8.5.2 Structure after the Second and Third Passes141 8.8 Hot Rolling Simulation 144 8.8.1 Introduction 144 8.8.2 Strength During Hot Rolling 144 8.8.3 Structural Evolution 145 8.9 Discussion 147 8.9.1 Introduction 147 8.9.1.1 Original Grain Size 147 8.9.1.2 Surface Heat Transfer Coefficient During Air Cooling 148 8.9.2 Hot Rolling of 316L 150 8.9.2.1 Strength During Rolling 150 8.9.2.2 Microstructural Evolution During Hot Rolling 155 8.9.3 Hot Rolling Simulation 159 8.9.3.1 Simulation of Microstructural Evolution 159 8.9.3.2 Strength and Temperature Simulation 163 8.10 Conclusions 165 CHAPTER 9 HOT ROLLING SIMULATION BY PLANE STRAIN COMPRESSION TESTS 167 9.1 Introduction 167 9.2 Plane Strain Compression versus Axisymmetric Compression Tests 168 9.3 Temperature Evolution During Plane Strain Compression Tests 169 9.4 Hot Rolling Microstructure Simulation 172 9.5 Hot Rolling Strength Simulation 177 9.6 Discussion 179 9.6.1 Plane Strain Compression versus Axisymmetric Compression Tests 179 9.6.2 Temperature Evolution During Plane Strain Compression 181 9.6.3 Simulation of Hot Rolling Microstructure 183 9.6.4 Simulation of Hot Rolling Strength 187 9.7 Conclusions 190 CHAPTER 10 SUGGESTIONS FOR FURTHER WORK 192 ACKNOWLEDGEMENTS REFERENCES APPENDICES TABLES FIGURES SIMULATION OF HOT WORKING OF STAINLESS STEEL SUMMARY The published literature on the strength and structural changes occurring during and after hot working of AI5I316 and 304 austenitic stainless steels are reviewed. Isothermal plane strain compression tests have been carried out with the purpose of determining relationships to describe the kinetics of static recrystallization, the recrystallized grain size, the isothermal grain growth rate and the strength during hot rolling of AISI316 steel. The kinetics of static recrystallization were also studied in samples tested in axisymmetric compression, or hot rolled. The effect on the kinetics of static recrystallization of the strain distribution in samples tested in plane strain compression was analysed. The set of equations determined for 316 steel was used in a computer model modified from the one developed by Leduc (1980) for simulation of hot rolling loads and microstructural evolution. Partially recrystallized microstructure was generated in a laboratory hot rolling mill and was reasonably simulated by the use of the computer programme. Non-isothermal plane strain compression tests were carried out for direct simulation of laboratory hot rolling results. Comparison between experimental hot rolling and plane strain compression data has shown reasonable levels of agreement in the microstructural simulations undertaken in the present work. The mean plane strain strengths from non- isothermal plane strain compression tests were higher than the ones from hot rolling. This may have been caused by thermal gradients inside the sample being tested. CHAPTER 1 Introduction Hot working operations are those generally carried out . at -60% of the metal melting point and at strain rates - within the range of 0.1 to 1000 s 1 . Most finished metallic products have been hot worked at some stage during their manufacturing route. The careful control of processing as well as material variables during hot rolling can be used to generate materials with better mechanical properties. The simulation of hot rolling operations has been carried out in the past by numerical methods and by direct simulation using mechanical testing. Mechanical tests such as torsion or plane strain compression can provide information on the strength and structural behaviour of the material concerned. This information is translated into equations which can be used in a computer model to predict temperature, load and structural development during a given hot rolling schedule. A number of hot workability tests have been used for hot rolling simulation. These are reviewed in chapter 4. Most simulations however, have been carried out under isothermal conditions. The few non-isothermal simulations which have been performed were not satisfactory since the cooling rate of the samples and interpass times differed from the ones in the hot rolling process. Recently, non- isothermal hot rolling simulations were carried out in which the cooling rate of the specimen was controlled inside the test furnace so that it coincided with the one from the hot rolling slab. This technique allowed a direct comparison between microstructures with the specimen from the hot rolled slab. The hot rolling loads could also be suitably simulated (Foster,1981). However, in most simulation work, the material entering the following deformation was either fully recrystallized, e.g C-Mn steels for instance in Leduc's work (1980) or fully deformed, e.g Nb-steels (Foster,1981); Al- 1%Mn (Puchi,1983). In the present work, complete hot rolling schedules have been undertaken on an experimental rolling mill using austenitic stainless steel type 316. This material presents partially recrystallized structures in between hot rolling passes, which permitted a more critical appraisal of the simulation techniques used. It is expected that the methods employed in the present work may be applied to simulate industrial hot rolling schedules. CHAPTER 2 Strength During Hot Deformation 2.1 Flow stress Relationships. When stress-strain behaviour is examined over a wide range of different hot working conditions, it is usual to report a number of curves as typical examples and characteristic values of the flow stress as functions of temperature and strain rate. In order to correlate data at different temperatures, the Zener-Hollomon parameter is used, hence constant values of the activation energy, independent of the temperature, may be related to those for the rate-controlling process (Jonas et al.,1969). Sellars and Tegart(1972) have reviewed several equations which are attempts to fit simple algebraic functions to the stress- strain curve obtained at a constant temperature and strain rate. While recognizing the limitations of the expressions reviewed, they suggest that it is advantageous to apply them to experimental data so that constants can be reported from which flow stresses or the work done for any strain can be computed. The steady-state data at low stress are best described by a power relationship • A' n E = 11. a* (2.1) where n is a temperature independent constant (Loizou and Sims,1953; Alder and Phillips,1954-55; Jonas et al.,1969). The steady-state data at high stresses are best described by an exponential relation n ; = A exp ( B a* ) (2.2) where is a temperature independent constant (Loizou and B Sims,1953; Alder and Phillips,1954-55). The similarity between relations (2.1), (2.2) and the ones used for the steady-state creep led Sellars and Tegart(1966) to propose the expression n' E = A ( sinh a a* ) exp (-Q / (R T) ) (2.3) where A, aand n' are temperature independent constants and Q is an activation energy. The constants a, B and n' are related by , B a n (2.4) At low stresses (a a*<0.8) equation (2.3) reduces to a power relation (equation (2.1)) and at high values of stresses (a a*>1.2) to an exponential relation (equation (2.2)). Figure(2.1) shows that equation (2.3) can be used successfully to correlate creep as well as hot rolling data for aluminium deformed under several different kinds of tests (Wong and Jonas,1968). The previous equations can be used to predict a particular value of stress at a given deformation condition. However, these relationships restrict the application of the predicted value of stresses to strain conditions equivalent to those under which a* was obtained. Clearly, relationships capable of describing the stress at any strain for a given temperature and strain rate are required. For alloys which present a peak stress, Leduc(1980) has used the following set of equations, which apply to C-Mn steels: a -= a e if E<(x c P) (2.5) a = a e — Pa if E>(x Ep) (2.6) where a e = alo + B (1 -exp -C e )in (2. 7) (Sah et al., 1969) I- —1 I-- -x -1m' E Ep_ pa = B/ 1 - exp - k (2.8) E,,, P L - - where B = a (2.9) ss(e) — ao B (2.10) ' = a ss(e) - ass 6 - I- ---1 r- -11/m ao C = - 10 in 1 - (2.11) B - - _ - The a subscripts o,ss,ss(e) stand for zero strain, steady- state and steady-state extrapolated using equation (2.7). c P is the peak strain, n-0.8 for C-Mn steels and n, m, m' are temperature independent constants. Equations (2.5) and (2.6) give a complete description of the stress-strain curve provided that the original grain size and deformation conditions are known. Figure(2.2) illustrates the computational procedure used to calculate a stress-strain curve for C-Mn steel. At the same time an experimental curve is shown for comparison purposes. 2.2 Strength During Hot Working of Austenitic Stainless Steels. The maximum hot stress, ap , and the stress to a strain equal to 0.1' '01/ obtained from several different . sources for austenitic stainless steels type 316 and 304 hot worked under different kinds of testing conditions, with temperatures ranging from 800 to 1200 C and strain rates no higher than 100s-1 but mostly less than 5s-1 are shown in tables (2.1) and (2.2). It can be seen from table(2.1) that Q the activation energy for deformation, varies from def, author to author although the 3 reported values are for materials with nearly the same chemical composition and tested under hot torsion. It can be written then that 456 kJ/mol 7def = where the bar stands for average. The reported values of Q for 304 type steel are slightly higher for torsion than def the ones calculated from axisymmetric compression tests. The average value of 0 304 steel being -clef for 405 kJ/mol 7def. = therefore it may be inferred that def316 = 1.12 CYdef304 It is interesting to note that the strengths of 316 and 304 steels are in similar proportion to their Qdef values. Figure(2.3) and (2.4) show the dependence of a and 10.1 for the 316 steel on the Zener-Hollomon par amenter. It seems that an exponential type of equation describes reasonably the stress dependence on Z for all levels of stresses reviewed. As expected, the scatter obtained when 10.1 is plotted is bigger than that obtained for aP. This is simply explained in terms of the steepness of the stress-strain curve in the work hardening region. It is interesting to note that a is approximately equal to ao .1 at Z values of -107 (T-1200 C at c -5s-1 ). ap then becomes increasingly higher thanas temperature decreases. The same 10.1 characteristics shown by the 316 steel can be seen in the 304 type as depicted in figures (2.5) and (2.6).