Dilatometric investigation on the phase transformations during thermal treatment of a low silicon TRIP-aided multiphase steel M l i I S I TUDelft UCL Delft U n i v e r s t t v of Tecnn Université catholique de Louvain This work is submitted as part fulfilment for the Degree of Materials Science Engineer. Supervisors : Prof. F. Delannay Prof. S. van der Zwaag Valéry ROLIN Academic Year '99 - '00 Acknowledgements In the chronological order of the elaboration of this thesis work, I would like to thank Professor Francis Delannay for having helped me to go and study at the TUDelft I thank especially Dr Lie Zhao for his interest in my work and the time he spent with me. I also thank Professor Sybrand van der Zwaag, Dr Jilt Sietsma, Theo Kop, Yvonne van Leeuwen and Pieter van der Wolk for their help, their judicious advices and their sympathy. I still would like to thank Pascal Jacques for his 'internet' pieces of advice. And I owe a special acknowledgement to Anne Mortens for all the time she has given to me, and for her conscientious help. 2 Abstract TRIP-aided multiphase steels owe their high strength and high formability mostly to the austenite that they contain at room temperature. This is what makes of them the challenging material for automotive industry. In the low-alloyed steels, the retention of the austenite is obtained by a specific thermal treatment, which includes a bainitic transformation. In order to prevent the precipitation of cementite in the enriched austenite, a graphitising element such as silicon is usually added to the composition. But the presence of silicon creates several problems within the finished products, this is why researches are carried out on low-silicon TRIP-aided multiphase steels. The main experimental technique that was used is dilatometry. (1) In a first time the allotropic transformation a ^ y upon heating was studied, A Matlab program was designed for the calculation (on the basis of the experimental data) of the amount of austenite that appears in a sample during an intercritical annealing, (2) In a second time, several thermal treatments have been designed in order to get information for the drawing of TTT diagrams. Therefore, samples were quenched from the austenitic region to several temperatures where an isothermal holding was applied for 15 minutes. Once again, the measured data was used by a Matlab program for the calculation of the fraction transformed, which finally lead to the TTT diagram. Scanning electron microscopy as well as optical microscopy were used on the samples in order to verify the results found by dilatometry and calculation. (1) Image analysis allowed to measure the distribution of phases determined by the regulation of the intercritical annealings. (2) And, by comparing the samples having undergone the different isothermal holding, it was possible to determine the influence of the heat treatments on the microstructures. 3 Table of contents 1. INTRODUCTION 6 1.1 Objectives 6 1.2 TRIP-aided multiphase steels 7 1.2.1 1.2.2 1.2.3 1.2.3.1 1.2.3.2 1.2.4 2. TRIP effect Usual processes for the production of TRIP steels Stabilisation of austenite during the bainitic transformation Bainitic transformation The incomplete reacüon phenomenon Low silicon TRIP-aided multiphase steels M A T E R I A L AND M E T H O D S 2.1 2.2 2.2.1 2.2.2 2.3 3. 13 Material 13 Characterisation Dilatometry Microstructural characterisation 16 16 18 Calculations 2.3.1 Dilatation-Phase 2.3.1.1 Lever rule 2.3.1.2 Calculation based on the lattice parameters 2.3.2 Newton-Raphson 2.3.3 Matlab fraction RESULTS 3.1 3.1.1 3.1.2 3.1.3 3.1.4 3.2 20 20 20 21 24 25 26 First measurements Characteristic temperatures Expansion coefficients Transformation curves MTData calculation of the equilibrium 26 26 28 29 33 Calculation upon the heating data 3.2.1 Calculation of the expansion coefficient of the ferrite 3.2.2 Lattice parameter of the ferrite and the cementite 3.2.3 Transformation curve 3.2.3.1 Calculadon 3.2.3.2 Microstructure analysis 3.2.4 Fitting parameters 3.3 7 8 9 9 10 11 34 35 35 37 37 43 45 3.3.1 3.3.2 3.3.3 Bainitic transformation Isothermal holdings Microstructure analysis Calculation on the bainidc holding 46 46 52 55 3.4.1 3.4.2 3.4.3 Intercritical annealing at 750°C : test Introduction Dilatometry Microstructure 57 57 59 61 3.4 4 4. DISCUSSION 4.1 Heating calculation 4.2 Bainitic transformation 4.2.1 Synthesis of the results on the isothermal holdings 4.2.2 Quenches 4.2.3 CCT Diagram 4.2.4 Stability ofthe calculadons 4.3 T T T diagram for the annealing at TSO^C 4.4 Decayed series Quenches from 900°C Elements for CCT diagrams 4.4.1 4.4.2 4.5 Remedy: Formula applied upon the quench 4.6 Intercritical annealing at 750°C : test Explanations for the gap between the annealings at 750°C Microstructure 4.6.1 4.6.2 4.7 Amount of retained austenite 5. CONCLUSIONS 6. APPENDIX 6.1 GuidelinesManual bainitic transformation analysis program 6.2 Programs 6.3 Three-dimensions T T T diagram 1. Introduction Objectives 1. Introduction 1.1 Objectives As suggested in its title, this work is an investigation on the thermal treatments for the production of a low silicon TRIP-aided multiphase steel. This material belongs to the family of high-strength foimable steels. The exceptional mechanical properties of the TRIP-aided multiphase steels have been studied for several years by now, and they will be detailed in this introduction. What is more recent is the interest bom to the low silicon family, which should be more appropriated on a technological point of view for industrial production. Practically, a low carbon - low silicon steel was chosen to be studied in a first time by means of dilatometry, and eventually by other chai-acterisation techniques : optical microscopy, scanning electron microscopy and X-ray diffraction. Besides the experimentation, the second main part of the work has been the development of a calculation method for the interpretation of the dilatometric data. Two kinds of transfomiations were analysed by this method: (1) the allotropic transformation a-^y upon heating, i.e. the calculation of the fraction of austenite that appears during an intercritical annealing, (2) the isothermal transformation in the bainitic region following a quench from the austenitic region. The idea of these calculation was to get data on the fraction transformed for the drawing of TTT diagrams corresponding to three annealing temperatures : two intercritical, and one over Ac3. In the whole set of dilatometric experiments, some have served for an additional investigation on intercritical annealings. The obtained microstructure still constitutes a mystery since it cannot be explained from the thermal treatments undergone by the samples. 6 1. Introduction TRIP-aided multipl^ase steels 1.2 TRIP-aided multiphase steels Steel is still the first choice material for the construction of car bodies in the automotive industry. In the current conjuncture, the big challenge is the fuel consumption, which demands a reduction of the weight. I f the iron and steel industries want their material to keep its place, they must improve its strength. This can be achieved with the TRIP effect . Although they are low alloyed material, the TRIP-aided multiphase steels show an excellent combination of strength and ductility. These performances can be attributed to the TRansformation Induced Plasticity, i.e. the continuous transformation of retained austenite into maitensite during straining ^^'^^. 1.2.1 T R I P effect The schematical free energy curves on Figure 1 help to understand how the mechanically induced transformation of the austenite works. For a fixed composition. To is the equilibrium temperature between austenite and martensite, and Ms is the temperature at which the undercooling is sufficient to provoke transformation. I f Tj is an intermediate temperature between Ms and To, the austenite that exists at Ti is said to be metastable since its free energy curve is above the curve of the martensite. The fact is that the difference between the free energy curves at T, (AG^^"') has not yet reached the critical driving force (AG^^^"'). However, it is possible for the austenite at Ti to transfomi into martensite i f a sufficient mechanical energy is provided (U'). This mechanically induced transformation bears the name of TRIP effect. M. „.^^^S. Martensite s C3 O Austenite Ms Tl To Temperature Figure I: Free energy curves of tiie austenite and tiie martensite 7 1. Introduction TRIP-aided multiphase steels 1.2.2 Usual processes for the production of T R I P steels TRIP-aided multiphase steels can be produced in two ways : (i) heat treatment after cold rolling (i) and, (ii) a continuous thermomechanical treatment including a hot rolling . Figure 2 shows the heat treatment used for cold-rolled TRIP-assisted multiphase steels. The aim of this process is to stabilise some austenite at room temperature thanks to a two steps carbon enrichment. In a first time, the austenite is formed during the intercritical annealing and it is enriched in carbon coming from the neighbouring ferrite . Secondly, a bainitic holding provokes a partial transformation ofthe intercritical austenite into bainite, and the carbon enrichment of the remaining austenite, which is therefore not transformed into martensite during the fmal quench to room temperature . Those low alloyed steels usually contain up to 1.5 - 2.0 wt. % silicon in order to prevent the precipitation of cementite in the carbon-enriched austenite. During the further processing of the material, the metastable austenite can transform into martensite when there is a strong plastic deformation. (ii) The processing of TRIP steels via thermomechanical treatment is quite similar, except that the material is hot-rolled, then directly cooled to the intercritical region, where the annealing is carried out in a continuous way. The continuation ofthe process is identical to the one for cold-rolled steels (i). Figure 2: Typical heat treatment scheme for the production of TRIP-aided multiphase steel 1. Introduction TRIP-aided multipimse steels 1.2.3 Stabilisation of austenite during the bainitic transformation 1.2.3.1 Bainitic transformation Before entering into the specificities of the multiphase TRIP-aided steels, it is necessary to examine the bainitic transformation. It is worth remembering that the bainite is the microstructure that forms when a steel is quenched from the austenitic region to a range of temperatures below the femtic region and above the martensitic region. While the formation of ferrite is a diffusive transformation, the formation of martensite is displacive. What about bainite ? It has been accepted now that its formation is displacive, even though there is some diffusion in the nucleation process . Austenite Grain Boundary Figure 3: Sciiematic representation of tiie development ofa sheaf of bainite The growth of the bainite is sketched in Figure 3. The sub-units have the cristallographic lattice of the ferrite, and are sometimes called "bainitic ferrite". They nucleate at the grain boundaries of the austenite and grow very fast as a plate until the dislocation pile-up at the austenite/ferrite interface stops them. Then new nucleation occurs at the tip of the laths, leading to a sheaf stmcture. As their fonnation is displacive, the fenite laths are supersaturated with carbon during a short instant, after their formation, carbon then diffuses into the surrounding austenite. This becomes the place for caitide precipitation, unless silicon or aluminium has been added. These elements, which ai'e substitutional, do not diffuse during bainitic transformation. Two diffusion processes exist that lead to two kinds of bainite, as sketched in Figure 4. 9 1. Introduction TRIP-aided multipliase steels Formation o f a supersaturated Sub-Unit Cai-bon diffusion into austenite / 2 \ Carbon diffusion into austenite and carbide precipitation i n feixite C 3 Carbide precipitation f r o m austenite Upper Bainite 1 Lower Baiiiite Figure 4: Scliematic illustration of tiie formation of either upper bainite or lower bainite The difference between upper bainite and lower bainite comes from kinetic effects Upper bainite appears when the transformation is performed at such a high temperature that the carbon diffusion out of the ferritic laths can take place very quickly. On the other hand, at lower temperatures, a part of the carbon cannot diffuse out of the lath and thus, carbides precipitate inside. This is the case of the lower bainite. 1.2.3.2 T h e incomplete reaction p h e n o m e n o n The fact that some austenite can be stabilised during the formation of bainite is called an incomplete reaction ^^1 It will be showed hereafter that this incomplete reaction is possible because the bainitic transformation is displacive. Figure 5 presents the free energy curves of ferrite and bainite at the temperature T, represented as a function of the carbon content. The crossing of these curves defines the carbon concentration above which the austenite cannot transform into ferrite in a displacive way. The line that represents this maximum carbon content as a function of the temperature of transformation is called the To curve. The result is that, for an isothermal transformation at Ti, and i f there is no carbide precipitation in the austenite, the bainitic transformation will stop when the caiton concentration in the austenite reaches the value defined by the To curve. 10 1. Introduction TRIP-aided multipliase steels On the other hand, i f the austenite had transformed by a reconstructive process, the carbon concentration in the ferrite and in the austenite would have been respectively defined by the Aei and the Aea lines, according to the tangent mle. Carbon Concentration Figure 5: Scliematic illustration of tiie origin ofthe To cwve on a piiase diagram as resulting at each temperature of specific points of the free energy curves offerrite and austenite Besides the fact that the bainitic transformation must be displacive, a second condition for the retention of austenite is that there must not be any carbide precipitation. It is possible to get rid of that precipitation by adding silicon to the steel. Indeed, the solubility of the silicon in the cementite is very small and therefore carbon cannot precipitate ^''l I f this requirement is met, the high carbon content of the austenite has the effect to drop Ms below room temperature, and the austenite can therefore be retained. 1.2.4 Low silicon TRIP-aided multiphase steels Significant amount of austenite can be retained in bainitically transformed steels highly alloyed with a silicon concentration around 2 % and it is accepted that a conventional TRIP-aided multiphase steel must contain at least 1 wt. % of silicon ^ " l But the problem is that besides its good effect on the hindering of the cementite precipitation, silicon, when it is added to more than 0.5 wt. % in steel, creates problems on the finished product. Firstly, a silicon oxide layer appears on the material after the hot-rolling. Secondly, at the galvanisation, too much silicon provoke the formation of intermetallics Fe-Zn that renders the protection 11 1. Introduction layer fragile TRIP-aided multipiiase steels \ This is why a real interest exists for low silicon TRIP-aided multiphase steels. The steel that is going to be studied in this work has the following composition : 0.16 wt. % C, 1.5 wt. % Mn, and 0.4 wt. % Si, which is similar to the composition of typical coldrolled dual-phase steels '^^^l As a matter of fact, the silicon content is much lower than in conventional TRIP-aided multiphase steels, and it should be difficult to get retained austenite. However, the dilatometric-investigation is interesting since it can bring many infoimation on that grade of steel. 12 2. Material, and metixods Material 2. Material and methods 2.1 Material The one and only material studied in this work is a low silicon steel that was provided by the research and development department of Hoogovens As it was to be studied by dilatometry, we have received the samples of industrially produced hot-rolled FeCMnSi steel in the shape of solid cyhnders of 10 mm long and 4 mm in diameter. Wt. % Mn Si C 1.5 0.4 0.16 Table 1: Composition given by Hoogovens. This steel was said to have a composition with lean chemistries, and that means a maximum of 0.16 wt. % C, 1.5 wt. % Mn and 0.4 wt. % Si. Those values were retained for the calculations based on the lattice parameters. Meanwhile, in order to have a second source for the composition, we confided three samples, as they were received from Hoogovens, to the department of Chemical Technology of Delft. The samples were digested in a mixture of 20 ml aqua regia and 5 ml HF in a closed Teflon vessel using a microwave furnace. The ICP-OES technique was used to analyse the sample solutions. The concentrations found are : Weight [mg] 975.5 ± 0 . 8 Wt. % Mn Si C 1.47 ±0.015 0.27 ±0.015 0.14 ± 0 Table 2: Composition measured at tiie TUDelft. The silicon concentration is much lower than the previous value of 0.4 wt. %. That would mean that this is a "very low silicon steel". Anyway, we will see that it will not be a problem for the calculations as the silicon concentration does not play any role. An explanation that was proposed for this lower measured value was that a precipitate including a part of the silicon forms in the batch, so that this part is not blown in the plasma torch. On the other hand, the measured concentration for the carbon was also lower than the value given by Hoogovens (0.14 < 0.16). This has more critic consequences as it influences the results of the calculation. Nevertheless, we made the choice to work with the first numbers. We asked our contacts in Hoogovens to repeat the same composition measurements with more details (Table 3). The results follow in weight percent: 13 2. Material and methods Wt. % Material Mn Si C Al Ni Cr Cu P S Mo, Sn 1.48 0.414 0.154 0.046 0.022 0.019 0.015 0.012 .0.011 <0.001 Tahle 3: Composition measured by Hoogovens. These measurements confirm the choice to take into account the three first alloying elements (Mn, Si, C), and to assume that their concentrations are 1.5, 0.4 and 0.16 wt. % réspectively. Internet provides some information on steels: the web site of the university of Cambridge, department of H.K.D.H.Bhadeshia, can release TTT and CCT diagrams '^^"l 1200 •TTT •CCT 1100 1000 P 900 |- 800 700 0.16*C, 0.4»Si, 1.5»In, m\i OSSMo, Oürcr, OSfT, OjfCo, 0 rt.ppm E Austenitizing Temperature = U73K Cooling Rate Range = 0.01 <-> ISOK/s 600 500" 0.01 I I 11 ml oml L 0.1 10 100 1000 Time (s) Figure 6: TTT and CCT diagrams calculated on Cambridge web site ^'''l The chart on Figure 6 assumes that the material has been austenitised at 900°C. Pictures 1 and 2 show SEM micrographs of the material as it was received from Hoogovens. At a low magnification, picture 1 shows the strongly banded stmcture oriented in the rolling direction. This is due to the microsegregation that takes place during the solidification of the liquid metal. Dendrites of ferrite 6 form in an oriented way and the manganese remains preferably in the liquid phase. The banded stmcture is created by the mechanical deformation at high temperature of those dendrites. The presence of pearlite (seen on picture 2) is strongly dependent on the local concentration of manganese since this element has the effect to move the eutectoïd point to the left. Moreover, as the manganese lessens the eutectoïd level ^^^^i.e. the A l temperature), its distribution has an effect on the microstructures that form upon cooling or heating through the (a,y) phase transfonnation. When cooling, the first ferritic grains will appear in the regions poor in manganese. When heating, the first austenitic grains 14 2. Material and metiiods Material will appear in the regions rich in manganese. The pictures 1 and 2 allow to think that the average grain size is around 5 pm. Picture 1 (AR): SEM micrograplr siiowing tlie hot-rolled microstructure ofthe received from Hoogovens. A strongly banded structure is visible. material Picture 2 (AR) : SEM micrograph showing the ferritic-pearlitic microstructure of tlie material received from Hoogovens. The grain size is 5-10 jlm. 15 2. Material and metiiods 2.2 CItaracterisation Characterisation 2.2.1 Dilatometry The main technique used in this investigation is dilatometry. A l l the experiments have been caiTied out in the Materiaalkunde at the Technische Universiteid Delft on a BAHR805. This appai-atus belongs to the new generation of the technical instruments. Figure 7 might help to understand how the dilatometer works. Thermocouples LVDT Sample Induction coil Quartz rods Figure 7: Scliematic illustration ofa dilatometer. The sample, a solid cylinder 10 mm long and 4 mm in diameter is wedged between two quartz rod tensed by a spring. Two coils surround the sample ; one is for the heating by high frequency induction and the other one projects a cooling gas during the possible quenches. Two cooling gases are available ; nitrogen and helium. Nitrogen was used during the first experiments that required a quench, but it appeared cleariy that it was not efficient enough. Thus helium was chosen, because of its higher calorific capacity, although it is more expensive. Two thermocouples are welded on the surface of the sample. Only the temperature measured by the first one (welded in the middle of the sample) will be taken into account for the application of the temperature program, however the data measured by the second thermocouple can be used for the calculation of the temperature gradient that exists between the middle and the tips of the sample. The dilatation measurement employs a device called "Linear Variable Displacement Transducer". The value of Al(T) is set to zero at the beginning of the program, and this is always at the room temperature. 16 2. Material and metliods Characterisation Experiment Quenching mode Bainitic holding Temperature range Gauging experiment No No , 20-900 °C For image analysis Yes No 20-800 °C Isothermal trans. Yes Yes 20-900 °C Test: 750 °C Yes Yes 20-950 °C Tahle 4: Set of dilatometric experiments peifonned in tiiis tiiesis work. In order to have an idea of the range of temperatures covered by the experiments, one may look at the Table 4. About 55 experiments have been carried out. The two first ones were "gauging experiments", i.e. the aim was to measure the characteristic temperatures of the steel as well as its expansion coefficients. It is just a slow heating to the austenite region, followed by a slow cooling. A few experiments called here "For image analysis" consisted in an annealing, intercritical or not, followed by a quench to room temperature. Most of the work was actually spent on the "Isothermal transformations" group; about twenty five experiments have been carried out according to the following process : The sample is heated at the rate of 100 K/minute to one among three annealing temperatures : 750°C, 800°C or 900°C. It is annealed for 10 minutes, then quenched with hehum gas to a level between 100°C and 500°C by steps of 50°C. This level is maintained for 15 minutes and is followed by a free cooling to the room temperature at the rate of 100 K/min. Those treatments are illustrated on Figure 8. Treatments Time [mini Figure 8: Representation ofthe dilatometric experiments peiformedfor isothermal transformations. 17 tiie analyse of 2. Material and methods Characterisation The horizontal dotted lines define A c l (= 725°C) and Ac3 (= 850°C). Finally, a few more "exotic" experiments, which were called "Test at 15Q°C\ were performed, A maximum temperature of 950°C is reached on the whole set. One must be aware that the BAHR805 is not just a conventional dilatometer. Indeed, a conventional device is just able to measure a change in length while the temperature is evolving. It is thus adapted for gauging measurements : slow heating, slow cooling. On the other hand, the apparatus used in this work is a "quench" dilatometer. It means that one can include quenching modes in the program, and the big interest is to measure the dilatation that takes place during an isothermal holding that follows the quench. This option is essential for someone who wants to draw TTT diagrams. It is very important to check that the sample did not move between the rods during the experiment because it would introduce a jump in the change in length data. Unfortunately, it often happens that the gas blown destabilises the sample during the quench, ant it renders the experiment decayed. When performing dilatometry experiments, one should always be aware of the decarburisation problems. At high temperatures, some carbon close to the surface may leave the sample because of the strong diffusion. If so, the following measurements and calculations would be falsified since the composition would have been locally changed. This is why it is important to look at the surface of a slice cut in the sample in order to see i f there is, or not, a segregation between the edge and the centre. Concerning this work, a checking was done on some samples austenitised during 10 minutes at 950°C and no decarburisation was observed. Indeed, this phenomenon can appear only from higher temperatures (at least 1100 °C). 2.2.2 Microstructural characterisation Some of the samples analysed by dilatometry were chosen for microstructural examination. Two slices about 1 mm thick were cut in each of them : one was taken in Louvain-ia-Neuve for microscopical observation, and the other one was kept by Dr. Lie Zhao, from the Materiaalkunde, TUDelft, for X-ray analysis. Those samples were cut very carefully with a diamond saw so as to avoid the mechanically induced transformation of retained austenite. (TRIP effect). Microstructures were studied by scanning electron microscopy (SEM) and by optical microscopy. The polishing has been done to a fineness in the diamond powder of 0.25 p.m. In order to make possible the distinction between retained austenite and martensite by SEM observation, specimens were first annealed for 2 hours at 200°C and then etched with 2 % 18 Characterisation 2. Matenal and methods nital (Norvanol + 2 % HNO3). Because of the carbide precipitation during the annealing, the maitensite appears as finely cracked grains, while austenite grains remain perfectly smooth [16] The image analysis was performed on pictures scanned from the SEM with a semi-automatic routine working with Visilog. The application was the measurement of the fraction of phase in quenched samples. It required fifty pictures magnified around 1400 times and taken' all around the facet of the sample. For each picture, a brightness threshold has to be defined in order to distinguish the ferrite from the martensite. It is important to take pictures properly scattered on the entire available surface because there may be some variation of the phase's fraction depending on the situation with respect to the edge of the sample. 19 Calculations 2. Material and metiwds 2.3 Calculations 2.3.1 Dilatation-Phase fraction As for the majority of the materials, steel undergoes a dilatation when it is submitted to a rise in temperature. I f there is no phase transformation during the heating, the dilatation can be described by mean of an expansion coefficient. If there is a transformation, one must take into account the different crystallographic phases that coexist at a given temperature. Two conventional techniques for the calculation of the phase fractions, for instance during a cooling from the austenitic region to the ferritic region, ai"e presented here. The first one bears the name of "lever rule", whereas the second method involves the lattice parameters. (This lever rule should not be mistaken with the lever rule relevant for the phase diagrams.) The second method constitutes the basis of all further calculations in this work. 2.3.1.1 L e v e r rule The volume fraction of austenite can be calculated as follows: fer-aust The lever rule method is illustrated on Figure 9 and by equation (1). The application of this method requires the assumption of proportionality between the phase fraction and the length change. By virtue of extrapolation of the linear expansion and contraction curves of the ferrite phase and the austenite phase, we can define these values : • far = Length change of a heated sample that would remain 100 % ferritic. • aust = Length change of a cooled sample that would remain 100 % austenitic. • cil (change in length) = Actual change in length of a sample cooled from 900 °C at 3K/min. 20 2. Material and metiiods Calculations Lever rule 110 30 500 550 600 650 700 750 Temperature P d 800 Figure 9: Illustration of tiie 'lever rule' on a dilatometric cooling curve. Those values are temperature dependent, and, in this example, it is at 700°C. The lever rule is very easy to apply, but the assumption of proportionality is too strong. Furthermore, using this technique could not help to measure the amount of a new phase growing during the isothermal level of an intercritical annealing, or of a bainitic holding. As a matter of fact, precisely that kind of calculation was to be performed in this thesis work. Another kind of calculation has thus to be used. 2.3.1.2 C a l c u l a t i o n b a s e d on the lattice parameters The following developments mainly come from an article of Lie Zhao ^ ^ ' l As explained in the previous pages, the dilatometer allows to measure the dilatation of a sample, which follows a temperature program, previously defined by the user. But it is technically easier to measure a length change (AI = 1-IQ) than a volume change (AV = V-VQ), and those values can be linked thanks to the following formula. 1+ AV (2) 0 Al 0 1 AV (3) 3 V0 Another way to write the equation (3) is: 21 2. Material and methods Calculations Where Al - l(T) - k . The values k and Vo characterise the initial dimensions of the sample. These values are going to be the reference in comparison with which the variation is calculated. The initial dimensions are defined as the dimensions of the sample at the beginning of the experiment, or at the beginning of the isothermal transformation. V'(T) is the instantaneous volume and it is a function of the temperature. Let us consider now the case of a phase transformation taking place upon cooling. We suppose that there is only one product phase and one parent phase involved, for instance, the ferrite (a) phase and the austenite (y) phase. We have to consider now the volume fractions and fy. The instantaneous volume V'(T) of the equation (4) can be expressed as follows : The sum of the volume fractions of the phases remains very logically equal to 1. Equations (4) and (5) establish the relation between the volume fraction and the length change. The next step will be to decompose the terms Va and Vy by means of the lattice parameters and the expansion coefficients multiplied by the temperature. This will introduce the link between the change in length and the temperature. Here is the application of this type of calculation to a transformation that occurs during an isothermal bainitic holding. Some values like the lattice parameters and the expansion coefficients are still unknown but the calculations that will be made on the heating curve of the gauging experiments will give them. Anyway, those values will be used in a formula that figures out the fraction of retained austenite all along the isothermal holding. Two different formulas must be written : one relevant for the completely austenitised samples, and the other one for the cases when the quench is carried out from an intercritical region. Austenitised samples : A/ _ (2 * fa-B ^0 * « a - B + fy-B * ^J-B) ' «r-A (6) 3*4_. The sign '-A ' means "in the austenitising region" and '-B ' stands for "bainitic". As a matter of fact, it is considered in the following calculations that the transformation that occurs during the isothemial holding produces bainite, although we are aware that it is not pertinent in the 22 2. Material and metiiods Calculations case of a maitensitic transformation for instance. As bainite is mainly composed of ferrite, its contribution in the volume is measured via the ferrite lattice parameter 'aa-B, In this equation, just as in the following one related to the intercritically annealed samples, what is looked for is the value of ' / « - b ' (which is equal to 1 - I t represents the fraction of bainitic ferrite, while the interlamellar cementite will be included in the ' ' term. The part of cementite in a steel of such a composition is quite low. The change in length 'Al' is the data measured by the dilatometer, while 7' is the length of the sample : 10 mm. The different lattice parameters must be written as is : Clfj^ — a^jQ ay - (ayQ Ci ferrile + C ] * Xl + C 2 * X J ) * OC austenite * ^ One should remember that x\ and X2 are the weight concentration of carbon and manganese in the austenite, and c\ and ca are appropriate coefficients for the effect of the carbon and the manganese. These elements have an influence on the size of the lattice parameter of the austenite, in which the alloying elements have a higher solubility than in the ferrite lattice. As the manganese stands in the iron lattice as a substitutional element, we may assume that it diffuses slowly, and thus X2 is constant. On the contrary, the carbon is much more mobile, and it obliges us to apply the following assumption : the cai'bon concentrates in the austenite. This is why x\ must be written : fr !-ƒ« On a mathematical point of view, it is interesting to note that a nice form of the solution of the complete equation cannot be found easily. This is why the Newton-Raphson method is a good choice for solving this equation. Intercritically annealed samples : A/ _ (2 lo * al_, + 2 * f , _ , * a l , + f^_, * a%) - (2 * f„_, * a^, + f^_, * ) 3*(2*/a-;*4-7+/r-/*4-/) '-ƒ ' indicates the "intercritical region". In this case it must be taken into account that there is already some ferrite inside the sample before the isothermal transformation of the austenite 23 2. Material and metliods Calculations begins. This is why the term '2* f^_, *al_,\ which represents the intercritical ferrite, is present in V' and Vo at the same time. Note that 'ƒ„_/' is a constant, either 0.1 or 0.55, depending on the temperature ofthe intercritical annealing, 800°C or 750°C. What is going to be calculated is ' fy_,', which represents the fraction of (retained) austenite and also the fraction of interlamellar cementite that is produced by the bainitic transformation. Then it will be easy to find ' fa-B='^-fa-I ', the fraction of bainitic ferrite, by using this formula : -fy-B (10) The details for the expressions of the lattice parameters are the same than in the case of the completely austenitised samples. 2.3.2 Newton-Raphson Newton-Raphson is the name of an iterated calculation technique that allows to find easily a root of any equation, and it is especially interesting for equations that cannot be solved in an analytic way. The equation that must be solved should be written in the following way : F{x) = 0. The origin of the formula can be explained by the development of F(x) in a Taylor series starting from a point xo. (X-XQ) F{x) = F{Xo) + {x-Xo)F'(Xo)+' ^^"^ 2 F"(A-o)+... (11 ) If this Taylor series is truncated after the term of the first order, and i f we are looking for a root, i.e. F{x) = 0, we get 0=F(x) = F(xo) + ( 12 ) (A--A-O)F'(XO) and thus ^ - = ^ 0 - - ^ (13) As the Taylor series was tmncated, the equation (13) is only an approximation of the solution. A better approximation can be found by repeating the operation as suggested by the following formula : ^M=Xi-T:7r^ (14) 24 2. Material and metixods Calculations This method is extremely powerful but it needs the evaluation of the value of the derivative F{xi). This can be done easily in the following way : ^,.,) = Z < i ± f ) _ £ ( £ ^ ,,,, where £ is a fixed small number. Once the difference between JCi+i and x\ has come under a defined threshold, the iteration is stopped. The user also has to define a starting value XQ ; this one should be chosen close to the expected root in order to improve the convergence. The Newton-Raphson method has been used in this work for the resolution of all the equations involving the phase fractions, function of the lattice parameters, who are themselves function of the phase fraction. 2.3.3 Matlab Most of the calculations have been performed with the mathematical software MATLAB. Indeed, it is very convenient for the handling of big data files such as those produced by the dilatometer. A non-expert user can quickly manage with it as the programming language is simplified in comparison with a language like Pascal. It is obviously very adapted to the functional programming, i.e. one can define functions that will be used by different programs. Another advantage is that no compilation is necessary so the programs can be modified pretty easily. And a great interest of using Matlab is that one can present his results on very functional and readable charts. Unlike with Microsoft Excell, for instance, the user does not have to settle a lot of parameters in the picture, and, furthermore, the pictures do not need lots of memory on the hard drive of the computer, because the file format is postscript. 25 3. Results First measurements 3. Results This chapter contains three types of results : dilatometric observations, calculations based on the dilatometric data, and microstructural examinations. A l l of them are distributed throughout four sections. Section 3.1 is about information on the low silicon steel that were obtained thanks to gauging experiments. The second section ( Section 3.2 ) develops a calculation based on the heating part of the gauging experiment. Section 3.3 , the biggest part, contains examinations of the bainitic holdings as well as calculations. The chapter ends with the section 3.4, which contains an analyse of a quite exotic dilatometric experiment. 3.1 First measurements This part comprises results that could be obtained by the analyse of the data of the first gauging experiments. A slow heating to the austenitic region followed by a slow cooling allowed to measure the characteristic temperatures, the expansion coefficients and the transformation curves upon cooling and heating as well as at the equilibrium. 3.1.1 Characteristic temperatures The first dilatometric experiment that was performed aimed to get basic information on the material such as the temperatures A c l , Ac3, A r l and Ar3. For this, a sample was heated to 900°C at the rate of 3 K/min, which is the industrial practice, then it was kept at this level during 30 minutes, and finally cooled at 3 K/min. The whole experience lasted 10h30 ; this is sketched on Figure 10 hereunder. 120 Temoerature f-Cl Figure 10: Dilatation ofa sample heated to 900°C at 3 K/min, then cooled at 3 K/min. 26 3. Results First measurements One can properly see the phase transformation that takes place upon the heating as well as the one that takes place upon the cooling. We can notice that, at POO-C, the sample is completely austenitised. The second chart also represents the change in length, but this time as a function of the temperature. Therefore it is possible to measure the characteristic temperatures. "C Acl Ac3 Arl Ar3 728 848 626 738 Table 5: Ciiaracteristic temperatures of tiie low-silicon steel. 'c' stands for 'citauffer' ('to heat' in French), and Y stands for 'refroidir' ('to cool' in French). The temperature A2 is the one at which the iron becomes ferromagnetic when cooling down. It is possible to measure it by looking at the curve that shows the electric power spent in the coil as a function of the temperature (figure 11). As a matter of fact, there is a big step at 750°C that indicates the A2 temperature. The ferromagnetic transition demands a special amount of energy, just like a fusion would do. Power 50 40 30 20 10 0 0 200 400 600 Temoerature PCI 800 1000 Figure 11: Electric power spent in tiie induction coU upon iieating ofa sample. As we ai-e dealing with the characteristic temperatures of a steel with a determined composition, we are able to calculate the temperatures corresponding to the 'bainite start' and the 'martensite start'. Here are Andrew's formulas ^^^^: Bs = 830 - 270 * [C] - 90 * [Mn] - 37 * [ M ] - 70 * [Cr] - 83 * [Mo] (16) Ms = 539 - 423 * [C] - 30.4 * [Mn] -17.7 * [Ni] -12.1 * [Cr] - 7.5 * [Mo] (17) 27 3. Results First measurements For our steel composition, we get Bs = 652°C Ms = 426''C Those values agree with the TTT and CCT diagrams obtained from Bhadeshia's web site ^^''l 3.1.2 Expansion coefficients Another important infomation that a dilatometer can bring is about the expansion coefficients. It is very important to have accurate values for them since they enter into account for all the calculations. Just by looking at the dilatation curve of this low silicon steel, one can set his ideas about those coefficients. A deeper research will follow in the section 3.2. Alpha and gamma 130 500 600 700 800 Temperature f^Cl 900 1000 Figure 12: Dilatation curve upon iieating ofa sample at 3 K/min. Figure 12 shows the change in length as a function of the temperature during the heating. The rings indicate the boundaries of the sections on which the expansion coefficient are calculated. The derivative of this curve is plotted on the Figure 13. The mean values of the expansion coefficients are calculated between the boundaries, and we get : aa = 17.14*10"^ K"' , for the ferrite, and Oy = 23.62*10"'^ K'" for the austenite. Of course, these pai-ameters do not depend on the temperature here although they should. Oa is just a mean value between 550°C and 725°C, and (Xyis between 850°C and 950°C. In the further development, a more accurate coefficient will be obtained for the ferrite, but we will keep 23.5*10"'^ for the austenite. 28 3. Results First measurements Expansion coefficients 30 20 Ferrite E C : 17.14 K^-1 Austdnite E C : 23.62 k^-1 ^ 10 o O Q. X . LU -20 -30 500 600 700 800 Temperature f-Cl 900 1000 Figure 13: Measured expansion coefficient as a function of tlte teinperature. The given values are for the averages on the regions defined hy the rings. 3.1.3 Transformation curves This comprises the cooling part and the heating part. What is meant by 'cooling part' is the transformation of the austenite into pearlitic ferrite during the experiment at 3 K/min. Figure 14 illustrates the phase transformation upon cooling. How can one measure the austenite fraction that disappears during the cooling ? As explained earlier, we can do it with the lever i-ule described in figure 9, or with a calculation based on the lattice parameters. Cooling part 600 650 700 750 Temoerature 1=01 800 Figure 14: Dilatation curve measured upon cooling. The result of the lever rule method is plotted on Figure 15. It is necessary to remember the previously estabhshed characteristic temperatures: A r l = 626°C and Ar3 = 738°C. The tips of the lever rule curve seem to be a little bit too much on the right. 29 3. Resuhs First measurements Lever rule 600 650 700 750 Temoerature PCI 800 Figure 15: Calculated fraction of tiie austenite that disappears upon cooling. By tiie 'lever rule' metiiod. It is worth trying another Idnd of measurement for the phase fraction. The curve on Figure 16 is the result of a calculation that involves the lattice parameters : Theo Kop, from the Materiaalkunde in TUDelft, proposed a program applied to the pearlitic transformation during the cooling of a completely austenitised steel. The result seems in better agreement with the measured values of A r l and Ar3. Both lever rule and Theo Kop's program show an angle in the curve when the last 20 % of austenite fmally transform into pearlite. Theo Kop's program 600 650 700 750 Temperature f=Cl 800 Figure 16: Calculated fraction ofthe austenite that disappears upon cooling. By a metiiod based on the lattice parameters, and programmed by Theo Kop. As a matter of fact, a quick calculation gives about 20 % of austenite when the eutectoïd level ^ ^ 0.16-0.02 I S reached ; = 18.5%. 0.78-0.02 30 3. Results First measurements After this quiclc loolc at the cooling part, the investigation continues with the heating part. The ring in the inflexion on the curve of the Figure 17 indicates the end of the decomposition of the cementite contained in the pearlite. The fraction of coming austenite can be calculated by the lever rule method. It requires to draw linear extensions for both ferrite and austenite (Figure 18), and then the equation (1) is applied. The result is displayed on Figure 19. Heating part 700 750 800 850 900 Temoerature i-Cl Figure 17: Dilatation curve upon iieating at 3 K/min. 750 800 850 900 Temoerature f^Cl Figure 18: Application ofthe 'lever rule' metiiod upon heating. Extensions for the ferrite and for tiie austenite have been drawn. 31 3. Results First measurements Lever rule 80 0 700 750 800 850 900 Temoerature l-Cl Figure 19: Fraction of austenite calculated by 'lever rule' upon heating. One should remember that A c l = 728°C and Ac3 = 848°C. These values are fitting quite well with the chait that yields the fraction of austenite during the heating. One can still observe a slight inflexion around 20 % of austenite. It corresponds to the end of the decomposition of the pearlite. The introduction of this thesis talks about an intercritical annealing, i.e. a thermal treatment in which a steel is maintained for several minutes at a temperature comprised between A c l and Ac3. The idea is to get, at the end of this intercritical annealing, a microstructure that contains both ferrite and austenite. It is worth remembering that most of the experiences performed in this research includes a bainitic or a martensitic holding preceded by either a complete austenitising or an intercritical annealing. It is therefore time to choose the parameters of these treatments. The phase fraction depends on the chosen temperature, as can be seen on Figure 19. As this curve corresponds to the heating, it is a good starting point for the choice of two intercritical temperatures. I f the first one must give around 20 % of austenite, 750°C seems to be a good choice. And i f we want more than 50 % of austenite, we can take 800°C as a second intercritical temperature. Finally, the choice of an austenitising temperature must be done according to the conventional rule : = Ac3 + 50 K. This is why 900°C was chosen. When the distribution of the phases during cooling and heating at low rates is known, one must check it with an MTData calculation. The relative positions of the curves with respect to the equilibrium curve should fit. 32 3. Results First measurements 3.1.4 MTData calculation ofthe equilibrium The MTData software allows to calculate the distribution of the phases at the equilibrium, just on basis of the composition ofthe alloy ^^^1 The assumption intended by 'equilibrium' is that every alloying element would have enough time and kinetic energy to diffuse from one phase to another. For instance, all the carbon and the manganese would go in the austenite, while the silicon would go in the ferrite. Applied to our case, the crystallographic phases that must appear in the current calculation are • ferrite : Body Centred Cubic. • cementite. • austenite : Face Centred Cubic. MTData; results 80 B C C A2 60 1 50 f8 40 FCC Al .c Q. r 30 20 10 CEMENTITE 850 900 950 1000 1050 1100 1150 Temperature fK] Figure 20: Output data of an MTData calculation of the equilibrium. Three phases are taken into account: ferrite, austenite and cementite. Figure 20 gives the concentration of unit cells of those phases as a fiinction of the temperature. The number of cementite unit cells is very low, even under 950 K, because this steel has a low carbon content (0.16 wt. %), and because the cementite unit cell is quite big compared to the ferrite and the austenite cells. Beside this, it is obvious that the ferrite (at low temperatures) has approximately two times more unit cells than the austenite (at high temperatures). This result can be drawn in such a way that we get the percentage of austenite as afiinctionofthe temperature. Indeed, this is the third curve of Figure 21. 33 3. Results Calculation upon heating 80 I 60 ZJ m "5 § 40 ••8 ^ 20 600 650 700 750 800 Temperature l°C] 850 900 Figure 21: Synthesis ofthe previously calculated curves for the austenite fraction. The first curve in figure 21 is thefractionof austenite during the cooling calculated by Theo Kop's program, the second one coiresponds to the cooling as well but calculated by the lever rule, while the last curve corresponds to the heating, by lever rule. The approximate positions of Acl, Ac3, Arl and Ar3 help to understand that the equilibrium curve is properly situated in the middle with respect to the heating and the cooling curves. A good thing would have been to calculate the para-equilibrium curve. In this case, the assumptions are that the carbon can still diffiise perfectly, but the bigger atoms like manganese and silicon, which are in a subtitutionnal solution position, cannot move, i.e. they remain well distributed among each phase. The para-equilibrium is a situation that can be reached in a few minutes, to the opposite of the complete equilibrium that requires several hours, maybe several days. An intermediate assumption is closer to the reality of an intercritical annealing of 10 minutes. 3.2 Calculation upon the heating data This part deals with different calculations based on the dilatometric data coming from the slow heating of the gauging experiment. The calculation method that is employed here is the one developed in the section 2.3.1.2. First results are about the ferrite (3.2.1 and 3.2.2); while others allow to produce a profile curve for the transformation of the ferrite into austenite (3.2.3). An interest of these calculations is the fitting of several parameters, which are summarised in the last part (3.2.4). 34 3. Results Calculation upon heating 3.2.1 Calculation of the expansion coefficient of the ferrite Here follows the results of a program that calculates the expansion coefficient of the ferrite. By using the least square method, it fits a parabolic curve with the experimental heating curve of the change in length as a function of the temperature. Figure 22 presents the experimental curve as well as the fitting curve. The second degree equation obtained for the parabola is : -2.939 +0.131* r+0.00003747 =0 (18) where the temperature is expressed in Celsius degrees. Let us remark that the second root of this equation should give the temperature of the room where and when the experiment was performed. As a matter of fact, the change in length is set to zero at room temperature. In this case it was 22.4°C. A correct result for the expansion coefficient can be found by dividing the 2 last terms by T. a f.,. = (0.131 + 0.00003747 * T) * lO"'* [K"^] =(13.1+ 0.003747* 7)* 10"^ [K"^] Exp coeff of ferrite in R730 Temperature f°Cl Figure 22: Fit ofa parabolic curve (red) to the heating part of a experimental curve (blue). 3.2.2 Lattice parameter of the ferrite and the cementite In the previous paragraph, a value for the expansion coefficient of the ferrite was calculated. Actually, our material is composed of ferrite with some cementite and the expansion coefficient used in the calculation should take into account the presence of cementite. The object of this part is the calculation of values for the initial (read at T = 20°C) lattice parameters for the ferrite phase and the cementite phase. One way to do that is to plot an 35 Calculation upon heating 3. Results experimental curve of a heating from 20°C to Acl, beside a second plot of a simulated change in length using given coefiBcients. The simulation can be done by using the formula (4) described earlier. A/_F'(r)-Fo As in this range of temperature the alloy is composed of ferrite and cementite, one needs to know the proportion of the phases. For a steel containing 0.16 wt. C, if we consider that all the carbon resides in the cementite, a quick calculation shows that there is 2.1 % of FesC. VQ is the initial relative volume, i.e. it is equal to P when T = To = 20°C. Here is an expression for V'(T), the current relative volume of the sample (it depends on the current temperature) : r{T) = 2* 0.979 *al{T) + y^* 0.021 * al{T) (20) where a a is the lattice parameter of the ferrite and ae is the lattice parameter ofthe cementite. Simulation for ferrite 0 200 400 600 Temperature PC] 800 Figure 23: Fit ofa calculated dilatation airve (red) to an experimental dilatation curve (blue). Figure 23 holds the experimental dilatation curve (blue) and the calculated dilatation curve (red and dotted). The deviation between them has been drawn on the Figure 24. Using the parameters aao = 2.8830 A, aeo = 4.5234 A, éeo = 5.0883 A, ceo = 6.7426 A, we have a correct estimation of the dilatation, since the difference remains small under A c l . This calculation takes into account only two phases, so it is not correct anymore once cementite starts to dissolve as austenite appears, i.e. once Acl has been reached. 36 3. Results Calculation upon Pleating Difference between experimental and simulation ^•4 c -6 D) C ^ -8 Ü -10 200 400 600 Temperature f^Cl 800 Figure 24: Difference between tiie curves siiowed on the figure 23. 3.2.3 Transformation curve Here comes an important result of this work. Using a calculation that implies the lattice parameter and the change in length as a function of the temperature, it was possible to determine the amount of austenite that appears during the heating of this low silicon steel. 3.2.3.1 Calculation Only two phases can be taken into account in the calculation : ferrite and austenite. That is why the temperature range on which it is acceptable starts at the end of the decomposition of the pearlite, i.e. when the only phases that remain are ferrite and austenite. Here is the expression for the change in length, adapted from equation (6) ^^'^: M 2*f,_j*al+f,_j*a'-Vo (21) 3*Va YQ /n (•0 ^ The -7 stands for intercritical. The idea is to calculate/y./ ( = 1 -fa-i) as the temperature and the change in length are known. The lattice parameter of the ferrite is given by the following equation : = « « 0 * 0 + 13-04*10-^* r-l-0.003702*10-^*7^) (22) and the lattice parameter of the austenite is (flyo+ci *A-, +C2*X2)*(1 + 23.5*10-^*D (23) Equations (22) and (23) are identical to the equations (7) except for the values of the expansion coefficients, which have been modified according to the above calculation. As the 37 3. Results Calculation upon heating solubility of alloying elements is much higher in the austenite, their concentrations have an important effect on its overall lattice parameter. One way to take this effect into account is to add a term including the weight concentration (x) multiplied by a coefficient (c). In the case of this alloy, the important elements in solution are the carbon and the manganese. The weight concentration of the carbon in the austenite is written xi while X2 stands for the manganese. Usual values for ci and ca are 0.033 and 0.00095 ^""^^1 Let us notice that the effect ofthe carbon is much stronger than the effect of the manganese. The silicon prefers to go in the lattice of the ferrite, so it does not exert a big influence on the lattice of austenite An important assumption that must be done was previously presented as the equation (8). In the intercritical region, all the carbon concentrates in the austenite. Indeed, carbon is gammagene, and diffusion is high enough at temperatures where austenite can appear, i.e. above Acl, since the carbon atom is small and diffuses easily. The solution ofthe complete equation can be found by using the Nev^on-Raphson method. Let us look at the result for heating up to 900°C. Annealing temperature : 900 "C 10 15 Time fminl Figure 25: Representation of the end of a heating to 900°Cfollowed by an intercritical annealing of 10 minutes The chart of Figure 25 describes the heating to 900°C of a sample in the dilatometer. The X-axis represents the time of the experience. As the heating rate is 100 K/min, 900°C is reached after 9 minutes. The dotted blue line is the temperature. The continuous line is the 38 3. Results Calculation upon heating change in length of the sample. And the third line represents the fraction of austenite, calculated with the equation (21). Simulation for austenite i 700 1 I ' 750 800 850 Temperature f-Cl Figure 26: Calculated fraction of austenite that appears upon heating to 900°C. This first result (showed again on Figure 26) was used in order to set parameters such as the expansion coefficient of the austenite and the coefficients for the carbon and the manganese. Let us look at the fraction of austenite as a function of the temperature. The upper part should remain at 100 % and it should be flat. The first thing is to define an expansion coefficient for which the slope of the upper part was equal to zero, and then define the coefficients c; and C 2 for carbon and manganese for which the plateau was set at 100 %. As a matter of fact, ci and C2 are fitting parameters. The finally chosen values are c\ = 0.046, C2 = 0.00103 and oCy = 23.5*10"^ K-'. Let us see now where goes this new "heating curve" with respect to the lever rule curves that were talked about in the part 2.2.2.4. On Figure 27, the green curve is the one calculated presently and that is plotted on Figure 26. Remember that the blue curves correspond to the cooling part, the black one is the equilibrium and the red one is the fraction of austenite during the heating calculated by the lever rule. 39 Calculation upon heating 3. Results 600 650 700 750 800 Temperature [°C1 850 900 Figure 27: Synthesis ofthe calculated curves for the austenite fraction as a function of the temperature. (Same chart than this of the figure 21, but with the curve of the figure 26.) Now that we have values for the fitting parameters, the calculation can be applied to a heating up to 750°C followed by an intercritical anneahng of 10 minutes. Annealing temperature: 750 °C 10 1200 12 14 Time fminl Figure 28: Representation of the end ofa heating to 750"Cfollowed by an intercritical annealing of 10 minutes. On Figure 28, the dotted line still represents the temperature just like on Figure 25, the continuous line is the change in length and the interrupted one is the fraction of austenite. One can notice that once 750°C has been reached, there is still some transformation all along the annealing of 10 minutes. At the end, the calculation of the equation (21) gives an austenite amount of about 46 %. Remembering the assumption that all the carbon concentrates in the 40 3. Results Calculation upon heating austenite, the carbon concentration can be calculated with the equation (8). The result is showed on Figure 29 and it stabilises at 0.35 wt. % C at the end of the annealing. This number will have an important influence on the fiiture transformation(s) of this austenite, since carbon slows down the formation of ferrite upon cooling Annealing temperature : 750 "C 100 80 'I 0.8 £> CT O Final fraction of austenite : 46 % 60 w 0.6 (0 •B c 40 0.4^ O S O ZI O (O Final [C] In austenite: 0.35 % 20 O 0.2 LL 10 12 14 Time fminl 16 18 Figure 29: Representation ofthe calculatedfraction of austenite, as well as the carhon concentration in the austenite during cm intercritical annealing at 750"C. Annealing temperature : 800 °C 1201 ' , , ' I i 1 I 5 10 15 20 Time fminl Figure 30: Representation ofthe end ofa heating to 800"Cfollowed by an intercritical annealing of 10 minutes. The third heat treatment in the heating part is an intercritical annealing at 800°C. Results of the calculation based on the equation (21) is showed on Figure 30. We can expect that there will be more austenite formed by the end ofthe annealing than in the case of the annealing at 41 Calculation upon heating 3. Results 750°C. The curves of Figure 30 show obviously that more than 10 % of the fmal austenite has been formed after the 800°C level was reached. According to the calculation, the fraction of austemte should be 91 % at the end of the 10 minutes anneahng. That would mean an austenite charged with 0.18 wt. % C, which is not very different from the overall concentration (figure31). Annealing temperature : 800 "C 100 Final fraction of austenite: 91 % 80 0.8 o c 1 60 0.6Bo (0 c ZJ O A0\ Final [C] In austenite: 0.18 % O (0 0.4§ n> O.2I 20 3 10 15 20 Time fminl Figure 31: Representation ofthe calculatedfraction of austenite, as well as the carbon concentration in the austenite on an intercritical annealing at 800°C. In order to set the ideas concerning the effects of the different annealing treatments, one can look at the pictures showed in the Figure 32 to 34. Remember that those resuhs are yielded by the calculation based on the equation (21). Only the phase fractions presented hereafter will be taken into account in the further calculations. 900 " C Austenitised at 900°C during 10 minutes. Carhon concentration in the austenite: 0.16 %. Figure 32 42 3. Results Calculation upon heating 800 " C Annealed at 800V during JO minutes. Carbon concenh'ation in the austenite: 0.18%. Annealed at 750V during JO minutes. Carbon concentration in the austenite : 0.35%. Figure 34 During the ulterior cooling, the ferrite will remain the same. What is going to interest us is what will happen to the austenite in the continuation ofthe thermal treatment. 3.2.3.2 Microstructure analysis The usual way to measure the fraction of phase in an intercritically annealed sample is to quench it to the room temperature and practice image analysis on the metallographic specimen. A sample was heated according to the temperature program described on Figure 35 and then quenched so that the austenite was completely transformed into martensite. Time [mini Figure 35: Heat treatment for the image analysis of a sample annealed at 750V. 43 Calculation upon heating 3. Results After having followed the procedure described in the section 2.2.2, the final result for the sample annealed at 750°C (picture 3) is a fraction of 44.2 % for the bright phase, which is the martensite. The standard deviation for the whole data is 2.77 %. The fraction of austenite is therefore around 44 % as well. 1.39kX UCillM 20kU HDilShird L. S; r r 7 P.00081 _ Picture 3 (RR7): SEM micrograph ofa sample intercritically annealed at 750°Cfor 10 minutes, then quenched to room temperature. Magnification : 1400 X. 4.09kX 10un 20kU UDUemm 8:06000 P i d S a s a Picture 4 (RR8): SEM micrograph ofa sample intercritically annealed at SOO^Cfor 10 minutes, then quenched to room temperature. 44 Calculation upon heating 3. Results The SEM micrographs of the sample annealed at 800°C were also analysed with Visilog, The result obtained yields 58,1 ± 5.2 % of martensite, i.e. austenite before the quench, 3.2.4 Fitting parameters Here is a table that summarises the whole set of coefficients that have just been defined. It includes the expansion coefficients, the lattice parameters, and the coefficients c; and C2 of the equation (23), These numbers are mostly inspired from a paper of Dyson and Holmes and have been refined to fit the calculation. In a first time, the assumption is that the composition of the alloy is the one given by Hoogovens, i.e. from the table 1, Mn Si C 1,5 0.4 0.16 Wt. % Table 1: Composition given by Hoogovens. For this composition, the parameters are presented in the Table 6 : = 2.883 [A] atO°C a = (13.1 +0.003747*T)*10"^ T expressed in °C ClQO = 4.5234 [A] at 20 °C bm = 5.0883 [A] at 20 °C Ceo = 6.7426 [A] at 20 °C a = Ferrite : Cementite : 5.311*10'^ - 1.942* 10'^*(T+273) + T expressed in °C 9.655* 10"'^*(T+273)^ Austenite : fl-yO = 3.5972 [A] a = 23.5*10"" Cl = 0.046 C2 = 0.00103 at 25 °C Table 6: Ciwsen parameters when the composition is defined by the tahle 1. The parameters have also been calculated assuming the composition that has been measured in Delft, i.e. from the table 2. Wt. % Mn Si C 1.47 0.28 0,14 Table 2: Composition measured at the TUDelft. 45 3. Results Bainitic transformation In this case, the only parameters that are different from those of the Table 6 are cj and C2> from the equation (23). As a matter of fact, these are the only parameters who depend on the concentration of the alloying elements. In this case, they must be set at: Cl 0.052 C2 0.0011 Table 7: Parameters for the influence oftite carbon and the manganese according to the composition defined in table 2. Nevertheless, it seems more appropriate to work with the composition of the table 1 because of the complexion problems that may have appeared during the chemical analysis with the ICP. 3.3 Bainitic transformation Firstly, the dilatometric curves will be observed and compared according to the thermal treatment applied to the samples. In the second part, there will be a short analysis of the microstructures obtained for the different annealings. And finally, we will see the results obtained by the calculations presented in the section 2.3.1 and applied to the data measured in 3.3.1. 3.3.1 Isothermal holdings 750 120| ^,00- QlZ 0 ' to 300 ' < ^ , . , 1 10 20 Time fminl 30 40 Figure 36: Typical dilatation curve of an experiment that comprises a bainitic holding. 46 Bain itie transforma tion 3. Results As explained in the introduction of this text, the usual way to stabilise austenite down tb room temperature is to impose a bainitic transformation. The mechanism is favourable to the survival of this phase out of its equilibrium. This is why I have been inquiring on the bainitic transformation for the composition previously described. In a first approach we will consider that nothing happens during the quench and that the transformation occurs only during the 15 minutes holding. The figure 36 shows which part of the measurement is interesting for us. The part where the curve is thicker corresponds to the isothermal holding, in this case, at 300°C. What defines the beginning of the holding is the moment when the temperature has been stabilised at the very end of the quench. This point is indicated on the figure 37. 5501 ' Quench to 300-C ' ' 250 200' 1054 ' 1055 —' 1056 1057 Time fsecl ' 1058 ' 1059 Figure 37: Sitape ofthe end ofa quench. The ring defines the moment when the isotlienncd transformation starts to be measured. For each of the three different annealing temperature, the curves corresponding to every isothei-mal holding have been reported on one chart with a logarithmic time scale on the Xaxis. The figure 38 contains the curves of the change in length during 15 minutes corresponding to the completely austenitised samples, i.e. austenitised at 900°C. The absolute vertical position of a single curve should not be taken into account as there may have been moves due to vibrations during the experiment. What is important is the absolute increase between the beginning and the end of the isothermal holding, and this is illustrated on the figure 39. 47 3. Results Bainitic transformation Series 900 "C 7 o * c 0) C3) c (0 x: O 10" 10 10 10^ Time fsecl Figure 38: Set of dilatation curyes corresponding to the isothermal transformations that takes place at different holding temperatures in the case of completely austenitised samples. Series 900 "C, fielding: 15 mln 50 40 f 30 f 20 c (0 Ü—fl-10 100 200 300 400 Holdina temperature f C l 500 Figure 39: Total variation ofthe length upon the 15 minutes holdings showed on figure 38. The results showed on the figures 38 and 39 are not like one could expect. Indeed, the absolute change in length should increase with lower holding temperatures, because the thermodynamical driving force for the transformation is increased as well. This behaviour is observed here only for the holding temperatures of 450°C, 400°C and 350°C. On the other hand, one can notice that the transformations appearing for the holding temperatures of 300°C and under are very light in comparison to the upper levels. The fact is that, in those cases, a martensitic transformation has occurred during the quench, and the light increase of the change in length during the 15 minutes is due to a precipitation of carbides in 48 3. Results Bainitic transformation the martensite ^ ' . Generally, the incoherence is explained by the existence of phase transformations during the quench. This problem will be discussed in the fourth chapter. Here comes the measurements on the isothermal transformations of the intercritically annealed at 800°C (figures 40 and 41). Series 800 "C Time fsecl Figure 40: Set of dilatation curves corresponding to the isothermal transformations that takes place at different holding temperatures for samples intercritically annealed at 800V. Series 800 "C, holding: 15 min 15r < o 10 •6) c ffl 0) O) c ro x: O 100 200 300 400 Holdina temperature f C l 500 Figure 41: Total variation of the length upon the 15 minutes holdings showed on flgure 40. On a first look, the result seems to be quite equivalent to the case of the samples completely austenitised (Figure 38 and Figure 39). But actually,ft)rthe highest holding temperatures, the relative variation is about 2.5 times less (look at the scale ofthe charts) : for the 15 minutes isothermal transformation at 350°C, the variation is here of 13*10"^ and it was of 30*10"^ 49 3. Results Bainitic transformation previously. This is surprising when one thinks that the starting amounts of austenite were of +91 % (according to the calculation) and 100 %, i.e. not very different. The explanation for such a difference in relative variation of the change in length must be given in the fourth chapter of this paper (section 4.2.1). What about the other intercritical annealing : 750°C ? Series 750 °C 80 ^ 60 o * t c «J c 40 0) ^ 20 m JZ Ü 10"' io'' 10° io' Time fsecl Figure 42: Set of dilatation curves corresponding to the isothermal tiansformations that takes place at different holding temperatures for samples intercritically cmnealed at JSOV. Series 750 °C, fiolding : 15 min 25 I ' ' i . r- < o •6) c 10¬ 0) O) c 5 . 5Qj l l l l 100 M i l l I l l l l I l l l l I l . l l 200 300 400 500 Holdina temoerature f C l I I 600 Figure 43: Total variation of the length upon the 15 minutes holdings showed on figure 42. One can still observe the gap between the high and the low holding temperatures, but this time, 300°C belongs to the group that allows an important transformation. It means that the 50 Bainitic 3. Results transformation temperature for the martensitic transformation (Ms) has decreased, hideed, i f we repeat the calculation of Ms with Andrew's equation (17), but this time for an austenite that contains 0.35 wt. % C, we get 290°C. This value is more than 100 K under the Ms of the completely austenitised steel. Another interesting remark is that the mean variation of the change in length all along the 15 minutes is slightly higher in this case than for the annealing at 800°C although there was less austenite to be transformed (45 % instead of 90 % ) . The charts of the figures 44 to 46 indicate the variation of the change in length for the first minute of the isothermal holding, When compared to the chaits for 15 minutes, it becomes obvious that most of the transformation happens during that first minute, as there is almost no difference between the results presented in these charts and those previously showed. Series 900 -C, holding: 1 mln Series 800 -C, holding: 1 mln 50 40 30 20 10 o —&• -10 100 200 300 400 Holdina temoerature f-Cl 500 100 Figure 44 200 300 400 Holdina temoerature f»Cl 500 Figure 45 Series 750 °C, holding : 1 min Ciiange in lengtii after 1 minute of isotiiermal iioldingfor : Austenitised samples (figure 44). Samples annealed at 800°C (figure 45). 100 200 300 400 500 Holdina temoerature f-Cl Samples annealed at 750°C (figure 46). 600 Figure 46 What is worth to be noticed is the value of the "750°C" series corresponding to the holding temperature of 300°C ( Figure 46). It is quite lower for a holding of 1 minute (7.5*lO"'^) than 51 3. Results Bainitic transformation for the 15 minutes (18*10"'*). It means that that treatment causes an isothermal transformation more widely spread in the time. Indeed, 300°C is still a little bit higher than Ms, and it is cold enough to slow down a diffusive transformation. 3.3.2 Microstructure analysis What is the effect of the annealing temperature on the bainitic transformation ? It is visible by the shape of the dilatation curve during the isothermal holding. A comparison between three experiments might help. Three bainitic holdings at 350°C have been plotted on the Figure 47: Quenches to 350°C -20' 0 ' 10 • 20 Time fminl • 30 ' 40 Figure 47: Dilatation curves for experiments with different intercritical annealing temperatures (750"C, 800T and 900V), followed by an isothermal holding at 350V. The three experiments showed on the figure 47 and, separately, on the figures 48 to 50 differ by their austenitisation conditions and have the same temperature of isothermal holding: 350°C. The annealing temperatures were 900°C, 800°C and 750°C. What is interesting for us is the shape of the curve after the quench; the three charts of the figures 48 to 50 have the same scale, so that the curves can be properly compared. Independently of the amplitude ofthe variation (that has been partly explained earlier), let us look at the slope of the curves, which gives an idea of the transformation rate. It is very fast in the case of the completely austenitised sample, whereas the higher carbon content of the third sample tends to slow down the isothermal transformation. Firstly, the rate of the transformation of austenite into ferrite is very dependent on the carbon concentration. Furthermore, it is not necessarily the same phase that forms since Ms depends on the carbon concentration in the austenite. After a full austenitisation at 900°C, Ms is around 400°C, and this means that the phase formed at 350°C is martensite. On the contrary, after an intercritical annealing at 750''C, Ms is around 300°C. 52 3. Results Bainitic transformation Microstractures corresponding to tlie three different treatments are visible on the pictures 5 to 7. One can see on the picture 5 that the austenitising treatment has increased the grain size from 5 pm to about 10 pm (It can be seen even better on the picture 11). On the other hand, the microstructures showed on the pictures 6 and 7 look quite hke those of the pictures 4 and 3 respectively, in what concerns the phase proportions. But the microstructure visible on the picture 7 is decomposed bainite, since the bainitic holding was performed at 350°C and Ms is around 300°C. From SOO^C 20 22 Time fminl 24 22 Time fminl Figure 48 24 Figure 49 From 750^0 Dilatation curves of experiments witii an isotiiermal Jiolding at 350"C, following a quench, from: 900°C (figure 48) SOO^C (figure 49) 20 22 Time fminl 24 750''C (figure 50) 26 Figure 50 53 3. Results Bainitic transformation Picture 5 (R935): SEM micrograpii ofa sample austenitised at 900''Cfor 10 min, then quenched to 35 "C and held at that temperature for 15 min. Picture 6 (R835): SEM micrograph ofa sample austenitised at 800°Cfor 10 min, then quenched at 350''C and held at that temperature for 15 min. 54 Bainitic 3. Results transformation Picture 7 (R735): SEM micrograpii ofa sample austenitised at 750°Cfor 10 min, then quenched at 350°C and held at that temperature for 15 min. 3.3.3 Calculation on the bainitic holding The section 2.2.1 has already described the equations that will be used in this part. Equation (6) will be applied to the completely austenitised samples, while the equation (9) stands for the intercritically annealed samples. The calculation is now possible because the dilatometric data is available since the section 3.3.1, and also because parameters have been summarised in the section 3.2.4. gOOi'G to 450^C 900^0 to 450^0 Figure 51: (a) Calculated fraction of austenite that disappears during the isothermal holding at 450°C, following a quench from 900''C. (b) Calculated fraction of bainitic ferrite that appears during the isothermal holding. 55 Bainitic 3. Results transformation Figure 51 shows the result for the isothermal transformation at 450°C, coming from 900°C. One should be aware that the scale on the Y-axis of the two charts are different. Unfortunately, this result is obviously wrong. It is simply impossible to keep more than 60 % of untransformed austenite at 450°C with this kind of steel. The reality is that there are not anymore 100 % of austenite at the beginning of the isothermal holding. We will try to solve that problem in the fourth chapter. What about the result for a sample intercritically annealed at 800°C ? (Figure 52) SOO^C to 4 0 0 S C 800^0 to 400^0 Time fsecl Time fsecl Figure 52: (a) Calculated fraction of austenite titat disappears during tiie isotiiermal holding at 400°C, following a quench from 800''C. (b) Calculated fraction of bainitic ferrite tiiat appears during the isothermal holding. Although 400°C is very far from the austenitic region, the fraction goes from 90 % to hardly 68 %. The problem is the same as in the case of the austenitised samples : there was not 90 % of austenite at the end of the quench. It seems that it is worse in this case : the calculation foresees the formation of 23 % of bainitic ferrite versus 37 % for the previous experience. At last, there is the isothermal transformation of a sample annealed at 750°C (Figure 53). The left picture suggests that there is a little bit more than 10 % of austenite remaining. But do not forget that it includes the cementite that is produced by the bainitic transformation. It is very acceptable in comparison to the two previous results; it seems that these data do not meet the same problem, i.e. some transformation of the austenite during the quench. Therefore, the experiments of the series "750°C" are chosen in order to draw a TTT diagram. 56 3. Results Intercritical annealing at 750 "C : test ySO^^C to 350^0 10 Time fsecl 750^0 to 350=0 10 10 Time fsecl 10' Figure 53: (a) Calculated fraction of austenite tiiat disappears during tiie isotitennal holding at 350°C, following a quench from 750°C. (b) Calculated fraction of bainitic ferrite that appears during tiie isothermal holding. 3.4 Intercritical annealing at 750-C: test This section is based on the study of a very particular experiment: the idea is to carry out an intercritical annealing at 750°C, but this time, coming from high temperatures. In a first time, the experiment is described, then the dilatometric results are presented, and the microstructure photographs come at the end. 3.4.1 Introduction Sybrand van der Zwaag has suggested a strange experiment: why not compare an intercritical anneahng that would follow a heating from room temperature as usual (figure 54), with an intercritical annealing that would be preceded by a full austenitisation at 950 °C (figure 55) ? R735 20 30 Time [mini 40 50 Figure 54: Classical heat treatment for the production of TRIP-aided multiphase steel. The intercritical annealing at 750°C is peiformed coming from low temperatures. 57 3. Results Intercritical annealing at 750 °C: test There are several ideas hidden behind this experiment: • To compare the amounts of austenite contained in the samples at the end of the intercritical annealing. • To compai'e the growth of the austenite grains inside a ferritic matrix with the growth of the ferrite grains inside an austenitic matrix. • To observe the influence of the starting microstructure on the kinetics of the bainitic transformation. • To look at the grain size of the austenitised samples. R9735 1000 _ l 800 a> a g. 600 § 400 200 0 0 10 20 30 Time [mln] 40 50 Figure 55: Heat treatment witli an inteixritical annealing at 750"C peifonned coming from a iiiglier temperature. Another way to understand this experiment is to look at the figures 56 and 57. During heating, when the dilatation curve crosses the dotted line at 750°C, the transformation has already begun. Whereas when cooling, the formation of ferrite hardly begins at 750°C. Now, what happens during the 10 minutes of annealing ? One may think that the volume fraction of austenite is going to evolve towards the equilibrium described by the MTData curve in the section 3.1.4. 58 3. Resuhs Intercritical anneahng at 750 V: test Heating and cooling at 3 K/min 600 650 700 750 800 Temperature \°C] 850 900 Figure 56: Dilatation heating curve (red) and cooling curve (blue). The vertical dark dotted line shows the temperature of the intercritical annealing. Ar3 100 ' ^ r Ac3 y I/ / 80 i 60 ^— O I Cool no/ Heatinc 40 (a 20 AH 600 650 700 750 800 Temperature ["Cl 850 900 Figure 57: Distiibution ofthe phases during cooling (blue) and heating (red). The dark dotted curve shows the temperature ofthe intercritical amiealing. 3.4.2 Dilatometry Before we observe the bainitic transformations, let us look at the annealings. The charts ofthe figure 58 and figure 59 show that although the annealings are performed at the same temperature (750°C) and for 10 minutes, the difference between the dilatations ofthe samples is quite important. Afirstexplanation for this deviation is that the phase distributions at 750°C is very diflFerent in the two cases. A quick look at figure 57 teaches that the sample that is cooled to 750°C contains a lot more austenite than the one that is heated to 750°C. Indeed the 59 3. Results Intercritical annealing at 750 "C: test 10 minutes holding cannot re-establish the equilibrium, And since the austenite lattice is more compact than the ferrite's, the sample with a lot of y phase presents a lower dilatation. 1401 ' < ' ' ^ ^ , Time fminl Figure 58: Dilatation curves of the experiments described by the figures 54 (red) and 55 (blue), but it is stopped at the end of the intercritical annealings. 1000 Figure 59: Dilatation curves ofthe experiments described by the figures 54 (red curve) and 55 (blue curve), but it is stopped at the end of the intercritical annealings. Let us look now at the bainitic transformation that follows these intercritical annealings. The figure 60 contams the complete curves of the experiments presented on the figure 54 and figure 55. The transformations that occur at 350°C after the quench have really different profiles. While the usual treatment, i.e. without austenitisation, yields a quite slow transformation, the other one produces a very fast reaction. The reason for this resides in the mutual austenite concentrations. Indeed, since the y phase ofthe austenitized sample is larger. 60 3. Results Intercritical annealing at 750 °C: test it has a lower carbon concentration than the y phase of the other sample. And it is well known that the the higher the carbon content in the austenite, the more the phase transformations are slowed down 3.4.3 Microstructure 120 ^100 < o ^ 80 s: 1 c 60 O) ro .c Ü 40 20 0^ 0 10 20 30 Time [mini 40 50 Figure 60: Complete dilatation curves ofthe experiments described by figures 54 and 55. Lookmg at the micrographs will help to compare the microstructures : in the first case, the austenite has grown in the ferrite, and in the second case, the ferrite has grown in the austenite. The microstructure of a sample intercritically annealed at 750°C has already been showed on the picture 3 in the section 3.2.3.2 devoted to the calculation during the heating. The austenite has nucleated on the grain boundaries of the pearlitic microstructure. The measurements showed that the sample contained around 44 % of austenite at the end of the annealing. It was investigated by both calculation and image analysis. Picture 8 that follows represents the sample that has undergone the treatment described by the figure 55. This picture is magnified only 65 times so that one can see the huge spots measuring nearly 1 millimetre. The microstmchire between the spots is banded, just Hke the one ofthe original samples received from Hoogovens. The big spots, visible on picture 8, measure more than 500 pm. They are fiilly martensitic with very large grains measuring sometimes more than 50 pm long (picture 10). On the other hand, the banded structure, which can be seen besides the martensitic spots on the picture 8, contains a mix of ferrite and martensite in similar proportions. Its grain size remains around 10 pm, according to the picture 9. This is more or less the same gram size than that ofthe samples completely austenitised and quenched under Ms (picture 5). It is obvious that everything that is martensite on the pictures was austenite before the quench to 350°C. 61 3. Results Intercritical annealing at 750 "C : test Picture 8 (R9735): SEM micrograpii at low magnificence of tiie sample tiiat lias undergone tiie treatment defined on tiie Figure 55. Picture 9 (R9735): SEM micrograph at high magnificence ofthe banded structure visible on the picture 8. 62 Intercritical annealing at 750 °C : test 3. Results • •: S i l l / • ' I / - , ;• ^ •'!•• i f , -Kl Picture 10 (R9735): SEM micrograph, at high magnificence ofa martensitic spot seen on the picture 8. 63 4. Discussion Heating calculation 4. Discussion The first section of this chapter (4.1) contains an interpretation of the calculation applied on the heating curve, which was developed in the section 3.2. It is foUowed by a short explanation of the results of the isothermal holding, and an investigation on the encountered experimental problems (4.2). The third point presents one of the most important outcome of this work : a TTT diagram (4.3), while the fourth part tries to retire information from the failed experiments (4.4). Another calculation method is presented in 4.5. The results of the exotic experiments on the intercritical annealing are discussed in 4.6. Finally, the appropriate ways for stabilising the austenite are presented in 4.7. 4.1 Heating calculation The results obtained in section 3.2 are summarised in Table 8. Calculation Image analysis Annealing at 750°C 46% 44.2 ± 2.8 % Annealing at 800°C 91 % 58.1 ± 5 . 2 % Table 8: Fraction of austenite calculated or measured at tiie end of tiie intercritical annealings. For the sample annealed at 750°C, the results of the calculation and the image analysis seem to agree quite well. Since the image analysis technique is accurate with a standai'd deviation of 2.77 % on 50 pictures, this is a good result. For the sample annealed at 800°C, the resuh ofthe image analysis yields 58.1 ± 5.2 % against 91 % for the calculation. A possible explanation for that great difference is that a part of the austenite has transformed into ferrite before Ms was reached. Looking at the curve that describes the quench (Figure 61), one can observe a slight hump in the slope, which could correspond to a partial transformation of austenite into ferrite This theory is confirmed by microstructural observations of the picture 4. Indeed, there are hints of ferritic laths peipendicular to the grain boundaries. This is the typical aspect of the Widmanstatten ferrite, which is nothing else than ferrite formed during a fast cooling. This 64 4. Discussion Bainitic transformation would explain the fact that the measured fraction of austenite is smaller than the calculated fraction since a part of it would have transform into Widmanstatten ferrite during the quench, 1401 ' Quench from 800 ' . ^ 1 120¬ . |iooi £ 80- § 60 • ö 40 ro I 20- O 0• .201 1075 ' 1080 ' ' 1085 1090 Time fsecl ' 1095 i 1100 Figure 61: Dilatation curve sixowing tlxe pitase transfonnation titat lias occurred during a quench from 800 "C to room temperature. A question that might be asked now is : "Why would there be a transformation during the quench in the case of the annealing at 800°C and not for 750°C ?", The explanation is that, in the first case, the carbon concentration in the austenite is high enough to prevent a transformation before Ms has been reached. In the second case, the cooling rate is not high enough to get rid of the formation of ferrite. According to the equation (8), the austenite of the samples annealed at 750°C contain about 0.35 wt. % C, against 0.18 wt. % C for the samples annealed at 800°C. 4.2 Bainitic transformation This section presents an interpretation of the results that were obtained in the section 3.3. Once the main problem is localised, it will be deeper investigated, with eventually the help of a CCT diagram. The last point of this section deals with the inaccuracies encountered with the stability of the calculation presented in the section 2.3.1.2. 4.2.1 Synthesis of the results on the isothermal holdings In the section 3.3.1, a big difference was measured between the change in length of the series 900°C (figure 39) and the series 800''C (figure 41) during isothermal holding, although the amounts of austenite that had to be transformed were close (100 % and 90 %). The average of the relative change in length was measured to be about 2.5 times less in the second case. This 65 4. Discussion Bainitic transformation problem can be explained by the fact that the quenches were not perfect, i.e. there were transformations during the quenches. In the case of the annealing at 800 °C, there was more transformation during the quench than in the case of the complete austenitising (900°C). Indeed, i f there is a big fraction transformed during the quench, the variation measured on the isothermal holding, which corresponds to the continuation of the transformation, is small. Another question evoked in the section 3.3.1 was : why is the change in length measured for the 750°C series (during isothennal holding (figure 43)) bigger than the change in length measured for the 800°C series (figure 41) although in this second case there is twice as much austenite to be transfomed ? The answer is that a big part of the austenite was transformed during the quench in the 800°C series, and nothing was transformed upon quenching in the 750°C series. The present section aims thus to investigate on what happens during the quench. The strange measurements of the section 3.3.1 have induced strange results in the calculations of the section 3.3.3. The results of the calculation applied to the dilatometric data of the isothermal holding are presented in the charts of the figures 51 to 53. It is deceiving for the series 900°C and 800°C, but it is acceptable for the series 750°C. Indeed, the proportions of stabilised austenite for the two first series are exaggerated. The problem resides in the fact that the program assumes that there is respectively 100 % and 91 % of austenite at the beginning of the isothermal holding. There was actually much less austenite left in those samples at that moment. Only the last series (annealing at 750°C) seems to present more acceptable results for the calculation. The following part attempts to give an explanation for this phenomenon. 4.2.2 Quenches Most of the experiments that were perfonned on the dilatometer BAHR805 presented a quench in their temperature program. One important advantage of that machine is that the sampling rate can be chosen up to 1000 Hz. When applying such a high sampling rate to the quench, it finally allows to draw a very accurate curve that describes the quench. In the set of the experiments performed, there are three different types of quenches, depending on the starting temperature : 900°C, 800°C or 750^0. 66 Bainitic 4. Discussion R910 transfonnation From 900=C to100=C 120 120 r 1140 1150 1160 1170 1180 Time fsec] 1190 1200 200 400 600 Temperature [-C] 800 1000 Figure 62: Dilatation curve ofa quench, from 900 °C showed (a) with the time as X-axis, (b) with temperature as X-axis. The charts of figure 62 represent the same quench from 900''C to 100°C : the first one with the time on the X axis and the second one with the temperature. An important transformation occurred ai-ound 600°C during the cooling. This is of course a problem for someone who wants to use that experiment to draw a TTT diagram. Actually, the cooling rate was not high enough. This is to be compared with quenches performed from intercritical temperatures. From 800^0 to 200^0 R820 1078 1080 1082 1084 1086 1088 1090 Time [seel 200 400 600 Temperature f-C] 800 1000 Figure 63: Dilatation curve ofa quench from 800°C showed (a) with time in abscise axis, (b) with temperature in abscise axis. Figure 63 show a quench performed from 800°C to 200''C, where there should be about 90 % of austenite at the beginning. An important transformation is visible around 700''C, which is sooner than in the case of the completely austenitised sample (figure 62). We will see later that those transformations at 600°C and 700°C are not exceptional phenomenons. Another 67 Bainitic 4. Discussion transformation characteristic of that quench is the existence of a plateau at the very beginning of the quench, and it is visible on the second chart. Finally, an analyse of the quench described by the figure 64, going from 750°C to 100°C, shows that it does not present any transformation before Ms (290°C) is reached. (Therefore that series could be used for the drawing of a TTT diagram.) R710 From 750»C to 100=0 Time [sec] Temperature [°C] Figure 64: Dilatation cwve ofa quench, from 750''C showed (a) witli time in abscise axis, (b) with temperature in abscise axis. One should remark that, alike the previous experiment, there is a plateau at the top of the slope on the second chait. Those plateaux are due to the effect of a temperature gradient from the core of the sample to its surface. When the helium blow begins, the surface is cooled earlier than the whole sample. And, as the thermocouple is welded on the surface, it indicates a lower temperature than the real overall temperature, which is naturally related to the exact change in length. Anyway, this artefact has no awkward consequences for the use of the data. AU the considerations established here are based on the analyse of several experiments for each one of the three cases. 4.2.3 C C T Diagram It has been stated that, for two series, the main problem in the quenching was the too low cooling rate. CCT diagrams are the appropriate tools to measure the critical cooling rate of a specific steel composition. The following diagram has been released by a program written by Pieter van der Volk, from the Materiaalkunde, TUDelft. The program is not finished yet, so the output (Figure 65) may look a little bit rough, nevertheless, the aim is achieved. 68 4. Discussion Bainitic transformation C C T diagram 0 1 2 3 loQ(Timefsecl) 4 5 Figure 65: CCT diagram for the composition described in table 1 and assuming that the material has been austenitised at 900"C. As usual, CCT diagrams are made for completely austenitised steels; in this case : at 900°C. Unfortunately, it does not produce CCT diagrams for steels that were intercritically annealed. The diagram is composed of four Hnes: FS (ferrite start), B S (bainite start), P E (pearHte end), (BE : bainite end). The user has to fmd his way through it by redrawing the curves with thicker plots. The program also calculates the position of a nose before which the ferrite cannot form. For this composition, the nose is at 6 0 I X and after 2.9 seconds. The critical cooHng rate values then: CCR - — = 2. .951 101.4 K/sec. There is no information about the critical cooHng rate required to get rid ofthe formation of bainite. 4.2.4 Stability of the calculations The results presented in the section 3.3.3. were yielded by a matlab program. It is important to know how the result can be influenced by a slight change in the input data. The figures 66 to 68 show the calculated fraction of bainite for three different input parameters. The three charts contain the so-called fractions of bainitic ferrite that appear during the isothermal transformations at 350°C of samples quenched from 750°C, 800°C and 900°C respectively. The curve in the middle is the one corresponding to the parameters of the table 6, while the upper curve corresponds to an increase of 0.1 % of the austenite lattice parameter, and the lower curve corresponds to an increase of 0.1 % of the ferrite lattice parameter. 69 4. Discussion TTT diagram for the annealing at 750"C Effect of a 0,1% variation on the 900 series Effect of a 0.1 % variation on the 800 series 0.25 10 10 10" Time fsecl 10" Time fsecl Figure 66 Figure 67 Effect of a 0.1% variation on the 750 series Calculated fi-action of bainiticferrite formed during an isothermal holding following an annealing at 900°C (flgure 66), 800V (flgure 67), 750V (flgure 68). The dark curve is the original, while the blue one corresponds to an increase of 0.1% of the austenite lattice parameter, and the red curve corresponds to an increase of 0.1% ofthe ferrite lattice 10 parameter. ^. , , 10' Time fsecl Figure 68 As one could expect, an artificial increase of the lattice austenite parameter induces an underestimation of the amount of this phase in comparison to the ferrite, which is therefore over estimated. And, logically, an increase of the ferrite lattice parameter has the opposite effect. What is very important to note here is that a slight change (0.1 %) in the input data can create, for a holding of 15 minutes, a variation of more than 5 % in the result. As a matter of fact, this calculation technique based on the lattice parameters is unstable, i.e. the error is quickly amplified. It means that it is dangerous to rely on the results without checking it by a different characterisation technique. This is a strong limitation to this type of calculation, and it is essential to be aware of it. 4.3 TTT diagram for the annealing at 750°C It was demonstrated in section 4.2 that the data corresponding to an intercritical annealing at 750°C were relevant to draw a TTT diagram since no transfonnation occurred during the quench. 70 4. Discussion TTT diagram for the annealing at 750°C Isothermal transformations - 1 -..-»rtÉ550°C --'-s^^^W500°C - Jf / n / / • U // / - 4500C /_».<*^4oo°c / / 300°C y250''C //:iC*-><^,»200°c ^ ^ . — • - ^ ' ^ ^ l 50°C VVWJyl»... 00°C ' 10° 10' 10 Time [sec] Figure 69: Calculatedfractions of transformed phase during isothermal holdings at 10 different temperatures The material was intercritically annealed at 750V. Figure 69 siiows tlie curves of tliefractiontransformed for the different holding temperatures, from 100°C to 550°C. This chart is available in the appendix of this paper for a better view. As thefractionof the so-called bainitic ferrite goes up to nearly 40 %, the Y-axis can be cut in seven pieces of 5 % in order to plot the TTT diagram. It is worth noticing that the 0 % transfonnation line cannot be defined this way, so it will be omitted. TTT diagram 6001 ' • Log Time fsl Figure 70: TTT diagram drawn on the basis of the calculatedfractions of phase transformed described in the figure 69. The diagram of the figure 70 is relatively regular except forthe holding temperature of SSO^C where there is a peak. There is no clear boundary between the bainite region and the ferrite 71 4. Discussion TTT diagram for the annealing at 750"C region, but this is normal for low alloyed steel ^^^\ On the other hand, we can see quite well that Ms is between 250°C and 300°C. The value of 290°C was calculated earlier with the equation (17). As a matter of fact, the martensitic transformation is extremely fast so that it occurs during the quench and the only thing that one can observe later is carbide precipitation, which does not produce an important change in length l^^-^'J. Because of kinetics reasons, the precipitation is more important at higher holding temperature, and it explains the slight levelling from 100°C to 250°C. Figure 71 and figure 72 show two camemberts as illustrations of the phase's disfribution inside the sample at the end of the isothermal holding at 500°C and 200°C, according to the calculation. 500 "C Bainite !35% Figure 71: Distribudon ofthe phases after the following treatment: 750^/ lOmin/ 500°C/ 15min, according to the Ferrite 55% calculation. 200 "C IVIart 25% Figure 72: Distribution of the phases after the following treatment: 750"C/ Ferrite 55% lOmin/ 200V/ IJmin, according to the calculation. Figure 71 : at 500°C, the phase that forms is bainite. According to the calculation, its amount goes up to around 35 %, so that there remains 10 % of untransformed austenite, which is quite a high volume fraction. The section 4.7 will come back to this part ofthe discussion. Figure 72 : at 200°C, we are between Ms and M f A linear relation between the fraction of martensite and the temperature leads to think that there must be something like 25 % of martensite versus 20 % of austenite remaining. This austenite will finally transform to martensite during the later cooling to the room temperature. Figure 73 shows a 3-dimensions TTT diagram based on this data. The surface contains the iso-transformation curves. This chart was drawn with the software Matlab. A bigger picture is available in the appendix. 72 4. Discussion Decayed series 3D T T T diagram Figure 73: Three-dimensions TTT diagram (the same as the one of figure 70). 4.4 Decayed series As described in the section 4.2, the data corresponding to the intercritical annealings at SOOT and 900°C were not relevant to plot TTT diagrams because of the parasite transformations taking place during the quenches. On the other hand, these dilatometric data contain many interesting information about the steel in a metallurgical point of view. The experiments were not pointless. 4.4.1 Quenches from 900°C 1201—• 1140 • 1145 Change in length • — 1150 1155 Time [sl 1160 1165 Figure 74: Dilatation curves of three quenches carried outfrom 900°C and called R910, RR9andRR9B. The quenches performed with the dilatometer present important inaccuracies. The user can be victim either of a lack of gas pressure during the blowing or of a lack of heat transfer by 73 4. Discussion Decayed series convection from the gas to the sample. Nevertheless, the use of helium is an amelioration compared to the nitrogen. In order to describe the difficulties that one meets when performing quenches, the charts of the figure 74 represent three quenches from 900°C under different aspects. Temperature • 10001—' 1140 1145 • • 1150 1155 Time fsl ' 1 1160 1165 Figure 75: Cun>es showing the temperature of the sample for 3 quenches from POOV. The first quench, called R910, was programmed at the cooling rate of 300 K/sec. Of course, one should be aware that the real cooling rate could never be so high, this is why the program put the quenching gas still available for 20 seconds more, which should be long enough for the sample to join the programmed isothermal holding temperature. Cooling rate 50 ' I A 1 - 50 5! 2- 100 O) 1-150 j^^^^^^^ RR9B tr° o Ü -200 RR9 -250 1140 1145 1150 1155 Time fsl 1160 1165 Figure 76: Instantly measured cooling rate for 3 quenches from 900 "C. RR9 was programmed to quench at the rate of 150 K/sec, and it managed quite well, in comparison with R910. Both transformations in R910 and RR9 are visible on figure 74 of course, but also onfigure75. The heat released by the transformation induces a slight hump in 74 4. Discussion Decayed series Picture 11 (RR9): SEM micrograpii ofa sample austenitised at 900''Cfor 10 minutes, then quenched to room temperature. It is fully martensitic. Grain size : ± 15 /um. (-1 (UJ I -•-^i Its.? - • ^ ¥ r / f h' n r wm -/}// Picture 12 (R910): SEM micrograph ofa sample austenitised at 900''Cfor 10 minutes then quenched to 100''C. Bainite or Widmanstatten ferrite. 75 4. Discussion Decayed series Picture 13 (R910): Optical micrograph, ofa sample austenitised at 900''Cfor 10 minutes then quenched to 100''C. Acicular ferrite of Widmanstatten. Figure 76 siiows the derivative of the curves showed in figure 75. It also gives an idea of the maximum cooling rates that have been reached (more than 200 K/s). The conclusion is that only the experiment "RR9" reaches Ms without having undergone any other transformation. A better control during the quenches for the whole set of experiments would have been possible i f hollow samples had been used. Indeed, hollow samples are lighter, which means a smaller weight of material that must be cooled with the same gas blow. Furthermore, it is possible to add a pipe in order to blow gas inside the sample. On the other hand, only solid samples allow to perform microscopy afterwards, since hollow samples are too thins. Picture 11 presents the microstructure of sample RR9, while picture 12 and 13 present the microstructure of sample R910. As expected, the first one contains 100 % of martensite, while the microstructure of the second one is more complex. The sample R910 has been firstly analysed with a scanning electron microscope (SEM) on the picture 12, and one could not say if the microstructure was constituted of bainite or Widmanstatten ferrite. According to H.K.D.H Bhadeshia, an optical microscope is more appropriate for the distinction between 76 4. Discussion Decayed series acicular ferrite and bainite. With an optical microscope, the bainite appears dark and the acicular ferrite appears clear, as can be seen on picture 13 R910 is acicular ferrite. 4.4.2 Elements for C C T diagrams If, for the intercritical annealing at 800°C and 900°C, the quenches are too slow for the construction of TTT diagrams, the experiments can still be useful to collect data for CCT diagrams. Indeed, the cooling rates were measured for each quench, as well as the temperatures where some transformation begin. The following figures might help to understand how measurements were done. R820 1000 1078 1080 1082 1084 1086 Time fsl 1088 1090 Figure 77: Measurement qf the cooHng rates after 0.5 and 2 seconds, and the average cooling rate. R820 120 ^100 ^ f 80 •a ^ 60 0) ? 40 ro 20 / 200 / 400 600 Temperature f°Cl 800 1000 Figure 78: Identification of the temperature of the transformation that occurs during the quench. 11 4. Discussion Decayed series The example showed on figures 77 and 78 is a quench from 800°C down to 200°C. On the first chart, one can see that the top and the end of the slope must be defined. Three values are calculated on figure 77: • the average cooling rate during the first half second. (135 IC/s in this case). • the average cooling rate during the two first seconds. (81 K/s), • the overall average cooling rate, (61 K/s). The second chart (figure 78) presents the change in length as a function of the temperature, which allows to identify the temperatures at which a transformation begins or ends. On this example, there is the end of a "temperature gradient effect" around 740°C (as related in the section 4.2.2), and the beginning of a transformation around 680''C. These measurements have been applied to all the quenches that have been performed in this work. The interest is, firstly, to see i f there are important variation for measurements that should be identical, and secondly, to get the transformations temperatures, for instance for the transformation that occurs during the quench from 800°C. The results for the quenches from 900°C are summarised in the table 9. From - To CR at 0.5 s CR at 2 s Average CR First Transf. 900-80 900-100 196 107 145 95 63 17 440 660 900-100 bis 41 41 38 600 400 900-150 132 107 54 560 "410" 900-200 137 111 57 560 "400" 900-250 140 106 61 600 "380" 900-300 135 103 51 600 900-350 134 137 85 "450" 400 900-400 130 119 86 "500" 400 900-450 126 111 77 580 900-500 149 140 120 "740" Sec. Transf. Table 9: Syntixesis ofthe parameters measured on samples quenched from 900"C. Except for the "900-100 bis", where the program was set at 40 K/s, and "900-80", which is an exception, the average cooling rates after 0.5 and 2 seconds do not vary too much, whereas the overall cooling rate is higher for shorter quenches, i.e. for quenches to higher holding temperatures. As one may notice that the instantaneous cooling rate does not stop to decrease 78 4. Discussion Decayed series all along the quench, it is normal that the average cooling rate of a longer quench will be slower. RR9b 1201— 0 1 200 r 1 400 600 Temoerature f»Cl 1 1 800 1000 Figure 79: Dilatation curve ofa quencit carried out from 900''C at 40 K/s. Concerning the temperatures of the main transformations, we can roughly identify 600°C and 400°C. In the table 9, the figures surrounded by quotation marks identify a less pronounced transformation. According to Andrew's formula, 600°C corresponds to the bainite start, while 400°C corresponds to the martensite start. The quench at 40 K/s aUows to see the formation of both bainite and niartensite. One can also notice that the slope of the curve is more important before the first transformation than after the second one. (oCaustenite > oCmartensite) From - To CR at 0.5 s CR at 2 s Average CR First Transf. Sec. Transf. 800-80 800-100 132 99 93 72 58 44 "740" "740" 700 700 800-150 128 88 67 "740" 700 800-200 135 81 61 "740" 680 800-250 114 74 61 "740" 700 800-300 103 71 64 "740" 700 800-350 129 94 84 "740" 700 800-400 138 91 86 "740" 700 800-450 101 71 67 "740" 715 800-500 142 97 92 "740" 680 Table 10: : Syntixesis of tiie parameters measured on samples quenciied from 800°C. The main characteristics of the quenches described by the table 10 are the end of the plateau around 740°C and the beginning of a transformation at already 700''C. At the beginning of the quench, the sample contains about 10 % of ferrite and the carbon enrichment of the austenite 79 4. Discussion Decayed series is around 0.18 wt. %. This amount of carbon is still low and cannot hinder a diffusive phase transformation, furthermore, the small ferrite phase (10 %) constitutes excellent nucleation sites. This explains the fact that in the case of an annealing at 800°C, the austenite transforms faster than after a complete austenitisation at 900°C (transformation at 700°C instead of óOO^C). From - To CR at 0.5 s CR at 2 s Average CR First Transf. Sec. Transf. 750-80 750-100 83 152 89 110 54 61 "725" "725" 300 290 750-150 130 94 64 "725" 295 750-200 101 103 79 "725" 300 750-250 81 72 61 "725" 290 750-300 96 79 69 "725" 750-350 120 94 90 "725" 750-400 107 78 71 "725" 750-450 77 72 71 "725" 750-500 113 102 102 "725" 750-550 132 102 104 "725" "680" Table 11: Syntiiesis ofthe parameters measured on samples quenched from 750"C. As for the 800°C series, the 750°C series, described on the Table 11, also show a pronounced "gradient effect" plateau whose end is around 725°C. For tempering at temperatures lower than 300°C, a fast phase transformation is observable near 290°C and it corresponds to the Ms temperature of the austenite charged with 0.35 wt.% C. No transformation was experienced above the martensite stait, and this is why the data coming from the 750°C series was kept for the drawing of a TTT diagram. Indeed, the reason why there was no parasite transformation is that the higher carbon content has stabilised the austenite enough to push the transformation noses to the right (on a TTT diagram) In a general way, one can see that, for comparable experiments, the values of the cooling rates differ quite much despite the fact that programmed cooling rate were identical. It is very difficult to get two times the same results, in what concerns the quenches. This illustrates the fact that even on a very good dilatometer, a quench is still something difficult to control, however it must be easier with hollow samples. 80 4. Discussion Remedy : formula applied upon the quench 4.5 Remedy: Formula applied upon the quench This part sketches out a technique for the calculation of the phase fraction transformed during a quench, in contrast to an isothermal tempering. In the equation (3) (— = express M=Y-YQ. V -V -), we can In the case of the isothermal holding, the reference (7o) for the calculation of the growth of the new phase was simply the change in length measured at the end of the quench, i.e. at the holding temperature, and when no transformation had occurred yet. This value could be kept constant as the holding was carried on in isothermal conditions. The method can easily be adapted to a non-isothermal transformation, if the reference 7o is properly dependent on the temperature. Hence in the coming calculation, Y will be the measured data while YQ will be calculated making the assumption that the phase fraction remains constant. Let us firstly look at the reference curve beside the data curve in the case of a quenchfrom800°C to 350°C on figure 80. Quench from QOO°C to 350''C Time fsecl Figure 80: Dilatation curves fi-om the beginning of the quench (8 OOV) to the end of the isothermal holding (350V). Red: experiment, blue: calculated assuming that the austenite does not trcmsform. Thanks to the logarithmic X-axis, it is easy to distinguish the quench, that lasts about 10 seconds, and the isothermal holding that goes on for 15 minutes. In this case, the reference curve YQ shows the change in length of a sample that would contain 90 % of austenite and 10 % of ferrite and that would not undergo any transformation. Something happens in the microstructure when the Y curve moves away from YQ during the quench (around 1 second). 81 4. Discussion Remedy : formula applied upon tlie quencit and we can see that there is still a transformation going on during the tempering because the change in length still increases. R835 1.51 • ' • . • 1 Figure 81: Fraction of bainitic ferrite calculated on tite basis ofthe results showed on figm-e 80. The values of AI = Y-YQ can now be used by the equation (6) or (9) in order to calculate the amount of bainitic ferrite. The figure 81 presents the result obtained for the example mentioned above. It indicates that the transformation starts after about one second, then it grows very fast until the end of the quench and it finally goes on slowly. A problem is that the bainitic ferrite fraction goes up to more than 100 %, which is impossible. That inaccuracy is mainly due to a bad estimation of the expansion coefficient of the austenite. On the figure 80, one can see that the calculated change in length at the temperature of 350°C is close to 0, which seems to low with regard to the previously observed experiments. From the beginning of this work, we have made the assumption that the expansion of the y phase as a function of the temperature is linear, and so that oty values 23.5*10"'' K"'. Actually, the expansion of the austenite is non-linear, and it is difficult to get good data for its expansion coefficient at lower temperatures. One way to refine this parameter is to choose a dilatometry experiment where we know that no transformation happened during the quench, and to make fit the calculated values of the change in length to the measured data. Indeed, the figure 82 shows the quench from 750°C to 350°C, The fit seems quite good in this case, as the curves remain close to each other, but looking at the figure 83, which is the calculated fraction of bainitic ferrite, we see that the growth of the ferrite phase is inverted when the YQ curve 82 4. Discussion Remedy: formula applied upon the quench happens to be above the 7 curve. It may be due to the fact that the experimental data are falsified by the "plateau" effect. This imperfection adds to the difficulty ofthe calculation. Quench from 7m°C to 350»C 100< O * 80- x: D) C 0) c <B O) c (Ö .c 60 • iY 40- O Vo 20 • 0^ 10 Time fsecl Figure 82: Dilatation curves from the beginning of the quench (VSOV) to the end of the isothermal holding (350V). Red: experiment, blue: calculated assuming that the austenite does not transform. 0.8| • • • ' 10° R735 — 0.61 -0.2' 10"^ • ^ 10^ • ' 10" Time fsecl Figure 83: Calculatedfraction of bainitic ferrite on basis offigure 82. As a final example, we may look at the figures 84 and 85, which show the result of this calculation applied to the quench of a completely austenitised sample, i.e. from 900°C. Hence there is a real problem with the accuracy of the evaluation of the expansion coefficient ofthe austenite phase. Solving this problem is quite difficult since a good estimation of this parameter would require new experiments, and in order to get a higher precision, the value 83 4. Discussion Remedy: formula applied upon the quench should be given by a polynomial equation taking the temperature into account to the third degree. Quench from 900°C to SSO^C I • 10"^ 1 • 10° 1 . 10^ 1 10" Time fsecl Figure 84:: Dilatation curves from the beginning of the quench (900V) to the end of the isothermal holding (350V). Red: experiment, blue: calculated assuming that the austemte does not transform. R935 1.5 a) 1 bai o c 0.5 raction »*o 0 .0.5i 10"' . ^ 10° ^ . 10' ^ 1 io" Time fsecl Figure 85: Calculatedfraction of bainitic ferrite on basis offigure 84. 84 4. Discussion Intercritical annealing at 750°C : test 4.6 Intercritical annealing at 750-C: test 4.6.1 Explanations for tlie gap between the annealings at 750"C The gap is visible in figure 58. Thi-ee explanations are faced : • The first explanation for the deviation between the two dilatation curves was linked to the difference in the phase fractions and to the fact that the austenite is more compact than the ferrite. It has been detailed previously. • A second track is the possible experimental deviation. Indeed, the absolute measure for the change in length is not always rehable : the height of two different dilatation curves can sometimes differ, especially when the treatment contains a quench, which might move the sample between the quartz rods (figure 7). But as there was no such operation for these experiments before the end of the annealing, this second explanation can be ignored. • Finally, a deviation can be seen in the fact that one of the two samples has undergone a holding at 950°C. As it has been austenitised, its pearlite has been decomposed and then it comes back in a different way. As a matter of fact, the pearlite formed after the hot rolling is not the same than the one that will be formed later, and thus the overall dilatation is changed. This theory was proposed by Theo Kop, from the Materiaalkunde in the TUDelft. 4.6.2 Microstructure The microstructure showed on the picture 8 is very strange because of its strong heterogeneity. Nobody could explain the reasons of that strange phenomenon. All the more, it cannot be due to a mistake since the experiment was performed twice, and since the dilatation data files prove the accuracy of the treatment. After a long time of thinking, the beginning of an explanation exists. The figures 56 and 57 show us that coming from 100 % of y phase at high temperatures and stopping at 750°C, we are really on the Ar3 point, which means that some ferrite should begin to appea:- in the austenite matrix. Actually, at Ar3, the driving force for the formation of ferrite is very low, thus very few nuclei of a phase succeed to reach the critic size. And, as the temperature is quite high, the diffusion is such that the surviving nuclei are able to grow quite fast. These words account for the partition of the microstructure in two : a fully austenitic region and a ferritic region. Now let us say that the austenitic region will become, during the quench, 85 4. Discussion Intercritical annealing at 750°C : test the fully martensitic structure that one can see on the picture 10, The problem now is : why is there a banded structure instead of huge ferrite grains ? As a matter of fact, the assumption of the growth of only a few ferritic grains does not hold since the picture 9 shows relatively smaU grains of ferrite beside grains of martensite (10pm). Nevertheless, the banded structure is related to the non-homogene repaitition of the manganese, when the metal is hot-rolled. As this element is in a substitutional position, it does not move a lot during the next thermal treatments, and thus it confers a so-called memory to the microstructure. Since the manganese is gammagene, austenite will appear preferably near it, and as a consequence, ferrite will appeal' preferably away from it. Finally, the distribution of the carbon through the microstructure is influenced by the distribution of the manganese, and it explains the fact that the pearlite is aligned in the sample "^^^l Furthermore, an important effect of this non-homogeneity is that the temperature A r l is different from one place to another depending on the local concentration in the alloying elements. This may have introduce different types of nucleation during the intercritical holding at 750°C. Unfortunately, it still does not give the key to the current problem. 86 4. Discussion Amount of retained austenite 4.7 Amount of retained austenite Since this research is partly an investigation on the possibilities of producing a low silicon TRIP-aided multiphase steel, it was interesting to observe the samples heat treated with the dilatometer and to look for possible retained austenite, Among the whole set of heat treatments, figure 86 recalls those that were applied for the study of multiphase steels. Treatments Time fmin] Figure 86: Tixermal treatments for tiie drawing of tiiree TTT diagrams. Three annealing temperatures were faced (750°C, 800°C, 900°C), and the duration of the annealings was of 10 minutes. Concerning the holdings, they were spread from 100°C to 500°C by steps of 50°C, and were lasting 15 minutes. Which of these thermal treatments are the most susceptible to give stabilised austenite ? As already written in the introduction (1,2,2), the stabihsation of the austenite is the resuh of a two-steps carbon enrichments : the first one during an intercritical annealing, and the second one during the formation of bainite, ideally on the second isothermal holding. Ever since, between the two annealing temperatures, the one that provides the best carbon enrichment is 750°C, as observed in the section 3.2.3. Then, for this series, which one of the holding temperature was the best ? Since the Ms temperature was calculated around 290°C for an austenite enriched at 0.35 wt. % C, and Bs was calculated at 600°C (with Andrew's formulas (16) and (17)^^^^), aU the levels comprised between Ms and Bs are worth to be analysed more closely. 87 4. Discussion Amount of retained austenite _ , — - — Picture 14 (R745): SEM micrograpii ofa sample annealed at JSO^Cfor 10 minutes, quenciied to 450"C, then held for 15 minutes. Picture 15 (R750); SEM micrograph ofa sample annealed at 750 °Cfor 10 minutes, quenched to 500°C, then held for 15 minutes. 88 4. Discussion Amount of retained austenite The samples corresponding to those treatments were thus analysed by scanning electron microscopy and X-ray diffraction (performed by Lie Zhao, from the TUDelft). The result of the microscopy analysis is that no stabilised austenite could be observed with the SEM, and the results of the measurements performed by X-rays prove to be very low. As a matter of fact, there was not enough silicon to impeach carbides precipitation in the austenite. The pictures 14 and 15 show the microstructures of samples annealed at 750°C and quenched respectively to 450°C and 500''C. One can see on both pictures 14 and 15 that the grain surrounded by ferrite is decomposed bainite. hideed, the clear lines that are crossing the grain are carbides that were precipitated on the sides of the ferritic laths during the bainitic transformation Retained austenite cannot be observed in these microstractures, neither by the SEM, nor by X-ray diffraction. Maybe this austenite is too thin to be detected by XRD. For high-silicon steels, large amounts of austenite had been obtained for a similar heat treatment : intercritical annealing at 750°C foUowed by a bainitic holding at 400-450''C for several minutes ^^^'^^l One can think that an unavoidable condition for stabilising austenite is to add a graphitising element such as silicon or aluminium in order to prevent cementite precipitation. This is not true and Pascal Jacques, from the Université Catholique de Louvain, has proved it. He has shown that it was possible to stabihse austenite in a low-sihcon steel and to obtain the TRIP effect For the composition : 0.18 wt.% C, 0.39 wt.% Si and 1.33 wt.% Mn, and by applying the following heat treatment; 730°C/5 min/370''C/l min, he could get up to 8.5 % of retained austenite. Furthermore, what influences the properties of a TRIP-aided steel is not only the amount of austenite that it contains, but also the stability of this phase. And as a matter of fact, the mechanical properties of the low-silicon TRIP-aided multiphase steel that was produced avowed to be excellent What explains the very low concentrations of retained austenite measured in the samples produced in the present work is the length of the isothermal holding. A bainitic holding of 15 minutes is too long (for a low silicon steel) since it aUows most of the austenite to transform by carbides precipitation ^^l (The Mössbauer spectroscopy measurements of Pascal Jacques give an amount of 2 % of retained austenite for a holding of 10 minutes ^^l) The austenite retention in low-silicon steels is only possible i f the kinetics of the bainitic transformation are taken into account. The bainitic holding must be long enough for the carbon to diffuse out of the supersaturated ferritic laths into the surrounding austenite, but it should be stopped before the transformation of this austenite. 89 4. Discussion Amount of retained austenite But one should keep in mind that one of the aims of the present work was to produce TTT diagrams, which explains the need to apply sufficiently long holding times, finally : 15 minutes. The samples could not therefore have undergone the ideal heat treatment for the production of TRIP-aided steels. 90 5. Conclusions 5. Conclusions This study investigated the heat treatments for the production of a low-siUcon low-carbon TRIP-aided muhiphase steel by means of dilatometry. Programs have been written for the interpretation of the dilatometric curves of, firstly the transformation a-^y upon heating, and secondly, the isothermal transformation during bainitic holding. The output of this second program have been used to release a TTT diagram for the phase transformations following an intercritical annealing at 750°C. For samples annealed at 800°C and 900°C, information on the transfomations that occurred during the quench have been reported. It may be useful to draw CCT diagrams, for instance. Moreover, a method for the measurement of the phase transfonnation during the quenches has been developed (Section 4,5). Besides the research for the TTT diagram, an experiment about the intercritical annealing has been canied out (Section 3.4). The observed microstmcture still constitutes a mystery. One should be aware that the calculation method developed in this thesis work require very accurate data for the different pai'ameters that describe the material. Moreover, the calculated phase fractions are very dependent on the input data such as the lattice parameters and the expansion coefficients (Section 4.2.4). Furthermore, perfect quenches are needed for the calculation of TTT diagrams: the use of hollow samples are therefore recommended for the dilatometry tests. The perspectives for the possible continuation of this work could be : • to get some new dilatometric data, but with hollow samples this time. • to try and refine the parameters for the calculations. • to integrate the programs in a more efficient programmatic language. For what concerns the steel grade that has been studied in this work, mechanical tests of this material are being cai-ried out currently at the university of Aachen, Germany. Furthermore, the possibilities of production of a TRP-aided multiphase steel of this composition have been investigated by Hoogovens. Laboratory simulations of a hot-dip galvanizing hne have proved to give a satisfying result ^^^l 91 5. Conclusions References [1] H, Shirasawa, "High-Strengtit steels for automative, symposium proceedings"; Slater, Baltimore, M D ,1994, pp 3-10. [2] I . Tamura, Metal Sc., 1982, vol 16, pp 245-252. [3] Anil K, Sachdev, Acta Metall., 1983, vol 31, n° 12, pp 2037-2042. [4] P. Jacques, PhD Thesis, UCL, Belgium, 1999. [5] P. Jacques, X. Cornet, Ph. Harlet, J. Ladrière, F. Delannay, "Eniiancement of tite Mecitanical Properties of a Low-Carbon, Low-Silicon Steel by Formation of a Multipitased Microstructure Containing Retained Austenite", Metall. Mater. Trans. A, 1998, vol 29A, pp 2383-2393. [6] H. Koh, S. Lee, S. Park, S. Choi, S. Kwon, N. Kim, Scripta Mater., 1998, vol 38(5), pp 763-769. [7] H. K, D. H. Bhadeshia, D.V. Edmonds, MetaU. Trans. A, 1979, vol lOA, pp 895-907 [8] M . Takahashi, H.K.D.H. Bhadeshia, Mater. Trans. JIM, 1991, vol 32, pp 689-695. [9] H.K.D.H. Bhadeshia, "Bainite in steels". The institute of Materials, London, 1992, pp 72-74. [10] O. Matsumai-a, Y. Sakuma, Y. Ishii, J. Zhao: Iron Steel Inst. Jpn. Int., 1992 vol 32 (10), pp. 1110-16. [11] Anne Mertens, Project for the FRIA, 1997. [12] G.R. Speich: "Fundamentals of Dual-Phase Steels", R.A. Kot and B.L. Bramfit, eds.. Trans. Met. Soc. AIME, Warrendale, PA, 1981, pp 3-45. [13] Jacobien Vrieze, Walter Vortrefflich, Laurens de Winter, Hoogovens Research report, 1999. [14] Bhadeshia H.K.D.H, "Thermodynamic analysis of diagrams", Metal Science, 1982, vol. 16, pp 159-165. http://Engm01.ms..ornl.gov/TTTCCTPlots.html [15] F. Delannay, "Compliments de Metallurgie Piiysique ", Cours MAPR 2420, UCL. [16] E. Girault, P. Jacques, K. Mois, P. Harlet, J. Van Humbeeck, E. Aernoudt, F. Delannay: "Material Ciiaracterisation", 1998, vol. 40(2), pp 111-118. 92 isotiiermal CE. transfonnation [17] L. Zhao, T. Kop, J. Sietsma, S. van der Zwaag, "Dilatometric analysis of bainitic transformation in TRIP steels", 1999, to be pubhshed in Euromat '99. [18] K.W. Andrews, J. h-on Steel Mst., 1965, pp 721-727. [19] Caian Qiu, Sybrand van der Zwaag, "Dilatation measurements of plain carbon steels and tiieir tiiermodynamic analysis", Steel Research, 1997, issue 1, pp 32-38. [20] D.J. Dyson and B. Holmes, J. t o n and Steel Institute, May 1970, pp 469-474. [21] N . Ridley, H. Stuart, L. Zwell, "Lattice Parameters of Fe-C Austenites at Room Temperature", Trans. Met. Soc. AIME, August 1969, vol 245, pp 1834-1836. [22] K. H. Jack, "Structural Transformations Martensitic Steels", Sept. 1951, pp 26-36, [23] J, Gordine, I , Codd, "Tiie influence of silicon up to 1.5 wt % on tiie tempering cliaracteristics ofa spring steel", J,of the Iron Steel Inst., April 1969, pp 461-467. [24] R.W.K. Honeycombe, H.K.D.H. Bhadeshia, "Steels", MMS, Edwai'd Arnold, 1995 (Sec. Ed,), pp 145-146. [25] A. A l i , M . Ahmed, F.H. Hashmi, A.Q. Khan, Metall. Trans. A, 1993, vol 24A, pp 2145-2150. [26] Y. Sakuma, D.K. Matlock, G. Krauss, Metall. Trans. A, 1992, vol 23A, pp 1221-1232. 93 in tiie Tempering of Higii-Carbon 6. Appendix 6. Appendix 6.1 Guidelines/Manual bainitic transformation analysis program Introduction This program calculates from a dilatometric data file the fraction of bainite that forms during the holding at the transformation temperature. It uses the lattice parameters of austenite, ferrite and cementite as well as their expansion coefficients. The calculation involves the solvation of an equation by the iteration method of Newton-Raphson. Two cases are taken into account : the quench is done from a complete austenisation temperature or from an intercritical temperature. The user is asked for the annealing temperature, and in the case it is intercritical, he must give the fraction of austenite that was in the sample before the quench. The user also has to introduce the holding temperature at which the isothermal transformation is meant to occur. Matlab environment To run this program, you need a Matlab software on your computer, In the main directory named ''matlab", a sub-directory (for instance -"bain") should be created in order to host the program files and the data files. This is also the place where the output files will be saved. At the beginning, the directory ''bain" should contain the following files which are the main program and its sub-routines : bainite.m,fprim.m, gtf.m. Pre-processing Make the input file. This is a table in wri format with 4 columns : anvthing(number of the value), time(s), temperature(°C), dilatation change r*10^V The table must start at the very first hne of the document, otherwise Matlab would not recocknize it as a matrix. Don't forget to put this wri file in the directory "bain". Processing hi the Matlab main command window, type : cd bain, then "enter", and bainite followed by "enter". After the program has started, you will be asked for the name of the input file. I f it is for instance data.wri, you must type : 'data' with the quotation marks. 94 6. Appendix Then you have to enter the name of the output file according to the same typing rules, for instance : 'output' and the file output.wri wiU be created at the end of the calculation and the results will be stored inside. Finally, you are asked for the annealing and the holding temperatures of the experiment. In the case it is intercritical, you have to type the fraction of austenite present in the sample at the end of the annealing. Post-processing The program has released two windows ; the first one contains a graph of the retained austenite as a function of the time, and the second one is the amount of bainite as a function of the time. The output file is a table of three columns : time(s), fraction of retained austenite, fraction of bainite. It can be converted then to an excell file or used as is by an other Matlab program. The interest of using Matlab is that the user can easily make modifications to the program, for instance: the lattice parameters. For details, see the Matlab Primer. 6.2 dispC Programs BAINITIC TRANSFORMATION'); % BAINITE figures out the fraction of retained austenite that appears % during the bainitic transformation of a low silicon steel % quenched from an intercritical temperature. The data needed % is a four columns text file that contains the time in the second % column, the temperature in the third and the change In length % in the fourth. BAINITE uses the Newton-Raphson method on the % function GRF, which has been written by Lie Zhao. % The output is a .wri file that contains three columns. The first % one is for the time, the second one is for the austenite fraction % and the third one is for the bainite fraction. global T, global DL, global FGI, global DLO; name = input('Name of the input file .wri ? '); eval(['load ',name,'.wri']); atemp = input('Annealing temperature ? '); If atemp == 900, FGI = 1; 95 6. Appendix else FGI = input('Fraction of austenite at the end of the annealing : '); end; htemp = input('Holdlng temperature ? '); [r c]=size(eval(name)); Time = eval([name,'(:,2)']); Temp = eval([name,'(:,3)']); deltal = eval([name,'(:,4)']); fgamma = zeros(r,1); bain = zeros(r,1); Time2 = zeros(r,1); counti = debut(name); % % The function "debut" finds the beginning of the isothermal holding, which defines DLO. DLO = deltal(countl); timeO = Time(countl); for count2 = counti :r, T = Temp(count2); DL = deltal(count2); fgb=0.5; twin=0; while (abs(fgb-twin)>0.0001), twin = fgb; fgb = fgb - (grf(fgb))/(fprim('grf',fgb)); if abs(fgb-twin)>1000, error('No convergence,'), end end; fgamma(count2) = fgb; Time2(count2) = Time(count2) - timeO; if ((Time(count2)<Time(count1)+900)+((Time(count2)>=Time(count1)+900)*(Temp(cou nt2)<htemp-5))==0), break, end end; % % % The "for" loop Is needed to go through the data. And the "while" loop is for the refining of the convergence in the Newton-Raphson method. bain = - (fgamma - FGI); figure(l); clf; semllogx(Time2(count1 :count2),fgamma(count1 :count2),'w'); title([num2str(atemp),'SG to ',num2str(htemp),'2C']); xlabel('Time [sec]'); ylabel('Fraction of retained austenite'); figure(2); 96 6. Appendix Clf; semilogx(Time2(count1 :count2),bain(count1 :count2),'w'); title([num2str(atemp);öC to ',num2str(htemp),'^C']); xlabel('Time [sec]'); ylabel('Fractlon of bainitic ferrite'); output = [Time2(count1 :count2),fgamma(count1 :count2),bain(count1 :count2)]; out = output'; fid = fopen([name,'op.wri -ascii'],'w'); fprintf(fid,'%4.4f\t %4.4f\t %4.4f\n',out); fclose(fid); function deb=debut(name) % DEBUT prend comme argument le nom d'un fichier % de donnees dilatometriques. II renvoie % alors I'indice de la ligne qui marque le debut de % la transformation bainitique. dat = [1090 1070 1025 1060 1030 910 1020 1025 870 858; 1200 1065 1075 1065 1040 910 1002 1020 861 0;1250 1157 900 1085 1125 870 995 1020 840 0]; asde = abs(name); ro = asde(2) - 54; te = 10*(asde(3)-48)+(asde(4)-48); CO = (te-5)/5; deb = dat(ro,co); function xprim = deriv(x) [r c]=size(x); xprim = zeros(r,2); forcount = 4:1:r-3, xprim(count,1) = x(count,2); xprlm(count,2) = (x(count+3,3)+4*x(count+2,3)+5*x(count+1,3)-5*x(count-1,3)4*x(count-2,3)-x(count-3,3))/(x(count+3,2)+4*x(count+2,2)+5*x(count+1,2)-5*x(count1,2)-4*x(count-2,2)-x(count-3,2)); end; function fpr = grfint(fgb) % GRFINT is a function used by the programme BAINITE. % The root of this function gives the value of the volume % fraction of retained austenite. This function is inspired % from the equation (13). global T, global DL, global FGI, global DLO; x i =0.16; 97 6. Appendix X2 = 1.5; aalpha = 2.883*(1+13.16-6*1+0.0037476-6*1/^2); agammab = (3.6008+x1/fgb*0,046+x2*.00103)*(1 +23.5e-6*(T-25))agammai = (3.6008+x1/FGI*0.046+x2*.00103)*(1+23.5e-6*(T-25)); fpr = (fgb*(agammab/^3-2*aalpha/^3)+FGI*(2*aalpha/^3agammai'^3))/(3*(FGI*agammai/^3+2*(l-FGI)*aalpha/^3))-((DL-DL0)/10000); 6.3 Three-dimensions TTT diagram

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