Surface Treatment and Corrosion
Strengthening via Grain Refinement in Lath Martensite on Low Carbon Fe–18Ni Alloys
2022 Volume 62 Issue 7 Pages 1502-1511
Details
2022 Volume 62 Issue 7 Pages 1502-1511
The lath martensite structure in steel offers high strength with a complex substructure, and its strength increases with carbon content. However, the mechanism of carbon strengthening is yet to be elucidated. In this study, we evaluate the tensile properties of as-quenched lath martensite without retained austenite in Fe–18Ni alloys containing 4–570 ppm carbon. In the 4 mass ppm carbon alloy, whose carbon is almost trapped by Ti(CN) particles, the work hardening behavior during uniform elongation is constant regardless of the size of the effective grain surrounded by a high angle boundary. In contrast, the yield point (YP), 0.2% proof stress (σ0.2%), 0.6% proof stress (σ0.6%), and maximum tensile strength (TS) in 7, 110, and 570 mass ppm carbon alloys increase with the refinement of their effective grain, consistent with the Hall–Petch relationship. The Hall–Petch intercepts for the YP, σ0.2%, σ0.6%, and TS are constant and unaffected by the carbon content. This suggests that the non-occurrence of solution hardening by solute carbon atoms in the lath martensite. The Hall–Petch coefficients for the YP, σ0.2%, σ0.6%, and TS increase with carbon content and are proportional to the square root of the carbon content. This indicates that the increase in carbon content increases the strength of the lath martensite via the refinement of effective grains and the increase in the effectiveness of grain refinement.
The lath martensite structure in steel is a beneficial for improving the strength of steel. It is widely used in advanced high-strength steels, e.g., hot stamping steels1) and dual-phase steels.2) However, the application of high-strength steels is restricted owing to their properties, which worsen as their strength increases. Although an increase in carbon content significantly increases the strength of martensite,3,4) it decreases the formability, weldability, toughness, and resistance of martensite to hydrogen embrittlement. Thus, the strengthening mechanism of martensite with increasing carbon content must be understood to improve the balance of the properties of high-strength steel.
Many studies have been conducted on the strengthening mechanism of lath martensite. Lath martensite comprises hierarchical and complex substructures,5,6,7) and carbon would increase the strength of martensite via several routes. Typically, the solution hardening effect of carbon is regarded as the most effective route.3,4,8,9) Similarly, grain boundary hardening is an important mechanism.10,11,12,13,45) Morito et al.10) reported that the effective grain of lath martensite is a block comprising laths that exhibit similar crystallographic orientations and the same habit plane.5) Because the block size decreases with increasing carbon content,5,14) the grain boundary hardening effect becomes more prominent as the carbon content increases. In addition, the dislocation density increases with carbon content;14,15,16) however, the dislocation hardening effect in lath martensite is yet to be elucidated. Although precipitation hardening increases with carbon content in tempered martensite containing cementite particles,17,18) this hardening mechanism is negligible in as-quenched martensite without cementite.
The strengthening of lath martensite with the increase in carbon content depends on solution hardening and grain boundary hardening; however, their proportions are unknown. In this study, we focused on the hardening effects in ultra-low- and low-carbon lath martensite structures. Solute hardening depends on the square root or cubic root of the solute element content;19,20) hence, the effect of solute carbon would be evident in low-carbon alloys.
This paper is based on a conference proceeding21) made at TMS 2019 148th Annual Meeting & Exhibition, March 10–14, 2019 in San Antonio, Texas.
Table 1 shows the chemical compositions of the four Fe–Ni alloys used in this study. In low-alloyed low-carbon steel, the martensite transformation start temperature (Ms) is relatively high; therefore, its lath martensite structure is affected by auto-tempering during quenching, and cementite particles begin to precipitate in the lath martensite structure.22) In contrast, in a highly alloyed steel whose Ms is much lower, its microstructure after quenching with subzero treatment contains residual austenite,23) and its strengthening mechanism becomes more complex because of the deformation-induced martensite transformation.24) To accurately evaluate the strength of lath martensite, we used Fe–18Ni alloys to avoid the effects of cementite and retained austenite. The total carbon contents in the alloys were between 4 and 570 mass ppm, as evaluated via infrared absorption after combustion. Alloys B, C, and D contained 0.005 mass% titanium and were able to trap 8 mass ppm nitrogen as large TiN particles. Alloy A contained 0.017 mass% titanium and was able to trap 4 mass ppm carbon and 8 mass ppm nitrogen as large Ti(CN) particles. These alloys contained approximately 25 mass ppm boron and exhibited a fully martensitic structure by delaying ferrite transformation.
| Alloy | C | N | B | Ni | Ti | Others | Ms |
|---|---|---|---|---|---|---|---|
| mass ppm | mass ppm | mass ppm | mass% | mass% | mass% | °C | |
| A | 4 | 8 | 27 | 18.4 | 0.017 | < 0.03 | 295 |
| B | 7 | 8 | 26 | 18.2 | 0.005 | < 0.03 | 293 |
| C | 110 | 8 | 24 | 18.2 | 0.005 | < 0.03 | 263 |
| D | 570 | 8 | 26 | 18.1 | 0.005 | < 0.03 | 215 |
The ingots of these alloys were melted in a vacuum induction furnace, heated at 1150°C, and hot-rolled at 900°C to sheets measuring 4 mm thick. After hot-rolling, the sheets were ground on both surfaces to remove decarbonized areas. The ground sheets with 3.0 mm thickness were austenitized at 800, 900, or 1000°C for 1.2 ks and quenched with water. We applied an additional heat treatment, which was sustained at 500°C for 10.8 ks before grinding, to alloy A for the growth of Ti(CN) particles.
The Ms values evaluated using a dilatometer during continuous cooling at 30°C/s after austenitization at 900°C were between 295 and 215°C, as shown in Table 1. Figure 1 shows the results of X-ray diffraction (Mo Kα source) on planes parallel to the sheet surface at half the thickness of the specimens quenched after austenitization at 900°C. In the samples evaluated in this study, peaks originating from austenite, which appeared in the reference result for the Fe-7 mass%Ni–0.5 mass%C alloy containing 8% retained austenite, were not observed as shown in Fig. 1. Figure 2 shows the results of the internal friction test from −50 to 300°C for the same samples. Sneak peaks at approximately 190°C, which correspond to the amounts of solute carbon,25,26) increased with the total carbon content. Although the relationship between internal stress and solute carbon content in lath martensite is yet to be elucidated,27) this tendency suggests that the solute carbon content increases with the chemical composition of the ingots.
XRD patterns of Fe–18Ni alloys quenched after austenitization at 900°C. Dotted line shows result of as-quenched Fe–Ni–C alloy containing retained austenite.
Internal friction spectrum measured at 3 Hz of Fe–18Ni alloys quenched after austenitization at 900°C.
We observed the lath martensite structure in the transverse direction at half the sheet thickness and evaluated the average prior austenite grain diameter (dγ) and average effective grain size (deff) by using an intercept method. Prior austenite grain boundaries observed in optical micrographs appeared due to nital etching. We evaluated high angle boundaries whose misorientations exceeded 10 degree via field-emission electron microscopy (JEOL-6500F) using an electron backscattering diffraction analysis system (OIM Data Collection ver. 7) and determined that they were effective grain boundaries corresponding to block boundaries in the lath martensite structure.5,10,28)
2.3. Tensile TestWe evaluated the tensile properties, namely, the yield point (YP), 0.2% proof stress (σ0.2%), 0.6% proof stress (σ0.6%), and maximum tensile strength (TS), via tensile testing using 13 B tensile test specimens in Japanese Industrial Standards (JIS Z 2201). The strain gauge length was 50 mm, and the nominal strain rate was 3.3 × 10−3 s−1. The YP is an elastic limit identified via comparison between a true stress–true strain curve and Young’s modulus of Fe–18Ni alloys.29) In the following, we describe these properties using the average number of two specimens per condition. We added error bars in graphs; however, most of them were hidden because they were smaller than the data dots.
Figures 3(a) and 3(b) show optical micrographs of samples of alloys A and D austenitized at 900°C. Their dγ values were 39 and 41 μm, respectively. Figure 3(c) shows the optical micrograph of the alloy A sample austenitized at 1000°C, whose dγ was 69 μm. Figure 4 shows the dγ of the entire sample. dγ was not affected by the carbon content. By contrast, dγ increased with the austenization temperature from 800 to 1000°C.
OM images of samples evaluated. (a) Alloy A austenitized at 900°C, (b) alloy D austenitized at 900°C, (c) alloy A austenitized at 1000°C. Bold line in (b) shows typical prior austenite grain boundary, which is less clear than that in alloy A shown in (a) and (c).
Relationship between average austenite grain diameter and square root of carbon content.
Figure 5 shows the inverse pole figure maps of the entire specimen. The black lines correspond to high angle boundaries as effective grain boundaries. dγ decreased with the austenitization temperature from 1000 to 800°C, thereby decreasing deff.7,10,30,31) Although the carbon content did not affect dγ, it is well known that increasing the carbon content decreases the size of the block, which comprises laths of the same habit plane and similar crystallographic orientations in the lath martensite structure.5,14) Figure 6 shows the effect of carbon content on deff. In this study, deff decreased as the carbon content increased at each austenitization temperature; this occurred because the blocks separating each packet in prior austenite grain became finer as the carbon content increased, as shown in Fig. 5.
Inverse pole figure maps of Fe–18Ni samples. Black lines correspond to effective grain boundaries whose misorientations exceeded 10 degree. (Online version in color.)
Relationship between effective grain diameter and square root of carbon content.
Figure 7 shows the true stress–true strain (SS) curves during uniform elongation in the lath martensite samples austenitized at 900°C. The ends of these SS curves correspond to the limits of uniform elongation, at which dσ/dε = σ in the true scale. The roundhouse type yielding behavior appeared in all the SS curves, as shown in Fig. 7; therefore, no clear yield points were observed. Figure 8 shows these SS curves focusing on their yielding behaviors. In this diagram, the YP are true stresses of clear elastic limits at which dσ/dε begins to decrease from the Young’s modulus of 173 GPa, as evaluated in Fe–18Ni alloys by Takaki et al.29) As shown in Fig. 8, the YP increased with the carbon content. Similarly, the σ0.2%, σ0.6%, and TS in Fig. 7 increased with the carbon content. Figure 9 shows the dependence of the YP, σ0.2%, σ0.6%, and TS on the carbon content. These stresses increased linearly with the square root of the carbon content, and the dependence increased with true strain, namely, in following order: YP < σ0.2% < σ0.6% < TS.
True stress–true strain curves during uniform elongation on samples quenched after austenitization at 900°C.21) Copyright 2019 by The Minerals, Metals & Materials Society. Used with permission. (Online version in color.)
The yielding behavior of samples quenched after austenitization at 900°C, whose true stress–true strain curves are shown in Fig. 7. Four arrows attached to true stress–true strain curves show their yield points, and gray lines correspond to Young’s modulus of Fe–18Ni alloys.29) (Online version in color.)
Figure 10 shows the SS curves of alloy A samples austenitized at 800, 900, and 1000°C, separately. In Fig. 10(a), although three curves are presented, it appeared as if only one curve is presented. This is because the differences among the SS curves of these samples were less than 5 MPa during uniform elongation, as depicted in Fig. 10(b), which shows a magnified view of the SS curves presented in (a).
True stress–true strain curves of alloy A samples austenitized at 800, 900, and 1000°C. (b) shows magnified true stress–true strain curves around uniform elongation. (Online version in color.)
Figure 11 shows the YP, σ0.2%, σ0.6%, and TS of these samples based on their austenitized temperatures. In these samples, the lath martensite structure refined as the austenitized temperature decreased, as shown in Fig. 5. However, these stresses were not affected by the austenitized temperature; therefore, their tensile properties were exactly the same regardless of their dγ and deff.
Relationship between tensile properties and austenitization temperature in alloy A. Δ means a difference from maximum value to minimum value for each tensile property, i.e. YP, σ0.2%, σ0.6%, and TS, in six specimens.
Figure 12 shows the SS curves of the samples of alloys B, C, and D. In the alloy B sample, as shown in Fig. 12(a), the three SS curves with several austenitized temperature appeared to be similar. However, their differences exceeded 15 MPa at the YP, σ0.2%, σ0.6%, and TS; hence, these three curves can be easily distinguished. The increase in flow stresses, as shown in the SS curves, with the decreasing austenitized temperature became more prominent as the carbon content increased. In the alloy D sample, as shown in Fig. 12(c), the stress differences were 65, 96, 88, and 103 MPa at the YP, σ0.2%, σ0.6%, and TS, respectively.
True stress–true strain curves during uniform elongation of specimens austenitized at several temperatures. (a), (b), and (c) show results for alloys B, C, and D, respectively. (Online version in color.)
It has been suggested that the strengthening of the lath martensite structure with the decrease in the austenitized temperature depends on the refinement of deff.10,11,12,13) Figure 13 shows the YP, σ0.2%, and σ0.6%, and TS of these samples vs. the inverse of their deff. Although these stresses were stable in alloy A, as shown in Fig. 11, they increased with the refinement of effective grains in alloys B, C, and D. These stresses increased linearly with the inverse of their deff in form of the Hall–Petch relationship,10,11,12,13) where σ = k·deff−1/2 + A. As shown in Fig. 13, kYP, k0.2%, k0.6%, and kTS, which are the Hall–Petch coefficients for the YP, σ0.2%, σ0.6%, and TS, respectively, were almost zero in alloy A, and they increased with the carbon content.
Relationships between tensile properties and inverse square root of effective grain diameter. (a),21) (b), (c), and (d) show results of YP, σ0.2%, σ0.6%, and TS, respectively. (a) Copyright 2019 by The Minerals, Metals & Materials Society. Used with permission.
It is well known that the strength of the lath martensite structure increases with decreasing dγ. It is speculated that this strengthening depends on the refinement of the effective grain size, namely, that of the packet,11,12) block,10) or lath.13,31) Morito et al.10) indicated that σ0.2% depended on the block size in 2 mass%Mn–0.2 mass%C lath martensite based on the Hall–Petch relationship and suggested that a block surrounded by high angle boundaries, such as ferrite grains in polygonal ferritic steel, corresponded to the effective grain in the lath martensite structure.
The effective grain evaluated in this study was almost equivalent to the block size; hence, the strength of the lath martensite tested in this study, except for alloy A, appeared to depend on deff based on the Hall–Petch relationship, as shown in Fig. 13. Table 2 shows the coefficients and intercepts of the Hall–Petch relationship, which were calculated via the least-squares method using six datasets (two specimens by three austenitized temperatures) in each alloy. Furthermore, Fig. 14 shows the Hall–Petch coefficients vs. the square root of the carbon content. The Hall–Petch coefficients for all stresses evaluated were almost zero in alloy A and increased with the carbon content.
| Alloy | Carbon content | Yield point | 0.2% proof stress | 0.6% proof stress | Maximum tensile strength | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| kYP | AYP | R2 | k0.2% | A0.2% | R2 | k0.6% | A0.6% | R2 | kTS | ATS | R2 | ||
| mass ppm | MPa·m1/2 | MPa | MPa·m1/2 | MPa | MPa·m1/2 | MPa | MPa·m1/2 | MPa | |||||
| A | 4 | −0.040 | 136 | 0.61 | −0.038 | 622 | 0.39 | 0.006 | 730 | 0.04 | 0.017 | 757 | 0.17 |
| B | 7 | 0.167 | 116 | 0.99 | −0.169 | 588 | 0.80 | 0.187 | 701 | 0.92 | 0.196 | 732 | 0.91 |
| C | 110 | 0.377 | 77 | 0.99 | 0.312 | 615 | 0.97 | 0.334 | 740 | 0.96 | 0.333 | 797 | 0.84 |
| D | 570 | 1.196 | 111 | 0.98 | 0.832 | 541 | 0.99 | 0.750 | 734 | 0.98 | 0.993 | 780 | 0.92 |
Relationship between Hall–Petch coefficients and square root of carbon content. White dots correspond to coefficients of alloy A, replotted to zero on horizontal axis.
In this study, it was presumed that the solute carbon content in alloy A was smaller than 4 mass ppm by heat treatment when growing Ti(CN) particles at 500°C prior to austenitization. The white dots in Fig. 14 show the coefficients of alloy A replotted at zero mass ppm on the horizontal axis. The black dots corresponding to the coefficients in alloys B, C, and D and white dots appear to be straight lines in Fig. 14. This suggests that the effect of grain refinement strengthening in the lath martensite structure, which occurred due to the solute carbon and its parameters, namely the Hall–Petch coefficients, increased linearly with the square root of the solute carbon content. This relationship seems to correspond to the strength of lath martensite which increases linearly with the square root of the solute carbon content,4,12,45) as shown in Fig. 9.
Takaki et al.32,33,34) reported the dependence of the Hall–Petch coefficient, kYP, on the solute carbon content in fully ferritic steels. In their study, kYP increased parabolically with the solute carbon content from 1 to 97 mass ppm, as evaluated via an internal friction test. They suggested that this effect was due to the carbon segregation at the boundaries of polygonal ferrite grains. These segregated carbon atoms stabilize dislocation sources on grain boundaries; hence, it is difficult for the strain to be distributed by the dislocation propagating over the grain boundary with the increase in the number of segregated solute carbon atoms, and the applied stress required for plastic deformation will increase.35)
Figure 15 shows AYP, A0.2%, A0.6%, and ATS, which are Hall–Petch intercepts for the YP, σ0.2%, σ0.6%, and TS, respectively, to the square root of the carbon content. The AYP in all the alloys did not depend on the carbon content, and they were approximately 100 MPa. Similarly, A0.2%, A0.6%, and ATS were almost constant at approximately 600, 720, and 750 MPa, respectively. The intercept in the Hall–Petch relationship included the effects of whole strengthening mechanisms without effective grain refinement; hence, the intercept was affected by the solution hardening effect of carbon,9,19,20) which implies that the solute carbon atom in the bcc iron crystal trapped the dislocation moving with the applied stress. However, in this study, intercepts for whole stresses were independent of the carbon content, as shown in Fig. 15. This indicates that solution hardening by carbon atoms did not occur in the lath martensite structures evaluated in this study. Similarly, it is suggested that dislocations induced during martensitic transformation, which increases with carbon content,15,16) did not affect the strength.
Relationships between Hall–Petch intercepts and square root of carbon content. White dots correspond to intercepts of alloy A, replotted to zero on horizontal axis.
Strengthening by carbon in the low-carbon lath martensite depends entirely on the refinement of deff and the increase in the effectiveness of grain refinement represented by the Hall–Petch coefficient. Furthermore, solution hardening by solute carbon atoms and dislocation hardening by dislocations induced during transformation did not appear to be active. Table 3 shows the recalculation results using the Hall–Petch relationship based on our understanding of strengthening. We considered the Hall–Petch intercepts in alloys B, C, and D as average stresses in alloy A, as shown in Fig. 11; therefore, AYP, A0.2%, A0.6%, and ATS were fixed at 125, 613, 731, and 761 MPa, respectively. The Hall–Petch coefficients in alloys B, C, and D were recalculated using the least-squares method. Figure 16 shows the recalculated coefficients vs. the square root of the carbon content. The coefficients for each stress, i.e., the YP, σ0.2%, σ0.6%, and TS, increased with the carbon content and increased linearly from the starting point of the graph to those in alloy D containing 570 mass ppm carbon.
| Alloy | Carbon content | Yield point | 0.2% proof stress | 0.6% proof stress | Maximum tensile strength | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| kYP | AYP | R2 | k0.2% | A0.2% | R2 | k0.6% | A0.6% | R2 | kTS | ATS | R2 | ||
| mass ppm | MPa·m1/2 | MPa | MPa·m1/2 | MPa | MPa·m1/2 | MPa | MPa·m1/2 | MPa | |||||
| A | 4 | 0.002 | 125 | −0.10 | 0.001 | 613 | 0.01 | 0.002 | 731 | 0.02 | 0.001 | 761 | 0.01 |
| B | 7 | 0.137 | 0.95 | 0.083 | 0.59 | 0.089 | 0.66 | 0.098 | 0.67 | ||||
| C | 110 | 0.223 | 0.82 | 0.318 | 0.97 | 0.363 | 0.95 | 0.446 | 0.74 | ||||
| D | 570 | 0.531 | 0.67 | 0.631 | 0.93 | 0.757 | 0.98 | 1.048 | 0.92 | ||||
Relationship between Hall–Petch coefficients recalculated in Table 3 and square root of carbon content. White dots correspond to coefficients of alloy A, replotted to zero on horizontal axis. Gray dots show Hall–Petch coefficients of polygonal ferrite structure reported in previous studies.32,36,37)
The gray dots in Fig. 16 correspond to kYP on polygonal ferritic steels reported in previous studies.32,36,37) kYP increased linearly with the square root of the solute carbon content evaluated via an internal friction test at less than 100 mass ppm.32,33) kYP saturated at values exceeding 100 mass ppm.36,37,38) Takaki et al.32,33,34) explained this tendency based on the segregation behavior of solute carbon at the grain boundaries. Below 100 mass ppm, the sites on the grain boundaries were not filled by solute carbon atoms; hence, some dislocation sources on the grain boundaries, whose density would decrease with the increase in segregated carbon atoms, would be active and assist in the strain distribution over the grain boundaries.35) By contrast, at values exceeding 100 mass ppm, the number of solute carbon atoms was larger than that required to fill the sites on the grain boundaries; therefore, the maximum effect of whole grain boundary trapping dislocations moving with applied stress was attained, and kYP in ferritic steel saturated at 0.6 MPa·m1/2.36,37,38)
Similarly, kYP in the lath martensite structure increased linearly with the square root of the carbon content. However, the kYP in lath martensite evaluated in this study was lower than that in ferritic steel. It is speculated that the effective grain boundaries in lath martensite contained fewer solute carbon atoms. kYP in alloy D was less than 0.6 MPa·m1/2; therefore, some sites on the effective grain boundaries would not filled. In the lath martensite structure, many solute carbon trap sites appeared regardless of the effective grain boundary, i.e., lath boundaries with small misorientation39) and dislocations induced by transformation.39,40) We assumed that the stabilization of the dislocation source on the effective grain boundary by solute carbon in lath martensite was weaker than that in ferritic steel. This might have contributed to the disappearance of solution hardening by the solute carbon atoms in lath martensite, because these atoms were trapped in these trap sites and were poor in bulk bcc crystal.
As shown in Fig. 16, the Hall–Petch coefficients increased in the order of kYP, k0.2%, k0.6%,, kTS. This suggests that the strengthening by grain refinement increased with the plastic strain. Figure 17 shows the coefficients vs. the true plastic strain, where kTS was plotted on the true plastic strain axis at uniform elongation in each alloy sample austenitized at 900°C. The coefficients in alloys B, C, and D increased parabolically as a function of the true plastic strain.41) It is well known that the uniform elongation in lath martensite increases with the carbon content despite strengthening,42,43) as shown in Fig. 13. The increase in carbon content decreased deff and increased the values of the Hall–Petch coefficients, particularly when plastic strain was involved; therefore, the work hardening rate increased with the carbon content. Consequently, the uniform elongation, at which the flow stress crosses the work hardening rate, increased with the carbon content.
Relationship between Hall–Petch coefficients recalculated in Table 3 and true plastic strain induced by single axis tensile deformation.
As mentioned above, strengthening by solute carbon in lath martensite depended on the refinement of deff and the increase in the coefficients. By contrast, solution hardening by carbon atoms did not occur. Therefore, these results indicate that the strength of lath martensite without carbon, as shown in Fig. 11, was unaffected by deff. Although the lath martensite without carbon was softer than that with carbon, it was much harder than fully ferritic steel of a similar deff. It would be difficult to explain this behavior based on the classical understanding of the strengthening mechanism of lath martensite. We hypothesized that the high strength of lath martensite without carbon was caused by the increasing dislocation density during plastic deformation, which would be completely different from that in ferritic steel. This is because the YP in lath martensite without carbon (125 MPa) was similar to that in polygonal ferrite, i.e., approximately 100 MPa,32,38) and the strength difference between lath martensite and ferrite was generated in the early stage of plastic deformation. Some studies14,29,44) focused on the behavior of dislocation density and the development of dislocation substructures during plastic deformation in lath martensite structures. These behaviors differed from those of the polygonal ferrite structure, and it was implied that the dislocation cells, which were formed in the early stage of plastic deformation by the ordering of dislocations induced by martensite transformation, strengthened the lath martensite structure.
The aim of this study was to clarify the strengthening mechanism of the lath martensite structure. We evaluated the tensile properties of as-quenched lath martensite specimens that were transformed from prior austenite grains of different sizes in Fe–18Ni alloys containing 4 to 570 mass ppm carbon.
(1) The prior austenite grain was refined as the austenitization temperature decreased, regardless of the carbon content. In addition, the effective grain refined owing to an increase in the carbon content and the refinement of the prior austenite grain.
(2) The tensile strengths, i.e., the YP (elastic limit), σ0.2%, σ0.6%, and TS, in specimens austenitized at 900°C increased linearly with the square root of the carbon content. In addition, the uniform elongation improved with increasing carbon content.
(3) For alloy A, which contained 4 mass ppm carbon and would be contained in large Ti(CN) particles, the YP, σ0.2%, σ0.6%, and TS were constant, regardless of the change in deff with the austenitization temperature.
(4) In alloys B, C, and D containing 7, 110, and 570 mass ppm carbon, respectively, the YP, σ0.2%, σ0.6%, and TS increased linearly with the inverse square root of deff in each alloy. This tendency corresponded to the typical Hall–Petch relationship.
(5) The Hall–Petch coefficients kYP, k0.2%, k0.6%, and kTS in alloy A were almost zero, whereas those in alloys B, C, and D increased with the carbon content. By contrast, the Hall–Petch intercepts AYP, A0.2%, A0.6%, and ATS in all alloys were unaffected by the carbon content. This indicates that the strengthening by carbon in this study originated from the refinement of the effective grain and the increase in the values of the Hall–Petch coefficient. Similarly, it was suggested that solution hardening by solute carbon atoms was not active in Fe–18Ni lath martensite containing 570 mass-ppm or less carbon.
(6) Based on the assumption that the Hall–Petch intercepts were constant regardless of the carbon content, it was discovered that the Hall–Petch coefficients were proportional to the square root of the carbon content. The effect of grain refinement on the strength became more prominent as the plastic strain increased.
The authors would like to express their sincere gratitude to Dr. Shigekazu Morito and Dr. Taisuke Hayashi (Shimane University, Japan) for their valuable comments and fruitful discussions.
