01_107A_2.qxd 5/14/03 7:27 PM Page 1237
Effect of Prestrain and Deformation Temperature on the Recrystallization Behavior of Steels Microalloyed with Niobium B. DUTTA and E.J. PALMIERE The evolution of microstructure during the hot working of steels microalloyed with Nb is governed by the recrystallization kinetics of austenite and the recrystallization-precipitation interaction. The present study focuses on the effects of prestrain and deformation temperature on the rectrystallization behavior in these steels. The extent of recrystallization is characterized by a softening parameter calculated from a series of interrupted plane strain compression tests carried out at different deformation temperatures and strain levels. The results indicate that at low temperatures, softening is caused by static recovery, while at higher temperatures, static recrystallization is the predominant mechanism. The recrystallization-stop temperature (T5pct ) and the recrystallization-limit temperature (T95pct ), marking the beginning and end of recrystallization, respectively, are determined as a function of strain. In order to achieve a homogeneous microstructure, finish rolling should be carried out outside the window of partial recrystallization (T5pct < T < T95pct ), as determined in this study. The Nb(CN) precipitation kinetics have been calculated using a model proposed in an earlier work, and these results are used to estimate the precipitate pinning force under the given processing conditions. Based on these estimations, a criterion has been proposed to predict the onset of recrystallization. The predicted results are found to be in reasonably good agreement with the experimental measurements.
I. INTRODUCTION
INDUSTRIAL production of flat-rolled products such as plate, sheet, and strip involves complex thermomechanical processing. In general, these products are aimed at achieving high strength as well as good impact toughness. The key to obtaining tailored microstructures and, hence, optimum properties is through obtaining a proper understanding of the microstructure evolution phenomenon during the processing, and evaluating the role of the different process parameters. Two rolling practices that are commonly in use are conventional controlled rolling (CCR) and recrystallization controlled rolling (RCR). The RCR is carried out at temperatures where the austenite microstructure is completely recrystallized (e.g., > T95pct ), where a sufficient amount of precipitate-induced grain-boundary pinning prevents a further grain growth and retains the fine recrystallized grain size. In contrast, CCR is carried out at temperatures below the recrystallisation-stop temperature (e.g., < T5pct ) whereby a completely deformed, but unrecrystallized, austenite microstructure is obtained. Subsequent cooling leads to nucleation of the low-temperature transformation product on grain boundaries and sub-boundaries of deformed austenite, and results in a refined and uniform microstructure.[1,2,3] However, if the finish rolling is carried out at a temperature between the two previously mentioned temperatures, a partially recrystallized microstructure results, B. DUTTA, formerly a Research Associate with the Department of Engineering Materials, The University of Sheffield, is now a Research Associate with the Department of Materials Science, Physical Metallurgy Institute, Technical University Darmstadt, Darmstadt, 64287, Germany. E.J. PALMIERE, Senior Lecturer, is with the Department of Engineering Materials and the Institute for Microstructural and Mechanical Process Engineering, The University of Sheffield (IMMPETUS), Sheffield S1 3JD, United Kingdom. Contact e-mail:
[email protected] Manuscript submitted March 6, 2001.
METALLURGICAL AND MATERIALS TRANSACTIONS A
which is inhomogeneous and causes a deterioration of properties.[4] Hence, it is extremely important to avoid finish rolling in the regime of partial recrystallization. The upper and lower limits of the partial recrystallization regime are commonly known as the recrystallization-limit temperature (T95pct ) and the recrystallization-stop temperature (T5pct ), respectively. Both of these temperatures depend on several factors.[5] Intrinsic parameters, such as material chemistry, which determines the precipitation potential, play an important role in determining these limits. Palmiere et al.[5] have studied the effect of the Nb concentration in these steels, and have shown that the recrystallization-stop temperature is a strong function of the Nb supersaturation (and, consequently, the Nb content) in the steel. In addition to the intrinsic parameters, there are a large number of extrinsic parameters that influence the recrystallization behavior of the steels. Interpass pass time and strain per pass are found to be among the key process variables controlling the recrystallization[6,7] and, hence, influence the window of partial recrystallization. Bai et al.[8] have studied the effect of strain, strain rate, interpass time, and steel composition on the recrystallization-stop temperature (referred to in their work as the no-recrystallisation temperature). Based on the results of their experimental studies, they have proposed some empirical relations correlating the recrystallization stop temperature with strain. However, these studies were carried out under continuous cooling conditions, and hence, it is difficult to correlate the results of this study with the earlier studies on recrystallization behavior in Nb steels under isothermal conditions.[9,10,11] While the studies by Bai et al.[8] are closer to the practical situations faced in the rolling industry, understanding the results are not so easy due to the complex thermomechanical processes that occurred during multipass deformation coupled with continuous cooling. It is understood that the interaction between precipitation and recrystallization plays a key role in controlling the VOLUME 34A, JUNE 2003—1237
01_107A_2.qxd 5/14/03 7:27 PM Page 1238
extent of recrystallization under a given deformation condition.[1,2,4,5,9,11–13] If the precipitates are smaller than a particular size, they can effectively pin the grain/subgrain boundaries and retard the kinetics of recrystallization.[9,14] However, as the deformation temperature increases, the precipitates coarsen faster and loose their ability to prevent grain/subgrain boundary migration. Thus, the recrystallization kinetics are a result of a competition between the driving force for recrystallization and the precipitate pinning force. Even though a large number of workers[5,8–11,15] have investigated the recrystallization-precipitation interaction, the phenomenon is not yet fully understood, mainly because of the difficulties in accurately measuring the precipitate size distribution and volume fraction evolution.[16] The extremely fine size of the particles is one of the reasons behind this. Additionally, the transformation of the austenite matrix upon quenching makes it difficult to study the deformed austenite microstructure and to characterize the subgrain structure that existed just prior to the transformation. Different workers have employed different techniques for investigating the recrystallization kinetics in microalloyed steels. In recent years, a technique involving the measurement of the area under the flow curves has been successfully used by various people.[5,11,17] A distinct advantage of this technique is that the measurement of the area under a flow stress curve is a more simple, straightforward, and reproducible method as opposed to determining the yield stress, which was the basis for calculating the recrystallization kinetics in many earlier investigations.[10,18] This is particularly true for servohydraulic test frames, which may not show a clear distinction between elastic and plastic flow behavior. The present study involves characterizing the recrystallization kinetics using this technique. It is intended to examine the effect of strain per pass on the two temperatures defining the lower (< T5pct ) and upper (> T95pct ) limits of recrystallization. The precipitation kinetics have been evaluated using a model presented in an earlier work,[19] and the results have been used to estimate the magnitude of the grain-boundary pinning force and recrystallization driving force. Based on these evaluations, a criterion has been proposed to predict the microstructure and these results have been compared with the experimental observations.
high to assist in metallographic techniques associated with revealing prior-austenite grain boundaries. Samples were chromium plated to reduce the extent of oxidation during reheating at high temperatures. Reheating was carried out at 1200 ◦ C for 30 minutes. This reheating temperature was predetermined on the basis of an earlier work on steels of similar composition, which had experimentally measured a NbC precipitate dissolution temperature of 1100 ◦ C.[20] Hence, during reheating, all available Nb would be expected to be in solution in austenite. Following reheating, the steel specimens were cooled at a rate of ∼8 K/s to the required deformation temperature. The static recrystallization studies were carried out using interrupted plain strain compression tests on a purpose-built servohydraulic compression machine for multipass deformation simulations. The testing procedure consisted of subjecting the material to a given prestrain (ε1 ), unloading, holding for a predetermined delay time, and then subjecting the specimen to a second deformation of equal magnitude (ε2 = ε1 ) to that of the first one. Following deformation, specimens were water quenched to room temperature. For each deformation condition, an uninterrupted test was also carried out, which involved a monotonic deformation without any intermediate holding and of magnitude equal to the sum of the two deformations (ε2 + ε1 ) in the interrupted test. A softening index was calculated from the area under the flow stress curve in both tests. The details of this technique and the method of calculation are described elsewhere.[17] A total of five deformation temperatures, namely, 850 ◦ C, 900 ◦ C, 950 ◦ C, 1000 ◦ C, and 1050 ◦ C, and four different levels of prestrain, 0.1, 0.2, 0.3, and 0.4, were used for the present experiments. A constant true strain rate of 10 s−1 and a delay time of 10 s were used for all the experiments. It is worth noting that the deformation temperatures, strain levels, strain rate, and delay time chosen in the present study are typical of those used in the plate rolling industry. For microstructural observations, specimens were subjected to a prestrain (ε1 ), held for 10 seconds at the deformation temperature, and subsequently quenched to room temperature. Samples were sectioned and metallographic preparation was conducted on a plane parallel to the elongation direction and parallel to the compression axis. Polished specimens were etched with saturated aqueous picric acid at 60 ◦ C. Quantitative microstructural characterization was carried out using an optical microscope.
II. EXPERIMENTAL DETAILS A commercial Nb-microalloyed steel was used for the present study and the detailed composition of the steel is given in Table I. A relatively high concentration of manganese was used in order to provide added hardenability to minimize the amount of proeutectoid ferrite formation during quenching. This was required so that an accurate description of the prior-austenite grain size could be attained. The amount of sulfur in these steels was chosen to represent standard levels in grades where machinability of the final product is not a critical factor. The phosphorus level was intentionally kept
Table I. Steel Composition in Weight Percent C
Mn
P
S
Si
Nb
N
0.1
1.38
0.017
0.009
0.26
0.03
0.005
1238—VOLUME 34A, JUNE 2003
III. RESULTS A. High-Temperature Flow Behavior Figure 1 shows the flow stress curves at different temperatures from the uninterrupted tests. The curves clearly show continuous strain hardening throughout the deformation (even at the highest deformation temperature of 1050 ◦C), indicating a complete absence of dynamic recrystallization. Hence, any softening observed under present deformation conditions can be attributed exclusively to static softening events (i.e., recovery and recrystallization). Figures 2(a) through (e) show the flow stress curves obtained from both uninterrupted and interrupted tests at temperatures ranging from 850 ◦ C to 1050 ◦ C for a given nominal prestrain of 0.3 (i.e., ε1 = ε2 = 0.3). The calculated softening fraction is also marked on the figures. Results METALLURGICAL AND MATERIALS TRANSACTIONS A
01_107A_2.qxd 5/14/03 7:27 PM Page 1239
C. Microstructural Studies
Fig. 1—Variation of flow stress at different deformation temperatures during uninterrupted deformation. All tests were conducted at a constant true strain rate of 10 s−1 .
indicate an increase in softening with increasing temperature. Interestingly, the softening index shows a negative value at the lowest deformation temperature of 850 ◦ C. Similarly, Figures 3(a) through (d) show the flow stress curves obtained from both uninterrupted and interrupted tests for different nominal levels of prestrain ranging from 0.1 to 0.4 for a given deformation temperature of 950 ◦ C. It is clearly evident that an increase in the prestrain at constant temperature causes a higher amount of softening. B. Fractional Softening/Hardening Studies Based on the softening calculations, the overall softening/ hardening behavior of the Nb steel has been graphically depicted in Figure 4. The notable features are (1) for any given prestrain, the amount of softening increases with increasing temperature; and (2) at any given deformation temperature, the amount of softening increases with an increase in prestrain. At 850 ◦ C, all the softening curves exhibit negative softening or, in other words, hardening. All the curves exhibit a plateau between 900 ◦ C and 950 ◦ C temperatures. It is worth noting that at this level the softening is between 17 and 20 pct for all the conditions studied in the present investigation. The criterion that 20 pct of the overall softening is due to recovery has been employed to identify the onset of recrystallization,[3,5,18,21] and to subsequently determine the recrystallization-stop temperature (T5pct) for different prestrains. The results are shown in Figure 5. It is clear from this figure that an increase in prestrain leads to a decrease in the recrystallization-stop temperature. The upper limit of the partial recrystallization regime was determined by microstructural observation and will be described in detail later. The recrystallization limit (i.e., 95 pct recrystallization) thus determined was found to correspond to approximately 60 pct of the overall softening (as marked in Figure 4). The recrystallization-limit temperature (T95pct) corresponding to 60 pct softening is plotted as a function of true strain in Figure 5 and, like T5pct, also decreases with increasing prestrain. Hence, Figure 5 shows both the upper bound and the lower bound of the partial recrystallization regime. METALLURGICAL AND MATERIALS TRANSACTIONS A
Figure 6 shows the microstructure of a sample reheated at 1200 ◦ C for 30 minutes. Clearly, the prior austenite grains appear to be equiaxed and the grain sizes are fairly uniform throughout the matrix. The mean austenite grain size was measured to be 147 µm in the reheated sample. Figures 7(a) through (c) show micrographs of samples prestrained to 0.1 at temperatures 950 ◦ C, 1000 ◦ C, and 1050 ◦ C, respectively. Following deformation, the specimens were held isothermally at the deformation temperature for a period of 10 seconds and were then quenched to room temperature. The micrographs reveal a completely deformed and unrecrystallized microstructure at 950 ◦ C, while at 1000 ◦ C, there are indications that recrystallization has begun. The micrograph from the sample tested at 1050 ◦ C exhibits a partially recrystallized microstructure and clearly indicates that recrystallization is not yet complete at 1050 ◦ C. Figures 8(a) through (c) show the microstructures from another set of samples prestrained to 0.3 and held for a period of 10 seconds at 900 ◦ C, 950 ◦ C, and 1000 ◦ C respectively. The micrograph shown in Figure 8(a) exhibits a highly deformed structure with completely unrecrystallized grains, while that shown in Figure 8(b) exhibits the beginning of recrystallization and that shown in Figure 8(c) reveals a fully recrystallized microstructure, consisting of small equiaxed grains distributed uniformly throughout the matrix. These microstructural observations were used to verify the recrystallization-stop temperatures calculated using 20 pct softening criteria from the high-temperature flow curves. As discussed previously, the completion of recrystallization (i.e., 95 pct recrystallization) was also identified from microstructural observations, and the results were used to determine the recrystallization-limit temperature (Figure 5). The recrystallization kinetics, as calculated from volume fraction measurements, are presented in Table II and Figure 9. For comparison, the values in parentheses in Table II correspond to the measured fractional softening data from Figure 4. With the exception of the steel prestrained to 0.1, there is a negative deviation between the overall fractional softening and the fraction recrystallization. This deviation is similar to results reported from other previous investigations,[17,22,23] and is related to the heterogeneity of deformation between recrystallized and unrecrystallized regions. Clearly, the recrystallization kinetics are enhanced by an increase in prestrain for a given deformation temperature. Figure 10 shows a plot of the average aspect ratio of the prior-austenite grains as a function of deformation temperature for various prestrains. The aspect ratio decreases, as the recrystallization proceeds and is almost equal to 1.0 in a fully recrystallized microstructure. IV. DISCUSSION The softening curves shown in Figure 4 describe the static recrystallization behavior of the Nb steel studied in the present investigation. All the softening curves exhibited a negative softening (i.e., hardening) at 850 ◦ C, the lowest deformation temperature in the present study. This hardening is caused by the strain-induced precipitation of Nb(CN) during the 10-second interpass delay time, as reported previously by separate and independent microstructural investigations on steels of similar composition.[5,24,25] Additionally, the VOLUME 34A, JUNE 2003—1239
01_107A_2.qxd 5/14/03 7:27 PM Page 1240
(a)
(b)
(c)
(d)
(e) Fig. 2—Flow stress curves from (•) uninterrupted and (◦) interrupted tests at various deformation temperatures: (a) 850 ◦ C, (b) 900 ◦ C, (c) 950 ◦ C, (d) 1000 ◦ C, and (e) 1050 ◦ C. Interrupted tests are carried out with a 0.3 prestrain, unloading and holding for 10 s, and subjected to a second deformation of 0.3 strain. The uninterrupted tests involved a monotonic deformation to 0.6 strain. Prior to deformation, specimens were reheated at 1200 ◦ C for 30 min. All the tests were carried out at a constant true strain rate of 10 s−1 .
precipitation kinetics of the Nb(CN) precipitates have been modeled in an earlier work,[19] and will be described briefly in a later section of this discussion (Figure 11). It is understood that the softening mechanisms, namely, static recovery and recrystallization are slow at this temperature and, therefore, precipitation hardening dominates. A further increase 1240—VOLUME 34A, JUNE 2003
in temperature leads to softening, which is followed by a plateau between the temperatures 900 ◦ C and 950 ◦ C. This stage of initial softening (up to 20 pct of total softening) is attributed to the recovery process alone. Because the stacking fault energy of austenite is relatively low (75 mJ/m2 ), softening due to recovery is expected to be low in this METALLURGICAL AND MATERIALS TRANSACTIONS A
01_107A_2.qxd 5/14/03 7:27 PM Page 1241
(a)
(b)
(c)
(d)
Fig. 3—Flow stress curves from (•) uninterrupted and (◦) interrupted tests at various prestrains for a constant deformation temperature of 950 ◦ C. Interrupted tests involved a prestrain, unloading and holding for 10 s, and were subjected to a second deformation equal to the prestrain. The applied prestrains were (a) 0.1, (b) 0.2, (c) 0.3, and (d ) 0.4. Prior to deformation, specimens were reheated at 1200 ◦ C for 30 min. All the tests were carried out at a constant true strain rate of 10 s−1 .
the softening curves is a result of the saturation of the recovery process and, beyond this regime, further softening is caused by the static recrystallization of the material. The recrystallization-stop temperature (T5pct ) for each level of prestrain was determined from the curves shown in Figure 4 by employing the criteria that 20 pct of the total softening is due to recovery.[3,5,18,21] This resulted in the relationship between the recrystallization-stop temperature and amount of deformation such that T5pct = 936 ε−0.014
Fig. 4—Overall softening behavior of the Nb steel as a function of temperature for four different levels of prestrain. The 5 pct recrystallization (Rxn) and 95 pct recrystallization (Rxn) limits are also marked on the figure. The reheat temperature, interpass delay time, and strain rate were held constant at 1200 ◦ C, 10 s, and 10 s−1 , respectively.
steel.[26] This result is in agreement with the findings of previous investigators, who had also observed similar levels of softening due to recovery.[3,5,18,21] The observed plateau in METALLURGICAL AND MATERIALS TRANSACTIONS A
[1]
The results of this research program clearly show that the precipitation-recrystallization interaction plays a major role in the microstructural evolution of the Nb-microalloyed steel. In the past, there have been some attempts to determine the recrystallization-stop temperature during multipass rolling under continuous cooling conditions.[8] The results have been correlated to the interaction between recrystallization and precipitation. However, these studies employed isothermal kinetic expressions for both recrystallization and precipitation in nonisothermal situations. Because the present experiments were conducted under isothermal conditions, the current results offer a unique opportunity to test VOLUME 34A, JUNE 2003—1241
01_107A_2.qxd 5/14/03 7:28 PM Page 1242
Fig. 5—Effect of prestrain on the recrystallization-stop temperature (T5pct —corresponding to 5 pct Rxn) and the recrystallization-limit temperature (T95pct —corresponding to 95 pct Rxn).
Fig. 6—Microstructure of a sample reheated to 1200 ◦ C and quenched, representing the initial structure prior to deformation. Equiaxed prior austenite grains were revealed by etching in saturated aqueous picric acid.
the applicability of these models and a better understanding of the precipitation-recrystallization interaction in Nbmicroalloyed steels. Later in this section, the precipitation kinetics under the given conditions are estimated using a model proposed in an earlier work.[19] This has been used to evaluate the precipitate pinning force. Predictions have been made based on the evaluation of pinning force and recrystallization driving force, and results are compared with the experimental observations. Figure 11 shows the precipitation-start times (5 pct precipitation) as calculated using the model[19] for the different deformation temperatures and strain levels used in the present study. Results indicate that at 850 ◦ C, 5 pct precipitation occurs after a 11.7-second delay time following a 0.1 prestrain. It can be recalled that in the present study, the delay time was kept constant at 10 seconds for all the testing conditions. Additionally, the softening calculations revealed that at 1242—VOLUME 34A, JUNE 2003
Fig. 7—Micrographs depicting (a) 0 pct recrystallization, (b) 11.5 pct recrystallization, and (c) 52 pct recrystallization after a true strain of 0.1, followed by a 10 s delay time at the respective deformation temperatures of 950 ◦ C, 1000 ◦ C, and 1050 ◦ C. All steels were initially reheated to 1200 ◦ C, and deformation occurred at a constant strain rate of 10 s−1 .
850 ◦C, the material prestrained to 0.1 exhibited −20 pct softening, which was caused by precipitation hardening.[27,28] Microstructural evidence also revealed that the austenite was unrecrystallized after a delay time of 10 seconds at 850 ◦ C following a 0.1 strain. These results highlight the importance METALLURGICAL AND MATERIALS TRANSACTIONS A
01_107A_2.qxd 5/14/03 7:28 PM Page 1243
Thus, the criterion of selecting the 5 pct precipitation and 5 pct recrystallization intersection as the recrystallizationstop temperature is not a necessary requirement.[29] Instead, it is the continuous evolution of the precipitation process and, therefore, the precipitate pinning force that is possibly the determining factor for retarding the recrystallization. Figure 12(a) shows the precipitate size and volume fraction evolution at 900 ◦ C for a material prestrained at 0.1, while Figure 12(b) shows the corresponding changes in the precipitate pinning force. The pinning force (Fpin ) was calculated using the subgrain boundary pinning force model:[9] Fpin =
3σ V f l 2πR 2
[2]
where σ is the interfacial energy per unit area of boundary, V f and R respresent the respective volume fraction and radius of the precipitates, and l is the average intercept distance of the subgrains. It is clearly seen from Figure 12(a) that with increasing time, as the precipitate volume fraction increases, the pinning force also increases. Although the increase in precipitate size has a decreasing effect on pinning force, in the time ranges typical of interpass delay times observed in practice, this effect is negligible. However, this effect can have a significant impact after the completion of precipitation (this impact will have more relevance during high-temperature grain growth). The recrystallization driving force is also plotted in Figure 12(b). Following[30,31,32] the recrystallization driving force (Frxn) is given by Frxn =
µb2 ρ 2
[3]
where µ is the austenite shear modulus, b is the Burgers vector, and ρ is the increase in dislocation density due to deformation. An estimation of ρ is obtained from the increase in flow stress ( σ ) due to deformation:[33]
ρ =
Fig. 8—Micrographs depicting (a) 0 pct recrystallization, (b) 8 pct recrystallization, and (c) 96 pct recrystallization after a true strain of 0.3, and a subsequent 10 s delay time at the respective deformation temperatures of 900 ◦ C, 950 ◦ C, and 1000 ◦ C. All steels were initially reheated to 1200 ◦ C, and deformation occurred at a constant strain rate of 10 s−1 .
of the effect of precipitation on the softening mechanisms and indicate that even for cases where less than 5 pct precipitation has occurred, particles can play a significant role in determining the operative softening/hardening mechanism. METALLURGICAL AND MATERIALS TRANSACTIONS A
25 σ 2 µ2 b2
[4]
By convention, 5 pct recrystallization is assumed to mark the onset of recrystallization and any material with a recrystallized volume fraction less than 0.05 is called unrecrystallized. In the present study, it is assumed that there is no change in recrystallization driving force until the 5 pct recrystallization limit. In reality, though, the recrystallization driving force will start decreasing as and when the recrystallization begins, and at 5 pct recrystallized fraction, the driving force will be less than the initial force. However, this decrease is not expected to be significant before 5 pct recrystallization. Results shown in Figure 12(b) indicate that after a certain time, 1.6 seconds in the present case, the precipitate pinning force becomes greater than the recrystallization driving force, and hence, from this time onward, the precipitates will be able to pin the grain/subgrain boundaries effectively. Hence, this time is termed as the critical time for the pinning (tpin ) of a subgrain boundary by strain-induced precipitates. The preceding discussion clearly indicates that the occurrence of recrystallization in Nb-microalloyed steels is a result of a complex interaction between the precipitation and recrystallization. If tpin is less than the trxn (time for 5 pct recrystallization), the precipitates will be able to suppress recrystallization. In addition to this, the recrystallization can VOLUME 34A, JUNE 2003—1243
01_107A_2.qxd 5/14/03 7:28 PM Page 1244
Table II. Measured Recrystallized Volume Fraction as a Function of Temperature for Different Prestrains* Temperature
Prestrain
(◦ C)
0.1
0.2
0.3
0.4
850 900 950 1000 1050
0.00 (–0.15) 0.00 (0.11) 0.00 (0.17) 0.12 (0.30) 0.52 (0.48)
0.00 (–0.10) 0.00 (0.12) 0.00 (0.18) 0.62 (0.50) 1.00 (0.86)
0.00 (–0.08) 0.00 (0.11) 0.08 (0.19) 0.96 (0.66) 1.00 (0.96)
0.00 (0.06) 0.00 (0.15) 0.63 (0.22) 1.00 (0.78) 1.00 (0.82)
*Values in parentheses represent the overall fractional softening (or hardening, in the case of negative values) of austenite as measured from the area under the flow curves.
Fig. 9—Variation of measured recrystallized fraction as a function of deformation temperature for different levels of prestrain.
Fig. 11—Precipitation start times (corresponding to 5 pct of the total precipitation) for Nb(CN) as calculated using the model proposed in Ref. 19 for different levels of prestrain.
observations. The time for 5 pct recrystallization, trxn, is calculated using the relation proposed by Sellars:[34,35] 300,000 trxn = 6.75 × 10−20 d02 ε−4 exp RT 2.75 × 105 [5] − 185 [Nb] exp T
Fig. 10—Variation in the average prior-austenite grain aspect ratio as a function of deformation temperature for different levels of prestrain.
also be suppressed if trxn is greater than the interpass delay time (td ). Hence, if either of these two conditions or both are fulfilled, the resultant microstructure will be unrecrystallized. Table III shows the results predicted by these conditions and draws a comparison with the present experimental 1244—VOLUME 34A, JUNE 2003
where d0 is the original grain size in microns, ε is strain, R is the universal gas constant, T is the deformation temperature in Kelvin, and [Nb] is the amount of Nb in solution in austenite in weight percent. The results shown in Table III indicate a very good agreement for the higher strain levels, namely, 0.2, 0.3, and 0.4, except for the 0.3 prestrain at 950 ◦ C. In this case, the proposed criteria predict that recrystallization has started. This is also supported by the microstructural observations. However, the fractional softening studies indicate an unrecrystallized microstructure. Recalling the results from the softening studies, it is worth noting that the steel prestrained to 0.3 exhibited a recrystallization-stop temperature of 948 ◦ C. This shows that the onset of recrystallization is around 950 ◦ C for this material. In contrast to the good agreement between the predicted and experimental results discussed previously, there is a distinct discrepancy between the predictions and experimental observations for the material prestrained at 0.1. While the METALLURGICAL AND MATERIALS TRANSACTIONS A
01_107A_2.qxd 5/14/03 7:28 PM Page 1245
(a)
(b) Fig. 12—(a) Variation in the radius and volume fraction of the Nb(CN) precipitates as a function of time for the steel isothermally held at 900 ◦ C following a prestrain of 0.1. The results were calculated using the model developed in Ref. 19. (b) Variation of the recrystallization driving force (Rxn force) and precipitate pinning force per unit area as a function of time for the steel isothermally held at 900 ◦ C after a prestrain of 0.1. The time when the precipitate pinning force becomes greater than the recrystallization driving force is indicated by tpin .
experimentally observed microstructures revealed partial recrystallization at 1000 ◦C and 1050 ◦C, the proposed criteria predict an absence of recrystallization. A closer look reveals that although the pinning force is far lower than the driving force for recrystallization, the time for the onset of recrystallization, trxn, as calculated from Eq. [5] is higher than the given delay time (i.e., 10 seconds) in both the cases. Evidently, trxn, as predicted by Eq. [5] is an overestimation of the real time taken for the onset of recrystallization. It is worth noting that [Nb], i.e., the amount of Nb in solid solution at the deformation temperature, is one of the key parameters in Eq. [5]. The ambiguity in determining solubility products has been discussed in detail elsewhere,[20] and it has been shown that there exists a range of values for solubility product of Nb in austenite. In order to estimate the role of Nb on trxn, it is essential to know the exact amount of Nb in solid solution. The preceding discussion indicates that there is a need to review the validity of Eq. [5] for all Nb steels. However, this issue is beyond the scope of the present investigation. It is important to note the difference between the criteria for the beginning of recrystallization, proposed in this work, METALLURGICAL AND MATERIALS TRANSACTIONS A
and that normally used in previous investigations. From the earlier discussions, it is evident that recrystallization is retarded only when the precipitate pinning force becomes greater than the recrystallization driving force. If this occurs before the onset of recrystallization, a significant retardation in the recrystallization kinetics is achieved. Therefore, an accurate estimation of both the precipitate pinning force and the driving force for recrystallization is very important in order to predict the onset of recrystallization. Because many of the earlier studies have used rolling as a means of deforming the material prior to recrystallization, direct measurement of flow stress was not possible. This, in turn, leads to an inaccurate evaluation of stored energy and, hence, the recrystallization driving force. In the present study, the use of well-controlled plane strain compression enabled a more accurate determination of the increase in flow stress and hence, the stored energy. However, it is the estimation of the precipitate pinning force that possibly makes the biggest difference for the present study. It is well recognized that the precipitate volume fraction plays a key role in controlling the recrystallization kinetics. Some of the previous investigations have used the equilibrium volume fraction of precipitates for calculating the precipitate pinning force, Fpin . However, the fact that the precipitation is a time- and temperature-dependent phenomenon makes this assumption invalid. Besides this, some of the models assume a uniform dispersion of precipitates throughout the matrix. This, in turn, implies that the volume fraction of precipitates at the austenite subgrain boundary, where the precipitates would be most effective in retarding the recrystallization, would be identical to the volume fraction throughout the bulk matrix. Electron microscopic investigations have clearly revealed that the precipitates are situated preferentially on prior-austenite grain boundaries, subgrain boundaries, deformation bands, etc.[4,10,15,25] This renders the assumption of uniform precipitate distribution invalid. Investigations involving direct measurement of precipitate volume fraction also contain some inherent drawbacks. Techniques using extraction replica are dependent on extraction efficiency and are not suitable for a precise determination of precipitate volume fraction.[36] Electron microscopic investigations are often unable to resolve the fine precipitates nucleated on dislocations, subgrain boundaries, deformation bands, etc., leading to an underestimation of precipitate volume fraction. The present study involves an estimation of the precipitate volume fraction using a model for strain-induced precipitation.[19] The use of this model enables the evaluation of the precipitate volume fraction evolution as a function of time. It incorporates an experimentally determined expression for the solubility of NbC in austenite for a steel composition similar to that used in this present study.[5] Additionally, this model assumes heterogeneous precipitation on dislocation nodes, which makes it more realistic. The magnitude of Fpin gradually increases as the precipitation proceeds (Figures 12(a) and (b)) until the precipitate volume fraction reaches the equilibrium volume fraction. Further holding at temperature leads to a decrease in the pinning force due to a decrease in the precipitate number density caused by coarsening of the precipitates. In contrast, the magnitude of Frxn gradually decreases (or remains almost constant until 5 pct recrystallization). Whenever the pinning force becomes greater than the recrystallization driving force, the VOLUME 34A, JUNE 2003—1245
01_107A_2.qxd 5/14/03 7:28 PM Page 1246
Table III. Calculated Values of tpin (the Time When the Precipitate Pinning Force Exceeds the Recrystallization Driving Force) and trxn (the Time for 5 Pct Recrystallization), along with the Predictions and Observations about the Resulting Microstructure; the Interpass Delay Time is Represented by td Recrystallization has Started? Observation Temperature (◦ C) 850
900
950
1000
1050
Strain
td (s)
trxn (s)
0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4
10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10
7704 481 95 30 1431 89 17 5.6 305 19 3.8 1.2 73.5 4.6 0.9 0.3 19.7 1.2 0.2 0.1
tpin (s) td < trxn tpin < trxn 2.9 4.6 5.8 6.5 1.6 2.6 2.9 3.7 — — — — — — — — — — — —
yes yes yes yes yes yes yes no yes yes no no yes no no no yes no no no
precipitates are able to effectively pin the subgrain boundaries and suppress recrystallization. The present study also shows the effect of prestrain on the upper bound of the partial recrystallization regime. This has been determined from a combined analysis of the softening curves and the quantified recrystallized microstructures. Results indicate that for the present experimental conditions, 60 pct overall softening is associated with a completely recrystallized microstructure. A mathematical fit to the data yields the following relation between the recrystallizationlimit temperature (T95pct ) and prestrain (ε): T95pct = 916.66ε−0.07
[6]
It is worth noting that there has been very little quantitative work done to determine the recrystallization-limit temperature as a function of prestrain, and the present study explicitly shows the relation between the prestrain and the recrystallization-limit temperature for isothermal conditions. Thus, Figure 5 shows the regime of partial recrystallization as a function of prestrain. In order to achieve a homogeneous microstructure, all finish rolling passes must be conducted outside of this window.
yes yes yes yes yes yes yes yes no no no no no no no no no no no no
Prediction
Fractional Softening
Microstructure
no no no no no no no no no no yes yes no yes yes yes no yes yes yes
no no no no no no no no no no no yes yes yes yes yes yes yes yes yes
no no no no no no no no no no yes yes yes yes yes yes yes yes yes yes
softening is caused by recovery. This was further confirmed by quantitative microstructural observations. The results indicate that an increase in prestrain decreases the recrystallization-stop temperature. 4. The fractional hardening (i.e., negative softening) observed at lower temperatures is attributed to the precipitation hardening caused by Nb(CN) and the subsequent suppression of static recrystallization. 5. A criterion has proposed to predict the austenite recrystallization behavior. Although the predictions are in reasonably good agreement in most of the cases, there are some discrepancies (associated with low levels of prestrain) between the observed experimental results and the predictions of the proposed criteria. 6. From quantitative microscopy, the recrystallization-limit temperature (T95pct ) has been determined as a function of prestrain, and the results reveal that the recrystallization limit is coincident with a 60 pct overall softening for the steel composition studied in the present investigation. This discrepancy between the measured fraction recrystallized and the overall fractional softening is attributed to the heterogeneity of deformation between recrystallized and unrecrystallized regions during plane strain compression testing.
V. CONCLUSIONS 1. An increase in the deformation temperature increases the amount of softening at a constant strain rate and delay time. 2. An increase in prestrain leads to an increase in the amount of softening for any given deformation temperature. 3. The recrystallization-stop temperature (T5pct ) is determined by applying the criterion that 20 pct of the overall 1246—VOLUME 34A, JUNE 2003
ACKNOWLEDGMENTS The authors thank Corus (Research, Development and Technology—Swinden Technology Centre) and the Engineering and Physical Sciences Research Council (EPSRC Grant No. GR/M13893) for providing the materials and funding that made this research possible. METALLURGICAL AND MATERIALS TRANSACTIONS A
01_107A_2.qxd 5/14/03 7:28 PM Page 1247
REFERENCES 1. L.J. Cuddy: Thermomechanical Processing of Microalloyed Austenite, Pittsburgh, PA, A.J. DeArdo, G.A. Ratz, and P.J. Wray, eds., TMSAIME, Warrendale, PA, 1982, p. 129. 2. L.J. Cuddy: Metall. Trans. A, 1981, vol. 12A, pp. 1313–20. 3. W. Roberts and B. Ahlblom: Acta Metall., 1978, vol. 26, p. 801. 4. T. Tanaka: Int. Met. Rev., 1981, vol. 26, p. 185. 5. E.J. Palmiere, C.I. Garcia, and A.J. DeArdo: Metall. Mater. Trans. A, 1996, vol. 27A, pp. 951–60. 6. C.M. Sellars: Mater. Sci. Technol., 1990, vol. 6, p. 1072. 7. F. Siciliano, Jr. and J.J. Jonas: Metall. Mater. Trans. A, 2000, vol. 31A, pp. 511–530. 8. D.Q. Bai, S. Yue, W.P. Sun, and J.J. Jonas: Metall. Trans. A, 1993, vol. 24A, pp. 2151–59. 9. S.S. Hansen, J.B. Vander Sande, and M. Cohen: Metall. Trans. A, 1980, vol. 11A, pp. 387–402. 10. M.J. Luton, R. Dorvel, and R.A. Petkovic: Metall. Trans. A, 1980, vol. 11A, pp. 411–20. 11. O. Kwon and A.J. DeArdo: Acta Metall. Mater., 1991, vol. 39, p. 529. 12. J.G. Speer, J.R. Michael, and S.S. Hansen: Metall. Trans. A, 1987, vol. 18A, pp. 211–22. 13. J.G. Speer and S.S. Hansen: Metall. Trans. A, 1989, vol. 20A, pp. 25–38. 14. L.J. Cuddy: Recrystallization and Grain Growth in Multiphase and Particle Containing Materials; 1st RISO Int. Symp. on Metallurgy and Materials Science, Denmark, N. Hansen, A.R. Jones, and T. Leffers, eds., Risø National Lab., Roskilde, Denmark, 1980, p. 317. 15. L.J. Cuddy, J.J. Bauwin, and J.C. Raley: Metall. Trans. A, 1980, vol. 11A, pp. 381–86. 16. M.G. Burke, L.J. Cuddy, J. Piller, and M.K. Miller: Mater. Sci. Technol., 1988, vol. 4, p. 113. 17. O. Kwon and A.J. DeArdo: Acta Metall. Mater., 1990, vol. 38, p. 41.
METALLURGICAL AND MATERIALS TRANSACTIONS A
18. R.A.P. Djaic and J.J. Jonas: Metall. Trans., 1973, vol. 4, pp. 621–24. 19. B. Dutta, E.J. Palmiere, and C.M. Sellars: Acta Mater., 2001, vol. 49, p. 785. 20. E.J. Palmiere, C.I. Garcia, and A.J. DeArdo: Metall. Mater. Trans. A, 1994, vol. 25A, p. 277. 21. R.A. Petkovic, M.J. Luton, and J.J. Jonas: Can. Metall. Q., 1975, vol. 14, p. 137. 22. W.C. Leslie, F.J. Plecity, and J.T. Michalak: Trans. AIME, 1961, vol. 221, p. 691. 23. D.R. Barraclough and C.M. Sellars: Met. Sci., 1975, vol. 13, p. 257. 24. R.M. Poths, R.L. Higginson, and E.J. Palmiere: Scripta Mater., 2001, vol. 44, p. 147. 25. W.M. Rainforth, M.P. Black, R.L. Higginson, E.J. Palmiere, I. Prabst, P. Warbichler, and F. Hofer: Acta Mater., 2002, vol. 50, p. 735. 26. W. Charnock and J. Nutting: J. Met. Sci., 1967, vol. 1, p. 123. 27. B. Dutta and C.M. Sellars: Mater. Sci. Technol., 1986, vol. 2, p. 146. 28. B. Dutta, E. Valdes, and C.M. Sellars: Acta Metall. Mater., 1992, vol. 40, p. 653. 29. B. Dutta and C.M. Sellars: Mater. Sci. Technol., 1987, vol. 3, p. 197. 30. J.E. Bailey and P.B. Hirsch: Proc. R. Soc. (London), 1962, vol. A267, p. 11. 31. J.W. Martin and R.D. Doherty: Stability of Microstructure in Metallic Systems, Cambridge University Press, Cambridge, 1976, p. 40. 32. R.W. Cahn: in Recrystallization, Grain Growth and Texture, H. Margolin, ed., ASM, Metals Park, OH, 1966, p. 99. 33. A.S. Keh: in Direct Observation of Imperfections in Crystals, J.B. Newkirk and J.H. Wernick, eds., Wiley-Interscience, New York, NY, 1962, p. 213. 34. C.M. Sellars: in Hot Working and Forming Processes, C.M. Sellars and G.J. Davies, eds., The Metals Society, London, 1980, p. 3. 35. C.M. Sellars: HSLA Steels 85, Chinese Society of Metals, Beijing, Peoples Republic of China, 1985, p. 12. 36. M.F. Ashby and R. Ebeling: Trans. AIME, 1966, vol. 236, p. 1396.
VOLUME 34A, JUNE 2003—1247
