Recovery and Recrystallization in
C-Mn Steels following Hot
Deformation
Proefschrift
ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus Prof. dr. ir. J.T. Fokkema, voorzitter van het College voor Promoties,
in het openbaar te verdedigen op dinsdag 18 april 2006 om 15.30 uur
door
Ali SMITH
Master of Engineering
Dit proefschrift is goedgekeurd door de promotor: Prof. dr. ir. S. van der Zwaag
Samenstelling promotiecommissie:
Rector Magnificus, voorzitter
Prof. dr. ir. S. van der Zwaag, Technische Universiteit Delft, promotor Dr. ir. J. Sietsma, Technische Universiteit Delft, toegevoegd promotor Prof. dr. ir. L. A. I. Kestens, Technische Universiteit Delft
Prof. dr. M. Militzer, University of British Columbia, Vancouver, Canada Prof. Dr.-Ing. K. Steinhoff, University of Kassel, Kassel, Germany Prof. dr. R. Boom, Technische Universiteit Delft
Dr. A. Miroux, Netherlands Institute for Metals Research, Delft
This research was carried out under the project number MP97013A, in the framework of the Strategic Research Program of the Netherlands Institute for Metals Research (NIMR) in the Netherlands (www.nimr.nl).
ISBN 9077172203
Keywords: Recrystallization, recovery, steel, stress relaxation, laser-ultrasonics, intercritical deformation
Copyright ¤ 2006 by Ali Smith
All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilised in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and retrieval system, without permission from the author
Contents
Page
1 Introduction 1
1.1 Hot rolling of C-Mn and related steels 1 1.2 Microstructural evolution during hot rolling 2 1.3 Improving the final properties of hot rolled strip 3
1.4 Intercritical rolling 4
1.5 Scope of the thesis 4
2 Recovery Processes in the Ferrite Phase in C-Mn Steel 8
2.1 Introduction 8
2.2 Recovery in metals 9
2.3 Experimental 12
2.4 Results and Discussion 14
2.4.1 Effect of temperature on recovery kinetics 14 2.4.2 Comparison of model with experiment 15 2.4.3 Activation energy for recovery 15 2.4.4 Activation volume for recovery 17 2.4.5 Influence of strain and strain rate 20 2.4.6 Analysis of deformation substructures 21
2.5 Conclusions 23
3. Laser-Ultrasonic Monitoring of Ferrite Recovery 26
in Ultra Low Carbon Steel
3.1 Introduction 26
3.2 Effect of microstructure on ultrasonic velocity and attenuation 27
3.2.1 Dislocation damping 27
3.2.2 Magnetomechanical damping 29
3.2.3 Texture effects 30
3.2.4 Grain scattering effects 30
3.2.5 Total effect of microstructure 31
3.3 Experimental 32
3.4 Results 34
3.4.2 Effect of temperature 36
3.4.3 Effect of applied strain 38
3.5 Discussion 39
3.5.1 Discussion of dominating microstructural effects 39 3.5.2 Estimation of dislocation density and pinning point separation 41
3.6 Conclusions 50
4. Laser-Ultrasonic Monitoring of Austenite Recrystallization 54
in C-Mn Steel
4.1 Introduction 54
4.2 Effect of microstructure on ultrasonic velocity and attenuation 55
4.2.1 Texture effects 56
4.2.2 Grain scattering effects 56
4.2.3 Dislocation damping 57
4.2.4 Total effect of austenitic microstructure 57
4.3 Experimental 57
4.4 Results 59
4.4.1 Microstructural evolution 59
4.4.2 Ultrasonics and stress relaxation: effect of strain 61 4.4.3 Ultrasonics and stress relaxation: 63
effect of temperature and strain rate
4.5 Discussion 65
4.5.1 Discussion of dominating microstructural effects 65 4.5.2 Comparison of stress with ultrasonic velocity 68 4.5.3 Calculation of recrystallized grain size 70
4.6 Conclusions 73
5. A Physical Analysis of the Stress Relaxation 76
Kinetics of Deformed Austenite in C-Mn Steel
5.1 Introduction 76
5.2 Modelling approach 77
5.3 Experimental 84
5.4 Results and Discussion 85
5.4.1 Modelling recovery kinetics 85
5.5 Conclusions 92
6 Modelling the Stress Relaxation Kinetics 95
of Intercritically Deformed Austenite and Ferrite in C-Mn Steel
6.1 Introduction 95
6.2 Modelling approach 96
6.2.1 Recovery and recrystallization of intercritical austenite 97 6.2.2 Recovery of intercritical ferrite 98
6.2.3 Strain and stress partitioning 98
6.2.4 Overall softening model 99
6.3 Experimental 100
6.4 Results 101
6.5 Discussion 107
6.5.1 Calculation of ferrite recovery model parameters 107 6.5.2 Calculation of strain and stress in each phase 109 6.5.3 Comparison of model with experiments 110
Chapter 1
Introduction
1.1 Hot rolling of C-Mn and related steels
During industrial steel making one of the most important forming operations is the hot rolling process. In a conventional hot strip mill, steel slabs, formed from casting with a thickness of around 225 mm, are fed into a reheating furnace. There they are reheated to around 1200°C, before being fed into the roughing section of the hot strip mill. Here the slabs are deformed to a thickness of around 37 mm. In the finishing section the thickness is further reduced to the final thickness in the range 1.5 – 20 mm. Then, the strip is cooled in a controlled manner on the run-out table to the coiling temperature. Finally the strip is coiled [1]. After coiling the strip may be processed further to improve the surface quality and further reduce the thickness. These last steps are performed typically by pickling, cold rolling and annealing [2].
Figure 1.1 shows a schematic of part of the hot strip production process. Shown are the roughing, finishing and cooling stages only. Also shown is the evolution in temperature and thickness as the steel slab travels through the process.
Time Th ic k ne ss / Te m pe ra tu re Time Th ic k ne ss / Te m pe ra tu re
An alternative to the conventional hot rolling process described above, are the processes of thin-slab casting and direct rolling. In this case the cast slab is produced by a thin slab caster. Here slabs with a thickness of around 70 mm are produced (compared to 225 mm for conventional hot strip production). The slabs are then fed into a temperature homogenisation furnace, before being fed into the rolling stages as shown in figure 1.1. The thin-slab casting process is advantageous since the combined cost of casting and rolling is less. This is partly due to the smaller energy consumption, due the omission of the reheating furnace. A disadvantage is the low production capacity compared to the conventional hot strip mills [1].
1.2 Microstructural evolution during hot rolling
During the hot rolling process the microstructure of the steel changes. For a given steel composition, two key parameters that influence microstructure are temperature and deformation. The effect of temperature is shown by the iron-carbon phase diagram in figure 1.2. Normally the hot rolling process is controlled, such that during the roughing and finishing stages the microstructure present consists only of austenite (J). During the cooling stage the austenite decomposes i.e. undergoes a phase transformation [3]. For carbon concentrations between 0.02 and 0.79 wt%, the austenite decomposes into a mixture of ferrite (D) and austenite. On further cooling below around 727°C, the remaining austenite transforms to a mixture of cementite (Fe3C) and ferrite. These changes can also occur during coiling.
The effect of deformation also plays a significant role in microstructural development. As shown above, during hot rolling this entails the deformation of an austenitic microstructure. The grains are deformed and a high density of dislocations is created, causing an increase in the internal energy of the austenite. Aided by the high temperature, the deformed austenite then lowers its stored energy by the processes of recovery and recrystallization. During recovery the stored energy is reduced by annihilation and rearrangement of dislocations into lower energy configurations e.g. cells or subgrains. During recrystallization strain-free nuclei appear in the deformed structure. The nuclei typically are the subgrains formed during recovery. These nuclei grow, consuming dislocations and thus lowering the stored energy. The new grains then impinge on each other, resulting in a microstructure that typically consists of small equiaxed austenite grains. At higher rolling temperatures these grains coarsen. At lower temperatures these grains retain their size up to the next rolling pass.
The processes of recovery and recrystallization can occur both during deformation i.e. dynamically, or they can occur after deformation i.e. statically.
1.3. Improving the final properties of hot rolled strip
For plain carbon and related steels, the final properties of the hot rolled strip, e.g. yield strength, toughness, ductility, depend, amongst other things, on the average ferrite grain size. Since the ferrite is formed from austenite and takes place predominantly at grain boundaries, the austenite grain size prior to the transformation is of great importance. This grain size is in turn controlled by the recrystallization process. Thus, it can be seen that by controlling austenite recrystallization, one can influence the final properties of the hot rolled strip.
been demonstrated [6,7], there is still a lack of ultrasonic studies specifically on recrystallization in steels following hot deformation. Thus, as a precusor to any online monitoring system for hot rolling, further study is required.
1.4 Intercritical Rolling
As indicated in figure 1.1, strip thickness changes and strip temperature changes are coupled. Hence, for a lower hot rolled strip thickness, the fully austenitic state can no longer be maintained and a (D+J) two-phase microstructure is present. This changes rolling conditions and microstructural development considerably. In recent years it has been realised that the occurrence of a two-phase microstructure is not only a complication, but also leads to new intercritical rolling strategies for thinner strip with interesting mechanical properties [1,8,9].
However, the control of the final properties is much more complex in intercritical rolling compared with conventional hot rolling. The origin of the increased complexity is firstly due to the deformation of a two-phase material, which leads to a distribution of strain and stress between the phases. Secondly, there is the possibility of several processes/softening mechanisms occurring in parallel: austenite recovery, austenite recrystallisation, deformation-enhanced austenite to ferrite transformation, ferrite recovery and ferrite recrystallisation.
Whilst the deformation behaviour of two-phase materials has received much attention, e.g. [10-13], the softening mechanisms during and after intercritical deformation have received less attention [14,15]. In addition, the investigations that concerned softening after intercritical deformation have primarily been experimental in nature. Another useful approach which has not been explored, is to use validated physically based models for the softening behaviour of the separate phases, and combine these using the proper mixture rules, to predict the overall material behaviour in the intercritical region.
1.5 Scope of the thesis
explored to study the softening processes in single-phase ferrite and austenite. These combined approaches lead to a better understanding of the separate ferrite and austenite softening processes, and give insights into the softening processes occurring during intercritical rolling of steel strip. In addition the use of laser ultrasonics will demonstrate the potential of this technique to be used in online-monitoring of the hot rolling process.
The contents of this thesis are arranged as follows:
In chapter 2 the static recovery kinetics of deformed ferrite in 0.19 wt% C, 1.5 wt% Mn steel are investigated. The recovery kinetics are characterised using the stress relaxation technique. The results are analysed using a physically based recovery model in the literature, the main parameters being activation energy and activation volume [16]. Analysis of these parameters enables the rate controlling mechanism of ferrite recovery to be established.
Chapter 3 describes a further investigation into ferrite recovery. The static recovery kinetics are investigated for ferrite in an ultra-low carbon steel (0.0024 wt% C). The experimental techniques used are in-situ laser ultrasonics and stress relaxation. The ultrasonic parameters measured are wave velocity and attenuation. From these two parameters, estimates of the evolution of dislocation density and pinning point separation during recovery are obtained. A comparison of these values with those obtained from stress relaxation measurements is made. The differences are discussed with reference to the sensitivities of these techniques to dislocation structure.
In chapter 4 the static recrystallization kinetics of hot deformed austenite in 0.19 wt% C, 1.5 wt% Mn steel are characterised by a combination of laser ultrasonics and stress relaxation measurements. The stress relaxation kinetics are compared to the observed decrease in ultrasonic velocity and attenuation. The recrystallized grain size is calculated using the ultrasonic attenuation results. The values are compared to those obtained from optical microscopy and the relation between the two data sets discussed.
of the model with experimental stress relaxation data allows interesting insights to be obtained, regarding recrystallization nucleation and grain boundary mobility.
References
[1] A. Bodin: PhD. Thesis, Delft University of Technology, The Netherlands. (2002). [2] R. Petrov, L. Kestens, P. Zambrano, M. Guerrero, R. Colas and Y. Houbaert, ISIJ Int., Vol. 43, (2003), pp. 378-385.
[3] M. Onink, PhD Thesis, Delft University of Technology, The Netherlands, (1995). [4] J. H. Beynon and C. M. Sellars, ISIJ Int., Vol. 32, (1992), pp.359-367.
[5] S. Cho, K. Kang and J. J. Jonas, ISIJ Int., Vol. 41, (2001), pp.766-773.
[6] E. Ulmgren, M. Ericsson, D. Artymowicz and B. Hutchinson, Mat. Sci. Forum, Vols. 467-470, (2004), pp. 1353-1362.
[7] S. Kruger, A. Moreau, M. Militzer and T. Biggs, Mat. Sci. Forum, Vols. 426-432, (2003), pp. 483-488.
[8] S. Godha, K. Watanabe and Y. Hashimoto, Trans. Iron Steel Inst. Jpn., Vol. 21, (1981), pp. 6-15.
[9] S. Godha, K. Watanabe, Y. Hashimoto, H. Hirayama and S. Kijima, Trans. Iron Steel Inst. Jpn, Vol. 21, (1981), pp. 360-369.
[10] Y. Tomota, M. Umemoto et al., ISIJ Int., Vol. 32, (1992), pp. 343-349.
[11] A. Bodin, J. Sietsma and S. van der Zwaag, Scripta Mater., Vol. 45, (2001), pp. 875-882.
[12] O. Bouaziz and P. Buessler, Advanced Engineering Materials, Vol. 6, (2004), pp. 79-83.
[13] M. Nygards and P. Gudmundson, Comp. Mat. Sci., Vol. 24, (2002), pp. 513-519. [14] A. Bodin, J. Sietsma, J and S. van der Zwaag: Metall. Mater. Trans. A, Vol. 33A (2002), pp. 1589-1603.
[15] H. Luo, J. Sietsma and S. van der Zwaag, Metall. Mater. Trans. A, Vol. 35A, (2004), pp. 1889-1897.
Chapter 2
Recovery Processes in the Ferrite Phase in
C-Mn Steel
2.1 Introduction
Intercritical rolling is one of the new, very promising hot rolling strategies for making thin hot rolled steel strip for C-Mn steels [1-5], as it enables the production of thinner strip without requiring higher rolling forces and mill investments. However, the control of the sheet thickness and the final sheet properties is much more complex than in the standard austenitic rolling strategies. The origin of the increased complexity is in the concurrency of several processes: austenite recovery, austenite recrystallisation, deformation stimulated transformation, ferrite recovery and ferrite recrystallisation. Much research has been done on some of these processes, in particular the recrystallisation of the austenite [6-8] and the deformation stimulated transformation [2,9,10], but so far recovery, in particular recovery in the ferritic state, has received only little attention [11]. However, for the development of a reliable integral model for microstructure development during intercritical rolling a better understanding of recovery kinetics after deformation in the ferritic region is highly desirable.
Barrett and Nix [15], Gibbs [16] and Evans and Knowles[17]) have been developed, which can be used to explain the rate controlling mechanisms of dislocation motion during deformation. Therefore for the current investigation, this literature shall be used to discuss the rate controlling mechanisms for recovery in ferrite.
Finally the substructure after deformation is presented in the form of scanning electron micrographs and an electron backscattering diffraction orientation map, which were obtained from specimens quenched during stress relaxation tests.
2.2 Recovery in Metals
Recovery generally involves both the annihilation of dislocations and their reorganisation into lower energy configurations, e.g. cells or subgrains. These two processes can occur both during deformation (dynamic recovery), and on subsequent annealing, (static recovery). As stated earlier, this investigation is concerned only with static recovery.
Generally static recovery models in the literature can be grouped according to the detail in the dislocation structure that they consider. In the most simple approach, recovery is modelled via the reduction of an overall dislocation density [12]. In a more sophisticated model [18], a distinction is made between dislocations within subgrains and those that make up the subgrain boundaries. Recovery is then related to the dislocation density within subgrain interiors and to the subgrain size. However, when applying this model there are seven fitting parameters to consider. Whilst four parameters can be calculated, two of these parameters still require knowledge of dimensionless constants which need to be determined from experiments. Finally, one parameter can vary by several orders of magnitude, depending on the initial dislocation density within the cells.
Because of the above uncertainties, a model based on just the dislocation density is preferred for modelling the experimental results in the present study. The models that are known in the literature are now discussed.
In the description of Friedel [20] it is assumed that the recovery proceeds via thermally activated cross-slip of dislocations. The rate of decrease of the internal stress is given by:
¸¸ ¹ · ¨¨ © § : T k V Q dt d B d d exp ( 0 V ) V , (1)
where Vd is the stress due to dislocations, t is time, kB is Boltzmann`s constant, T is
temperature,: is a factor having the dimensions of Pa s-1, Q0 is the activation energy
for recovery and V is the activation volume. This volume can be written as:
a
l b
V 2 , (2)
where is the Burgers vector and is an activation length [21]. According to Nes [21], it is approximately equal to the spacing of the rate-controlling obstacles to dislocation glide, e.g. the spacing of jogs, or the spacing between solute atoms.
b la
The activation length is therefore expected to be of the order of nanometres. For an aluminium-2.5 wt% Mg alloy Verdier et al [12] found that the activation volume varied between 22 b3 and 46 b3. Withb for aluminium being equal to 0.286 nm [19],
this corresponds to activation lengths around 10 nm.
The model can be experimentally tested, by fitting the model expression to the data usingQ0,V and : as fitting parameters.
A more recent approach is due to Verdier, Brechet and Guyot [12]. The model assumes that the internal stress relaxation is due to thermally activated dislocation annihilation and reorganisation, and therefore to plastic relaxation. The plastic relaxation rate is related to the change in internal stressHx Vd by:
E dt d d x H V , (3)
where E is Young’s modulus. The relation between and the dislocation behaviour
is given by:
x
H
bv
where M is the Taylor factor ( M = 2 for BCC metals [1] ), U is the dislocation density, and vis the dislocation velocity. The dislocation velocity is thermally activated and influenced by Vd according to:
¸¸ ¹ · ¨¨ © § ¸¸ ¹ · ¨¨ © § T k V T k Q bv v B d B D V sinh exp 0 , (5)
where QD is the Debye frequency. This results in the following overall equation for the relaxation of the internal stress:
¸¸ ¹ · ¨¨ © § ¸¸ ¹ · ¨¨ © § T k V T k Q M v b E dt d B d B D d U V V sinh exp 0 2 . (6)
The dislocation density is then converted to a stress due to dislocations only, using:
U D
Vd M Gb , (7)
whereG is the shear modulus and D is a constant of the order of 0.3 [18]. The shear
modulus dependency on temperature for ferrite is given by [22]:
1 0.00044 300
0.032( 573)2
64000 T T
G , (8)
where G is in MPa and T is in Kelvin. Combining equations (6) and (7)
withG 3E/8, the following is obtained:
¸¸ ¹ · ¨¨ © § ¸¸ ¹ · ¨¨ © § T k V T k Q v E M dt d B d B D d d V D V V sinh exp 9 64 0 2 3 2 . (9)
To test the model on experimental stress relaxation data requires Q0 andV to be used
as fitting parameters.
Comparison of equations (1) and (9) shows that the exponential term in equation (1) is replaced by a sinh term in equation (9), and secondly that : in equation (1) is replaced by E M d 2 3 2 9 64 D V in equation (9).
It should be noted that models previously developed to describe the high temperature steady state creep of metals [15,16] are similar in form to equations (1) and (9). According to Barrett and Nix [15] the steady state creep rate (strain rate) is given by:
¸¸ ¹ · ¨¨ © § ¸¸ ¹ · ¨¨ © § ¸¸ ¹ · ¨¨ © § x T k V T k Q D b B d B s 2 sinh exp 2 0 1 3 0 V D I SU H , (10)
where Us is the mobile screw dislocation density, I is the number of atoms per unit
cell, D0 is the lattice parameter and D1 is a constant. The reason for the similarity is
that in both processes the rate is thermally activated and influenced by an acting stress.
2.3 Experimental
The steel used for the present study has the composition 0.19 wt% C, 0.445 wt% Si, 1.46 wt% Mn, 0.033 wt% Al, with balancing Fe.
Cylindrical samples were machined from rolled plate, with diameter 10 mm and length 12 mm. The samples were machined with the axis parallel to the rolling direction.
To investigate the static recovery kinetics, a Gleeble® 3500 thermo-mechanical simulator was used. Each test comprised of three stages. Firstly a heat treatment schedule was applied. Samples were heated via electrical resistance heating (under vacuum) to 1100°C to austenitise for 3 minutes. Then samples were cooled to 679°C (in the two-phase region) and held for 10 minutes. (This was done for comparison with future intercritical deformation tests.) Next, the samples were cooled at a rate of 5°C/s to the desired test temperature and held for 5 minutes.
In the second stage the samples were deformed in compression. Lubrication was provided via graphite paste. To protect against the possibility of carbon pick-up during the test, tantalum sheets were used as a protective layer between the sample and the lubricant.
After 50 minutes, samples were water quenched at a quenching rate of around 200°C/s. In addition some samples were quenched after 120 minutes relaxation.
Samples quenched after relaxation provided material for examination via electron backscattering diffraction (EBSD) and scanning electron microscopy (SEM) techniques.
Three series of stress relaxation tests were carried out. In the first series the effect of temperature on the recovery kinetics was investigated. Test temperatures used were in the range 150°C – 650°C. The strain for each test was 0.15, whilst the strain rate used was 0.1 s-1.
In the second series of tests the effect of strain was investigated by carrying out tests with strains in the range 0.05 – 0.25. The strain rate was kept constant at 0.1 s-1, whilst the temperature used for each test was 550°C.
In the third series of tests the effect of strain rate was investigated using rates of 0.01 s-1 – 0.6 s-1. The strain was maintained at 0.15 for each test whilst the temperature used was 550°C.
In addition, multiple measurements were performed to test the reproducibility.
Finally one relaxation test was carried out with a higher strain of 0.5, using a strain rate of 0.6 s-1.
To compare the experimental data with the recovery model, the experimental flow stress values during relaxation need to be converted to stress values due to dislocations Vd. This is achieved by using the equation:
0
V V
Vd f , (11)
where Vf is the experimental flow stress and V0 is an equilibrium stress that contains
the contributions from other sources e.g. friction stress, grain size, solute atoms etc. For experimental stress relaxation data V0 is assumed to be the minimum stable stress
obtained during annealing. For high temperature data V0is easily obtained since it is
Finally, since the carbon concentration of this steel is 0.19 wt%, the V0 value obtained
from each experiment is an upper estimate of the real value for ferrite, due to the presence of pearlite or bainite.
2.4. Results and Discussion
2.4.1. Effect of temperature on recovery kinetics
Example stress relaxation curves are shown in figure 2.1, for the series of tests concerning the effect of temperature.
Firstly, considering only the experimental curves, we can see that for every temperature the stress decreases with time. This is due only to recovery, since there is no distinctive three-stage curve as would be observed if recrystallisation had occurred [23].
The effect of increasing temperature on the recovery kinetics is twofold. Firstly the initial stress decreases. Secondly the stress relaxation rate increases.
The first effect is due to a larger degree of dynamic recovery during deformation. The second effect is explained by the model, i.e. the motion of dislocations can be considered to occur by thermally activated mechanisms.
0 50 100 150 200 250 300 0.1 1 10 100 1000 10000 Time (s) V d (M P a) A B C D
Figure 2.1: Stress relaxation curves for test temperatures of: A) 450°C, B) 500°C, C) 550°C
and D) 600°C. Strain is 0.15 and strain rate is 0.1 s-1. Experimental data is indicated by
2.4.2. Comparison of model with experiment
Figure 2.1 also shows the curves obtained using equation (9). The best fits to the data were obtained by allowing both Q0and V to vary for each separate curve. Attempts to
fit the model to all the experimental data by using a single value for Q0 and a
temperature dependent value for V did not give satisfactory results. As can be seen, there is good agreement between experiment and model.
Figure 2.2 shows the dislocation density evolution with time for both experimental data and the model. Dislocation densities were calculated from experimental
d
V values by applying equation (7). The modelled dislocation densities were obtained by applying equation (7) to the Vdvalues resulting from the model calculations.
From figure 2.2 it can be seen that the dislocation density generally decreases with increasing temperature. The exception is for the temperature of 600°C, where during the early stages of recovery, the dislocation density is higher than for the lower temperatures. This is likely to be caused by the error in determining Vdand the fact that G from equation (8) does not take into account the effect of composition.
0 2 4 6 8 10 12 14 16 0.1 1 10 100 1000 10000 Time (s) D is loc at ion de n si ty ( 10 14m -2) A B C D
Figure 2.2: Evolution of dislocation density during recovery. A = 450°C, B = 500°C, C =
550°C, D = 600°C. Strain is 0.15 and strain rate is 0.1 s-1. Experimental data is indicated by
markers and the model fit by solid lines.
2.4.3. Activation energy for recovery
The activation energies that gave the best fit for each temperature investigated are presented in figure 2.3.
As can be seen from figure 2.3, Q appears to rise with increasing temperature until 450°C after which it remains approximately constant. The activation energy for temperatures between 150°C and 300°C appears to be close to that for dislocation
600°C, the experimental data is in reasonable agreement with the activation energy for lattice self diffusion ( Qs = 251 kJ/mol [22] ) in Į-iron. For the temperature range
300°C – 450°C the data suggests a transition region between the two processes.
0 50 100 150 200 250 300 100 200 300 400 500 600 Temperature (°C) Q0 (kJ /m o l) Qc = 174 kJ/mol(17) Qs = 251 kJ/mol(17)
Figure 2.3: Effect of temperature on activation energy for recovery. Data for strain 0.15 and
strain rate 0.1 s-1 is shown by closed markers. Data shown by open markers corresponds to the
data for other strains and strain rates, shown in table 2.1.
This result compares well with the work of Michalak and Paxton [24], who studied the recovery of zone-refined iron during annealing between 300°C and 500°C. Their work suggested a stress independent activation energy (i.e. equivalent to Q0 ) of
around the value for lattice self-diffusion. In the present study however, at temperatures of 300°C, 335°C, and 375°C, the analysis indicates a contribution from dislocation core diffusion to the observed activation energy.
In addition, a very similar dependency of the activation energy on temperature shown in figure 2.3, has been observed for creep in aluminium, copper, thalium and tungsten [17]. At low temperatures the creep activation energy is due to dislocation core diffusion whilst at higher temperatures the activation energy is due to lattice self diffusion.
The climb of edge dislocations involves the formation and migration of jogs. If it assumed that the jogs are pre-existing, or form without thermal nucleation, the activation energy for jog migration and therefore recovery is given by [25]:
d vm
vf E E
E , (12)
where Evf is vacancy formation energy, Evm is the vacancy migration energy and Ed is
the self-diffusion activation energy. The activation energy for vacancy migration, and therefore jog migration can be smaller than Ed since vacancies can diffuse also along
the dislocation lines, i.e. Ed becomes equal to the value for core diffusion [25].
The glide of jogged screw dislocations also involves the migration of jogs controlled by vacancy diffusion. Thus, the same argument presented above for climb of edge dislocations, also applies for this case, i.e. the activation energy will be either equal to that for self-diffusion, or equal to the core diffusion value.
Since both the above processes can have the same activation energies and both are likely to occur at the same time, the experimental activation energy, i.e. close to the core diffusion value or the self-diffusion value, does not enable a distinction to be made between these two processes.
2.4.4. Activation volume for recovery
From figure 2.4 it can be seen that the activation volume appears to be approximately constant at about 3 x10-28 m3 between 150°C and 375°C. Above 375°C it appears to rise to a peak value at 450°C before decreasing with increasing temperature.
0.00 1.00 2.00 3.00 4.00 5.00 6.00 100 200 300 400 500 600 Temperature °C Ac ti va ti o n v o lu m e (x 10 -2 8 m 3)
Figure 2.4: Effect of temperature on activation volume. Data for strain 0.15 and strain rate 0.1
s-1 are shown by closed markers. Data shown by open markers corresponds to the data for
Comparison of figures 2.3 and 2.4 suggests that when the activation energy is close to the value for dislocation core diffusion, the activation volume can be treated as constant. When the activation energy is close to that for lattice self diffusion, the activation volume is a decreasing function of temperature.
The activation volumes observed in the present experiments can be used to calculate the activation length from equation (2). Using b for BCC iron as 0.248 nm [19] gives values between 3 nm and 9 nm for the data in figure 4. According to Leslie [26] the activation volume for pure iron deformed at room temperature is around 3.8 x 10-28 m3. This corresponds to an activation length of 6 nm, which is of the same order as found in this study.
For recovery controlled by thermally activated glide of jogged screw dislocations, the observation of decreasing activation length with increasing temperature above 450°C is in contrast with that predicted by theory. If the activation length is assumed to be only due to the jog separation on screw dislocations, an Arrhenius type temperature dependence is expected, that is, the jog separation (activation volume) should increase with temperature according to [16]:
¸¸ ¹ · ¨¨ © § ¸¸ ¸ ¹ · ¨¨ ¨ © § x k T Q b v b l B j s j j 5 . 0 exp 2 1 2 0 1 H O N N , (13)
where lj is the steady-state or equilibrium jog separation established during
deformation (assumed constant during subsequent annealing), N1 and N2 are material
constants, vj0 is a prefactor, the reciprocal of O represents the number of lattice points
a segment of a screw dislocations must glide through before cross slip occurs, is the strain rate produced by the dislocations and Q
x
s
H
j is the activation energy for jog
migration.
Equation (13) stems from the fact that during deformation (and also on annealing) there will be both annihilation of jogs via lateral motion and creation of new jogs due to interaction of dislocations. When the rate of jog annihilation equals the jog creation rate an equilibrium jog separation is established. The ratio of the jog velocity
( ¸¸ ¹ · ¨¨ © § T k Q v B j
j0exp ), to the velocity of the screw dislocation ( ), determines the
size of the separation.
x
s
The trend of increasing activation length with increasing temperature has been observed experimentally for pure BCC iron [13,27], magnesium [28] and pure niobium [14]. However, according to Arieta and Sellars [29], for niobium containing HSLA steel, the activation volume for austenite was found to generally decrease with increasing temperature.
This difference in behaviour can be due to the effect of solute atoms (i.e. niobium) which can retard the lateral drift of jogs [18]. If the jog velocity is reduced, it follows that the ratio of the jog velocity to the screw velocity can decrease as the temperature is increased. From equation (13) this will cause the equilibrium separation to decrease with increasing temperature.
In the current steel, examination of quenched samples (section 2.4.6) suggests that carbon segregates to dislocations during deformation or relaxation. Thus the carbon atoms can act to retard the lateral drift of jogs on screw dislocations causing the observed reduction in activation volume with increasing temperature.
For the case of recovery controlled by climb of edge dislocations, if it is assumed that their annihilation consists of a glide movement followed by a climb movement, the activation length is given by [18]:
¸¸ ¹ · ¨¨ © § c g a l l b l 1 , (14)
where lg is the glide length and lc is the climb length. The activation length is expected
to remain constant during annealing. Since the equilibrium dislocation density decreases with increasing temperature, lg/lc should increase i.e. la increases with
temperature [18].
For the case of solute atoms exerting a drag effect on the edge dislocations, lg/lc will
still increase with temperature but with a slower rate i.e. la is increasing. Thus it is
expected that the observed decreasing activation length with increasing temperature is better explained by a rate controlling process involving the thermally activated glide of jogged screw dislocations which are decorated in this case by carbon atoms.
study suggests that climb of edge dislocations is not the rate controlling step for the motion of dislocations in ferrite at high temperatures.
2.4.5. Influence of strain and strain rate
The effect of strain and strain rate on Q and for a fixed temperature of 550°C is shown in table 2.1. The values are also plotted in figures 2.3 and 2.4.
0 V
Table 2.1: Effect of strain and strain rate on recovery activation energy and activation volume. Temperature of deformation and relaxation is 550°C.
Strain Strain rate (s-1) Q0 (kJ/mol) V (10-28 m3)
0.05 217 1.6 0.15 231 2.6 0.25 0.1 228 2.6 0.01 223 2.4 0.1 231 2.6 0.15 0.5 226 2.7 0.5 0.6 236 2.2
As can be seen, strain and strain rate appear to have no significant effect on activation energy and volume. All of the values appear to be within the range of scatter indicated in figures 2.3 and 2.4.
Increasing the strain however, is expected to cause a reduction in the activation volume for migration of jogged screw dislocations, since the jog density is increasing. Thus, the jog separation will decrease with increasing strain due to the equilibrium separation described by equation (13). This trend is confirmed by the results of Verdier et al [12], for Al- 2.5 wt% Mg alloy.
2.4.6. Analysis of deformation substructures
The substructures obtained after deformation at 550°C to a strain of 0.5 with strain rate 0.6 s-1, and to a strain of 0.15 with strain rate 0.1 s-1, are shown in figures 2.5 and 2.6 respectively.
In figure 2.5 A) a clear subgrain structure is visible (thinnest black lines correspond to a misorientation between 0.5° and 2°), together with precipitates present on both subgrain boundaries and grain boundaries. Figure 2.5 B) confirms the subgrain structure suggested by the EBSD map. In addition there is evidence of precipitation on the grain boundary and also the subgrain boundaries. The precipitates were identified, both from the EBSD pattern and by energy dispersive spectroscopy (EDS), as cementite. In addition, it was found that the precipitates on the subgrain boundaries in figure 2.5 A) were present where the misorientation was more than 3°.
B)
Figure 2.5: A) EBSD image showing two ferrite grains and cementite in ferrite subgrain boundaries (black lines). B) SEM image from a different area of the same sample, showing two ferrite grains separated by a boundary. Both images from samples deformed to a strain of
0.5 with strain rate 0.6 s-1. Samples quenched after 7200 s relaxation. Black circles indicate
example areas of precipitation.
Figure 2.6 shows a boundary separating two ferrite grains. It can be seen that there is a small contrast difference within the ferrite grains but no clear subgrain structure is visible. In addition there is some evidence of precipitation of cementite on the grain boundary.
Figure 2.6: SEM image from sample deformed to strain of 0.15 with strain rate 0.1 s-1. Sample
The precipitates are likely to have been formed in the following way. First during deformation and subsequent relaxation, the carbon atoms in interstitial sites in ferrite can move towards the dislocations. This occurs by interaction of their elastic strain fields [30]. The carbon atoms then form atmospheres around the dislocations. On subsequent quenching of the microstructure the matrix becomes saturated with carbon and due to the fast diffusion of carbon in ferrite (even at room temperature), precipitation occurs [31].
2.5. Conclusions
1) It has been shown that the stress relaxation technique is able to reveal the recovery kinetics of ferrite deformed over a range of temperatures, strains and strain rates. The recovery model of Verdier et al [12] has been successfully applied to the experimental stress relaxation data.
2) The activation energy and volume for recovery were found to vary with temperature, whilst they did not vary with strain and strain rate. At low temperatures (150°C – 300°C) the activation energy was found to be close to that for dislocation core diffusion. At higher temperatures (450°C – 600°C) the activation energy agreed with that found for lattice self diffusion.
3) In the temperature range 150°C – 375°C the activation volume was approximately constant whilst between 450°C – 600°C it decreased with increasing temperature. This is in contrast with a number of experimental data in the literature, where the activation volume increases with temperature. It is suggested that a decreasing activation volume can occur, for a rate controlling process involving thermally activated glide of jogged screw dislocations contaminated by solute atoms (in this case carbon).
References
[1] A. Bodin: Ph. D. Thesis, Delft University of Technology, The Netherlands. (2002).
[2] A. Bodin, J. Sietsma, J and S. van der Zwaag: Metall. Mater. Trans. A, Vol. 33A, (2002), pp. 1589-1603.
[3] D. B. Santos, R. K. Bruzszek, P. C. M. Rodrigues and E. V. Pereloma: Mater. Sci. Eng. A, Vol. 346, (2003), pp. 189-195.
[4] D. P. Dunne, B. Feng and T. Chandra: ISIJ Int., Vol. 31, (1991), pp. 1354-1361. [5] L. Chabbi and W. Lehnert: J. Mater. Process. Technol., Vol. 106, (2000), pp. 13-22.
[6] P. Uranga, A. I. Fernandez, B. Lopez and J. M. Rodriguez-Ibabe: Mater. Sci. Eng. A, Vol. 345, (2003), pp. 319-327.
[7] N. Fujita, T. Narushima, Y. Iguchi and C. Ouchi: ISIJ Int., Vol. 43, (2003), pp. 1063-1072.
[8] H. S. Zurob, C. R. Hutchinson, Y. Brechet and G. Purdy, Acta Mater., Vol. 50 (2002), pp. 3075-3092.
[9] Z. Yang and R.Wang: ISIJ Int., Vol. 43, (2003), pp. 761-766.
[10] M. R. Hickson, P. J. Hurley, R. K. Gibbs, G. L. Kelly and P. D. Hodgson: Metall. Mater. Trans. A, Vol. 33A, (2002), pp. 1019-1026.
[11] K. Mukunthan and E. B. Hawbolt: Metall. Mater. Trans. A, Vol. 27A, (1996), pp. 3410-3423.
[12] M. Verdier, Y. Brechet and P. Guyot, Acta Mater., Vol. 47, (1999), pp. 127-134. [13] R. W. Evans and L. A. Simpson: Phil. Mag., Vol. 19, (1969), pp.809-819. [14] G. A. Sargent: Acta Metall., Vol. 13, (1965), pp. 663-671.
[15] C. R. Barrett and W. D. Nix: Acta Metall., Vol. 13, (1965), pp. 1247-1258. [16] G. B. Gibbs: Phil. Mag., Vol. 23, (1971), pp. 771-780.
[17] H. E. Evans and G. Knowles: Acta Metall., Vol. 25, (1977), pp. 963-974. [18] E. Nes, Acta. Mater., Vol. 43, (1995), pp. 2189-2207.
[19] F. J. Humphreys and M. Hatherly: Recrystallization and Related Annealing Phenomena, Pergamon, Oxford, (1996).
[21] E. Nes: Prog. Mat. Sci., Vol. 41, (1998), pp. 129-193.
[22] J. Frost and M. F. Ashby: Deformation-Mechanism Maps, Pergamon, Oxford, (1982).
[23] L. P. Karjalainen: Mater. Sci. Technol., Vol. 11, (1995), pp. 557-565.
[24] J. T. Michalak and H. W. Paxton: Transactions of the Metallurgical Society of AIME, Vol. 221 (1961), pp. 850-857.
[25] D. Hull and D. J. Bacon: Introduction to Dislocations, Pergamon, Oxford, (1984).
[26] C. W. Spencer and F. E. Werner: Iron and its Dilute Solid Solutions, Interscience, (1963).
[27] K. K. Mani Pandey, Om Prakash and B. Bhattacharya: Mater. Let., Vol. 57, (2003), pp. 4319-4322.
[28] G. B. Gibbs: Phil. Mag., Vol. 13, (1966), pp. 317-329.
[29] F. G. Arieta and C. M. Sellars: Scr. Mater. Vol. 30, (1994), pp. 707-712.
[30] V. T. L. Buono, M. S. Andrade and B. M. Gonzalez: Metall. Mater. Trans. A, Vol. 29A, (1998), pp. 1415-1423.
Chapter 3
Laser-Ultrasonic Monitoring of Ferrite
Recovery in Ultra Low Carbon Steel
3.1 Introduction
Laser Ultrasonics is a relatively recent technique that uses laser light pulses to generate and detect ultrasonic waves in materials. Due to the interaction of the microstructure with the ultrasonic waves, various phenomena can be studied. The literature on ultrasonics has mostly focused on: grain size measurements [1-3], monitoring of phase transformations [4], recrystallization [3,5,6,7], magnetic domain effects [8,9] and dislocation behaviour [9-13].
A key advantage of this technique is that it is non-contact and non-destructive. Thus it has great potential to be used in industrial online monitoring of microstructural development during materials processing. Indeed trials have already been performed during the processing of steel strip [14], sheet [15] and a system has been continuously operating for a few years for monitoring tube thickness and austenite grain size [16].
Whilst some progress has been made, there is a lack of ultrasonic studies of annealing behaviour following warm or hot deformation of steels. The studies mentioned earlier concerning recrystallization were performed on samples annealed after cold deformation only. Similarly, the ultrasonic studies concerning dislocation behaviour were mainly focused on creep [10], ageing [11] and fatigue [12,13]. Thus, if ultrasonics is to be used for online monitoring of recovery and recrystallization after hot forming in steels, then further study is required.
This investigation focuses on the recovery process in ferrite following warm deformation. An ultra low carbon (ULC) steel was chosen for this investigation, since it is known (and confirmed here) that recrystallization following warm deformation is unlikely to occur, except for longer annealing times [21-23].
In the current investigation, measurements of ultrasonic velocity and attenuation have been made during annealing for a variety of deformation conditions and at various temperatures. Stress relaxation measurements were made simultaneously.
In addition samples were quenched after various annealing times and analysed by optical microscopy.
3.2 Effect of microstructure on ultrasonic velocity and attenuation
Microstructural features cause changes in ultrasonic velocity and attenuation. The ultrasonic velocity mainly depends on texture e.g. [5,6], the dislocation structure e.g. [12,13], magnetomechanical effects e.g. [24] and on scattering effects e.g. [3]. Scattering is caused by acoustic inhomogeneities, like grains, porosity, cracks, etc. Given the perfection of the steel samples used, in this study only grain scattering needs to be considered.The attenuation of ultrasonic waves is due to grain scattering e.g. [2] and absorption effects. Absorption is mainly due to the dislocation structure [10-13] and magnetomechanical effects [8,9].
Thus the ultrasonic velocity and attenuation during annealing should be due to a combination of some or all of the above effects, depending on the deformation and temperature conditions. In the following sections the theory for each of these effects is discussed.
3.2.1 Dislocation damping
inhibited by a drag force. The magnitude of this depends on a combination of thermal vibrations (phonons), electrons, and impurity atoms.
Assuming strain amplitude independent damping, the velocity change
¸¸ ¹ · ¨¨ © § ) 0 ( ) 0 ( ) ( d d d v v v U
and attenuation Dd (in dB/s) due to the presence of dislocations with
densityU and average pinning point separation L, are given by equations [25]
¸¸¸ ¸ ¸ ¹ · ¨¨ ¨ ¨ ¨ © § ¸¸ ¹ · ¨¨ © § ¸¸ ¹ · ¨¨ © § 2 2 2 2 2 4 2 2 1 1 4 ) 0 ( ) 0 ( ) ( g C L Gb v v v d d d E E E S U U (1)
¸¸¸ ¸ ¸ ¹ · ¨¨ ¨ ¨ ¨ © § / 2 2 2 2 0 5 2 1 115 . 0 4 g Cf L fGB d d E E E S U D , (2)
where vd(U) is the velocity due to dislocations, vd(0) is the velocity when there are no
dislocations, G is the shear modulus, b is the Burgers vector, C is the dislocation line tension, B is the damping constant, f is the frequency of the ultrasonic waves, f0d is the
resonance frequency of the dislocations and / is the density of the material. The factorsE and g are given by:
d f f 0 E (3) B f b g 2 /S2 2 0d . (4)
A maximum in attenuation occurs at the resonance frequency, given by:
2 2 2 0 4 b L C f d / S . (5) WhenE and 2 2 g E
are small, then equations (1) and (2) can be approximated by:
As can be seen from equations (1-5), for isothermal annealing, the velocity change and attenuation are dependent on the dislocation density and pinning point separation only.
3.2.2 Magnetomechanical damping
The interaction of magnetic domain walls with ultrasonic waves gives rise to magnetomechanical damping. In the absence of an applied magnetic field two effects dominate: micro-eddy current damping and hysteresis damping. For ultrasonic waves in the MHz range (used in this study), the first effect dominates [26].
In the micro-eddy current mechanism, ultrasonic waves cause the movement of magnetic domain walls. This leads to changes in local magnetization, giving rise to micro-eddy currents [27]. This contribution depends on the ultrasonic frequency but not on its amplitude [28].
The velocity change ¸¸
¹ · ¨¨ © § ) 0 ( ) 0 ( ) ( me me i me v v v P
and attenuation Dme in this case are given by
[29]: ¸¸ ¹ · ¨¨ © § ¸¸ ¹ · ¨¨ © § ¸¸ ¹ · ¨¨ © § 2 2 2 0 2 / 1 225 . 0 ) 0 ( ) 0 ( ) ( s sat s i r me me i me I E f f v v v P P O , (8) ¸¸ ¹ · ¨¨ © § ¸¸ ¹ · ¨¨ © § ¸ ¹ · ¨ © § 2 0 2 0 2 2 / 1 / 115 . 0 45 . 0 r r s sat s i me f f f f I E f P O D , (9)
where vme(Pi)is the velocity in the presence of magnetic domains and is the velocity when there are no domains, P
) 0 (
me
v
i is the initial permeability, Os is the
magnetostriction constant, Esat is the Young’s modulus at saturation, Is is the
saturation magnetisation and f0r is a relaxation frequency given by (10):
2 0 24 i d e r D R f P S , (10)
where Re is the electrical resistivity and Dd is the domain size.
The initial permeability in equations (8) and (9) also depends on the internal stressVi.
Thus it can be seen, in micro-eddy current damping, the presence of internal stresses will act to reduce the velocity change and attenuation.
3.2.3 Texture effects
In the presence of texture, the longitudinal ultrasonic velocity vLx is given by [5]:
¸ ¸ ¹ · ¨ ¨ © § ¸ ¸ ¹ · ¨ ¨ © § ¸ ¸ ¹ · ¨ ¨ © § / 400 2 35 2 32 2 1 yW vLx O P S , (12)
where / is the density of the material, O,P and y are single crystal elastic constants and W400 is a texture coefficient. This coefficient comes from a series expansion of the
crystallographic orientation distribution function. For an orthorhombic aggregate of cubic crystallites W400 is one of the lowest order non-zero texture coefficients in the
Roe notation [5,15].
During isothermal conditions the elastic constants and density can be assumed constant. In addition in most metals the texture term 2 400
35 2 32
yW
S is much smaller than the constant term
O2P
, thus equation (12) can be simplified to:
400 eW d
vLx , (13)
where d and e are constants. Thus from equation (13) the velocity is linearly related to the texture coefficient.
3.2.4 Grain scattering effects
Grain scattering affects both the velocity and attenuation of ultrasonic waves. The relationships between velocity and grain size or attenuation and grain size depend on the ratio of the ultrasonic wavelength in the materialOu to the grain size Dg. For the
experimental results presented here, the ultrasonic wavelength in the material is around an order of magnitude larger than the average deformed grain size. Thus, assuming the Rayleigh regime (Ou>>Dg), the group velocity vLGg and attenuation DLg
for longitudinal waves are given by [30,4]:
where A is a single-crystal anisotropy factor and SL is the scattering factor in the
longitudinal direction.
The wave numbersk1 and k2 in equation (14) are given by [30]:
S v f k1 2S , (16) L v f k2 2S , (17)
wherevs is the shear wave velocity.
For equation (15), the scattering factor for longitudinal waves SL, is given by [31]:
¸¸ ¹ · ¨¨ © § /2 2 5 5 2 4 2 3 0308 . 0 s L L a L v v v S S P , (18)
wherePa is related to the anisotropy of the grain, and is defined as: 44 12 11 c 2c c a P , (19)
where c11,c12 and c44 are the elastic constants of the cubic crystal.
It should be noted that in the above equations the grains are assumed to be spherical. Thus for the majority of results in this study, where a deformation strain of 0.15 was used, equations (14) and (15) should give reasonable estimates of the grain scattering effect.
3.2.5 Total effect of microstructure
To summarise, the overall velocity change
T v v ¸¸ ¹ · ¨¨ © § ' 0
and attenuation DT due to
microstructure, can be expressed as:
¸¸ ¹ · ¨¨ © § ¸¸ ¹ · ¨¨ © § ¸ ¸ ¹ · ¨ ¨ © § f f ¸¸ ¹ · ¨¨ © § ¸¸ ¹ · ¨¨ © § ' ) 0 ( ) 0 ( ) ( ) 0 ( ) 0 ( ) ( ) ( ) ( ) ( ) 0 ( ) 0 ( ) ( 400 0 me me i me d d d LGg LGg g LGg Lx Lx Lx T v v v v v v v v D v v v W v v v P U (20) g me d T D D D D (21)
Where vLx(0) and vLGg(f) are the velocities in the absence of texture (W400 = 0,
equation (12)) and grain scattering (Dg= f, equation (14)) respectively. In obtaining
In the case of recovery in ferrite following plastic deformation, the grain size should be constant (i.e. constant
¸ ¸ ¹ · ¨ ¨ © § f f ) ( ) ( ) ( LGg LGg g LGg v v D v
) and there should be a constant
texture (i.e. constant ¸¸
¹ · © § ) 0 ( ) 0 ( ) ( 400 Lx Lx Lx v v W v
¨¨ ). This means that as recovery proceeds, any
change in T v v ¸¸ ¹ · ¨¨ © § ' 0
will be due only to dislocation damping and magnetomechanical
damping.
Using equation (15) the grain size effect can be subtracted from experimental measurements of attenuation therefore:
me d
T D D
D (22)
Furthermore, from equations (8-11) the magnetomechanical damping is expected to be small during the initial stages of recovery (large internal stress) and should increase as recovery proceeds.
3.3 Experimental
The composition of the ULC steel used in the experiments is shown in table 3.1.
Table 3.1: Steel composition shown in [wt %].
C Mn Si Al Fe
0.0024 0.561 0.147 0.038 Bal.
Cylindrical samples were machined from rolled plate, with diameter 10 mm and length 12 mm. The samples were machined with the axis parallel to the rolling direction.
interferometer. The signals are digitised and recorded for further processing. Figure 3.1B shows an example of a signal obtained after deformation. The signals are used to calculate the ultrasonic velocity and attenuation. The velocity was determined by the ratio of the distance travelled through the material (twice the sample diameter) to the time delay between generation and the first echo. The attenuation (determined for a range of frequencies) was obtained from the ratio of the amplitude of the first echo to the second echo. This allowed an attenuation vs frequency curve to be obtained for each measurement. Finally, this curve should be corrected for diffraction effects to provide the true attenuation of the material. However due to the sample geometry present after deformation (barreled cylinder), a diffraction correction could not be made. Generation laser Gleeble thermomechanical simulator Detection laser Interferometer Computer Sample Optical fibers A) -0.1 -0.05 0 0.05 0.1 -1 1 3 5 7 9 11 13 15 Time (Ps) A m p lit u d e ( a.u ) Echo 1 Echo 2 Generation B)
To investigate the relaxation kinetics after plastic deformation, a Gleeble® 3500 thermo-mechanical simulator coupled with a laser ultrasonic monitoring device was used. Each test comprised of three stages. Firstly the desired starting microstructure was made via austenitisation at 1100°C for 3 minutes under vacuum. Then, the samples were cooled to the desired test temperature in the ferritic state. Secondly, after holding for 5 minutes, the samples were deformed in compression. Lubrication was provided via graphite paste. To protect the steel against the possibility of carbon pick-up during the test, tantalum sheets were used as a protective layer between the sample and the lubricant. Just before deformation the Gleeble® chamber was filled with argon, since this provided better conditions for the generation of ultrasonic waves.
Finally in the third stage, the annealing kinetics after deformation were monitored via both the stress relaxation and laser ultrasonics techniques. In the stress relaxation technique the stress required to maintain a constant strain in the sample is recorded. In the laser-ultrasonics technique the ultrasonic signals were recorded for later calculation of velocity and attenuation.
To investigate the microstructural development during annealing, selected samples were water quenched after different annealing times in the third stage. To provide less interference with the ultrasonic measurements, the quenching was carried out using a separate Gleeble® 3500 for the same experimental conditions. Samples were quenched with a rate of approximately 200°C/s. The samples were then analysed by optical microscopy after suitable metallographic preparation.
3.4 Results
3.4.1 Microstructural evolution
Figures 3.2, 3.3 and 3.4 show examples of the microstructural changes during annealing.
After 36 seconds annealing at 730°C for a strain of 0.15, figure 3.3A shows a deformed grain structure. Some grains however seem to have a clean interior and have negative curvature. After 200 seconds ( figure 3.3B ), the structure appears similar. Thus it is difficult to decide whether or not recrystallization has begun.
After 14 seconds annealing at 800°C for a strain of 0.15, figure 3.4A shows a deformed structure with some grains possessing a clean interior. After 300 seconds (figure 3.4B), the structure appears partially recrystallized with very large grains. In light of the uncertainty in determining the transition between pure recovery and the start of recrystallization, only the first 10 seconds of annealing will be considered in the following results and discussion for T = 730°C and T = 800°C. This is highlighted by the dotted lines in figure 3.5. For T = 550°C the whole time range is considered.
Figure 3.2: Optical micrograph of ULC steel after 3000 seconds annealing. Deformation and
annealing temperature = 550°C, strain = 0.5, strain rate = 0.1 s-1.
A) B)
Figure 3.3: Optical micrographs after annealing at 730°C. Strain = 0.15, strain rate = 0.1 s-1.
A)
B)
Figure 3.4: Optical micrographs after annealing at 800°C. Strain = 0.15, strain rate = 0.1 s-1.
A) 14 seconds, B) 300 seconds.
3.4.2 Effect of temperature
Figure 3.5 shows the effect of temperature on stress relaxation, ultrasonic velocity and attenuation. It should be noted that in all figures concerning ultrasonic velocity, the fractional change in velocity ¸¸
¹ · © § ' 0 v v
¨¨ is plotted. In each experiment v0 was taken to be
the value at 100 seconds annealing.
Analysis of the fractional ultrasonic velocity change in figure 3.5B yields similar trends. The initial values decrease with increasing temperature (although for 730°C and 800°C the values are similar) and the rate of change in ¸¸
¹ · ¨¨ © § ' 0 v v
with time appears to
decrease slightly from 550°C to 800°C.
From figure 3.5C, the ultrasonic attenuation appears generally larger for a higher temperature. In addition, the attenuation at 550°C and 730°C appears constant, whilst at 800°C it tends to increase. 0 50 100 150 200 250 300 0.1 1 10 100 1000 Time (s) St re ss ( M Pa ) A) 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 0.1 1 10 100 1000 Time (s) F racti o n al vel o ci ty ch an g e 1 2 3 4 5 0.1 1 10 100 1000 Time (s) U ltr aso n ic att en u at io n (d B /µ s) B) C)
Figure 3.5: A) Stress, B) fractional ultrasonic velocity change and C) attenuation for strain =
0.15 and strain rate = 0.1 s-1. Open triangles = 550°C, open diamonds = 730°C and open
3.4.3 Effect of applied strain
Figure 3.6 shows the effect of strain on stress relaxation, ultrasonic velocity and attenuation.
The stress relaxation data in figure 3.6A indicate that a higher strain gives rise to a higher initial stress and that both curves are almost parallel, indicating similar rates of softening.
Analysis of the fractional ultrasonic velocity change in figure 3.6B shows that for the higher strain the initial value after deformation is higher. In addition, the rate of change in ¸¸ ¹ · © § ' 0 v v
¨¨ with time appears similar for both strains.
From figure 3.6C, it can be seen that the ultrasonic attenuation is higher for the lower applied strain. In addition, the attenuation fluctuates during annealing for both strains.
100 150 200 250 300 350 0.1 1 10 100 1000 Time (s) St re ss ( M Pa ) A) 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 0.1 1 10 100 1000 Time (s) F racti o n al vel o ci ty c h an g e 0.0 0.5 1.0 1.5 2.0 2.5 0.1 1 10 100 Time (s) U lt ra soni c a tt enu at ion (dB /µ s) B) C)
Figure 3.6: A) Stress, B) fractional ultrasonic velocity change and C) attenuation for T =
550°C and strain rate = 0.1 s-1. For open triangles, strain = 0.15. For crosses, strain = 0.5.
3.5 Discussion
3.5.1 Discussion of dominating microstructural effects
As explained earlier, for a constant grain size and texture the values of
0 v
v
' should only change with time due to changes in dislocation damping and magnetomechanical damping. For the attenuation the values of DT should also depend on the above effects
with the addition of a grain scattering effect, since not the change in DT, but the
absolute value is considered.
The contribution of magnetomechanical damping to the observed velocity changes and attenuation can be assessed with reference to figures 3.5B, 3.5C and the Curie temperature. For the steel used in this investigation the Curie temperature is around 768°C [9]. Hence differences in the data for T = 550°C (ferromagnetic behaviour) and
T = 800°C (paramagnetic behaviour) may reveal the magnitude of the effect.
From figure 3.5B there is a decrease in the velocity change between 550°C and 800°C suggesting the loss of the magnetomechanical effect described by equation (8). However with reference to figure 3.5A, at 550°C there is a much higher stress (dislocation density) compared to that at 800°C. Thus it is more likely that the decrease in the velocity change is due to a decrease in dislocation damping i.e. in UL2
from equation (6). In addition when dislocations are present their stress fields should interact with domain walls, causing a reduction in the magnetomechanical damping i.e. equation (11). Hence it is concluded that the magnetomechanical damping in these experiments gives a small contribution to the results.
Further evidence is provided by the attenuation results in figure 3.5C. The values at 800°C are significantly higher than at 550°C. There is no drop in attenuation at 800°C, which would be expected from equation (9) if there was significant magnetomechanical damping. Assuming a constant grain size, the trend of increasing attenuation with increasing temperature in figure 3.5C should be only due to a change in dislocation damping, i.e. an increase in UL4 from equation (7).
From figure 3.6B it is concluded that the change in
0 v
v
be due to an increase in UL2. Other factors that control the initial values of
0 v
v
' are texture and grain scattering effects. However the effects are difficult to estimate since firstly equation (14) assumes spherical grains and secondly, W400 in equation (13) can
be positive or negative, thus the velocity change can increase or decrease during deformation.
The smaller attenuation values observed in figure 3.6C for the higher strain are expected to be due to a combination of dislocation damping, i.e. smallerUL4 for larger strains and a difference in grain scattering compared to the lower strain case.
For the attenuation results, a constant contribution due to grain scattering effects during recovery is expected. This effect can be estimated from equation (15), (18) and (19) provided that the grain size, velocities vL and vs, and the single crystal elastic
constants are known. The grain size was obtained from analysis of optical micrographs. For each experiment around 200 grains were analysed and the average equivalent circle diameter (ECD) obtained. For vL, values were obtained from
experimental data using the values after 100 seconds of annealing, whilst vs was
assumed equal to 0.5vL. The single crystal elastic constants were assumed equivalent
to those for pure iron. In the literature Rayne and Chandrasekhar [32] have measured these constants up to room temperature. However the experiments performed here were at higher temperatures, thus the reported temperature variation of the elastic constants was extrapolated to obtain values relevant to this study. The theoretical attenuation due to grain scattering for each of the experiments is shown in table 3.2. Also shown are the calculated scattering factors and the average equivalent circle diameters.
Table 3.2: Theoretical calculation of attenuation due to grain scattering
Temperature
(°C) Strain (x 10-10SL s3/m3) Average ECD (µm) Calculated8 MHz (dB/µs)Dg at
550 0.15 6.9 50 0.35
550 0.50 6.2 41 0.17
730 0.15 9.0 49 0.43
