2020 Volume 61 Issue 4 Pages 668-677
The changes in the states of carbon (C) together with hardness and the tensile properties of low C steel (0.045C–0.34Mn in mass%) quenched from 710°C and aged at 50°C were investigated as a function of aging time using TEM and atom probe tomography. Vickers hardness increases at about 1.1 × 104 s, exhibits significant increase at 5.8 × 104 s (16 h) and maintains peak hardness untill 8.6 × 105 s (10 d) followed by a decrease after further aging time. At the start of peak aging, C clusters form with an irregular shape that resembles a sphere about 10 nm in diameter. The number of C atoms is about 700, and the C content is in the range of 1–2 at% at 1.0 × 105 s (28 h), where no enrichment of elements except for C is observed. At the end of peak aging, the plate-shaped precipitates (about 1 nm wide and 12 nm long) having a C content greater than 10 at% are distributed with the {100} habit plane, thus confirming the transition from C clusters to fine carbides. Lower yield strength (LYS) is the lowest for the specimen with solute C, and significantly increases for the specimen with C clusters and fine carbides in this order. LYS is determined presumably by the cutting mechanism for the C cluster specimen and the Orowan mechanism for the fine carbide specimen. The work hardening for the solute C and C cluster specimens is high, while the carbide specimen shows less work hardening. The C cluster is assumed to be decomposed into solute C through shearing by dislocations, causing work hardening and relatively good uniform elongation. Post uniform elongation (l-El) was the lowest for the C cluster specimen followed by the fine carbide specimen with the same strength level. This is because dynamic strain aging caused by solute C promotes the strain localization leading to the deterioration in l-El.
This Paper was Originally Published in Japanese in J. Japan Inst. Met. Mater. 83 (2019) 353–362.
Changes in Vickers hardness and state of carbon with aging time at 50°C.
The low temperature aging of the quenched specimens from the high temperature ferritic region of low carbon steel exhibits a remarkable increase in hardness.1,2) This implies the prominent strengthening capability of carbon (C) clusters and/or extremely fine iron carbides compared with solid solution hardening by C. Despite previous analyses on the C clusters and extremely fine iron carbides conducted using TEM (Transmission Electron Microscopy), their actual states have not been fully clarified. Furthermore, industrial use of a prominent hardening has yet to be implemented. However, there have been many studies on the low temperature tempering effect on martensite with the complicated hierarchical structure. Recently studies on martensite using APT (atom probe tomography) have been conducted. However, the structure of martensite is extremely complicated with various lattice defects. Therefore, research on the quench and aging of ferrite single phase steel is anticipated to provide fundamental findings on the strength mechanism of martensitic steel.
Abe et al.1,2) conducted an experiment in which low carbon Al-killed steel (0.046C–0.01Si–0.35Mn–0.02P–0.018S–0.04Al–0.0060N (mass%)) was water-quenched from 700°C followed by iso-thermal aging at 35–300°C for various times untill 5 × 106 s. The changes in the states of C were investigated by hardness measurement together with the combined exploitation of electrical conductivity and thermo-electric power. The two stages of hardening behavior were revealed in a temperature range of 35–75°C. The first stage with small hardening was assumed to be caused by the segregation of solute C to dislocations, whereas the second stage with significant hardening was caused by the formation of C clusters and extremely fine iron carbides. During iso-thermal aging at 100–200°C, metastable carbide (ε carbide) formed, which led to slight hardening in the early stage of aging followed by softening in the later stage. When the aging temperature increased as high as 300°C, the stable carbide (θ carbide) formed, where the softening proceeded with aging time. However, no changes in the C states with aging were directly observed. Moreover, for mechanical properties, the hardness measurement was the only test conducted and no tensile test was performed. Therefore, neither the influences of C clusters and fine iron carbides on yielding and subsequent work hardening behaviors nor ductility were reported.
Vyhnal3) investigated the influence of the cooling rate on the quench aging behavior of pure Fe–0.019C alloy (no Al addition) using TEM and micro hardness measurement. An extremely rapid cooling rate as fast as 25000°C/s following the solution heat treatment of 710°C–30 min was achieved. The aging temperatures were both 25°C and 100°C, showing that the morphology of carbides, the amount of age-hardening and the aging kinetics differed significantly depending on the cooling rate. When the cooling rate was as fast as 25000°C/s, C-V (carbon-vacancy) pairs were maintained during low temperature aging. Thus, they acted as the nuclei of precipitation resulting in the extremely fine carbides. Fine globular carbides as small as 10 nm formed at intervals of 10 nm after aging of 25°C–1000 h in the case of an ultra-fast cooling rate over 3000°C/s. For the relatively slow cooling rate of several 100°C/s, 50 nm fine globular carbides formed at intervals of 200 nm. Moreover, the C-V pair promoted the growth of carbides, which was possibly caused by the C-V pair relaxing the coherent strain in the interface between the carbide and matrix leading to precipitate coarsening. However, the usual cooling rate was presumed to no longer produce the C-V pair. The fine carbides were observed only by TEM, but were not evaluated by APT. For the mechanical properties, only the hardness measurement was conducted, and neither the effect of the cooling rate on yielding and subsequent work hardening behaviors nor the effect on ductility were examined.
Kobayashi et al.4) investigated the changes in both the hardness and the state of C with time during room temperature aging in C supersaturated ferrite using APT. The increase in hardness was presumably caused by the formation of the C enriched region (C cluster). Furthermore, the formation of the C cluster was suppressed by the presence of solute Ti and Nb presumably due to the attractive interaction between them and C. However, the transition from C cluster to carbides during long time aging was not examined, nor was any tensile test performed.
Ohtani et al.5) reported that the formation of C clusters may be caused by the spinodal decomposition during the quench and low temperature aging of ferrite. Similarly, Olson et al.6) reported that C clusters are formed as a precursory phenomenon prior to the carbide precipitation in the early stage of low temperature tempering of martensite, the mechanism of which was assumed to be the spinodal decomposition.
Many studies have also been conducted the formation of C clusters and fine carbides during the low temperature tempering of martensite.7,8) Fe–Ni–C alloys with low martensitic transformation temperature (Ms) are often used to prevent the auto-tempering of martensite during quenching. Zhu et al.7) confirmed the relatively high C enriched region (C cluster) of as much as 10 at% during martensite tempering at 20–150°C by APT, and the C cluster was implied as the precursory phenomenon of ε carbide precipitation. However, no attempt was made to connect these changes in the C states with mechanical properties. Lu et al.8) revealed the formation of η carbides in Fe–15Ni–1C martensitic steel after room temperature aging as long as 2–3 years by both APT and TEM, and revealed that disk-like η–Fe2C precipitated in the {521} habit plane of martensite after long-term aging. Contrary to the previous idea that the nm order transition carbides precipitate at over 100°C, they were confirmed to form even at room temperature aging for a long time. However, the relationship between the disk-like transition carbides and mechanical properties has not been reported. Moreover, according to the recent result of the first principle calculation by Liu et al.,9) the formation energy of η carbides at room temperature was the lowest among various carbides.
Concerning the effect of clusters on tensile properties, there is much literature on Al alloys, but few studies on steels. We have already investigated the effects of clusters and fine precipitates on tensile properties in the 6000 series Al–Mg–Si alloy by forming clusters aged at 100°C, and fine precipitates β′′ aged at 180°C following the solution treatment at 550°C. Three specimens of as-solution treated, as-aged with Mg–Si clusters and as-aged with fine precipitates having the same hardness value were subjected to the tensile test. The specimen with clusters exhibited a good balance of strength and ductility, most likely due to the increase in work hardening in a large strain region presumably caused by shearing clusters by dislocations and decomposing clusters into solute Mg and Si leading to the retardation of dynamic recovery. To verify whether the positive effect in Al alloys also holds for steel in terms of improving the strength-ductility balance, we investigated the tensile behavior of specimens aged at low temperature after the quenching of low carbon steel.
Abe et al.11) conducted tensile tests using specimens with 1) C in solid solution by quenching the Fe–C alloy with ferrite single phase from 700°C and 2) fine iron carbides subsequently aged at 200°C for 1 h. The specimen with solute C exhibited dynamic strain aging during the tensile test even at room temperature with a usual strain rate, which promoted the strain localization during the tensile test. On the other hand, the specimen with very fine iron carbides as small as 300 nm by low temperature aging was fractured within the Lueders band prior to work hardening. However, no specimens with various C states were not systematically subjected to the tensile test.
Considering the situations in the previous studies, our study placed particular focus on preparing specimens with different C states by changing the aging times at 50°C after quenching a specimen from 710°C using 0.046C steel. The first objective was to accurately evaluate the state of C, which was the problem in the past research, by simultaneously exploiting APT and TEM. The second was to investigate the influence of the states of C on tensile properties. Here, the effects of the states of C on yielding and work hardening behaviors are examined as well as ductility from the aspect of the interaction between low temperature products and dislocations.
Table 1 shows the chemical compositions of low C Al-killed steel used in the present study. The starting material was a vacuum-melted ingot with small additions of Si, Mn and P of 0.045C–0.015Si–0.34Mn–0.02P–0.017S–0.038Al, which is very similar to the steel used by Abe et al.1) Material was heated at 1250°C for 60 min followed by hot rolling at the finish delivering temperature of 950°C in an austenite region. Subsequently, material was air-cooled to 600°C and held for 1 h followed by air cooling to room temperature. Material 4 mm thick was ground to 3 mm from both sides and was cold-rolled to 1 mm with a reduction of 66%. Material was annealed at 710°C for 20 min followed by water quenching. Thus, the microstructure of the annealed specimen consisted of equiaxed grains with an average grain size of about 15 µm. The quenched material was then aged at 50°C for 1 × 102 s∼1 × 107 s in order to change the C states such as C in the solid solution, C clusters and very fine iron carbides. Furthermore, most of the nitrogen (N) as an interstitial element is considered to be fixed as AlN. Therefore, the phenomena related to the interstitial atoms are caused by C. Special attention was paid to prevent room temperature aging of the quenched specimen by keeping specimens in liquid nitrogen except for the period for sample preparation and testing.
As for C in the as-quenched specimen, about 0.02%C and remaining C among 0.045%C are expected to exist as C in solid solution and coarse cementite, respectively. Hereafter, the quenched specimen is called the solute C specimen. According to the research by Abe et al.,1) the solute C is expected to change into C clusters and extremely fine iron carbides with aging time at 50°C.
In the present study, the observations by TEM and APT were conducted in order to evaluate the C clusters and very fine iron carbides. A thin foil specimen for TEM observation was prepared in the usual manner: both surfaces of the specimens were first mechanically polished to obtain a thickness of 100 µm and the specimen was then perforated with a twinjet electro-polishing machine. A H-8000 TEM (Hitachi) was used for TEM observation at an accelerating voltage of 200 kV. The needle sample for APT was first cut from a sheet into a bar and then finished by electro-polishing. APT measurements (LEAP 4000X HR, Cameca Instrument) were performed using either voltage mode or laser mode. The conditions for voltage mode were as follows: the specimen temperature 65 K, pulse fraction 20%, and the pulse repetition rate 200 kHz, while the conditions for laser mode were as follows: the specimen temperature 50 K, laser pulse energy 30 pJ, and the pulse repetition rate 250 kHz. The quantification method of C and other alloying elements under the above condition was already established in a separate paper.12) Since the detection ratio of ion in the present equipment is about 38%, the number of elements comprising cluster and precipitate was estimated by multiplying 1/0.38 to the measured value. The total number of measured ions was set to be 20 M (million) in multiple areas. Three-dimensional representation of the measured data was performed using IVAS software (Cameca Instrument). The present steel contains Si and N; however, the mass-charge ratio of 14N+ and 28Si2+ belongs to the same 14Da, which makes it impossible to distinguish them. Therefore, the expression of Si+N was used.
The specimens were kept in liquid nitrogen or a refrigerator at −30°C except for the sample preparation period in order to prevent the change in the state of C due to room temperature aging. Here, the periods during thin foil preparation for TEM observation and the needle sample preparation for APT were inevitable. However, the substantial aging time at room temperature was less than 1 d, and the diffusion distance of C at room temperature was estimated to be less than 1/5 of that during aging at 50°C for 28 h. Therefore, the change in the C states caused by room temperature aging was judged to be negligible.
2.2.2 Mechanical propertiesThe change in hardness with aging time was evaluated using the Vickers hardness tester of MVK-G3 (Akashi, Ltd., Japan) at room temperature. After removing the surface oxide layer using abrasive paper, the average of values measured at five positions was used with a weight of 9.8 N applied to the top surface.
The tensile tests were conducted for tensile specimens of Japanese Industrial Standard (JIS) No. 5 with a gauge length of 50 mm using the autograph AG-10TA tensile machine (Shimazu, Ltd., Japan). The crosshead speed (strain rate) was 1 mm/min (3.33 × 10−4 s−1) at room temperature. Moreover, the work hardening rate dσ/dε was evaluated. Here, σ and ε are true stress and true strain, respectively. Since serrations were observed in the nominal stress-nominal strain curves of the solute C specimen and the C cluster specimen, the problems with vibration and accuracy occurred for the work hardening rate dσ/dε obtained from the serrated stress-strain curves. Therefore, the true stress–true strain curves were first approximated with the polynomial of a power of true strain, making it possible to obtain the smooth and reliable work hardening rate dσ/dε.
Figure 1 shows the change in Vickers hardness (Hv) with aging time at 50°C. The prominent hardness peak is clearly recognized in a range of 5.8 × 104 s (16 h) and 8.6 × 105 s (10 d). The hardness of the as quenched specimen was 140 Hv, while it increased to 200 Hv under the peak hardness condition. Moreover, the hardening commences at about 1.1 × 104 s, whereas the softening starts after 8.6 × 105 s. These results reproduce the change in hardness with time quenched and aged at 50°C reported by Abe et al.1)
Change in Vickers hardness with aging time at 50°C of the quenched specimen.
The C states both at the early stage of peak hardening (1.0 × 105 s (28 h)) and the later stage of peak hardening (8.6 × 105 s (10 d)) were investigated by TEM and APT.
Figure 2 shows the bright field images observed from [001] by TEM for the two types of specimens. The specimen in the early stage of peak aging (28 h) exhibited the indistinct strain contrast images presumably caused by the very fine particles (Fig. 2(a)). On the other hand, the specimen in the later stage of peak aging (10 d) showed the clearer dense strain contrast images (Fig. 2(b)). Presumably the fine iron carbides with the disk shape precipitated; however, no diffraction pattern corresponding to the precipitates was identified. Judging from the strain contrast, the fine disk precipitates having the habit plane of {100} were estimated to distribute with intervals of about 30 nm.
TEM bright field images showing contrasts caused by clusters and precipitates aged at 50°C for (a) 28 h and (b) 10 d.
Figures 3 and 4 show the results of APT in the specimens aged for 28 h and 10 d. Figure 3(a) indicates the modulated thick and thin contrast of the C content of the specimen in the early stage of peak aging (28 h). Assuming that the amount of solute C at 710°C corresponds to the solubility limit of C 0.093 at% (0.02 mass%), the fact that the average C content in the whole of the area measured was about 0.07 at% suggests that the average state in the present steel was correctly observed. The modulated structure in terms of the C content was observed, and it had the irregular shape resembling that of a sphere 10 nm in diameter, which was distributed at intervals of about 20 nm. The interface between the modulated structure and matrix was indistinct and diffuse, suggesting the existence of the C cluster. Hereafter, the material having C as the C cluster is called the C cluster specimen. Figure 3(b) shows the 3D elemental maps in a 20 nm × 20 nm × 20 nm box. The average number of C atoms comprising the C cluster is estimated to be about 700, and the concentration profile of C crossing the C cluster shown in Fig. 3(c) reveals C content as much as 1–2 at% (0.2–0.4 mass%). It is suggested that more than 10 times of C in comparison to the solubility of C 0.093 at% (0.02 mass%) enriched into the C cluster. No enrichment of Mn, Si, N, P and Al was detected in the C cluster, indicating that no partitioning of the alloying element takes place during the C cluster formation. In the specimen aged untill the later stage of peak age (10 d), Fig. 4 shows that the disk-like precipitates (width: ∼1 nm, length: ∼12 nm) with the C content higher than 10 at% densely form at intervals of about 30 nm. Hereafter, the material having extremely fine carbides is called the fine carbide specimen. The average number of C atoms comprised of fine carbides is estimated to be about 1600, and increased in comparison to the C cluster specimen aged for 28 h. The number density decreased to half that of the C cluster, which indicates that the further capture of C atoms as well as Ostwald ripening occurred during aging from 28 h to 10 d at 50°C. The disk-like precipitates have the habit plane of {100}. The small enrichment of C at the rear edge of the disk carbide was recognized in the measurement direction; however, this is an artifact of APT, not the real C distribution, probably caused by the delayed evaporation of C remaining on the surface of the specimen.13) Furthermore, the width of the disk carbide having the {100} habit plane enclosed by a rectangle seems to expand; however, this is another artifact of APT caused by the local magnification effect. The electron diffraction pattern from the fine disk carbides was not obtained because of their small size, but the fine carbide is assumed to be the early stage of ε carbide judging from the habit plane. No enrichment of Mn and Al was detected in the disk carbide, but the slight enrichment of Si+N and P was detected (Fig. 4(b)). P presumably segregated in the interface between the carbide and matrix, and N was taken into carbide together with C.
3D elemental maps (a), (b) and concentration profile of C (c) in the specimen aged for 28 h at 50°C.
3D elemental maps (a), (b) and concentration profile of C (c) in the specimen aged for 10 d at 50°C.
To show the influence of the change in the states of C during low temperature aging at 50°C on tensile properties, the solute C specimen, the C cluster specimen (5.8 × 104 s (16 h)) and the fine carbide specimen (8.6 × 105 s (10 d)) were subjected to the tensile test. Here, the aging time for the C cluster specimen subjected to TEM and 3DAP observations was 1.0 × 105 s (28 h), while that of the specimen for the tensile test was slightly shorter (5.8 × 104 s (16 h)). These two specimens are considered identical in the sense that both of the specimens were common in the early stage of peak aging and C cluster formation. Furthermore, the hardness values of these specimens are almost the same as that shown in Fig. 1. Figure 5(a) shows the nominal stress-nominal strain curves as a function of the states of C, while Fig. 5(b) is the enlargement of the curves to show the difference in yielding behavior between the specimens. Table 2 summarizes the tensile properties. It is obvious that the quenched specimen showed no clear yield drop, while the aged specimens exhibited the upper yield followed by yield point drop. Moreover, the solute C specimen had the lowest lower yield stress (LYS) of 320 MPa, while LYSs of the aged specimens with C clusters (16 h) and fine iron carbides (10 d) were 489 MPa and 507 MPa, respectively. The LYS significantly increased with low temperature aging and the fine carbide specimen had a slightly higher LYS than the C cluster specimen. Once specimens underwent the work hardening, the solute C specimen and the C cluster specimen commonly exhibited the high work hardening behavior. The fine carbide specimen showed almost no work hardening, except for the prominent work hardening in the early stage of plastic deformation presumably due to the dislocation pile up around carbides. Consequently, the C cluster specimen possesses higher TS of 596 MPa compared to the fine carbide specimen with TS of 537 MPa. Meanwhile, the solute C specimen with low strength had the largest uniform elongation (u-El) among the specimens, followed by the C cluster specimen and the fine carbide specimen. On the other hand, the local elongation (l-El), which is the post uniform elongation after the maximum load, is the largest for the solute C specimen followed by the fine carbide specimen and the C cluster specimen. The relation between the states of C and ductility will be discussed in Section 4.2.
(a) Nominal stress-strain curves of specimens quenched, and subsequently aged for 16 h and 10 d at 50°C, and (b) enlarged stress-strain curves near yield point.
Abe et al.1) reported that the combined analyses of electrical resistivity with thermo-electric power on the low temperature aging at 50°C of quenched low C steel exhibited the transition from C clusters to very fine iron carbides. Vyhnal et al.3) confirmed the formation of extremely fine iron carbides by TEM where the C-V pair was assumed to act as nucleation sites during low temperature aging owing to the quenched-in vacancies by the ultra-fast cooling. Kobayashi et al.4) observed C clusters with a diffused interface in ferritic steel during quench-aging at room temperature by APT. In the present study, the direct observation by TEM and APT revealed the transition from C clusters in the early stage of peak aging (28 h) to fine iron carbides in the later stage of peak aging (10 d) during quench-aging at 50°C.
The C cluster, which is presumably a precursory phenomenon of precipitation, has the modulated structure in terms of the C content, but has the same bcc crystal structure as the matrix phase. C is considered to have a repulsive interaction with the C atom itself;14) however, the formation of the C cluster is interesting itself. To the best of our knowledge, the reasons for this are as follows: 1) total energy decreases with the formation of the C cluster considering the multi-body interaction of C; 2) spinodal decomposition occurs from the aspect of free energy,5) resulting in the modulated structure in terms of the C content; 3) the C cluster may form owing to the C-V pair as nucleation sites.3,15) Here, 1) and 2) are basically the same, and these are plausible in the present study. Moreover, the transition from C clusters to fine iron carbides took place with the aging time at 50°C, which is presumably caused by the difference in free energy between them. Lu et al.8) observed the formation of very fine iron carbides after 2–3 years aging at room temperature using 1%C martensitic steel, indicating that the transition is caused by spinodal decomposition. Moreover, Shang et al.16) reported that the iron carbide is stabilized with the increase in the C content. However, the free energy of C in a standard state was Fe6C6, not the energy in the state of solid solution. Recently, Sawada et al.17) reported that the free energy decreases when ε-carbide precipitates considering the solid solution of C as the standard state. The calculated results were in good accordance with those by Shang et al.16)
4.2 Relation between changes in the states of C and tensile properties 4.2.1 Yield strengthThe solute C specimen scarcely shows a yield point phenomenon, while the specimens aged at 50°C exhibit it. This feature of the solute C specimen was also reported by Yoshimura et al.18) for which the residual unlocked mobile dislocations are responsible. The dislocations in the aged specimens are speculated to be immobile because of being locked by C, which makes it necessary to generate new dislocations resulting in an upper yield point. The grain boundary segregation of C, which takes place during aging, is also considered to be responsible for this phenomenon as discussed by Araki et al.19) This is because the emission of dislocations from grain boundaries is suppressed by the grain boundary segregation of C, which leads to the increase in the upper yield point.
Next, we will discuss the lower yield stress LYS of the specimens having three different states of C. When LYS of the solute C specimen is taken as a standard value, the increment in LYS of the C cluster specimen was 169 MPa, while that of the fine carbide specimen was 187 MPa (Table 2). Here, irrespective of the C cluster or fine carbide specimens, a part of 0.09 at% (0.02 mass%) solute C just after quenching is expected to remain as solute C. The increment in LYS during low temperature aging is judged to be the summation of precipitation hardening by the C cluster or fine carbide and solid solution hardening by solute C. In the present study, the amount of solute C for each aged specimen was examined by APT. Despite the reliability being low especially for the C cluster specimen because of its diffuse interface and the aberration problem with APT, Table 3 shows the estimated range of solute C in the matrix obtained. The solid solution hardening (MPa) by C was evaluated using the equation,20) 5000 × C (mass%), where the amount of solute C for each aged specimen is shown in Table 3. It was also confirmed that the solid solution hardening by C based on the above equation is in good agreement with those experimentally determined by the other papers.18,21) Therefore, the amount of precipitation hardening was evaluated by subtracting the solid solution hardening by C from the experimentally determined increment in LYS. Thus, the amount of precipitation hardening by the fine carbide was estimated to be in the range of 255–265 MPa, while that by the C cluster was in the range of 226–273 MPa. Here, the tensile test was carried out for the specimen aged for 16 h, while the observation of the C cluster by APT was conducted for the specimen aged for 28 h. Therefore, the specimens were not identical; however, the amount of precipitation hardening of the specimen aged for 28 h is presumably the same as that of the specimen aged for 16 h, because these two specimens show almost the same hardness values as shown in Fig. 1. Furthermore, as reported by Araki et al.,19) the increase in grain refinement hardening must be taken into consideration because the segregation of C in grain boundaries enhances the Hall-Petch coefficient with aging time. However, in order to quantitatively discuss the change in grain refinement hardening during aging, further study using current 0.045%C steel is required. This is because the dense C cluster or fine iron carbide exist in the present study, while the grain boundary C segregation together with relatively coarse carbides formation took place in 0.006C steel during aging in the specimen by Araki et al.19) These are subjects for future study. In this study the amount of rigorous precipitation hardening remains unclear by taking into account the increase in grain refinement strengthening during aging. However, it is suggested that the amount of the true precipitation hardening due to the C cluster or fine iron carbide is slightly lower than the value stated above.
Next, the precipitation hardening mechanism is discussed comparing the predicted Orowan stress using eq. (1) based on the Ashby-Orowan model.22) Irrespective of the C cluster or very fine carbide, the following two types of particle are considered: the Orowan-type strong particle leaving dislocation loops around the particle or the cutting-type weak particle being sheared by dislocation.
| \begin{equation} \sigma_{\text{Ashby-Orowan}} = 0.84M\frac{1.2Gb}{2\pi \lambda}\ln \left( \frac{x}{2b} \right) \end{equation} | (1) |
| \begin{equation} \lambda = 1/\sqrt{n_{s}} - x \end{equation} | (2) |
The estimated Orowan stress based on the Ashby-Orowan model is shown in Table 4. As for Taylor factor M, two cases of M = 2 and M = 2.75 frequently used in previous studies were assumed for calculating the Orowan stress.23–25) When the C cluster observed in the specimen aged for 28 h is assumed to have a sphere shape about 10 nm in diameter, the inter-spacing of particles in a slip plane λ = 41.8 nm is obtained. Therefore, the value of σAshby-Orowan is about 442 MPa assuming M = 2, while that of σAshby-Orowan becomes about 608 MPa assuming M = 2.75. These values are significantly large when compared with the experimentally determined ones (226∼237 MPa). On the other hand, fine iron carbides in the specimen aged for 10 d having a disk shape 12 nm in diameter are estimated to have the average inter-spacing of particles on a slip plane λ = 67.3 nm. Consequently, the value of σAshby-Orowan is about 289 MPa assuming M = 2, which is in close accordance with the experimental values (255∼265 MPa), while that of σAshby-Orowan is about 397 MPa assuming M = 2.75.
In an estimation of precipitation hardening by the Ashby-Orowan model, the parameters such as the inner-cut-off value, Taylor factor and so forth are assumed. Therefore, rigorous examination is difficult, because the assumed values are not necessarily valid. However, among the two specimens used in the present study, there is no difference in the parameters used except for the difference in aging time. Therefore, the relative comparison between them becomes possible and significant. The value of σAshby-Orowan for the C cluster specimen aged for 28 h is 1.5 times higher than that for the fine carbide specimen. This is attributed to the decrease in particle inter-spacing due to the high particle density of the C cluster. On the contrary, the amount of precipitation hardening experimentally determined by the tensile test considering the solid solution hardening by C exhibits a relatively similar value for two types of specimens, namely 226–237 MPa for the C cluster specimen and 255–265 MPa for the fine carbide specimen, respectively. This implies that if fine carbides are sheared by dislocations, C clusters are definitely sheared by dislocations. On the contrary, even if fine carbides are Orowan type particles, C clusters may be cutting type particles sheared by dislocations. The above analysis allows us to conclude that fine carbides are particles with strong interaction with dislocations, while C clusters are particles with weak interaction with dislocations. Concerning the precipitation hardening mechanism itself, various mechanisms such as the friction force effect, the chemical effect, the effect due to the difference in elastic modulus, the coherent strain effect and so forth have been proposed.26) The hardening mechanism for the two types of particles is not necessarily the same. In the present paper, we shall not examine this any further; however, the formation behavior of the C cluster and its interaction with dislocations are future subjects of interest.
The specimens in the peak aged condition from 5.8 × 104 s (16 h) (in the early stage of peak aging) to 8.6 × 106 s (10 d) (in the later stage of peak aging) exhibited almost the same hardness value; however, the state of C transited from C clusters to fine iron carbides and the hardening mechanism changed in association with the change in the states of C. Presumably the number of C atoms, size and morphology of precipitates changed with the aging time, leading to the particles with stronger interaction with dislocations from the cutting type to Orowan type. These changes were speculated to make a balanced contribution to the hardness, which was simultaneously affected by the changes in particle density, amount of solute C in the matrix, elastic strain in the interface between particle and matrix, and the grain boundary segregation of C. On the other hand, the decrease in hardness when aged longer than 8.6 × 106 s (10 d) is caused by the Ostwald ripening of fine iron carbides.
4.2.2 Work hardeningHere the work hardening behavior after yielding is examined. The C cluster specimen exhibited larger work hardening than that of the fine carbide specimen, and showed almost the same work hardening as the solute C specimen. These characteristics are obvious from the true stress-strain curves and superimposed work hardening rate dσ/dε shown in Fig. 6. The serrated stress-strain curves observed in the solute C specimen indicate the occurrence of dynamic strain aging during the tensile test at room temperature. Dynamic strain aging leads to the increase in work hardening,11,18,21) and the C cluster specimen increases the work hardening because of the occurrence of dynamic strain aging just like the solute C specimen. The C cluster specimen is expected to have more solute C than the fine carbide specimen before the tensile test. Moreover, the amount of solute C is speculated to increase during the tensile test. Since the C cluster is sheared by dislocations, a part of C composed of the C cluster is expected to be decomposed into solute C. Consequently, the C cluster specimen reveals large work hardening similar to the solute C specimen. The work hardening rate of the C cluster specimen is larger than that of the solute C specimen until the tensile strain reaches 0.1, which implies the redissolution of C from the C cluster. On the other hand, the fine carbide specimen shows the clear work hardening in the early stage of deformation because of the acceleration of dislocation pile up around particles. However, it is assumed that fine carbides do not contribute to the work hardening in the later stage of deformation.
True stress-strain curves of specimens quenched and subsequently aged for 16 h and 10 d at 50°C together with their work hardening rates dσ/dε.
Concerning the interaction between the Mg–Si cluster or β′′ (Mg2Si) formed during low temperature aging of the 6000 series Al alloy with dislocation, the following findings have been reported.10,27) The Mg–Si cluster is sheared by dislocation resulting in the redissolution of Mg and Si, which leads to the superior balance of yield strength with high work hardening. On the contrary, in the specimen with β′′ (Mg2Si) formed at relatively high aging temperature, dislocation by-passes particles with dislocation loops. Consequently, high yield strength in the early stage of deformation and low work hardening in the later stage of deformation were confirmed. A similar phenomenon in terms of yielding and work hardening is considered to take place in the present study of the Fe–C specimen quenched and aged at low temperature.
4.2.3 DuctilityNext, the relationship between the states of C and ductility (u-El and l-El) is analyzed. The work hardening of the C cluster specimen is large next to the solute C specimen, and its u-El is superior to the fine carbide specimen (Table 2). Here, u-El of the solute C specimen with the lower strength level is the best among three specimen types. Considering that the stress level of the C cluster specimen is about 40% higher than that of the solute C specimen, it is significant that the C cluster specimen has relatively good u-El. However, the C cluster specimen is presumed to have inferior u-El to the solute C specimen, because the higher stress level of deformation of the C cluster specimen is assumed to result in the relatively earlier plastic instability, i.e. necking. The post uniform elongation, l-El, from the maximum load to fracture is the lowest for the C cluster specimen, and the highest for the solute C specimen. The C cluster specimen is speculated to show the lowest l-El, because a part of the C cluster, which is dissolved as solute C due to being sheared by dislocation, as well as the relatively high initial solute C cause the occurrence of dynamic strain aging during the tensile test, which resulted in the acceleration of strain localization.11,18,21) The fine carbide specimen exhibits relatively high l-El, because C is fixed as the stable iron carbide as well as less initial solute C. On the other hand, the solute C specimen shows relatively good l-El because of its considerably lower stress level, although the occurrence of dynamic strain aging due to solute C promotes the strain localization.
The states of C were varied by changing the low temperature aging time at 50°C from 1 × 102 s to 1 × 107 s following quenching of the low C Al-killed steel (0.045 mass%C) from 710°C in the ferrite phase. The change in the states of C with aging time was investigated in detail by TEM and APT. Furthermore, the change in mechanical properties such as hardness and tensile properties was simultaneously evaluated. The results obtained are summarized as follows.
