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In order to assess the importance of precise deformation conditions used in modelling of hot working processes, the effects of temperature and strain rate histories as well as that of the reversed deformation on the flow stress and recrystallisation behaviour of both the austenite and ferrite phases have been investigated in various steels.
According to the experimental results, the temperature history seems to have only an insignificant influence on the flow stress and recrystallisation rate of austenite. In microalloyed steels, during a temperature drop to a low temperature, precipitation can occur that may prevent the subsequent recrystallisation. However, in the rolling gap the surface temperature drops are very short in duration so that precipitation can hardly occur to any significant extent.
Under abruptly decreasing strain rate, in the dynamic recovery regime, the final flow stress remains higher than that at the corresponding constant final strain rate, close to the stress at the constant mean strain rate of the whole deformation history. This means that the mean flow stress is higher under the varying strain rate than at constant mean strain rate. The static recrystallisation rate lags even more than the flow stress so that it has a certain memory from the previous strain rate history. Following an abrupt decrease in the strain rate, the recrystallisation rate remains close to that at the high strain rate before the drop. However, because the effect of strain rate on the recrystallisation kinetics is weak, the effects are not very significant and the mean strain rate can be used for modelling with reasonable accuracy. The composition of the steel has no influence on that.
Reversing the direction of deformation from tension to compression results in the Bauschinger effect in the flow stress of austenite, with the magnitude order of 5%. The reversal leads to a retarded recrystallisation rate, the amount depending on the strain after the reversal (at a constant strain before the reversal). The rate is decreased as much as by 23 times, as the second strain is 0.020.04 and the first strain 0.2. Qualitatively this is consistent with observations from torsion tests. Decreasing the strain rate in the final stage of deformation after the reversal causes an additional retardation. Partial recrystallisation after the first deformation before reversing the strain enhances the recrystallisation, but the effect is not pronounced. No distinct effects of the reversal on the recrystallised austenite grain size were detectable.
In the ferrite phase, the influence of strain rate change on the flow stress level and the reecrystallisation kinetics was found to be qualitatively similar to that in the austenite phase. Strain reversal was found, by the doublecompression tests and by optical microscopy, to retard the recrystallisation of ferrite, and qualitatively its effect was similar as for the austenite. However, a pronounced coarsening of the ferrite grain size was observed at small reversed strains.
After changing the strain rate abruptly, the cell size formed in the ferrite seemed to be larger than at constant high strain rate revealing that the driving force for the static recrystallisation decreases rapidly due to the drop of the strain rate. The misorientation distribution of thePage 354grain boundaries was not affected by the strain rate change. The strain reversal also resulted in an increased cell size compared to that in monotonic straining. The misorientation distribution was also affected by the reversal, the number of lowest angle (the misorientation below 5°) boundaries being increased.
Finally, the transient behaviour of the flow stress in the ferrite following the abrupt change in the strain rate was modelled successfully in the ferrite using the Bergström’s model, although several assumptions had to be incorporated.
Traditionally, deformation resistance and recrystallisation kinetics are determined in tests carried out at constant strain rate and temperature. Equivalent or average values of these external variables are used in modelling.
Due to chilling effect of the rolls, temperature at the surface layer of a slab drops fast during the rolling pass but it increases again immediately after the exit due to the conduction of heat towards the surfaces from the hotter core. Fast temperature changes are possible to simulate and perform on a Gleeble apparatus due to the use of resistive heating of the specimen in the experiment. In the previous ECSC project [A6.1], tests on a 0.07C0.96Mn 0.046Nb0.011Ti (wt. %) steel indicated that the final temperature, i.e. the temperature at which the static recrystallisation occurred after the deformation, determined the softening kinetics, If the initial temperature was more than 50°C higher than the final temperature in the deformation, the driving force remained somewhat lower due to a faster dynamic recovery at the high temperature and consequently the recrystallisation process became retarded. However, the surface temperature decreases in the rolling gap, not increases, compared to that during the subsequent pass interval.
In hot rolling, in each stands the strain rate changes continuously, rises immediately to a maximum and as the material leaves the roll gap it falls to zero (see [A6.2]). When strain rate is changed during deformation, these changes seem to produce transients while the stress is not instantaneously defined by a mechanical equation of state. In a rolling pass, strain is so short that stable conditions cannot be reached. Moreover, the strain required to achieve a new steady microstructural state is still higher [A6.1,A6.3A6.5], and therefore the transients may have some influence on the recrystallisation kinetics subsequent to the deformation pass. These phenomena have been investigated in microalloyed steels earlier briefly by Karjalainen et al [A6.6,A6.7], but more results and firmer conclusions were searched in this project.
At the University of Oulu, experimental work was carried out aiming at investigating the influence of deformation history, i.e. the changes in temperature and strain rate in the course of deformation, on the flow stress and subsequent softening behaviour in the hotdeformed austenite and also in warmdeformed ferrite phase, and compare them with the behaviour of austenite investigated earlier at the University of Oulu and Corus (in compression) and also at CEIT (in torsion).
The effect of reversing straining was preliminarily investigated in the previous ECSC project in axial deformation and also in torsion [A6.1]. Some results have been published from axial compression tests in Refs. [A6.7,A6.8] and from torsion tests in Refs. [A6.9A6.11]. It has been noticed that the reversal causes a distinct Bauchinger effect in the flow stress and retardation in the static recrystallisation kinetics, which is dependent on the ratio of strains preceding and following the reversal [A6.8,A6.9]. Dynamic recrystallisation is delayed by the reversal [A6.9].
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In the present study further information was aimed at clarifying the influence of strain reversal on the flow stress and the static recrystallisation kinetics of C1.8Mn0.13Ti 0.067Nb and 42MnV7 steels. However, it was realised important to fix the experimental conditions even better than earlier, and therefore a relatively high number of tests were first carried out using the same Nb steel (0.15C1.42Mn0.033Nb) as in the previous project [A6.1].
Furthermore, the aim was to investigate the effect of decreasing strain rate after the strain reversal on the recrystallisation kinetics, this way simulating the real deformation conditions present in the rolling gap. To modify the dislocation structure after the first pass deformation, in a few tests, a holding time resulting in partial recrystallisation was applied before the reversed deformation.
At the University of Oulu, computer modelling was not intended to perform in the project, only experiments to generate data and to improve the knowledge on the extent of the history effects and their importance to be incorporated in the models by the other partners. However, simple constitutive modelling on the influence of an abrupt change in the strain rate was performed based on the Bergström’s model.
Before the experimental investigations of the constitutive behaviour, the evaluation of the existing constitutive models was performed by all partners. In fact, at the University of Oulu, the present research group uses regression models only, developed by partly the group itself and partly taken from the open literature. All regression models are based on average values of the deformation parameters. These models have been incorporated into some neural models to form an online hybrid model, installed at the moment in a steel company.
For the benchmark simulation, some calculations were carried out using the abovementioned regression models for the static recrystallisation in order to adjust the interpass times applied in hot rolling tests at TU Freiberg.
Two steels, a highTi bearing HSLA steel (marked here hTiNb) and a medium carbon steel 42MnV7, were used in the tests. Their chemical compositions are given in Table A6.1.
The cylinders 10 x 12 mm were machined from the prerolled plates for compression testing on a Gleeble 1500 thermomechanical simulator. The intention was to impose somewhat larger temperature changes than in the previous ECSC project [A6.1] and to investigate whether the chemical composition has any influence. Only the effect of abruptly reduced temperature, as the real case in rolling, was tested. Experimentally, a reasonable heating rate is 50°C/s so that the change of 100°C requires 2 s. The strain of 0.2 can be achieved within this time at the strain rate of 0.1 s^{1}.
The test details are given in Table A6.2. To ascertain that the final temperature has been reached accurately before the beginning of recrystallisation, special schedules were adopted in some cases. In these tests, the temperature change was already accomplished shortly before the end of compression (e.g. strain of 0.16 occurred in the heating stage and strain of 0.04 at the final temperature, i.e. the time of 0.4 s, long enough, was available to adjust the temperature).
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The lower strain rate of 0.01 s^{1} executed in some tests provided a longer time, while the initial deformation could be carried out isothermally at the lower temperature, followed by heating in the final deformation stage to the final temperature (e.g. schedules such as 0.15 strain at 900°C followed by 0.04 strain during heating at 50°C/s to 1100°C or 0.16 strain at 1000°C followed by 0.02 strain during heating at 50°C/s to 1100°C).
The final (i.e. recrystallisation) temperature selected was 1100°C (a few tests were performed at 1150°C and some isothermal tests at temperatures between 1025°C and 1150°C to confirm the kinetics) providing a convenient recrystallisation rate and absence of any interfering precipitation even in the hTiNb steel. The lowest start temperature was 900°C, i.e. the change was then 200°C.
The stress relaxation technique was applied to determine the recrystallisation rate. The method has been established in many previous studies (see Ref. [A6.12], for instance).
The strain rate changes taking place in the course of a rolling pass were simulated on a Gleeble 1500 simulator by three ways:

Starting at a low strain rate (0.01 s^{1} in most cases) to a short strain of about 0.02 (stage 1), increasing instantaneously to a high strain rate (1 s^{1} in most cases) to a certain strain (0.1 to 0.3) (stage 2), and finally decreasing instantaneously the strain rate back to a low value (stage 3).

Executing only the stages two and three (a high strain rate and the drop to a low strain rate) as described above.

The “continuous change” in the strain rate, one or two orders of magnitude, was created by changing the strain rate in small steps of 0.01 s^{1}. The strain rate was first increased to a maximum at the first half of the applied strain and then decreased back to the initial level.
Two steels, hTiNb and a medium carbon steel 42MnV7, were used in these tests (see Table A6.1). The cylinders 10 x 12 mm were machined from the prerolled plates for compression testing on a Gleeble 1500 thermomechanical simulator. The stress relaxation technique was applied to determine the recrystallisation rate.
All tests were carried out on a Gleeble 1500 simulator. The rods of 120 mm length and 10 mm in diameter, but the middle portion of 10 mm long thinned to the 9 mm diameter, were used. The thinned portion was essential to obtain a more uniform temperature zone where the deformation was concentrated. In this specimen, the gage length of 10 mm could be assumed, even though it appeared that this is not a very accurate estimate. It was found that the strain in the tension mode in the thinned portion became higher than nominal strain intended and after compression considerable bulging was present, so that the actual strain values had to be estimated from the diametric strains. The stress relaxation technique was employed to determine the recrystallisation rate. Due to experimental reasons revealed in the previous project [A6.1], in all tests the strain was tensile first following by a compressive strain in the second stage.
Three steels, Nbsteel, hTiNb steel and 42MnV7 were used in the tests. Various details were in the tests schedules as follows:
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Ordinary T/C reversal tests In all tests the first strain applied was constant, nominally 0.175, but the actual strain was about 0.2. The second strain was varied from the lowest value 0.0125, still controllable in the Gleeble, up to 0.4.
In addition, the austenite grain size was measured in the Nb steel after the reversed deformation varying the second strain between 0.05 and 0.125 in the tests.
T  C + decreasing strain rate A decreasing strain rate from 1 s^{1} (or 0.1 s^{1}) to 0.01 s^{1} was applied in the final stages (0.01 strain) of certain tests after the first tensile strain, followed by the equal compressive strain (nominally 0.175T/0.175C).
TholdingC reversal tests The holding stage of 3 s or 6 s after the first tensile strain at 1050°C was used in some tests to obtain a partially recrystallised structure before the straining in the compressive mode and finally followed by the stress relaxation.
The strain rate changes occurring in the course of a rolling pass were simulated on a Gleeble 1500 simulator by starting at a high strain rate (1 s^{1} in most cases) to a certain strain (from 0.1 to 0.6), and finally decreasing instantaneously the strain rate back to a low value.
In order to reveal the possible influence of chemical composition, four steels, lowcarbon, hTiNb, Ti IF and NbTi IF, were used in the tests. Their chemical compositions (wt. %) are given in Table A6.1. The cylinders 10 mm x 12 mm were machined from the prerolled plates for NbTi IF and low carbon steels, but smaller cylinders of 6 mm x 7.5 mm had to be used for Ti IF steel due to availability of the material. For IF steels, two prepasses with the 10 min holding at 1000°C were applied to refine the grain size of austenite by recrystallisation and to enhance the recrystallisation rate in ferrite, which is known to be quite slow [A6.13]. This procedure was also adopted in a previous ECSC project [A6.1]. In the low carbon steel, a completely homogeneous polygonal ferrite structure was obtained by the cooling at the rate of 5°C/s to 500°C and then rising the temperature to the deformation temperature (700°C in most tests).
The stress relaxation technique was first tried to apply to determine the recrystallisation rate, but its sensitivity was found to be quite poor so that in most cases doublecompression tests had to be employed, instead. The 5% total strain procedure was adopted [A6.12], in which the maximum stress (VER SIMBOLO EN PDF ADJUNTO 3) is the final stress after the strain rate change, i.e., at the strain 0.02 in most tests.
Optical microscopy was used to examine the grain structures in different stages of the softening. Comparisons were carried out between the structures after constant strain rate straining and changedstrain rate deformation to reveal differences in the recrystallisation rate.
Electron microscopic techniques were employed to study the dislocation structures. Comparisons were carried out between the structures after constant strain rate straining and changedstrain rate deformation to reveal differences in the dislocation density or distribution. The deformed specimens were sectioned parallel to the compression axis andPage 358the cut surfaces were examined metallographically using standard procedures. Specimens for thin foils were prepared by the twinjet electropolishing in the solution of perchloric acid and ethanol at about 35°C. The foils were studied in a Leo 912 transmission electron microscope. Bulk specimens were examined in the SEM (Jeol 6400) using the backscatter electron image contrast. The misorientation between grains and subgrains were further analysed in the SEM using the Nordif CD100/Oxford INCA EBSDunit attached.
The Armco iron was used to test the effect of strain reversal on the recrystallisation kinetics of ferrite. Stress relaxation technique was first tried, but the sensitivity was observed to be relatively poor so that the double compression technique (the 0.5% total strain [A6.12]) was employed instead. The first applied strain, always in tension, was kept constant, nominally about 0.18, but due to inhomogeneous deformation the diametric strain was higher, about 0.26. The second compression strain was varied from a small ( §0.02) value to about 0.7.
The specimens for dislocation studies were prepared similarly as described above in the case of the strain rate change tests.
The influence of the temperature change was investigated for the austenite phase only. Figure A6.1 shows examples of the compression stressstrain curves for the hTiNb and 42MnV7 steels obtained in isothermal tests and in tests with increasing temperature. As starting at a lower temperature the stress increases faster than in the isothermal test. However, finally the curves approach each other, so that the difference between the final flow stress levels is generally relatively small (see values in Table A6.2), although the flow stress of the isothermal tests tended to remain lower. The hTiNb steel is an exception, for as starting the deformation from 900°C, a pronounced difference remains between the final flow stress values (Fig. A6.1(b)).
Typical relaxation curves recorded are shown in Fig. A6.2. From the curves the fraction v time data were computed and the Avramitype equation fitted with the data. The complete data from the relaxation tests are given in Table A6.2, listing the stress in the beginning of relaxation, the Avrami exponent and the values t5, t50 and t95 for 5, 50 and 95% recrystallisation fraction, respectively.
The relaxation curves obtained for the hTiNb steel, with the start temperature of 900°C, are shown in Fig. A6.2(b). It is obvious from the straight relaxation lines that no recrystallisation takes place at all at 1100°C in this steel, even though recrystallisation is fast in the isothermal test at this temperature.
Recrystallisation behaviour is dominated by the total stored energy and its distribution (see e.g. Refs. [A6.14] and [A6.6]). The number of viable recrystallisation nucleation sites per unit volume (Nv) is dependent on local differences in the stored energy, whereas the growth rate is determined by the mean stored energy per unit volume (PD). Consequently, the kinetics is affected by both of them, approximately as:
[VER FORMULA EN PDF ADJUNTO]
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Where C is a constant (related to the mobility of grain boundary) and p is a coefficient related to the probability of finding a sufficiently large nucleus (in fact, the probability of a nucleus being formed depends primarily on the standard deviation of the subgrain size distribution and on the mean subboundary misorientation (VER SIMBLO EN PDF ADJUNTO) which is why probability decreases rapidly as [VER SIMBOLO EN PDF ADJUNTO] decreases), [VER SIMBOLO EN PDF ADJUNTO] a geometrical factor, Sv the grain boundary area per unit volume (dependent on strain) and [VER SIMBOLO EN PDF ADJUNTO] the subgrain size. PD consists of influences of the dislocation density [VER SIMBOLO EN PDF ADJUNTO], cell size [VER SIMBOLO EN PDF ADJUNTO] and also misorientation [VER SIMBOLO EN PDF ADJUNTO] as follows:
[VER FORMULA EN PDF ADJUNTO]
Where [VER SIMBOLO EN PDF ADJUNTO] is the critical angle for distinguishing between a grain and subgrain boundary [VER SIMBOLO EN PDF ADJUNTO], G the shear modulus and b is the burgers vector.
Hence, the recrystallisation kinetics is dependent on the stored dislocation density. At a lower temperature, at a given strain a higher stored energy in the form of numerous dislocations and vacancies can be expected owing to lesser dynamic recovery, enhancing the growth rate in the recrystallisation. Possible changes in the number and character of the nucleation sites are difficult to conclude.
The flow stress [VER SIMBOLO EN PDF ADJUNTO] is also dependent on dislocation density as follows (see e.g. Refs. [A6.15] and [A6.8]):
[VER FORMULA EN PDF ADJUNTO]
Where [VER SIMBOLO EN PDF ADJUNTO] is the friction stress dominated by the viscous drag of solute atoms segregated to the moving dislocations, [VER SIMBOLO EN PDF ADJUNTO] are constants, M is the Taylor factor. Therefore, the flow stress level should be a (rough) measure of the dislocation density and consequently, the driving force of recrystallisation.
As seen in Fig. A6.1, as starting compression in a lower temperature, the flow stress increases higher, which results from lower thermal activation for dislocation glide and perhaps from higher dislocation density. The flow stress level in the end of compression reflects the driving force achieved for the subsequent recrystallisation. It can be seen that the difference between the final flow stresses is quite small, and it also appeared that scatter was present. As a consequence of small difference in the driving force, only a small variation in the recrystallisation rate may be expected, as observed from the measurements (Table A6.2). Generally, the results indicated that the change in temperature in the course of deformation (i.e. previous temperature history) only affects minimally the subsequent softening behaviour, but the actualinterpass temperature determines the rate.
There are some other things to be noted, however. It is well known that the deformation conditions, often described by the ZenerHollomon parameter, vary in the thickness direction. The real temperature tends to be lower at the surface layer. The deformation rate varies in a complicated way. There may also be variation in the final strain reached in the deformation pass resulting from different deformation resistance in the layers at different temperatures. All these factors may result in differences in the recrystallisation kinetics in the thickness direction.
It should be noticed that if low temperatures below about 950°C exist (see Fig. A6.2(b)), they may cause prompt dynamic or/and static precipitation to occur which consequently retards significantly the recrystallisation. However, in practice, the duration of a rolling pass (strain/strain rate) is order of 0.3/3 [VER SIMBOLO EN PDF ADJUNTO] 0.1 s, i.e. very short, and the temperature rise is fastPage 360after the exit of the roll gap, so that enough time for any profound precipitation may not be available.
The tests details for the hTiNb steel are shown in Table A6.3. Figure A6.3 shows two examples of the strain rate histories applied by the first way and the corresponding flow stress curves are given in Fig. A6.4 (also at certain constant strain rates for comparison). Fractional softening curves are plotted in Fig. A6.5, following these strain rate changes or at constant strain rates.
Typical strain rate histories according to the second way are shown in Fig. A6.6 and the corresponding flow stress curves in Fig. A6.7 and the fractional recrystallisation curves in Fig. A6.8, the latter also containing curves at constant strain rate for comparison.
For medium carbon steel, the strain rate history is shown in Fig. A6.9(a) and the flow stress curves in Fig. A6.9(b). Stress relaxation curves and fractional recrystallisation curves are given in Fig. A6.10(a and b), respectively.
Immediately following an abrupt decrease in the strain rate, the control of the strain rate seems to be shortly poor, and the flow stress drops instantaneously to a low value but increases back to a proper level corresponding to the controlled strain rate.
It is obvious that the flow stress remains temporarily somewhat higher than the flow stress at a final strain rate in constant strain rate test (below or close to the level of the flow stress in a test at the constant average strain rate). Hence, the flow stress is slightly lagging as following the changes in the strain rate compared to that expected from the mechanical equation of state.
With increasing strain at the lower final strain rate, the flow stress gradually approaches the level of flow stress of a constant strain rate test. In the real rolling pass, the final strain is, however, extremely short (decrease of the strain rate so fast), so that it can be concluded that the flow stress at the exit is markedly higher than that based on the final strain rate (approaching zero).
In the instance of continuously changing strain rate, the final flow stress is practically independent of the previous strain rate history, as seen in Fig. A6.11(a). The recrystallisation rate is, however, dependent on the history so that the high strain rates applied results in faster recrystallisation kinetics than the lower ones, as seen in Fig. A6.11(b).
The previous results [A6.8] showed that the MFS of the deformation (strain 0.3) is about 12% higher under the varying strain rate than under a constant strain rate equal to the mean strain rate. The values of MFS were 87 MPa (at the changing H´) and 78 MPa (at 0.064 s^{1}). This may mean that the real rolling load tends to be higher than the value predicted from constant strain rate tests.
Recrystallisation rate (in the case of a short final strain, 0.0050.02 strain) is close to the value at the high strain rate applied, i.e. it lags clearly more than the flow stress (Figs. A6.5 and A6.8). Also, as shown earlier [A6.7,A6.8], the average strain rate can be used to model the static recrystallisation kinetics reasonably.
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At higher strains, and for 42MnV7 steel in particular, it seems that following the decrease in the strain rate, dynamic recrystallisation will be initiated which results in the decreasing rate of metadynamic recrystallisation, and even absence of recrystallisation in the case of 0.01 strain as seen in Fig. A6.10.
Both steels behave qualitatively in a similar way so that no significant effects of the chemical composition can be found. The peak strain of 42MnV7 steel is shorter than that of hTiNb steel. The results confirm the observations for Nbbearing steel obtained earlier [A6.7,A6.8]. Some discussion concerning the role of the internal state variables can be found in some previous papers [A6.7,A6.8].
The main interest was paid on the kinetics of SRX after a very short second strain following the reversal from tension to compression. Different results have been published regarding this behaviour. From axial compression tests results showed that the SRX kinetics is not affected by the short second strain and higher second strains are enhancing the rate, although the rate is always smaller than in monotonic deformation at a comparable total strain [A6.6]. In torsion tests, a retardation (a minimum) of the kinetics was observed at small second strain, i.e., the rate was slower than the rate without any second strain (here in the CEIT contribution) [A6.9,A6.10,A6.11]. At higher second strains the rate increased but remained lower than in monotonic deformation at a comparable total strain.
The main observations are as follows:
Tension  compression tests
The Bauschinger effect of about 5% is present in all the steels tested as shown by the flow stress curves in Fig. A6.12 in four examples.
As seen in Fig. A6.12, the flow stress in tension measured using the long rods is higher than that in compression determined using cylinders. This is probably due to differences in the distribution of deformation (centrally thinned specimen; shoulders) or in the prediction of the flow stress (problems to define the exact gauge length; nonuniform temperature).
The diametric strain (Cstrain) is higher than the longitudinal strain (Lstrain) indicating some barrelling occurring in the middle zone. Therefore, the actual strains before and after the reversal are higher than intended (nominal) ones. Control of small strain less than about 0.015 is difficult, for the proper stress level has not been reached at the 0.0125 strain, as seen in Fig. A6.13.
The time for 50% recrystallised fraction t50 is shown in Fig. A6.14, as a function of the second strain following the tensile strain of 0.175 (the actual Cstrain about 0.2, calculated assuming the gage length of 10 mm). For all the steels tested, the trend in t50 is the same, first increasing with increasing second strain up to a maximum at about 0.04 strain (for NbhTi at about 0.02), which is smaller than 0.1 in torsion [A6.10,A6.11], and then decreasing towards the value determined for the metadynamic recrystallisation in the monotonic (i.e., without reversal) deformation, reached at about 0.5 strain in the case of Nbsteel (Fig. A6.14(a)). Previous data (nominal strains) fit the present data for the Nbsteel, but earlier only higher second strains were used. In the present tests, distinct reduction in the SRX rate is observed at small second strains, in agreement with the torsion test results from CEIT [A6.10,A6.11], such a behaviour which was not detected in the previous tests.
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For the Nbbearing steel, the maximum t50 (i.e. the minimum rate) is 3 times longer than that in monotonic deformation at 0.2 strain without any second strain (about 20 s and 6.2 s, respectively). The latter value of t50 is reached again at the 0.14 second strain, i.e., at the strain somewhat smaller than the first strain. The MDRX behaviour was reached at about 0.25 strain in the monotonic mode, and now in the reversed deformation at about 0.5, i.e. at the total strain of 0.7, or, in other words, the second strain of 0.5  0.14 = 0.36 is needed to enhance the SRX rate from the monotonic t50 value of 6 s to MDRX value of about 3 s. The MDRX rate is not affected by the reversal, as observed earlier [A6.8].
Tension  holding  compression
After the maximum, the slope log(t50) v log (time) curve is much lower than that in the monotonic deformation, i.e. the power of strain is lower in the reversed deformation than in the monotonic deformation (about 3 [A6.8]).
Retardation of the SRX rate can be explained by some kind of dissolution of the deformation dislocation structure due to reversed direction of straining [A6.8A6.11].
For the hTiNb steel, the retardation is somewhat smaller, about 2 times (Fig. A6.14(b and c)), for 42MnV7 steel about 3 times. Hence, the retardation is always of the same order for all these steels.
Tension  compression  decrease in strain rate
A few tests were carried out for Nb and 42MnV7 steels using reversed deformation 0.175T/0.175C and decreasing the strain rate from 0.1 s1 to 0.01 s1 in the end of second deformation for short 0.01 strain, before relaxation to determine the SRX rate (see Table A6.3). Figure A6.15 shows the flow stress behaviour and the relaxation curve recorded. The relaxation curves were of the proper shape so that the schedule is experimentally well under control. The data obtained are included in Fig. A6.14 for these steels revealing a slight retardation compared to the kinetics without decreasing the strain rate, but the effect is quite small. The effect of first/second strain ratio was not investigated.
A few tests were carried out to investigate the influence of holding during reversal on the subsequent SRX rate. During holding some SRX can occur and presumably rearrangements in the deformation dislocation structure. Medium carbon steel 42MnV7 was used in the tests. Two different holding times were selected, 3 and 6 seconds resulting in about 30% and 75% recrystallised fractions, respectively. The flow stress curves (L and C strain) as holding for 6 s are shown in Fig. A6.16 and the fraction v times curves obtained from the relaxation curves for two cases: without holding and with 6 s holding. From the fraction curves it can be noticed that the holding has slightly increased the softening rate, which might be explained as a result of elimination of first deformation effects in holding by recovery and recrystallisation so that the second strain (or the total strain) becomes more effective. Contrary to this behaviour, in the monotonic deformation, partial recrystallisation occurring between the passes would decrease the kinetics. The data are also inserted in Fig. A6.14. The second feature observable in the figure is that the final part of the fraction data falls well below the Avrami curve, even though predicted using a small Avrami exponent of 1.2. This might reflect the influence of those grains, which recrystallised during holding and have no retained deformation. As seen, the fraction curve for 0.175 strain without reversal is much steeper.
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The test details for IF steels and hTiNb steel are given in Table A6.4 and Table A6.5, respectively, and the tests details and main results for the lowC steel are listed in Table A6.6. Two examples of flow stress curves in tests carried out at 800°C at constant high (1 s^{1}) and low (0.01 s^{1}) strain rates and changing the strain rate in the later part of the test (the total strain 0.3) are plotted in Fig. A6.17. It is clear that for both Ti IF and NbTi IF steels, the final stress level in the strain rate change test remains above the flow stress at the lower strain rate, but below the level of the flow stress at the initial high strain rate. Qualitatively this is the same result as observed in the case of hotdeformed austenite.
Figure A6.18 gives examples of the recorded relaxation curves in the Ti IF steel, Fig. A6.18(a) for the austenite (at 1000°C) and Fig. A6.18(b) for the ferrite phase (at 800°C). It is obvious that the shape of the relaxation curve is much flatter for ferrite than for austenite, so that it is inaccurate to determine the recrystallisation start and finish times for the ferrite. Nevertheless, some data and the Avrami type curves fitted with the data for the recrystallised fraction v time are plotted in Fig. A6.19 and in Fig. A6.20. In the former figure, the data and curves are given for both austenite and ferrite to reveal the differences between them. They show that the recrystallisation kinetics in ferrite occurs over a longer time, i.e. the Avrami exponent is much lower that that for the austenite, 0.5 and 1.4 for the ferrite and austenite phases, respectively. It was observed in Ref. [A6.13] that the softening in deformed ferrite takes place mainly by the recovery process. It is known that the recovery decreases the Avrami exponent so that probably some influence of recovery is included the behaviour of ferrite, even though usually the recovery effects can be excluded by the stress relaxation analysis [A6.12,A6.16]. In Fig. A6.20 the data and curves from constant strain rate tests and from strain rate change tests are plotted, but distinct differences in the kinetics cannot be distinguished due to considerable scatter in the data. On the other hand, it can be concluded that the differences cannot be very pronounced.
Typical relaxation curves for the NbTi IF steel are displayed from two monotonic tests and from one strain ratechange test at 800°C in Fig. A6.21. However, one can notice that the recrystallisation of ferrite cannot be seen in the relaxation curves. Otherwise, the shapes of the curves are quite similar.
The kinetics of recrystallisation was expected to be relatively fast in lowcarbon grades so that one of them was selected as a material in the further tests (Table A6.6). However, the relaxation curves were insensitive to reveal recrystallisation so that the doublecompression technique was adopted to determine the softening kinetics (the 5% total strain procedure [A6.12] in a slightly modified way).
Typical behaviour of flow stress is displayed in Fig. A6.22 in two cases, the holding time 250 s or 400 s before the second pass (which does not affect the flow stress of the first pass, of course). The second strain following the change in the strain rate was only 0.02, so that the flow stress curve is short. It can, however, be seen that the flow stress is much below the level at the high strain rate, and in fact, closer to the flow stress at the lower strain rate, but anyhow lagging behind a mechanical equation of state.
In Fig. A6.23 data for the recrystallisation are plotted, after the monotonic deformation of 0.6 strain at 1 s^{1 }or 0.01 s^{1}, and after the strain rate change tests at 0.58 strain. The considerable amount of the data is to reveal that following the strainratechange deformation, the kinetics is retarded considerably and intermediate to those after monotonic deformations. However, the recrystallisation seems to be completed after the strainrate change deformation similarly as at 1 s^{1}, which is contrary to that at 0.01 s^{1}, when the kinetics is extremely slow and only small recrystallised fractions are achieved. Barnet et al [A6.17] have found the power of 0.15 for the strain rate, which does not fit with thePage 364present data, but Jansen et al [A6.13] reported that the complete recrystallisation is only achieved at high strains and high temperatures in ferrite.
Some relaxation tests were tried using Armco iron deformed at 800°C (0.28 at 1 s^{1 } + 0.02 at 0.01 s^{1 } expecting a faster kinetics. However, the relaxation curves were quite flat, so that the determination of recrystallisation kinetics seemed to be difficult.
Typical partially recrystallised grain structures in low carbon steel are shown in Figs. A6.24A6.27. These microstructures confirm nicely the results in Fig. A6.23 revealing that the softening is retarded considerably. Fully recrystallised grains are uniformly white in colour while the others are darker and their surfaces seem to be wrinkled due to the internal cell structure. Whether those grains are only deformed (dynamic recovery) or recovered after the deformation (static recovery) is more difficult to distinguish.
Examples of the dislocation structures in the TiIF steel after monotonous deformation and after the changedstrain rate deformation are shown in Fig. A6.28 and Fig. A6.29, respectively. It can be seen that in both cases the cell structure has formed. Measuring the diameter of about 100 cells in the constant strain rate test and the diameter of 425 cells in the changedstrain rate test the mean cell sizes were 1.4 µm and 1.8 µm, respectively. The values are given in Table A6.7. This seems to indicate that somewhat larger cells are present after changing the strain rate than at the constant (high) strain rate.
It appeared that the cell structure could be revealed on the surface of the bulk polished specimens by the SEMBEI contrast that enabled much easier measurements of the sizes of more numerous cells. Figure A6.30 and Fig. A6.31 show examples of the cell structures. Analysis of more than 2000 cells gave the values for the diameter as 2.2 µm and 2.8 µm for the constant and the changed strain rate deformation conditions, respectively. Once more, the cells seem to be larger after the changed the strain rate, in agreement with TEM observations. The cell size determined in SEMBEI is, however, much larger than that from TEM.
The distributions of misorientation of the grain boundaries were determined by SEMEBSD, and the results are shown in Fig. A6.32. It can be noticed that the change in the strain rate does not affect the misorientation distribution, neither in the highangle nor lowangle range. The same was observed for the lowC steel, too.
Typical flow stress curves in the strainreversed deformation are plotted in Fig. A6.33. A pronounced Bauschinger effect, about 12%, can be seen, i.e. higher than in the austenite. Figure A6.34 shows the recrystallised fraction in 40 s, during the holding time that was held constant in the first set of tests. It is seen that the recrystallised fraction remains distinctly smaller than without any second strain if the second strain is low, 0.02  0.15, i.e. a small reversed strain even retards the recrystallisation kinetics of the ferrite, similarly as observed earlier for the austenite. The time t50 increases from 20 s to 200 s, as shown in Fig. A6.35. These values are computed by fitting the Avrami type curve with the exponent of 0.9 with the measured fraction at 40 s. Figures A6.34(b) and A6.35(b) show the fractions after monotonic and reversed deformations as a function of absolute strain, i.e. the first tensile+second compressive strains. The maximum retardation can be estimated from Fig. A6.35(b), and it is about 8 times at the total strain of 0.35. It is also seen that there is no single power of strain in a reversed deformation, while in the monotonic deformation the power is –1.8. This value is somewhat lower than generally for austenite or reported for ferrite [A6.4].
Page 365
Recrystallisation was also followed by metallographic means and the retardation could be detected in optical microstructures. Another observation is that at small/intermediate reversed strains, not only the kinetics are retarded but also the recrystallised grain size tends to be much coarser, and particularly a few coarse (› 500 µm) grains appear in the partially recrystallised microstructure (Fig. A6.36). In recrystallisation (within 20 s) after compression to the strain of 0.20 at 1 s^{1}, the grain size became slightly coarser than the initial grain size (Fig. A6.37(a and b)). This is in consistence with the equation proposed by Barnett et al [A6.17] for the recrystallised grain size in the lowC ferrite. However, after small reversed strain, the grain size is much coarser, but it becomes refined with increasing total strain, as shown in the recrystallised microstructures (holding just until the complete recrystallisation (about 85% fraction) in each case), compare Fig. A6.37(bd), for instance. The evolution of the grain size is plotted in Fig. A6.38. In an AlMg alloy, Zhu and Sellars [A6.18] observed the grain size to become much coarser in the reversed straining with the increasing second strain.
The dislocation structures seen in TEM in Armco iron after compression at 1 s ^{1} to the 0.3 strain and after straining 0.23 in tension + 0.07 in compression are shown in Fig. A6.39 and Fig. A6.40 respectively. In the both cases, cell structure is present. The analysis of about 150 cells resulted in the cell size of 2.8 µm and 4.1 µm without the strain reversal and with the strain reversal, respectively (see Table A6.7). Hence, the reversed deformation seems to lead to distinctly larger cells.
The cell structures revealed by SEMBEI are shown in Fig. A6.41 and Fig. A6.42 for the deformation without and with the strain reversal, respectively. Surprisingly, measuring the size of 20002700 cells resulted in the identical size of 4.5 µm, for the both deformation histories.
The distributions of misorientation of the grain boundaries are shown in Fig. A6.43 revealing that there are more boundaries with a lowangle misorientation in the instance of reversed deformation than without the reversal. Hence, reversing the direction of straining tends to decrease the average misorientation between cells, i.e. increase the number of lowestangle boundaries (misorientation below 5°) at the expense of boundaries with the 68° misorientation.
A large number of strain rate tests on 55Cr3 steel were carried out and in cooperation with CSM, and their analysis was performed to include in the constitutive modelling (see the CSM report).
The transient observed in the flow stress in the ferrite (in austenite as well) following the abrupt drop of the strain rate was modelled in order to try to understand the factors controlling the evolution of the flow stress, lagging behind the mechanical equation of the state, as observed earlier. The Bergström’s model, a relatively simple approach used at MEFOS, for instance, to model the flow stress behaviour under constant deformation conditions was adopted. In the model, the flow stress is related to the total dislocation density and affected by the rates of dislocation immobilisation and remobilisation (recovery). The parameters have to be estimated under the transient conditions, changing exponentially after the drop of the strain rate.
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A number of physical material models have been developed by different research groups describing the evolution of flow stress during deformation, which essentially include the material dislocation density as a history parameter. Of the various models, the Bergström’s model [A6.19] for plastic deformation of metals is relatively simple, and it has been explored under constant deformation conditions in the present and the previous ECSC project by MEFOS, so that this model has been adopted in this study to model the effects of the abrupt change in the strain rate on the observed flow stress transient.
Recently Bianchi and Karjalainen [A6.20] have incorporated the change in the strain rate in the model for dynamic and metadynamic recrystallisation in rod rolling.
The true flow stress, [VER SIMBOLO EN PDF ADJUNTO], of crystalline materials is related to the total dislocation density [VER SIMBOLO EN PDF ADJUNTO] as
[VER FORMULA EN PDF ADJUNTO]
Where [VER SIMBOLO EN PDF ADJUNTO] is a strainindependent friction stress, [VER SIMBOLO EN PDF ADJUNTO] is a constant, G the shear modulus and b the dislocation burgers vector. The change in the dislocation density is
[VER FORMULA EN PDF ADJUNTO]
Where [VER SIMBOLO EN PDF ADJUNTO] is the measure of the rate of dislocation immobilisation and [VER SIMBOLO EN PDF ADJUNTO] is a measure of dislocation remobilisation (also termed as the recovery parameter). The integration results in
[VER FORMULA EN PDF ADJUTNO]
Where [VER SIMBOLO EN PDF ADJUNTO] is the “grownin” dislocation density, in the wellannealed materials order of 2x10^{12} m^{2}. Combining Equation (A6.6) with Equation (A6.4), the following [VER SIMBOLO EN PDF ADJUNTO] relationship is obtained.
[VER FORMULA EN PDF ADJUNTO]
The experimental and the fitted curves using Equation (A6.7) are plotted in Fig. A6.44. The values of the parameters obtained are listed in Table A.6.8.
It is assumed that [VER SIMBOLO EN PDF ADJUNTO] consists of an athermal component, [VER SIMBOLO EN PDF ADJUNTO] and a thermal component [VER SIMBOLO EN PDF ADJUNTO], i.e.,
[VER FORMULA EN PDF ADJUNTO] where k is a constant and n0 is the number of vacancies per unit volume, Do the diffusion coefficient and Qm the activation energy of grain boundary migration. For ferrite, using D0 value of 2 cm^{2}/s and considering Q(ferrite) = 2xQm (ferrite) [VER SIMBOLO EN PD ADJUNTO] 30000 cal/mol, and kn0 value of 1.85x10^{3} was obtained by Bergström. [VER SIMBOLO EN PDF ADJUNTO] in the present constant strain rate condition, obtained from fitting, is shown in Fig. A6.45. In the following, the modelling of transient behaviour is described.
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According to the definition of the recovery parameter,[VER SIMBOLO EN PDF ADJUNTO] it is a measure of the probability the immobile dislocations to remobilise. The athermal component [VER SIMBOLO EN PDF ADJUNTO] was determined experimentally to be 10.8 under the constant strain rate conditions (see Fig. A6.45). The value for [VER SIMBOLO EN PDF ADJUNTO] can be calculated from Eqiuation (A6.6) as function of temperature and strain rate.
However, the athermal component [VER SIMBOLO EN PDF ADJUNTO] obviously gets enhanced to a new value of [VER SIMBOLO EN PDF ADJUNTO] at the very moment of the strain rate change owing to the shift of a high dislocation density to the lower strain rate condition, amenable for remobilization and recovery. We assume that the enhancement is relative to the ratio of dislocation densities, i.e.
[VER FORMULA EN PDF ADJUNTO]
Finally the total [VER SIMBOLO EN PDF ADJUNTO] in the start of the transient is
[VER SIMBOLO EN PDF ADJUNTO]
Now the value of [VER SIMBOLO EN PDF ADJUNTO] initial is known and the final value of : is that at the constant second (final) strain rate. However, to model the behaviour of : during the transient, the duration of the transient must be known.
We can assume that the ratio of dislocation densities affects the time before the remobilization of immobile dislocations. According to Bergström, the average rest time the immobilized dislocations remain in rest before remobilization is
[VER FORMULA EN PDF ADJUNTO]
Hence, under the transient
[VER FORMULA EN PDF ADJUNTO]
For instance, for the change from 1 s^{1} to 0.01 s^{1} [VER SIMBOLO EN PDF ADJUNTO] is 18.8 s.
The length of the transient strain is
[VER FORMULA EN PDF ADJUNTO]
Under constant strain rate conditions, [VER SIMBOLO EN PDF ADJUNTO] at 1 and 0.01 s^{1 }are 0.087 s and 5.55 s, respectively ( [VER SIMBOLO EN PDF ADJUNTO] at 1 and 0.01 s^{1 }are 11.5 and 18, respectively, from the fitted curves). See Table A6.8 for these values and the estimated transient strain.
Therefore, at the start of the transient, the time spent to mobilise dislocations for the recovery at 0.01 s^{1 }=› ( [VER FORMULA EN PDF ADJUNTO]) This means that, following the strain rate change, [VER SIMBOLO EN PDF ADJUNTO];changes from 42.2 to 18 in about 18 s ([VER FORMULA EN PDF ADJUNTO]) to reach the steadystate value of 18 and it has been assumed that there is an exponential change in [VER SIMBOLO EN PDF ADJUNTO] in the transient region (fitted by regression).
Then an exponential equation was assumed to describe the course of [VER SIMBOLO EN PDF ADJUNTO] during the transient:
[VER FORMULA EN PDF ADJUNTO]
The curves [VER SIMBOLO EN PDF ADJUNTO] strain are plotted in Fig. A6.46.
The abrupt drop in the strain rate leads to a high dislocation density inherited from the first (high) strain rate deformation. Following the strain rate change and during further straining at a low strain rate, the excess dislocations in the subgrains lead to a very high value of [VER SIMBOLO EN PDF ADJUNTO] and the friction stress drops to a very low value before increasing back to its steadystate value during the transient strain.
An attempt has been made to roughly estimate the friction stress at the start of the transient as using the Equation (A6.3) given by Furu et al [A6.15] reproduced below and some rough mathematical factors. The equation for the flow stress of work hardened materials based on the state variables, the dislocation density [VER SIMBOLO EN PDF ADJUNTO] and the cell size [VER SIMBOLO EN PDF ADJUNTO]
[VER FORMULA EN PDF ADJUNTO]
Where [VER SIMBOLO EN PDF ADJUNTO] is the Taylor factor. The friction stress [VER SIMBOLO EN PDF ADJUNTO] is dominated by the viscous drag of the solute atoms segregated to the moving dislocations and it can be expressed as
[VER FORMULA EN PDF ADJUNTO]
Where [VER SIMBOLO EN PDF ADJUNTO]is the drag force, Do the diffusion coefficient, Z the ZenerHollomon parameter and [VER SIMBOLO EN PDF ADJUNTO] the mobile dislocation density in [VER SIMBOLO EN PDF ADJUNTO]
Let us assume that [VER SIMBOLO EN PDF ADJUNTO] in Equation (A6.14) does not change significantly during deformation so that the factor [VER FORMULA EN PDF ADJUNTO] can be considered to be constant (Qdef is the activation energy of deformation).
Therefore, Equation (A6.16) can be rewritten as
[VER FORMULA EN PDF ADJUNTO]
Where K is a constant equal to [VER FORMULA EN PDF ADJUNTO]
It was experimentally determined from the constant strain rate flow stress curves (Fig. A6.44) that [VER SIMBOLO EN PDF ADJUTNO] values are about 35, 29, 25 and 20 MPa at 1, 0.1, 0.01 and 0.001 s^{1}, respectively.
The mobile dislocation density is not known, only the total one at the constant strain rate conditions. The relative values can, however, be written for the conditions 1 and 2
[VER FORMULA EN PDF ADJUNTO]
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Using Equation (A6.18) and the friction stress values at four measured strain rates, it can be shown that
[VER FORMULA EN PDF ADJUNTO] where the numbers in the suffixes represent the strain rate. Let the mobile dislocation density at [VER FORMULA EN PDF ADJUNTO]
A plot of [VER FORMULA EN PDF ADJUNTO] as using the data at constant strain rate conditions gives the following straight line relation (Fig. A6.47).
[VER FORMULA EN PDF ADJUNTO]
Further, it is assumed here that U (the measure of the rate of dislocation immobilisation) does not change significantly as a consequence of abrupt strain rate change and the values assigned at the constant strain rate conditions are still valid.
It is assumed that [VER SIMBOLO EN PDF ADJUNTO] in the instance of strain rate change gets approximately multiplied by the ratios of the U and [VER SIMBOLO EN PDF ADJUNTO] at the two strain rates. Therefore,
[VER FORMULA EN PDF ADJUNTO]
For instance, at the start of the transient [VER FORMULA EN PDF ADJUNTO]
From the plot [VER FORMULA EN PDF ADJUNTO] Fig. A6.47, the value of the friction stress can be obtained, about 3.7 MPa in the present example. This also suggests that the mobile dislocation density has approximately increased by nearly 0.0949x/0.014x = 6.8 times owing to the drop in the strain rate by two orders of magnitude from 1 to 0.01 s^{1}. Similarly, it can be shown that the friction stress values at the start of the transients at 0.1 and 0.001 s^{1} following 1 and 3 orders of magnitude drop in strain rate (from 1 s^{1}), respectively will be about 13.8 MPa and 1.1 MPa. The corresponding increase in mobile dislocation densities will be about 1.9 and 19.2 times that at the constant strain rates, respectively.
The course of the friction stress during the transient flow is not known. Therefore, it had to be obtained by the fitting with some experimental curves. This way, the equation describing the evolution of during the transient strain is
[VER FORMULA EN PDF ADJUNTO]
The curves are shown in Fig. A6.48.
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Finally, all parameters needed in Equation (A6.7) for the flow stress are known, and the flow stress can be predicted at constant as well as transient conditions. The results are shown in Fig. A6.49.
It is concluded that:

The final flow stress after compression under increasing temperature from 900 to 1100°C is only slightly higher than that after isothermal compression at 1100°C,i.e. the stored dislocation densities are almost equal. The chemical composition (microalloying) of the steel has no detectable influence on this behaviour.

The results indicate that the chilling effect of rolls in the course of deformation,i.e. the previous temperature history, only affects minimally the subsequent softening behaviour of the steel, but it is the actual interpass temperature which determines the softening rate.

In microalloyed steels, precipitation may occur at low testing temperatures preventing the subsequent recrystallisation. However, in rolling the surface temperature drops in the rolling gap are very short in duration so that precipitation can hardly occur to any significant extent.

Under abruptly decreasing strain rate, in the dynamic recovery regime the flow stress clearly lags behind the behaviour of a mechanical equation of state. After the drop, the final flow stress remains distinctly higher than that at the corresponding constant final strain rate, but it is close to or lower than the stress at the constant mean strain rate of the whole deformation history. Therefore, the mean flow stress is distinctly higher under the varying strain rate than at constant mean strain rate.

The static recrystallisation rate lags even more than the flow stress from the behaviour following the mechanical equation of state. The recrystallisation rate remains close to that at the high strain rate before the fast drop of the strain rate, if the strain at the low strain rate is short (0.005 to 0.02). However, because the effect of strain rate on the static recrystallisation kinetics is small, the average strain rate can be used to fair accuracy to model the static recrystallisation kinetics also after a strain rate change deformation.

If the strain rate drop takes place after a strain resulting in dynamic recrystallisation at the low strain rate, the subsequent metadynamic recrystallisation behaviour is affected significantly, the magnitude depending on the strain after the strain rate change. The recrystallisation may even be totally absent. The average strain rate is a poor variable for modelling this behaviour.

A special centrally thinned rods are used as specimens in the tests but it has been realised that reversal tests are difficult to control. Flow stress in tension seems to be higher than in compression of cylinders, obviously due to experimental difficulties to control the gage length as well as strain and temperature distributions along the rod.

Bauschinger effect can be seen in the flow stress in the connection with the strain reversal.
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Strain reversal causes retardation in the SRX rate in all the three tests used in the study, the amount depending on the magnitude of the second strain. The minimum rate occurs at about 0.020.04 second strain (if the first actual strain is 0.2), being 23 times lower than the rate without any second strain At second strains beyond 0.14, the SRX rate becomes faster than that without any second strain. This effect can be explained by partial dissolution of deformation dislocation structure after reversing the strain direction.

Changing the strain rate in the end of second strain results in a decreased SRX rate. Experimentally these effects are possible to investigate.

Partial recrystallisation after first strain before the reversed deformation seems to result in an enhanced SRX rate, even though the effect is relatively small.

Under abruptly decreasing strain rate, the flow stress of ferrite clearly lags behind the behaviour of a mechanical equation of state. After the drop, the final flow stress remains distinctly higher than that at the corresponding constant final strain rate. The behaviour is similar in Ti IF, NbTi IF and low carbon steels and qualitatively identical with the behaviour of austenite of the steels.

The static recrystallisation rate of the ferrite lags considerably from the behaviour according to the mechanical equation of state. The kinetics at the strain shortly after the strain rate change (strain 0.02) is between those at initial (1 s^{1}) and final strain rates (0.01 s^{1}).

The softening of ferrite is affected by the recovery. The stress relaxation technique is not very sensitive to reveal the recrystallisation behaviour.

In the ferrite (Armco iron), the strain reversal results in a decreased SRX rate at small reversed strains, the maximum effect being about 8 times.

In the ferrite, the reversal results in a significantly coarsened grain size at small reversed strains.

Dislocation cell structures can be revealed in the ferrite by TEM and SEMBEI. Grain boundary misorientation distributions can be determined by SEMEBSD.

After changing the strain rate abruptly, the cell size seem to be larger than at constant high strain rate revealing that the driving force for the static recrystallisation decreases rapidly after the drop of the strain rate.

The misorientation distribution is not affected by the strain rate change.

The strain reversal also results in an increased cell size compared to that in monotonic straining.

The misorientation distribution is also affected by the reversal, the number of lowest angle (misorientation below 5°) boundaries being increased.

The Bergström’s model can be used to model the transient in the flow stress in the ferrite following the drop in the strain rate, but several assumptions have to be made.
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References
A6.1 Zhou, M, et al: The effect of strain reversal and straintime path on constitutive relationships for metal rolling/forming processes, Report EUR 19891 EN, 2001.
A6.2 Sellars, C M: Recrystallization and Related Phenomena, MIAS, (1997), p. 87.
A6.3 Baxter, G J, Furu, T, Whiteman, J A and Sellars, C M: Mater. Sci. Forum, 217222 (1996), 459.
A6.4 Urcola, J J and Sellars, C M: Acta Metall., 35 (1987), 2649.
A6.5 Immarigeon, JP and Jonas, J J: Acta Metall., 19 (1971), 1053.
A6.6 Karjalainen, L P and Somani, M C: Effect of strain reversals on recrystallization kinetics and grain size in hotdeformed austenite, Proc. Intern. Conf. Recrystallization and Grain Growth, eds, G. Gottstein and D.A. Molodov, August 2731, 2001, Aachen, Germany, vol. 2, pp779784.
A6.7 Karjalainen, L P, Porter, D and Peura, P: Recrystallization of Timicroalloyed steels under constant and varying deformation conditions. The Fourth International Conference on Recrystallization and Related Phenomena, July 1316, 1999. Eds. T. Sakai and H.G. Suzuki. Proceedings of ReX’99 (JIMIS 10), 1999. pp721  726.
A6.8 Karjalainen, L P, Somani, M C, Peura, P A and Porter, D A: Effects of strain rate changes and strain path on flow stress and recrystallisation kinetics in Nb bearing microalloy steels, Thermomechanical Processing of Steels, 2426 May 2000, London, UK, pp130139.
A6.9 Bartolomé, R, Astiazarán, J I, IzaMendia, A and Gutiérrez, I: Mechanical and microstructural effect of the strain reversal on a microalloyed steel, Thermomechanical Processing of Steels, 2426 May 2000, London, UK, pp221230.
A6.10 JorgeBadiola, D, Bartolomé, R, Martin, S and Gutiérrez, I: Effect of the strain reversal on both the recrystallization and the straininduced precipitation in a Nbmicroalloyed steel, Intern. Conf. Thermomechanical Processing: Mechanisms, Microstructure and Control, 2326 June, 2002, Sheffield, UK.
A6.11 Bartolomé, R, JorgeBadiola, D, Astiazarán, J I and Gutiérrez, I: Mater. Sci. Eng.,A344, 2003, pp323330.
A6.12 Perttula, J S and Karjalainen, L P: Mat. Sci. Techn., 1998, 14, (7), pp626630.
A6.13 Jansen, E F M, Geisler, S, De Paepe, A, Underhill, R and Anelli, E: New hot rolled deep drawing steel qualities, Final Report, 2001, EUR 19889 EN.
A6.14 Sellars, C M and Zhu, Q: Mater. Sci. Eng. A280, 2000, pp17.
A6.15 Furu, T, Shercliff, H F, Sellars, C M and Ashby, M F: Mater. Sci. Forum, 1996,217222, pp453458.
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A6.16 Karjalainen, L P and Perttula, J: Characteristics of static and metadynamic recrystallization and strain accumulation in hotdeformed austenite as revealed by the stress relaxation method, ISIJ International, 1996, 36, (6), pp729736.
A6.17 Barnett, M R, Kelly, G L and Hodgson, P D: Metall. Mater. Trans. A, 2002, 33A,(7), pp18931900.
A6.18 Zhu, Q and Sellars, C M: Effect of deformation paths on static recrystallisation behaviour of an Al2Mg alloy, Proc. ReX’96, Third Intern. Conf. recrystallization and related phenomena, ed. McNelley, T R, Monterey, Ca, USA, 1996, pp195202.
A6.19 Bergström, Y: The Plastic Deformation of Metals – A Dislocation Model and its Applicability, Royal Institute of Technology, Tech. Report, Stockholm, 1982.
A6.20 Bianchi, J H and Karjalainen, L P: Modelling of dynamic and metadynamic recrystallisation during bar rolling of a medium carbon spring steel, J. Materials Processing Technology, Elsevier, (2005), vol. 160, No. 3, pp267277.
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Table A6.1: Chemical composition of the steels tested (wt. %)
Steel C Si Mn Al Ni V Ti Nb B(ppm) Nb 0.15 0.3 1.42 0.037 0.03 0.011 0.033 hTiNb 0.07 0.20 1.80 0.028 0.03 0.007 0.130 0.067 3 42MnV7 0.40 0.22 1.68 0.036 0.04 0.083 0.018 0.003 4 LowC 0.092 0.190 0.450 0.026 TiIF 0.002 0.004 0.128 0.024 0.022 0.071 NbTiIF 0.003 0.010 0.164 0.036 0.032 0.003 0.020 0.037 Armco 0.014 0.020
Table A6.2: Results of temperature history tests
Steel: hTiNb (0.071C1.8Mn0.067Nb0.13Ti0.007V)
RH 1250°C/ 5 min, followed by cooling at 2°C/s to Tdef,
15 s hold, followed by compression.
Grain size: [VER SIMBOLOS EN PDF ADJUNTO]
[VER TABLA EN PDF ADJUNTO]
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Concurrent heating at 5055.5°C/s during deformation
* Heating started while the deformation is being continued
Steel: 42MnV7 (0.398C1.68Mn0.018Ti0.083V)
RH 1250°C/5 min, followed by cooling at 2°C/s to Tdef,
15 s hold, followed by compression.
Grain size: [VER SIMBOLOS EN PDF ADJUNTO]
[VER TABLA EN PDF ADJUNTO]
*concurrent heating at 50°C/s during deformation
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Table A6.3: Strain rate change tests performed for htinb steel.
[VER TABLA EN PDF ADJUNTO]
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Table A6.3: Cont…
[VER TABLA EN PDF ADJUNTO]
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Table A6.4: Strain rate change tests performed for tiif steel.
[VER TABLA EN PFA ADJUNTO]
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Table A6.4: Cont…
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Table A6.5: Strain rate change tests performed for htinb steel
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Page 381
Table A6.6: Strain rate change tests performed for lowc steel
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Page 382
Table A6.7: Data concerning the deformation cells in the ifsteel and armco iron
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Page 383
Table A6.8: Experiments for modelling the transient behavior of ferrite. Some predicted data are also given.
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Fig. A6.1(ac): Typical flow stress curves in isothermal and temperature change tests
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Fig. A6.2(ac): Typical relaxation curves in isothermal and temperature change tests
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Fig. A6.3(a and b): Strain rate history in tests
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Fig. A6.4(a and b): Influence of strain rate history on flow stress.
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Fig. A6.5: Effect of strain rate history on fractional softening curves.
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Fig. A6.6: Strain rate history in the second group tests.
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Fig. A6.7: Influence of strain rate history on flow stress.
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Fig. A6.8: Effect of strain rate history on fractional softening curves.
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Fig. A6.9(a and b): Three strain rate histories (a) and their effects on flow stress (b).
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Fig. A6.10(a and b): Stress relaxation curves (a) and fractional softening curves (b). No softening following the strain rate change.
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Fig. A6.11(a and b): Effect of continuous change in strain rate on flow stress (a) and fractional softening (b).
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Fig. A6.12(ad): Typical flow stress behaviours in reversal tests, changing from tension to compression at 0.175 nominal strain.
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Page 398
Fig. A6.13: Control of the second strain below 0.015 is hardly possible
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Page 399
Fig. A6.14(ad): Effect of the second compressive strain on t50 time after 0.175 nominal tensile strain in various steels. (a) Nbsteel (b) Nbhti steel (c) another Nbhti steel (d) 42MnV7 steel.
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Fig. A6.15: Reversal/strain rate change test on the Nb steel, the flow stress behaviour and the corresponding relaxation curve.
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Fig. A6.16: Strain reversal t/c and tholding for 6 sc tests.
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Page 403
Fig. A6.17(a and b): Influence of strain rate history on flow stress of Ti IF steel at 800°C, in monotonic and strain rate change modes. Ti IF steel (a) and NbTi IF steel (b).
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Fig. A6.18(a and b): Comparison of typical relaxation curves for (a) austenite and (b) ferrite.
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Fig. A6.19: Fractional softening curves for austenite and ferrite. Notice the different Avrami exponents.
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Fig. A6.20: Effect of strain rate history on fractional softening of ferrite in TiIF steel
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Fig. A6.21: Effect of strain rate history on relaxation curves at 800°C in NbTi IF steel.
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Page 407
Fig. A6.22(a and b): Influence of the strain rate history on the flow stress of low carbon steel at 700°C. Holding for (a) 250 s (b) 400 s.
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Page 408
Fig. A6.23: Recrystallisation of ferrite after 0.6 strain at 700°C. Constant strain rate or strain rate change tests.
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Fig. A6.24: Recrystallisation of ferrite after 0.6 strain at 700°C in 2000 s. Constant strain rate of 0.01 s^{1}.
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Fig. A6.25(a and b): Recrystallisation at 700°C in 250 s (a) at 1 s^{1 }(b) strain rate change
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Fig. A6.26(a and b): recrystallisation at 700°C in 500 s after 0.6 strain at 1 s^{1}, (a) lower magnification (b) higher magnification.
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Fig. A6.27(a and b): Recrystallisation at 700°C in 500 s in strain rate change deformation (a) lower magnification (b) higher magnification.
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Fig. A6.28: Cell structure seen in TEM in the TiIF steel after straining at the constant strain rate of 1 s^{1}.
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Fig. A6.29: Cell structure seen in TEM in TiIF steel after the strain rate change
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Fig. A6.30: Cells on the surface of TiIF steel strained to 0.3 strain at the constant strain rate of 1 s^{1 }
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Fig. A6.31: Cells on the surface of TiIF steel strained to 0.27 strain at the changed strain rate
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Fig. A6.32: Misorientation distribution of the grain boundaries in TiIF steel after constant and changed strain rate tests
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Fig. A6.33: Flow stress in a strain reversal test followed by a second compression pass after 40 s
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Fig. A6.34(a and b): Recrystallisation within 40 s as a function of (a) second strain (b) absolute/total strain (also in monotonic compression)
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Fig. A6.35(a and b): Predicted t50 time as a function of (a) second strain, (b) absolute/total strain (also in monotonic compression)
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Fig. A6.36(ac): Grain structure after 40 s revealing large grains after certain reversed strain (a) 0.29T+0.05C (b) 0.27t+0.07C (c) 0.26t+0.15C
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Page 418
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Fig. A6.37(ae): Recrystallised grain structure after (a) without strain (b) 0.20C (c) 0.25t+0.11C (d) 0.27t+0.16C (e) 028t+0.25C
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Fig. A6.38: The ferrite grain size as a function of the second strain after the reversal
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Fig. A6.39: Cell structure in Armcoiron after compression to 0.3 strain
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Fig. A6.40: Cell structure in Armcoiron after reversed straining
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Fig. A6.41: Cell structure in Armco iron seen in SEM after compression to 0.3 strain
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Fig. A6.42: Cell structure in Armco iron seen in SEM after a strain reversal
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Fig. A6.43: Misorientation distribution with and without strain reversal (comp=compression; t/c=tension/compression; repeated tests for the both).
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Fig. A6.44: Measured and modelled flow stress curves at constant strain rates
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Fig. A6.45: The recovery parameter, the thermal and athermal components as a function of the strain rate
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Fig. A6.46: Modelled course of the recovery parameter during the transient
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Fig. A6.47: Estimation of the friction stress
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Fig. A6.48: Course of the friction stress during the transient
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Fig. A6.49: Measured and modelled flow stress curves with the transient
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