 80 K, respectively. XRD measurements evaluated changes in FWHMs of the ferrite diffraction peaks due to V addition. Diffraction intensity profiles ranging from 40° to 140° in diffraction angle (2θ) at 0.1° intervals were measured using a Rigaku Ultima-III diffractometer, with a Cu target operated at 40 kV and 40 mA. The measured diffraction profiles were fitted using the Lorentz function, and the lattice strain in the ferrite was analyzed from the FWHM obtained by the fitting.

3. Results

3.1. Microstructure

Figure 2 shows the SEM images of heat-treated specimens. The microstructure was identified as full pearlite with no pro-eutectoid ferrite in all specimens. Finer pearlite was formed at lower temperature around 823 K. At holding temperature 873 K, the lamellar cementite changed to sheroidized structure by long time holding.

Fig. 2.

SEM micrographs of V-free/0.1 V steel after isothermal holding.

Figure 3 shows the average lamellar spacing as a function of the isothermal holding time at 823 K and 873 K. The average lamellar spacing increased to almost maximum within 900 s in holding time. It is suggested that the finer lamellar region preferentially spheroidized during isothermal holding, and the relatively coarser lamellar region remained undivided.^14,15) The lamellar spacing increased in the order of V free-823 K < 0.1 V-873 K < V free-873 K in the specimens isothermally held for 180 s.

Fig. 3.

Lamellar spacing of V-free/0.1 V steel isothermally held under several temperature and time conditions.

3.2. Hardness and Tensile Properties

Figure 4(a) gives the Vickers hardness (Hv) as a fuction of the isothermal holding time. The specimens treated at a lower holding temperature or shorter holding time became harder. Comparing the specimens held at 873 K, 0.1 V steel was harder by about Hv50. Previous studies¹⁾ has also reported that a 0.1% V addition increases the hardness of Hv30–60 in the 873 K isothermally transformed specimens, so our result would be reasonable for the V addition strengthening amount. Figure 4(b) presents the relation between hardness and lamellar spacing along with a curve estimated with the Hall–Petch like law (Hv = H₀ + kλ⁻¹: λ is average lamellar spacing). V-added (0.1 V) steel was found to be harder than the V-free one by about Hv30, compared at similar lamellar spacing. This suggests that the V itself increased the resistance of dislocation motion.

Fig. 4.

Measured Vickers hardness of V-free/0.1 V steel as a function of (a) isothermal holding time and (b) pearlite lamellar spacing.

Figure 5 shows the tensile properties. Figure 5(a) illustrates the stress–strain curves of specimens isothermally held at 873 K. The yield strength and the ultimate tensile strength increased as a result of V addition. It is noted that the 0.1 V specimen isothermally held for 180 s at 873 K can bring out a high strength without a trade-off in elongation. The tensile elongation further increases with increasing holding time. The 0.1 V-3600 s specimen achieved much higher elongation compared to the V-free 180 s specimen with same strength level. Figures 5(b) and 5(d), respectively, give the 0.2% proof stress and the ultimate tensile strength as functions of isothermal holding time. Tensile strength increased with lower isothermal holding temperature, shorter holding time, and V addition. Figure 5(c) illustrates the 0.2% proof stress as a function of lamellar spacing along with a curve estimated with the Hall–Petch like law as mentioned in Fig. 4. The increase in the proof stress by V addition was estimated as about 100 MPa. Figure 5(e) presents the work-hardening estimated from the difference between the ultimate tensile strength and 0.2% proof stress. The amount of work-hardening increased with higher isothermal holding temperature and decreased with longer time holding or the addition of V. Comparing specimens held for 180 s, the work-hardening amount increased in the order of V free-823 K < 0.1 V-873 K < V free-873 K, showing the same tendency as that of lamellar spacing. Figure 5(f) gives uniform elongation. As seen in Fig. 5(a), specimens held for 180 s showed almost the same elongation regardless of the V addition, while elongation significantly increased with the holding time.

Fig. 5.

Tensile properties of V-free/0.1 V steel isothermally held under several temperature and time conditions. (a) Examples of stress–strain curve, (b)(c) 0.2% proof stress, (d) ultimate tensile strength, (e) work hardening (difference between tensile strength and proof stress), (f) uniform elongation.

3.3. Characterization of Precipitates by TEM and 3D-AP

In order to clarify the strengthening mechanisms by V addition, we attempted to observe the microstructure and chemistry of precipitates by TEM and 3D-AP. Figure 6 shows the TEM images of 0.1 V steel isothermally held at 873 K for 180 s or 3600 s. Clear contrast of VC was not observed in the specimen held for 180 s, while the specimen held for 3600 s, fine VC precipitation was observed in lamellar ferrite. The particle size of VC was about 3–4 nm in diameter. The VC particles had a Baker–Nutting orientation relationship with the ferrite matrix, and precipitated with multiple variants. In general, the interphase precipitation of alloy carbides has only one variant in three variants that satisfy the Baker–Nutting relationship.^3,16,17) Therefore, it is suggested that the VC observed in the specimen held for 3600 s with multiple variants was formed not by interphase precipitation but by aging precipitation in the ferrite matrix after transformation completion.

Fig. 6.

TEM micrographs of 0.1 V steels isothermally held at 873 K for (a) 180 s and (b) 3600 s.

Figure 7 shows 3D mapping images of V and C atoms by 3D-AP analysis with 0.1 V steel held at 873 K for 180 s or 3600 s, and Fig. 8 shows concentration of V in ferrite and cementite. Niether V-enriched clusters nor precipitates were observed in the specimen held for 180 s (Fig. 7(a)). This suggests that V exists as a solid solution not as VC precipitates in the ferrite matrix. In the specimen held for 3600 s, rod or plate shaped precipitates with V and C are observed. The size and morphology of the precipitates suggest that VC has been formed in the lamellar ferrite. But this VC might be different from interphase precipitation characterized as regularly spaced bands of VC. As shown in Fig. 8(b), V was also concentrated in cementite. The average V concentration in cementite increased from about 0.22 at% to 0.51 at% with increasing holding time. The average V content in ferrite decreased from 0.11 at% to 0.07 at% to compensate the concentration of V in cementite by aging. It has been confirmed that the partitioning of C, Mn, Cr, and Si to ferrite and cementite was negligibly affected by V-addition.

Fig. 7.

3D elemental maps (carbon and vanadium) of 0.1 V steels isothermally held at 873 K for (a) 180 s and (b) 3600 s. (Online version in color.)

Fig. 8.

Vanadium compositions of 0.1 V steels isothermally held at 873 K for 180 s and 3600 s. (a) V in ferrite and (b) V in cementite.

According to the results above, VC interphase precipitation, presumed to be a major strengthening factor, was not observed via TEM analysis and 3D-AP attempted in this study. The other strengthening mechanisms should be discussed to understand the effect of V addition on the pearlite steel.

4. Discussion

4.1. Factors Controlling Yield Strength

Yield strength (0.2% proof stress) as well as ultimate tensile strength remarkably increased with the addition of 0.1% V, while no clear VC interphase precipitation could be observed in TEM and 3D-AP in the specimen isothermally held for a shorter time. In this section, we consider the following three factors that may have caused the increase in the yield strength (Δσ_0.2~100 MPa) by 0.1% V addition presented in Fig. 5(c).

4.1.1. Solid Solution Strengthening by V Addition in Ferrite and Cementite

The First hypothesis is that the yield strength is increased by solute V. The strengthening resulting from the V solid solution in ferrite (α) phase and cementite (θ) phase was estimated respectively. Here, the yield strength of pearlite was calculated by a simple rule of mixtures of the two phases: the yield strength of ferrite (σ_α) and the shared stress due to elastic deformation of cementite (product of cementite elastic modulus, E_θ and deformation 0.2%).¹⁸⁾ It has been estimated that the amount of strengthening by solute V in ferrite (Δσ_SS(α)) is about 20 MPa/at% in terms of yield strength,¹⁹⁾ and those in cementite (ΔE_SS(θ)) is about 6 GPa/at% in terms of elastic modulus.²⁰⁾ The V concentration in ferrite and cementite were 0.11 at% and 0.22 at% respectively in the specimen isothermally held for 180 s, the amount of solid solution strengthening in each phases is estimated as   

$$\mathrm{F}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}:\mathrm{\hspace{0.17em} }\mathrm{\Delta }{\sigma }_{\mathrm{S}\mathrm{S}(\alpha )}\times 0.11\mathrm{\hspace{0.17em} }\mathrm{a}\mathrm{t}\%=2.2\mathrm{\hspace{0.17em} }\mathrm{M}\mathrm{P}\mathrm{a},$$(1)

  

$$\mathrm{C}\mathrm{e}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{e}:\mathrm{\hspace{0.17em} }\mathrm{\Delta }{E}_{\mathrm{S}\mathrm{S}(\theta )}\times 0.22\mathrm{\hspace{0.17em} }\mathrm{a}\mathrm{t}\%\times 0.2\%=2.64\mathrm{\hspace{0.17em} }\mathrm{M}\mathrm{P}\mathrm{a}.$$(2)

Summing these values by proportionally dividing ferrite/cementite volume fraction in eutectoid steel (f_α:f_θ = 89%:11%), the total amount of solid solution strengthening is extremely small:   

$${\sigma }_{\mathrm{S}\mathrm{S}}=2.2\mathrm{\hspace{0.17em} }\mathrm{M}\mathrm{P}\mathrm{a}\times 89\%+2.64\mathrm{\hspace{0.17em} }\mathrm{M}\mathrm{P}\mathrm{a}\times 11\%=2.2\mathrm{\hspace{0.17em} }\mathrm{M}\mathrm{P}\mathrm{a}.$$

Therefore, the V solid solution is not considered the major strengthening factor.

4.1.2. VC Particle Dispersion Strengthening in Ferrite

The second hypothesis is that the VC was too fine to observe in TEM and 3D-AP. Although no clear precipitation was observed in TEM and 3D-AP, the amount of particle dispersion strengthening was estimated assuming that very fine VC was formed in the ferrite. The strength increment was calculated by Ashby–Orowan equation (Eq. (3)) commonly used in the particle dispersion strengthening theory:^21,22)   

$${\sigma }_{\mathrm{P}}=0.84M_{\mathrm{T}}(1.2Gb/2\pi L)\mathrm{l}\mathrm{n}(x/2b).$$(3)

where M_T is the Taylor factor (2.0), G is the stiffness of the ferrite matrix (83100 MPa), and b is the Burgers vector (0.248 nm). L is the spacing between the precipitated particles on the slip plane, and x is the particle diameter on the slip plane. Assuming that the spherical precipitated particles with diameter d are randomly dispersed in ferrite, L and x can be calculated as follows.²³⁾   

$$x=\sqrt{\text{2/3}}\times d$$(4)

  

$$L=\sqrt{\pi \text{/6}f}\times d-x=\left(\sqrt{\pi \text{/6}f}-\sqrt{\text{2/3}}\right)d$$(5)

where f is the volume fraction of the precipitated particles. The average concentrations of V and C in the ferrite measured by 3D-AP were 0.11 and 0.07 at%, respectively. It was assumed that all of the supersatulated C atoms combined with 0.07 at% of V atoms in a ratio of 1:1 to form VC. Considering a simple structure composed of pure iron (αFe) and VC particles, the volume fraction of VC particles in the ferrite matrix (f_VC), was estimated to be 0.107%, from calculations using the atomic weight (Fe: 56, V: 51, C: 12) and density of each phase (αFe: 7.9 g/cm³, VC: 5.8 g/cm³).

Figure 9 shows the dependence of precipitation strengthening on grain size in ferrite was estimated by the Ashby–Orowan equation. The maximum yield strength was predicted as 94 MPa, which corresponds to 29 in terms of Hv. The yield strength was supposed to reach to maximum if the particle diameter (d) was 1.4 nm and (L) was 72 nm, according to Eq. (5). Since the above estimation was based on the ferrite matrix without other phases, the amount of precipitation strengthening in pearlite structure needs to be estimated by multiplying the ferrite volume fraction (f_α= 89%) in pearlite, resulting 84 MPa in yield strength and 26 in Vickers hardness. These values are comparable to the amount of strengthening in the present 0.1% V addition: Δσ_0.2~100 MPa and Hv~30. The Ashby–Orowan model by VC particles could be acceptable only if VC with the diameter of about 1.4 nm have been uniformly dispersed. However, this model has also predicted that the amount of precipitation strengthening reduces as the particle size is refined than 1.4 nm due to the term of ln(x/2b) in Eq. (3).²³⁾ Y.-J. Zhang et al. suggested that 1.2–1.3 nm was the limit size for identification that gives a clear image of VC in 3D-AP observations, under the same conditions using the same equipment as those in this study.²⁴⁾ Even if there are the VC particles that are too fine to be identified, the amount of strengthening cannot reach to 100 MPa according to Eq. (3). Therefore, the second hypothesis unlikely support the present estimation, and the Ashby–Orowan mechanism is not considered the major strengthening factor.

Fig. 9.

Estimated strength increment based on the Ashby–Orowan model.

In a previous study, one of the authors evaluated the precipitation strengthening in 0.3% V-added medium carbon steel mainly composed of pearlite, where the interphase-precipitated VC was clearly observed in lamellar ferrite. It has been reported that the hardness increase by V addition can be explained using the modified Ashby–Orowan model where x in Eq. (3) is tripled.¹⁾ It was because the precipitation strengthening estimated by the original Ashby–Orowan model was smaller than the increase in hardness in the V-added steel. It was suggested that the discrepancy was reduced by modifying the range of elastic field around dislocation that interacts with VC particles, based on the precipitation strengthening theory. From another perspective, the discrepancy might be explained by the lattice strain. As discussed in the next section, even in alloys where VC interphase precipitation is clearly observed, the lattice strain may increase in ferrite with V addition and contribute to strengthening. Thus, this lattice strain can actually lead to a hardness increase larger than the precipitation strengthening amount evaluated using the original Ashby–Orowan model.

4.1.3. Strengthening by Elastic Strain in Ferrite

Lattice strain is also an important factor for strengthening. The third hypothesis is that the lattice strain can lead to a hardening larger than the amount of precipitation strengthening. The elastic strain of ferrite phase in pearlite strengthened by V addition was identified by analyzing the XRD intensity profile. To calculate the lattice strain (ε_L), the Williamson–Hall equation²⁵⁾ (Eq. (6)) was used according to a previous study¹³⁾ in which elastic strain was analyzed from the ferrite diffraction peak width in pearlite.   

$$\beta (\mathrm{c}\mathrm{o}\mathrm{s}\theta /{\lambda }_{\mathrm{X}\mathrm{R}})=0.9/D+2{\epsilon }_{\mathrm{L}}(\mathrm{s}\mathrm{i}\mathrm{n}\theta /{\lambda }_{\mathrm{X}\mathrm{R}})$$(6)

Here, β is the diffraction peak width (FWHM). λ_XR and D are the X-ray wavelength and crystallite size respectively. The ferrite diffraction peaks of (110), (211), and (220) were used in this analysis. The relationship between the diffraction angle (θ) and peak width (β), which were obtained as a result of fitting each peak intensity profile, was subjected to linear regression analysis using Eq. (6), and ε_L and D were calculated as the fitting parameters.

Figure 10(a) gives the lattice strain (ε_L), as a function of isothermal holding time. The lattice strain increases with shorter holding time and with V addition, showing exactly the same tendency as that of strength. It is considered that the decrease in lattice strain with longer time holding is attributed to the misfit relaxation caused by atomic diffusion near the ferrite/cementite interface during spheroidization after pearlite transformation.¹³⁾ Figure 10(b) represents the relationship between lattice strain (ε_L) and tensile strength. It is noted that the 0.2% proof stress is almost positively proportional to lattice strain with and without V.

Fig. 10.

Lattice strain of ferrite phase estimated by XRD analysis. Relationship between lattice strain and (a) isothermal holding time, (b) tensile properties, and (c) lamellar spacing.

In Fig. 10(c), the lattice strain (ε_L) is plotted with the reciprocal of lamellar spacing (1/λ). The lattice strain increases monotonically with 1/λ. As described by Tanaka et al., it is understood that the lattice strain caused by misfit at the ferrite/cementite interface tends to increase in proportion to 1/λ.²⁶⁾ Figure 10(c) also indicates that the lattice strain is enhanced by V addition. This suggests that V-added steels are strengthened by increasing the lattice strain.

Dislocation is another possible factor increasing lattice strain. However, the contrast of dislocation has been rarely observed in lamellar ferrite. The lattice strain identified in pearlite is attributed to elastic strain, not plastic strain caused by dislocation.⁹⁾

The V concentration at the ferrite/cementite interface is another possible cause of lattice strain increase. In the 3D-AP results as shown in Figs. 7 and 8, V was concentrated in the cementite phase, particularly near the interface with ferrite phase. The measured V concentration in cementite in the specimen isothermally held at 873 K for 180 s was 0.22 at% on average and probably higher near the interface, immediately after pearlite transformation. If the V enrichment enlarges the cementite lattice size, the difference between the lattice parameters of ferrite and cementite may increase, causing an increment in the interphase misfit. Nakada and Kato estimated the elastic strain due to the misfit between ferrite and cementite by a calculation using micromechanics.²⁷⁾ They suggested that the elastic strain energy changes according to the crystal orientation relationship and the lattice parameter gap due to distribution of alloying elements between the two phases.²⁸⁾

To consider the effect of V distribution on the lattice strain, we attempted to evaluated the principal strain and elastic strain energy of the misfit based on the literature data.²⁷⁾ The lattice parameter data of cementite (Fe₃C) and its alloyed counterparts, which were studied by Razumovskiy and Ghosh using first-principles calculation,²⁹⁾ were referred. Here, the cementite lattice parameters are a_θ, b_θ, and c_θ, in ascending order. Table 2 shows the data examples of the lattice parameter and unit cell volume (V_θ = a_θ × b_θ × c_θ) of these cementite alloyed counterparts. When Mn, Cr, or V replaces Fe, two or more of the lattice parameters (a_θ, b_θ, and c_θ) increase, leading to increases in the unit cell volume (V_θ) in the order of Mn₃C < Cr₃C << V₃C. The tendency that the volume of Cr₃C is larger than that of Mn₃C is consistent with the experimental data in the literature³⁰⁾ as shown in the Table 2. Thus, it is expected that the lattice parameter increment by V is larger than those by Mn and Cr.

Table 2. Lattice parameters of Fe₃C and its alloyed substitutes, and corresponding α/θ misfit strain.

(Fe, M)3C	Calculated in ref. 29)				Experimental30)	Calculated misfit strain under Pitsch–Petch OR27)
	Lattice constants			Cell volume	Cell volume	Principal strain		M value
	aθ/nm	bθ/nm	cθ/nm	Vθ/nm3	Vθ/nm3	ε*11	ε*22
Fe3C	0.4482	0.5029	0.6726	0.1516	0.1554	−0.05834	0.09050	0.00807
Mn3C	0.4264	0.5218	0.6790	0.1511	0.1558	−0.09879	0.12469	0.01709
Cr3C	0.4511	0.5195	0.6628	0.1553	0.1595	−0.04998	0.12377	0.01369
Fe2VC	0.4527	0.5100	0.6675	0.1541	−	−0.04852	0.10543	0.01006
FeV2C	0.4713	0.5091	0.6803	0.1632	−	−0.01497	0.10975	0.01117
V3C	0.4194	0.5627	0.7877	0.1859	–	−0.11111	0.20961	0.04076

The lattice strain was calculated using the lattice parameters of the cementite alloyed counterparts shown in Table 2. Generally, when calculating lattice strain using micromechanics, it is assumed that each phase has homogeneous structure. Here, there is a hypothetical structure assumed in which the lattice parameter is constant throughout the cementite without local enrichment of alloying elements. According to a method proposed by Nakada and Kato,^27,28) the principal misfit strain (ε^*₁₁, ε^*₂₂) and M value are calculated under the two-dimensional lattice correspondence condition at the ferrite/cementite coherent interface in pearlite lamellae. The M value is an index (Eq. (7)) indicating the magnitude of elastic strain energy.   

$$M={({\epsilon }^{*}{}_{11})}^2+{({\epsilon }^{*}{}_{22})}^2+2/3\times {\epsilon }^{*}{}_{11}\mathrm{\hspace{0.17em} }{\epsilon }^{*}{}_{22}.$$(7)

In this calculation, the Pitsch–Petch orientation relationship^31,32) is introduced. For the ferrite lattice parameter, the value a_α = 0.28311 nm in Reference 29) was used. Since the amount of solute alloying element in ferrite was relatively small, the effect of the alloying elements on a_α was not considered. The calculated principal strain and M value are shown in Table 2. Compared to Fe₃C, the M value increased 1.25 times for Fe₂VC, 1.4 times for FeV₂C, and 5 times for V₃C. Although the actual V concentration observed was considerably lower than that for the hypothetically alloyed cementite counterparts, an increase in the elastic strain energy M in such substituted structures suggests that lattice strain can increase due to the change in the cementite lattice parameter. Additionally, compared to Mn₃C and Cr₃C, V₃C has the largest M value. Therefore, among Mn, Cr, and V, which easily dissolve in cementite, V is the most likely to increase the lattice strain.

As shown in Fig. 8(b), the V concentration in cementite increased with longer-term holding at 873 K, while the lattice strain shown in Fig. 10(a) decreased with the longer holding in 0.1 V steel as well as V-free steel. This seems to be inconsistent with the previous consideration that the V concentration in cementite increases the lattice strain. However, this is probably because the contribution of misfit relaxation mechanisms such as cementite spheroidization and introduction of misfit dislocations was more dominant. As a result, the lattice strain in both V free and 0.1 V may decrease, in the same manner, with aging.

The lattice strain by XRD might include effects of solid solution atoms and precipitates or clusters. It is known that when fine clusters or coherent precipitates are formed in ferrite, the ferrite peak angle changes and the peak width increases in XRD measurement.^33,34) In this study as well, there might be fine clusters that cannot be observed by 3D-AP, and the lattice strain due to the coherency between the clusters and ferrite matrix might contribute to strengthening. However, there are no clarified explanations so far to give the factors that cause lattice strain, the relationship between lattice strain and strengthening mechanisms such as Orowan and cutting, and the factors for strengthening. A systematic investigation on the relationships among precipitation amount, lattice strain, and strength, using pearlite steels with a wide range of V addition, including the case in which clear VC precipitation can be observed, will have to be conducted. It is also expected to evaluate the effect of lattice strain on the strengthening mechanism due to clusters and coherent precipitates in simpler low-carbon ferritic steels.

4.2. Factors Controlling Work Hardening

Figure 10 shows that yield strength (0.2% proof stress) is likely proportional to the lattice strain, while the correlation between ultimate tensile strength and the lattice strain varies slightly. Among the specimens held at 873 K, strength plots of longer holding time seem to deviate from the correlation line to a lower side. This indicates that factors different from lattice strain may be involved in the work-hardening behavior after yielding. As shown in Fig. 5(e), the amount of work hardening decreases with increasing isothermal holding time. According to Koga et al.,¹¹⁾ the yield behavior of pearlite is governed by the elastic strain (lattice strain), whereas the work-hardening behavior strongly depends on the lamellar structure, especially on spheroidization of the lamellar cementite. Therefore, the lamellar cementite spheroidization due to longer time holding reduced work hardening, and the ultimate tensile strength became smaller than the tendency indicated by the lattice strain.

The work-hardening amounts of specimens with a shorter holding time of 180 s, which is less affected by spheroidization, are plotted with lamellar spacing in Fig. 11. Work hardening after yielding increased with lamellar coarsening. The increase in work hardening due to V addition was as small as about 10 MPa, if the effect of lamellar spacing was subtracted. The strengthening mechanism by V addition was examined from two viewpoints: VC precipitation in ferrite and V concentration in cementite.

Fig. 11.

Relationship between lamellar spacing and work hardening of specimens isothermally held for 180 s.

First, as in the discussion described in 4.1.2, a very fine VC was formed in the ferrite and the contribution to work hardening was estimated. Nakada et al. estimated the work hardening experimentally based on Ashby’s theory,³⁵⁾ in which it is explained that work hardening by nanoprecipitates in ferritic steel is caused by an increase in the density of dislocations (GN dislocations) that occur near the grain boundary during deformation.³⁶⁾ According to this theory, the amount of work hardening by hard precipitates, such as VC, at a true strain of 3% (difference between the flow stress at true strain of 3% and 0.2% proof stress) is given by the following formula using the precipitate volume fraction (f_P) and particle size (d).   

$$\mathrm{\Delta }{\sigma }_{\text{WH}}=\text{4}\mathrm{\hspace{0.17em} }\text{300}\times \sqrt{f_{\text{P}}\text{/(}d\text{/nm)}}\mathrm{\hspace{0.17em} }\text{MPa}$$

Where f_P is f_VC = 0.107%, which is the VC volume fraction used in the above considerations on yield strength increment, d = 1.4 nm, which is VC particle size giving the maximum precipitation strengthening amount. Substituting these values leads to the following estimation.   

$$\mathrm{\Delta }{\sigma }_{\text{WH}}=\text{4}\mathrm{\hspace{0.17em} }\text{300}\times \sqrt{\text{0}\text{.107\%/1}\text{.4}}\mathrm{\hspace{0.17em} }\text{MPa}=\text{119}\mathrm{\hspace{0.17em} }\text{MPa}$$

The contribution to strengthening of the entire pearlite structure is 106 MPa by multiplying the ferrite volume fraction f_α = 89% in pearlite. This value is an estimate at a true strain of 3%, before the tensile strength reaches its maximum. Nevertheless, it is almost 10 times higher than the experimental value of 10 MPa for the amount of V strengthening above. Therefore, even if there are VC precipitates or clusters in the specimens, they are unlikely to contribute to the increase in dislocation density. Therefore, VC precipitation is not considered to be the major strengthening factor in terms of work hardening.

Next, the contribution to work hardening was estimated assuming that the elastic modulus of cementite is changed by V concentration. Tomota et al. showed that cementite shared stress by elastic deformation even after macroscopic yield.³⁷⁾ Based on the elastic behavior, the deformation stress of cementite after macroscopic yield can be roughly estimated. Assuming that lamellar cementite continues elastic deformation up to the elongation at ultimate tensile strength (ε_u = 8%), the contribution to the cementite elastic deformation stress due to solute V can be obtained by the following formula with reference to the above Eq. (2).¹⁸⁾   

$$\mathrm{\Delta }{E}_{\mathrm{S}\mathrm{S}(\theta )}\times 0.22\mathrm{\hspace{0.17em} }\mathrm{a}\mathrm{t}\%\times ({\epsilon }_{\mathrm{u}}-0.2\%)=103\mathrm{\hspace{0.17em} }\mathrm{M}\mathrm{P}\mathrm{a}$$

Multiplied by the cementite volume fraction (f_θ = 11%), amount of the solid solution effect in the pearlite structure is estimated as 11 MPa, which is comparable to the experimental value. Therefore, the V contribution to the work-hardening behavior observed in this study can be explained without considering precipitation. This is consistent with the previous results of this study, which suggest that VC precipitation is not necessary for the increase in yield strength by V addition.

According to the above considerations, microstructure factors affecting tensile properties in V-microalloyed pearlite steel are schematically shown in Fig. 12. (1) First, the yield strength mainly depends on the lattice strain. The lattice strain is considered to include the effects of lamellar spacing, cementite spheroidization, and V addition. (2) Cementite shares macroscopic yield strength by elastic deformation. The elastic modulus can be increased by concentrating V in the cementite. However, because deformability, as well as the volume fraction of cementite, is small, the change in elastic modulus or solid solution strengthening due to V concentration is minor. (3) The work-hardening behavior after yielding seems to depend on the cementite morphology, such as lamellar spacing and spheroidization.¹¹⁾ (4) Fine precipitates in ferrite may increase the dislocations density and increase the work-hardening amount. However, if the amount of V added is so small that no clear precipitation is observed, the effect is small. (5) Cementite shares flow stress by elastic deformation even after macroscopic yielding. The small amount of V addition may contribute slightly to work hardening through elastic modulus increase because of the solid solution in cementite.

Fig. 12.

Schematic view of pearlite strength factors.

5. Conclusion

The strengthening effect of microalloyed V on eutectoid pearlite steel was investigated from the perspective of VC precipitation and lattice strain. The findings are as follows.

• In the pearlite specimens isothermally transformed at 873 K, hardness increased by about 50–60 in Hv and 0.2% proof stress increased by about 160–170 MPa with 0.1% V addition.

• The interphase precipitation of VC, regarded as the principal strengthening factor, was detected neither by TEM nor by 3D-AP, while the 3D-AP result showed V concentration in lamellar cementite.

• The lattice strain in lamellar ferrite, analyzed by XRD measurement, had a clear correlation with the proof stress. The lattice strain of 0.1% V steel increased with the same correlation as V-free steel.

• Theoretical calculation assuming the Pitsch–Petch orientation relationship qualitatively showed that the change in cementite lattice constant with V concentration could gain ferrite/cementite misfit, causing lattice strain increment.

• The increase in work hardening by 0.1% V addition was smaller than that estimated assuming VC precipitation based on Ashby’s theory.

Therefore, V addition to pearlite steel contributes not only to VC precipitation but also to an increase in lattice strain, and strength improvement may not necessarily be accompanied by the precipitation.

References

• 1)   G.  Miyamoto,  R.  Hori,  B.  Poorganji and  T.  Furuhara: ISIJ Int., 51 (2011), 1733.
• 2)   Y.  Daitoh,  S.  Torizuka and  T.  Hanamura: Tetsu-to-Hagané, 97 (2011), 480 (in Japanese).
• 3)   S. A.  Parsons and  D. V.  Edmonds: Mater. Sci. Technol., 3 (1987), 894.
• 4)   F. A.  Khalid and  D. V.  Edmonds: Mater. Sci. Technol., 9 (1993), 384.
• 5)  The Iron and Steel Institute of Japan: Proc. Symp. on Controlled Forging Group in “Fundamental Studies on Technologies for Steel Materials with Enhanced Strength and Functions”, The Iron and Steel Institute of Japan, Tokyo, (2010), 1 (in Japanese).
• 6)   K.  Han,  G. D. W.  Smith and  D. V.  Edmonds: Metall. Mater. Trans. A, 26 (1995), 1617.
• 7)   S.  Takaki: Fundamentals and Applications of Precipitation in Steels, ISIJ, Tokyo, (2001), 69 (in Japanese).
• 8)   K.  Hono,  T.  Homma and  D. H.  Ping: Fundamentals and Applications of Precipitation in Steels, 2, ISIJ, Tokyo, (2003), 46 (in Japanese).
• 9)   N.  Nakada,  N.  Koga,  T.  Tsuchiyama and  S.  Takaki: Scr. Mater., 61 (2009), 133.
• 10)   N.  Koga,  N.  Nakada,  T.  Tsuchiyama,  S.  Takaki,  M.  Ojima and  Y.  Adachi: Scr. Mater., 67 (2012), 400.
• 11)   N.  Koga,  N.  Nakada,  T.  Tsuchiyama and  S.  Takaki: CAMP-ISIJ, 25 (2012), 1243, CD-ROM (in Japanese).
• 12)   N.  Nakada,  N.  Koga,  T.  Tsuchiyama and  S.  Takaki: Proc. 2nd Int. Symp. on Steel Science, ISIJ, Tokyo, (2009), 163.
• 13)   N.  Nakada,  N.  Koga,  Y.  Tanaka,  T.  Tsuchiyama,  S.  Takaki and  M.  Ueda: ISIJ Int., 55 (2015), 2036.
• 14)   A. K.  Gogia and  A. M.  Gokhale: Metall. Trans. A, 11 (1980), 1077.
• 15)   O. E.  Atasoy and  S.  Ozbilen: J. Mater. Sci., 24 (1989), 281.
• 16)   A. T.  Davenport and  R. W. K.  Honeycombe: Proc. R. Soc. Lond. A, 322 (1971), 191.
• 17)   N.  Kamikawa,  Y.  Abe,  G.  Miyamoto and  T.  Furuhara: Fundamentals and Novel Approaches for New Demands on Work-Hardening Properties of Steels, ISIJ, Tokyo, (2011), 200 (in Japanese).
• 18)   S.  Takaki: 191st and 192nd Nishiyama Memorial Seminar, ISIJ, Tokyo, (2007), 17 (in Japanese).
• 19)   T.  Maki: Microstructure Control of Steels, Uchida Rokakuho, Tokyo, (2015), 110 (in Japanese).
• 20)   M.  Umemoto and  K.  Tsuchiya: Tetsu-to-Hagané, 88 (2002), 117 (in Japanese).
• 21)   T.  Gladman: The Physical Metallurgy of Microalloyed Steels, The Institute of Materials, London, (1997), 47.
• 22)   T.  Gladman: Mater. Sci. Technol., 15 (1999), 30.
• 23)   N.  Kamikawa,  G.  Miyamoto and  T.  Furuhara: Materia Jpn., 54 (2015), 3 (in Japanese).
• 24)   Y. -J.  Zhang,  G.  Miyamoto,  K.  Shinbo,  T.  Furuhara,  T.  Ohmura,  T.  Suzuki and  K.  Tsuzaki: Acta Mater., 84 (2015), 375.
• 25)   G. K.  Williamson and  W. H.  Hall: Acta Metall., 1 (1953), 22.
• 26)   Y.  Tanaka,  D.  Akama,  N.  Nakada,  T.  Tsuchiyama and  S.  Takaki: Tetsu-to-Hagané, 100 (2014), 1229 (in Japanese).
• 27)   N.  Nakada and  M.  Kato: ISIJ Int., 56 (2016), 1866.
• 28)   N.  Nakada and  M.  Kato: CAMP-ISIJ, 30 (2017), 379, CD-ROM (in Japanese).
• 29)   V. I.  Razumovskiy and  G.  Ghosh: Comput. Mater. Sci., 110 (2015), 169.
• 30)   D.  Fruchart,  P.  Chaudouet,  R.  Fruchart,  A.  Rouault and  J. P.  Senateur: J. Solid State Chem., 51 (1984), 246.
• 31)   W.  Pitsch: Acta Metall., 10 (1962), 79.
• 32)   N. J.  Petch: Acta Crystallogr., 6 (1953), 96.
• 33)   D. S.  Rickerby,  S.  Henderson,  A  Hendry and  K. H.  Jack: Acta Merall., 34 (1986), 1687.
• 34)   M.  Akhlaghi,  T.  Steiner,  S. R.  Meka,  A.  Leineweber and  E. J.  Mittemeijer: Acta Mater., 98 (2015), 254.
• 35)   M. F.  Ashby: Philos. Mag., 14 (1966), 1157.
• 36)   N.  Nakada,  T.  Tsuchiyama and  S.  Takaki: Fundamentals and Novel Approaches for New Demands on Work-Hardening Properties of Steels, ISIJ, Tokyo, (2011), 194 (in Japanese).
• 37)   Y.  Tomota and  T.  Suzuki: Bull. Iron Steel Inst. Jpn., 12 (2007), 71 (in Japanese).