Influence of strain rate on interpass softening

Influence of Strain Rate on Interpass Softening During the Simulated Warm Rolling of Interstitial-Free Steels P.R. CETLIN, S. YUE, J.J. JONAS, and T.M. M A C C A G N O Most laboratory simulations of hot rolling involve a scaling down of the strain rate from the much higher industrial levels. This leads to slower softening between each rolling pass, for which corrections must be made. In the present work, torsion testing simulations of "warm" rod rolling were conducted on a Ti-Nb interstitial-free (IF) steel at 840 ~ and 770 ~ (i.e., in the ferrite range). For this purpose, "strain rate corrected" interpass times were used, in addition to the more familiar corrections for the stress. The results are compared with those obtained from simulations using uncorrected industrial interpass times. At 840 ~ simulations using corrected interpass times led to high levels of softening between the stages of rolling, thus triggering the reinitiation of cycles of dynamic recrystallization. The initially high stress level at the start of these cycles was responsible for the large differences in the pass-to-pass mean flow stress behavior, compared with that observed when using uncorrected industrial interpass times, or continuous deformations. The differences were much less pronounced at 770 ~ where the rate of softening is much slower than at 840 ~ Predictions for softening based on the Avrami equation underestimated the softening observed using the continuous and uncorrected industrial interpass time schedules and overestimated it for the corrected ones. The former is due to the occurrence of recovery, which is not addressed by the Avrami relation, while the latter is due to the precipitation that takes place during the corrected (longer) interpass times. It was also found that simulations using continuous deformations are applicable only if the interpass softening that would be expected using the corrected interpass times does not exceed about 20 pct. I. INTRODUCTION H O T - W O R K I N G experiments carried out by trials in the mill are difficult and expensive to perform and can pose considerable risks to production equipment. An alternative is the laboratory simulation of hot-working processes, which can provide a great deal of useful information for optimizing microstructure, properties, and processing parameters. This has been carried out extensively with the aid of hot torsion machines, t'-tq various compression-type simulators, t12-~7] and reduced-scale rolling mills, t'z,~5,18,191 Such experiments have been employed to simulate strip, t1"5"61seamless t u b e , 12I and r o d ~3'4"71 rolling and ideally should have faithfully reproduced the industrial conditions. This was largely the case with respect to temperature, strain per pass, and interpass time. However, since laboratory equipment is usually unable to apply high industrial strain rates (e.g., up to 1000 s -1 in rod rolling), there was a scaling down of the strain rate in most of these simulations. The lower laboratory strain rates lead to lower stress levels and to coarser microstructures than those prevailing under industrial conditions, t5'6~but corrections can be made to allow for these effects. The lower strain rates, however, also retard the softening kinetics of the material; I2~ thus, the amount of industrial softening predicted from laboratory simulations can be too low. One P.R. CETLIN, on leave from the Departmento de Engenharia Metahirgica, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil, and J.J. JONAS, Professors, S. YUE, Associate Professor, and T.M. MACCAGNO, Research Associate, are with the Department of Metallurgical Engineering, McGill University, Montreal, QC, Canada H3A 2A7. Manuscript submitted August 25, 1992. METALLURGICAL TRANSACTIONS A way of overcoming this problem is to increase the laboratory interpass times to compensate for the slower rate of laboratory softening. Consider, for example, the strain rate (~) dependence of the time for 50 pct softening (tso) after dynamic recrystallization: t2~ ts0 oc 1/~" [1] For C-Mn steels, n = 0.6; t2m thus, an allowance can be made for a 100-fold decrease in the strain rate, from the industrial level to the laboratory one, by increasing the laboratory interpass times by a factor of 16 over the industrial ones. The objective of the present work was to investigate the suitability of using such a strain rate correction for interpass softening, in addition to the strain rate correction for stress level, in the simulation of rod rolling. This involved, first, an analysis of the kinetics of interpass softening, followed by laboratory hot-rolling simulations. Hot torsion testing was selected as the means of simulation because of the ease with which high strains, and multiple-step deformations, can be achieved. I'-'u The experiments were performed in the ferrite range on a TiNb interstitial-free (IF) steel, and all four stages of rod rolling were investigated: roughing, intermediate rolling, prefinishing, and finishing. The approach taken was to compare simulations using uncorrected industrial interpass times with those using interpass times corrected for the differences in strain rate between the mill and laboratory conditions. Since it has been suggested that multiple-step deformations with very short interpass times (e.g., rod mill simulations) lead to interrupted stress vs strain curves that are similar to continuous ones, c~2J results were also obtained for simulations using continuous deformation. VOLUME 24A, JULY 1993--1543 II. EXPERIMENTAL TECHNIQUES A. Materials and Torsion Testing The chemical composition of the material, which was supplied by Dofasco Inc., Hamilton, Ontario, Canada, as a laboratory cast ingot, is shown in Table I. In Ti-Nb IF steels, the usual practice is to add sufficient Ti to react with the N and S, leaving Nb to scavenge the C as NbC. On the basis of the stoichiometry of NbC, the amount of free Nb in the present IF steel is 93 Nb* = Nb (wt pct) - ~ C (wt pct) = - 0 . 0 0 3 2 5 [2] where the negative value suggests that there is insufficient Nb to react completely with the C. By contrast, the amount of Ti remaining after reaction with the N and S, and therefore available to react with the C, is 48 Ti* = Ti (wt pct) - - - N (wt pct) 14 48 - - - S (wt pct) = 0.0043 32 [3] This excess Ti probably reacts with some of the C so that the approximate amount of Nb remaining in solution is Nb* = N b ( w t p c t ) - ~ = C(wtpct) 0.0045 [4] The test specimens had a diameter of 6.35 m m and gage lengths of 22.5 or 5.6 mm. They were solid rather than tubular; thus, problems associated with specimen buckling were avoided. The measured torque, T, and twist, 0, were converted to von Mises effective stress, ~, and strain, e, using the following formulas: 122} 3.3rv = - oR - ~ = - - 27rR 3 ' [5] L~/~ where R and L are the gage radius and length, respectively, of the specimen. B. Determination o f Ar~ and Arl The torsion testing simulations were conducted in the ferrite range, but this first required the determination of the At3 and Ar] temperatures (i.e., the start and finish temperatures, respectively, of the austenite-to-ferrite transformation) pertaining to multipass deformation./TM This was done by applying successive deformation passes of e = 0.3, separated by 30 second interpass times, while the temperature was being decreased from 950 ~ at a cooling rate of 0.4 ~ The results were then plotted in terms of "mean flow stress" (MFS) vs the inverse absolute temperature (Figure 1). Here, the MFS is calculated by applying the mean value theorem of integral calculus to the ~ vs e curve for each pass t241 and evaluating for a strain of 0 . 2 5 - - a value typical of the reductions applied in each pass of a rod mill. From Figure 1, it is apparent that the material is entirely ferrite Testing was performed using a torsion machine consisting of a servohydraulic rotary actuator mounted on a lathe bed, with high speed control and data acquisition via an MTS Systems Corp., Minneapolis, MN, digital controller interfaced with a COMPAQ* 386 computer. T (~ 917 200 864 I 814 I ' ~ I * C O M P A Q is a t r a d e m a r k o f C o m p a q C o m p u t e r Corporation, Houston, TX. This equipment allows interpass times as short as 10 ms to be applied. The hydraulics and the tooling arrangements are described in more detail elsewhere. [2~] The specimen was heated with a tungsten lamp radiant furnace, also microprocessor controlled, mounted on the lathe bed. The specimen was protected from oxidation by enclosing it in a quartz tube through which high purity argon gas was passed. JArs = 895"C [ 1 15o rd~ o = O 100 Table I. Chemical Composition of the IF Steel Element Weight Percent C N Mn Si AI Ti Nb P S 0.003 0.0018 0.18 0.004 0.054 0.018 0.020 0.003 0.005 1544--VOLUME 24A, JULY 1993 50 i .8 I .84 A I .88 i I .92 i .96 1000/T ( K 1 ) Fig. 1 - - D e t e r m i n a t i o n of the At3 and Art t e m p e r a t u r e s for the present steel. METALLURGICAL TRANSACTIONS A at temperatures below about 860 ~ In order to be conservative, the maximum temperature for testing in the ferrite range was chosen to be 840 ~ Note that the values of At3 and Ar~ are in good agreement with ones previously measured for IF steel. 15'23] C. Determination of the Softening Kinetics No information was available in the literature conceming the softening kinetics of IF steels in the ferrite range. Thus, these were evaluated at 840 ~ and 770 ~ after deformation at strain rates of 0.1, 1, and 10 s -~. The shorter gage length specimens were used for the highest strain rate and also for the 840 ~ 1 s -~ case. The latter tests were carried out for comparison with results from longer specimens in order to ensure that the change in specimen geometry had no influence on the kinetics. A "double twist" technique was employed to evaluate the softening, which was similar to the "double hit" technique described in the literature for compression testing. ~24] A schematic representation of this method is shown in Figure 2. The softening experiments involve an initial deformation, followed by various waiting times, and then a second deformation. If the material softens fully during the wait, the curve for the second twist is the same as that for the first. If there is no softening, the second twist yields a stress vs strain curve that coincides with the extrapolation of the first twist (dashed line in Figure 2). The amount of softening between these two extremes, X, can be measured by determining the mean flow stresses for both twists, ~ and ~2, respectively, and comparing these to the mean flow stress associated with the extrapolation of the first curve, ~,,, according to the expression 1241 X (pet) - • 100 pet ~st Twist [6] ] The thermal schedules followed for the softening tests are shown in Figure 3. As regards the strain schedule, an initial "roughing" deformation of e = 0.8 was applied at 840 ~ This was followed about 5 minutes later by the "first twist" of e = 1.5, approximating the intermediate and prefinishing stages and which is beyond the dynamic recrystallization peak of IF steels warm worked in the ferrite range. 16j The specimens were held for periods ranging from 1 to 900 seconds, after which the " s e c o n d twist" of e = 1.5 was executed. Because of the short interpass times in the later passes of rod rolling, it is expected that strain accumulation takes place, leading to the initiation of dynamic recrystallization. [~'3j Thus, the softening kinetics measured using this technique are considered to be representative of postdynamic, as opposed to conventional statics softening, t25] D. Torsion Testing Simulation Schedules Experimental torsion testing simulations were carried out, in which the strains per pass and the interpass times were representative of those employed for a commercial wire rod rolling mill. 1261 Details of these schedules are presented in Table II, where the average pass strain rates and temperatures (for a final rod diameter of 5.5 mm) are also included. With respect to the strain per pass, it has been suggested in the literature that the heterogeneous strain associated with caliber rolling leads to an effective pass strain higher than that calculated directly from the initial and final cross sections. [4,27] By contrast, the partial reversal in strain path in successive passes, [28] leading to reversed shears, Iz9,3~ acts to offset the additional deformation contributed by the redundant strain. In order to keep matters simple, the area strain (i.e., calculated from initial and final cross sections) was employed throughout this work. Under the mill conditions, there is initial cooling from about 1050 ~ to 880 ~ followed by gradual heating back to about 1050 ~ Because the processing times are very short (Table II), it is difficult to achieve these temperature changes in the laboratory. For this reason, the industrial temperature profile was approximated by deforming isothermally at 100 ~ below the reheating temperature. [41 The thermal cycles employed are illustrated in Figure 3. Roughing was always performed at 840 ~ i 12~ i i i O.25 / ~" 950 -- 84o ~ 770 1to 0.25 ; i ~-------~i i i strain Fig. 2 - - S c h e m a t i c representation of the double twist technique for evaluating the softening kinetics. METALLURGICAL TRANSACTIONS A time Fig. 3 - - S c h e m a t i c representation of the thermal treatment of specim e n s in the interrupted torsion tests. VOLUME 24A, JULY 1993--1545 Table II. Industrial Rolling Parameters and Related Laboratory Simulation lnterpass Times Pass No. Area Strain Strain Rate (s -l) I(R) 2(R) 3(R) 4(R) 5(R) 6(R) 7(R) 8(1) 9(1) 10(I) 11(I) 12(P) 13(P) 14(P) 15(P) 16(F) 17(F) 18(F) 19(F) 20(F) 21(F) 22(F) 23(F) 24(F) 25(F) 0.37 0.34 0.22 0.24 0.32 0.31 0.32 0.33 0.24 0.31 0.22 0.26 0.17 0.30 0.21 O.23 0.20 0.22 0.22 0.25 0.21 0.25 0.22 0.24 0.21 0.68 0.63 0.84 1.80 1.57 2.40 3.49 5.25 5.08 12.98 9.75 25.50 16.65 46.19 37.08 83.65 71.17 121.38 151.42 314.38 221.15 498.13 420.98 867.51 782.44 Temperature (~ Interpass Time (s) 1050 980 955 945 940 915 895 880 880 880 900 920 --970 970 --------1050 14.5 7.6 6.1 4.8 3.5 2.6 4.8 1.4 1.3 0.65 3.03 0.66 0.56 0.41 3.45 0.079 0.061 0.047 0.036 0.028 0.023 0.018 0.014 0.011 -- Corrected Interpass Time: 840 ~ (s) 9.5 4.6 5.0 9.2 5.7 5.7 19.0 8.7 7.8 10.9 37.1 23.3 12.4 27.8 183.6 10.3 6.6 9.2 9.0 15.6 8.7 16.7 10.8 18.8 -- Corrected Interpass Time: 770 ~ (s) 11.5 5.8 5.5 6.8 4.6 4.4 10.2 3.8 3.5 3.0 11.8 4.7 3.0 4.1 30.2 1.1 0.80 0.83 0.73 0.88 0.59 0.75 0.53 0.64 (R): Roughing; (I): Intermediate; (P): Prefinishing; and (F): Finishing. and further processing was carried out either at this temperature or at 770 ~ For the simulations at 770 ~ the holding time after roughing (pass 7) was 180 seconds (60 seconds for cooling plus 120 seconds for stabilization of the temperature). As will be seen in Section III, this leads to nearly full softening of the material. All the simulations were conducted at a strain rate of 1 s -~. As will be demonstrated in Section III, the value of the softening parameter n (in Eq. [1]) for the present grade was 1.1 at 840 ~ and 0.6 at 770 ~ These values were used to determine laboratory interpass times corrected for the differences between the industrial and laboratory strain rates. The following relation, derived from Eq. [1], was used to calculate the laboratory interpass times, ttab: tlab -----/mill/'7--/ L 8lab J [7] The corrected laboratory interpass times (using e~ab = 1 S-1) are also shown in Table II. III. SOFTENING KINETICS The softening data obtained at 840 ~ and 770 ~ are shown in Figures 4(a) and (b), respectively. It is apparent that the softening curves at the higher strain rates (and particularly at the lower temperature) show a "plateau" in the softening kinetics, and this was attributed to precipitation taking place. The behavior expected in 1546--VOLUME 24A, JULY 1993 the absence of precipitation is represented as dashed lines. Support for the view that precipitation is responsible for the plateau comes from the observation that when retardation of the softening is evident, the stress level in the second twist is invariably higher than in the first twist. For example, the stress v s strain behavior in the absence of precipitation is illustrated in Figure 5(a) (840 ~ and = 1 s-~), where the curve for the second twist, which was performed after a waiting time of 7.3 seconds, follows the extrapolation of the curve for the first twist. This is not the case in Figure 5(b) (770 ~ g = 1 s -1, and waiting time of 300 seconds), where precipitation during the long waiting period raised the curve for the second twist a b o v e the extrapolation of the first curve. The occurrence of similar precipitation effects has already been reported in the literature for a Ti-Nb IF steel which was aged after warm rolling, t3u For the very high strain rates typical of the last passes of wire rod rolling, the rate of softening is expected to be much faster, with little time available for precipitation. However, precipitation can occur during the early passes, where the strain rates are lower and the interpass times are longer. In the absence of precipitation (dashed lines in Figures 4(a) and (b)), the dependence of the time for 50 pct softening (ts0) on strain rate can be described in terms of Eq. [1] and the following values of the exponent n: for 840 ~ n = 1.1; and for 770 ~ n = 0.6. These n values are in the same range as those reported in the literature for low carbon austenite, commercial purity aluminum, and AI-1Mg alloys, as can be seen in Table III. t2~ As mentioned in Section II, the above n METALLURGICAL TRANSACTIONS A 100 90 L - 100 ,'Vt I ' ' ' ' I ' ' ' ' I ' . , / / 80 80 70 eo 60 40 "~ 50 o ~ /Tempemture: s40*C [HoldingTime:7.3 ,, 40 20 * 0 30 "1 2 i 4 3 strain 20 (a) 10 i Ii 10 100 120 T=a40~ I ' J ' ' ' [ 0 1000 time (s) (a) 100 - 1 ~ ' Strengthening ~ ~ SO _ ! ~ / . lOO 90 ITI.Nb IF SteeI I T=770"C 80 / I fl o/ / / 7o Iq ]-] il lP. 60 20 I 0 ~ . . . . Ir.r.,~t~:770.c I 9 IH~ , . . . . , 1 2 ,/~ . . . . I , 3 . . . . 4 strain (b) ~ ~ 4o~ " 50 Fig. 5--(a) Absence of precipitationhardeningeffectsduringa 7.3 ~ 4o / s interruption. (b) Precipitation hardening effect during a 300 s interruption. 30 9.0 10 L~=0.1 s-1 I~ I 0 1 10 100 / 1000 time (s) (b) Fig. 4--Softening kinetics after prestraining at different strain rates: (a) 840 ~ and (b) 770 ~ values were used to calculate corrected interpass times (Table II), following the hypothesis that they are valid over the full industrial strain rate range. The typical sigmoidal plots for precipitation-free softening displayed in Figure 4 can be analyzed using the Avrami equation t33j as formulated by Sellars: t341 X= 1- exp -0.69 [8] where X is the fraction recrystallized, t50 is the time for METALLURGICALTRANSACTIONSA 50 pct softening, and k is determined by fitting a straight line to a plot of experimental values of In In [(1/(1 x)] vs in t (i.e., a so-called Avrami plot), see Figure 6. The values for k and ts0 are shown in Table IV. It can be seen that except for the case of 770 ~ and ~ --- 0.1 s -l, all the values for k fall in the range from 1.3 to 1.6, which is intermediate between the values reported in the literature for tl iron after dynamic recovery (k = 2) and dynamic recrystallization (k = 1). t351 A comparison of the curves in Figure 4 with similar results for zone-refined iron processed at lower temperatures t351 shows that the latter softens, after dynamic recrystallization at 650 ~ and a strain rate of 0.026 s -i, at approximately the same rate as the present IF steel, after deformation at 770 ~ at a strain rate of 1 s -l. The somewhat "slower" softening in the IF steel is probably due to the presence of fine Ti and Nb precipitates, t36] The softening that is predicted to occur after each pass of the industrial hot roiling schedule, outlined in Table II, was determined using Eq. [8] and the Avrami parameters listed in Table IV. The results obtained are presented in Figures 7(a) (840 ~ and (b) (770 ~ for both the uncorrected industrial and strain rate corrected interpass times. Note that these predictions are compared VOLUME 24A, JULY 1993--1547 2 I J Table IV. Avrami Equation P a r a m e t e r s for the S o f t e n i n g o f T i - N b IF Steels after D e f o r m a t i o n in the F e r r i t e R a n g e f TI-Nb IF Steel 1.5 T (~ 1 /x t~ ~', .5 ~ 0 ~ -.S ~ (s -l) ts0 (s) k 0.1 1 10 0.1 1 10 180 15 1.3 450 55 20 1.4 1.6 1.3 2.2 1.4 1.5 840 840 840 770 770 770 i . i , i , i Roughing -1 , i , i , i Intermediate Pre-Finishin 8 12 . i , i , t , i , i , Finishing I0O -1.5 .,~ -2 0.1 I I I 1 10 100 so 1000 40 time (s) (a) 92 0 l I 2 l 4 6 I0 14 16 I.8 20 22 24 Pass N u m b e r T i - N b IF Steel 1.5 ~ .5 -~ 9 p-q T = 770"C // o (a) D i i >; 100 i I Intermediate (770"C) i= g 0 6O ",,, \ -.5 , Roughing (840"C) ',P i e - F i n i s h i n g ~ (770"C) -i- [ I Finishing(770*C) =E INDUSTRIAL INTERPASS TLMES STRAIN RATE I CORRECTED I 40 6 = 0 . 1 s -I -I -1.5 2 4 8 10 12 14 . 16 18 20 22 24 Pass N u m b e r -2 1 I I I 10 100 I000 10 000 time (S) (b) Fig. 7 - - S o f t e n i n g levels predicted using the Avrami equation for processing at (a) 840 ~ and (b) 770 ~ (after roughing at 840 ~ (b) Fig. 6 - - P l o t of In In [1/(1 - X)] and (b) 770 ~ T a b l e III. vs time for softening at (a) 840 ~ V a l u e s o f n R e p o r t e d in the L i t e r a t u r e Material Low C austenite Low C austenite A1-1Mg AI 1548--VOLUME 24A, JULY 1993 n Reference 0.6 0.8 1.1 0.75 20 32 20 20 with the results of the hot rolling simulations in Sections IV and V. W h e n using a strain rate o f 1 s -~ at 840 ~ and the uncorrected industrial interpass times, the Avrami predictions suggest that almost no softening takes place between passes after the roughing stage (Figure 7(a)). The "envelope" of the multiple stress-strain curves obtained from a hot-rolling simulation at ~ --= 1 s-~ should, therefore, approximate the single curve for continuous deformation, as suggested by Yada e t al. 1~21 Similarly, other work 125j has indicated that when the strain is being accumulated, the softening kinetics after single- and multiple-pass processing are nearly the same (although METALLURGICAL TRANSACTIONS A the authors point out that this does not apply to passes executed after a large amount of softening, where the whole process of strain accumulation has to be restarted). The results presented in Section IV will confirm this. On the other hand, when the interpass times are increased to correct for the slower strain rates of the laboratory simulations compared to those of the mill, the calculations suggest softening fractions in the 40 to 60 pct range between most of the passes, with complete recrystallization taking place during the passage from one set of mill stands to the next (Figure 7(a)). At 770 ~ full softening is predicted to occur after the seventh pass, during the additional 180 seconds available during cooling from 840 ~ and temperature stabilization (Figure 7(b)). Otherwise, no significant softening is predicted to occur after either the industrial or corrected interpass times. In passing, it is worth noting that the information displayed in these figures is useful for determination of industrial rolling l o a d s 1371 and in predicting the final mechanical properties. 13sl 100 ' ' ' ' I ' ' ' ' ' ' Roughing ' ' I ' ' ' ' l ' ' ' ' Interm. Pre-fi~ I ' ' ' ' I ' ~ ' ' I , , , , Finishing ~ so r---r---40 20 0 , 0 I , , I , 2 , t , , , 3 , , , i 4 , , , , 5 6 7 strain (a) 100 ' ' ' " ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' _. . .Interm . . _P r e - f i. n Roughing ~ ' ' ' I ' i i , , , , , i Finishing it 80 60 IV. 840 ~ SIMULATION 40 Torsion tests were carried out, as described in Section II-D, using (1) single large deformations to represent each set of mill stands; (2) multiple deformations using the uncorrected industrial interpass times; and (3) multiple deformations using interpass times corrected for the differences in strain rates between the mill and the laboratory. These results are presented in Figures 8(a) through (c), respectively. It is evident that the envelope of the flow curves for the uncorrected (short) interpass times (Figure 8(b)) coincides with the uninterrupted flow curve of Figure 8(a). Thus, the contention of Yada et al. 1~21 that continuous stress-strain curves can be used in place of interrupted ones in the case of very short unloading times is supported by the present results. However, as will be demonstrated subsequently, this is unlikely to be the case /f the stress-strain curves are generated at the industrial strain rates. [10] This is because there is more softening during the longer unloading periods, particularly after the prefinishing and intermediate stages. Thus, the incremental pass strains keep returning the dynamic recrystallization flow curve to somewhere near the stress peak. In Figure 9, a comparison is made between the evolution of the MFS values for the simulations using the uncorrected industrial, and strain rate corrected, interpass times. It can be seen that the longer unloading intervals during the corrected simulation led to lower MFS values in passes 12, 13, 16, and 17 but to higher ones METALLURGICAL TRANSACTIONS A 0 , 0 1 2 i~ l 3 4 i i J 5 I 6 7 strain (b) 100 ' ' . ~ ' ' i ' ' ' ' 'q' Roughing ' ' Interm. so I ' ' ' ' I_ Pre-fin. T '11' ' I ' ' ' Finishing ' I , ' ' ' 'Eq.,x0) ( 20 ' i IY, F I1 [9] By contrast, the line fitted to the envelope in Figure 8(c) (i.e., corrected interpass times) has a lower slope, as given by ff = 75.0 - 0.33e(MPa) I 40 After the second pass in Figure 8(b), the flow stress can be described by the line shown in the figure, whose equation is # = 75.0 - 1.5e(MPa) i 20 , 0 i I 1 , , i 2 i J i i J 3 i I t 4 , i , , 5 6 7 strain (c) Fig. 8 - - S t r e s s - s t r a i n curves for the torsion testing simulation at 840 ~ using (a) continuous deformations to represent each stage of hot rolling; (b) the uncorrected industrial interpass times; and (c) the strain rate corrected interpass times. in passes 6 through 11, 14, 15, and 18 through 26. As already mentioned, this is because the increased softening due to longer interpass intervals can decrease the residual strain to such an extent that a new cycle of dynamic recrystallization is initiated, which reintroduces the high MFS values associated with the peak of the dynamic recrystallization stress-strain curve. VOLUME 24A, JULY 1993--1549 76 9 i , i , , 9 , i , i , , i , i , [ , i , i , i , i , Finishing [ Pre-Finishing 70 65 o 8o i 65 ~s ! [i Roughing J 50 , i 2 /I ] Intermediate t I 4 , I 6 , I 8 CoPa~zCTZD I i , I0 12 , 14 *1 , i 16 9 18 i , i 20 . 22 24 Pass Number Fig. 9 - - C o m p a r i s o n of the mean flow stress levels for the simulations at 840 ~ using the uncorrected industrial, and strain rate corrected, interpass times. The experimentally observed softening that takes place after each pass is displayed in Figure 10, for both the uncorrected industrial and corrected interpass times. It is now of interest to compare this observed behavior with the Avrami equation predictions (Figure 7(a)). For the uncorrected industrial (i.e., shorter) interpass time schedule, it is clear that the high softening levels predicted for the first two passes were not realized during the torsion testing simulation. This is because the softening kinetics typical of unloading after straining to a point before the dynamic recrystallization peak are much slower than the postpeak kinetics described by the Avrami relation. {2~ The accurate description of prepeak recrystallization behavior would have required the availability of a further set of data, similar to those displayed in Figures 4(a) and (b) but obtained after unloading at lower strains. Another difference between Figures 10 and 7(a) is that the overall level of softening for the simulation (Figure 10) is about 20 pet higher than the Avrami prediction (Figure 7(a)). This is attributable to the recovery and relaxation of the dislocation stress fields during unloading, a softening process that the Avrami relation does not address. , i , i , i , Roughing i , i , i Intermediate , i i , i , Pre-Finishln i , i . i . Finishing 100 "E g() ~ [ IINDUSTRIAL ] 6O 40 =i 1 0 , i 2 , i 4 , i i 6 8 , i , I0 i 12 , i i 14 16 , L 18 , i 20 i t , 22 i , 24 Pass Number Fig. 1 0 - - C o m p a r i s o n of the softening observed after each pass of the simulations at 840 ~ using the uncorrected industrial, and strain rate corrected, interpass times. 1550--VOLUME 24A, JULY 1993 By contrast, there is less discrepancy between the observations and predictions for the corrected (i.e., longer) interpass times. The observations followed the predictions relatively well after pass 5, although the observed higher level of softening after each pass delayed the strain accumulation required to satisfy the kinetics of Figure 4, with the result that the softening after pass 7 was significantly lower than the expected level of about 70 pet. Similar considerations led to the observed softening of about 85 pet after pass 11, being lower than the predicted softening level of about 95 pet. This discrepancy increased to 35 pet (observed) vs 85 pet (predicted) after pass 15. The situation in the finishing stage is similar to that pertaining to roughing and prefinishing: the predicted softening levels are again higher than the observed ones. When long interpass times are employed, there is sufficient time for precipitation to occur, an opportunity which is absent when the industrial interpass times are used. Because of the complexity of the phenomenology, no attempt was made to include the retarding effect of precipitation on softening when employing the Avrami relation. Accordingly, when the simulation allows sufficient time for precipitation to take place, there will be less observed softening than predicted by the Avrami kinetics. This is one drawback to the use of corrected (i.e., longer) interpass times. The low strain rates used in the laboratory (and therefore the low accumulated dislocation densities) mean that the fractional softening determined using the mill interpass times will lead to predicted softening levels that are too low for the high dislocation densities pertaining to mill conditions of straining. The use of corrected interpass times goes a long way in addressing this problem but leads to truly accurate results only when the longer time does not lead to significant volume fractions of precipitates. Thus, even when corrected interpass times are used in simulations, the measured fractional softening may still be lower than that occurring in the mill. Several conclusions can be drawn from the previous results. One is that the softening kinetics are highly sensitive to the amount of retained strain in a sequence of passes. When this is low, the rate of softening will be slow and close to that observed in undeformed materials. This means that even if dynamic recrystallization has been initiated, which can lead to rapid postdynamic softening, the latter, if it goes to completion, can lead to the subsequent complete loss of retained strain. In this case, slow interpass softening (i.e., conventional static recrystallization) is reintroduced at later stages of the process. Such increases and decreases in the softening rate may thus be responsible for the anomalous evolution of the MFS along the finishing stands of a strip mill, which has been reported in the literature, t39,4~ It also appears that the use of continuous curves to replace interrupted ones can lead to problems, unless there is only limited softening even when longer interpass times are employed. According to the present results, such softening should not exceed about 20 pet, signifying that little recrystallization has been initiated. METALLURGICAL TRANSACTIONS A V. 770 *C SIMULATIONS For the torsion tests carried out at 770 ~ roughing was performed at 840 ~ As this aspect of the simulation was described in Section IV, only the results obtained from the further processing stages will be presented 120 ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' ._ Intermed. _ I Pre-finish~.l_ I . . . . I ' ' ' , Finishing l ' ' ' ' ~ I here. The stress-strain curves for the simulation using continuous deformations for each stage, and for the simulation using the uncorrected industrial interpass times, are shown in Figures l l(a) and (b), respectively. The two sets of curves are similar, as expected from the softening predicti~s in Figure 7(b). The peak strain is higher than at 840 ~ and the flow curve envelope after the intermediate stage of rolling (pass 11) can be described by the following equation: IO0 ~ = 1 0 2 . 0 - 1.92e(MPa) 80 [11] 120 The stress-strain curves for the simulation using corrected interpass times are shown in Figure 1 l(c). Here, the softening levels are somewhat higher than in Figure 1 l(b), and there is a clear increase in the stress level after the prefinishing stage. The latter can be attributed to the occurrence of precipitation during the 30 second interpass time (Figure 5(b)). Since similar hardening effects were not observed after earlier passes, even though the accumulated time was of the same order, it can be concluded that the present type of precipitation phenomenon depends primarily on the time available after a given strain step. The equation for the envelope of the finishing stage in Figure 11 (c) is IOO # = 1 0 5 . 2 - 1.89e(MPa) 40 20 0 t 0 i i i | 1 1 1 I i , I i i I 2 , i i 3 i i I i I i i 4 I . i . , 5 ] , , i ,l 6 7 strain (a) 80 40 20 0 0 1 2 3 4 6 6 7 strain (b) .,,,i,.,~i..,, i., : Intermed. : Pre-finlsh. l . 120 IOO /v < ,.i,.,,i. Finishing ,, ,i, ,~, 9 [12] The comparison of Eqs. [11] and [12] shows that precipitation leads to a hardening effect of approximately 3 MPa. Since there is much less time available after each pass in industrial mills, Eq. [I 1] is more useful for practical purposes than Eq. [12]. The evolution of the MFS values for the industrial interpass times is compared to that obtained using the corrected ones in Figure 12, where the strengthening effect of precipitation can also be seen. In contrast to the results for 840 ~ (Figure 9), the increased softening associated with longer interpass times was not enough to reduce the residual strain to a level leading to the reinitiation of dynamic recrystallization. Even after pass 16, the MFS envelope is similar to the one observed using the short unloading intervals. Softening levels of about 20 pct were observed using r( 120 f u , , u . n 9 , . n , Eq.(12) INDUSTRIAL [k CORa~CTED INTC~ASS [/ AND AFFECTED BY TIMES 40 20 I 0 i 2 I . . . . 3 I 4 , , . . I 5 , , , , I . . 6 , . 7 strain (c) Fig. 11 - - S t r e s s - s t r a i n c u r v e s for the s i m u l a t i o n s at 770 ~ (a) u s i n g c o n t i n u o u s d e f o r m a t i o n s to represent each stage o f hot rolling; (b) using the uncorrected industrial interpass t i m e s for i n t e r m e d i a t e rolling and p r e f i n i s h i n g ; and (c) u s i n g the strain rate corrected interpass t i m e s for i n t e r m e d i a t e and prefinishing. METALLURGICAL TRANSACTIONS A i far.mutilate 60 , Pm-Fiaishiag i Finishing 1 I I I I I 9 11 13 15 17 19 I I 21 I I I 23 25 Pass I Number Fig. 1 2 - - C o m p a r i s o n o f the m e a n f l o w stress l e v e l s for the simulations at 7 7 0 ~ u s i n g the uncorrected industrial, and strain rate corrected, interpass t i m e s . VOLUME 24A, |ULY 1993--1551 the industrial interpass periods, which are higher than the Avrami predictions shown in Figure 7(b). This situation is similar to the one at 840 ~ where the difference was assigned to recovery and to the relaxation of the dislocation stress fields. An analogous comparison for the corrected schedules is displayed in Figure 13, where the pass 15 measurement excludes the precipitation hardening shown in Figure 12. (Note that no calculations were performed for passes 16 through 25, because these tests utilized one continuous deformation to simulate the finishing stands.) The fact that, in contrast to the 840 ~ case, the softening levels are now higher than the predicted ones can again be explained by the occurrence of recovery, which is not addressed by the Avrami relation. The comparison of Figures 9 and 12 indicates that substantial interpass softening (50 pet or more) is necessary in order for new cycles of dynamic recrystallization to be triggered, with their attendant increases in MFS level. VI. F L O W S T R E S S C O R R E C T I O N S FOR STRAIN RATE DIFFERENCES 1 s-t). The results for 840 ~ and 770 ~ are presented in Figures 14(a) and (b), respectively. Note that the MFS,,itt values corrected for strain rate are approximately double the laboratory values corrected for the interpass time only. Note also the "oscillations" in the MFS,,u values in going from pass to pass, which might not be apparent simply from inspection of Eq. [14]. It is of interest that higher values of the softening rate exponent, n, and of the rate sensitivity, m, were observed at 840 ~ than at 770 ~ These two observations may be linked, since an increase in strain rate leads to an increase in stored energy, which, in turn, is related to the driving force for softening. VII. CONCLUSIONS 1. Strain rate corrected (i.e., longer) interpass times should be used when high strain rate industrial processes are simulated using low strain rate laboratory tests. Compared with the results obtained using the uncorrected industrial interpass times, this more accurately reproduces the evolution of the mean flow stress values, particularly with respect to the behavior The strain rate dependence of the flow stress, for a given strain, is ~4~ or 225 [13] OC ~ m i , i , i , i Roughing The strain rate sensitivity m in Eq. [13] was evaluated using the peak stress measured at various strain rates in the softening experiments. The average m values were determined to be 0.15 and 0.11, at 840 ~ and 770 ~ respectively. By assuming that these values are valid right up into the industrial strain rate range, as well as for all levels of residual strain, Eq. [13] can be used to determine the expected mill MFS values as follows: . i , i . i , i , i , , I n t e r m e d i a t e ', Pie-Finishing', i . i , i , Finishing 200 ~u 175 ~a 150 125 100 75 MFSmiu = [14] MFS/ao k et,~bJ 50 2 Equation [14] was used to calculate the MFS values for a rod mill from the laboratory MFS values measured using the strain rate corrected interpass times and from the mill strain rates listed in Table II (recall that gt~o = 4 6 8 10 12 14 16 18 20 22 24 Pass Number (a) 225 i i i Pre-Finishing Intermediate i i , i , ~ , i , Finishing 200 i i i Intermediate v I Pre-Finishing Iml( IOO Finishing It ;: r~ ~ 175 :- MFS i AT i w 1so ~ s0 ~rEs I: \ i f ~,./ i "i , b I sT~'~ I 60 75 9 II 13 15 17 19 21 23 25 Pass Number 0 (b) \ 8 I0 12 14 16 Pass Number Fig. 1 3 - - C o m p a r i s o n between the predicted and observed softening levels for processing at 770 ~ using the strain rate corrected interpass times. 1552--VOLUME 24A, JULY 1993 Fig. 1 4 - - M e a n flow stress levels predicted for hot rolling at the industrial strain rates, using the corrections for the strain rate dependence of both the MFS and the interpass softening from torsion testing simulations conducted at (a) 840 ~ and ~ = 1 s -~ and (b) 770 ~ ande = 1 s-'. METALLURGICAL TRANSACTIONS A due to dynamic (and metadynamic) recrystallization. A drawback of this approach, however, is that precipitation can take place during the extended unloading periods, which can then retard the rate of softening and modify the stress levels. 2. High strain rate, multiple-step industrial processes can be simulated accurately using continuous low strain rate tests only if the interpass softening that would be expected using the corrected interpass times does not exceed about 20pct. 3. Postdynamic softening in the present Ti-Nb IF steel can be retarded, both at 840 ~ and 770 ~ by the occurrence of precipitation. In the absence of precipitation, the softening strain rate sensitivity exponents are n = 1.1 at 840 ~ and n = 0.6 at 770 ~ 4. Softening predictions based on the Avrami equation underestimate the softening observed using the continuous and uncorrected industrial interpass time schedules and overestimate it for the corrected ones. 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Jonas: Formability & Workability of Metals: Plastic Instability & Flow Localization, ASM, Metals Park, OH, 1984, p. 18. VOLUME 24A, JULY 1993--1553