Detailed technical report by Corus UK Limited
| Author | G. J. Watts- D. C. J. Farrugia- B. Cheong- Z. Husain- M. Zhou |
| Pages | 49-173 |
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Corus, in common with all the other partners is involved in reviewing constitutive models for the adoption or formulation of laws likely to be relevant for the materials and associated forming processes within their remit, particularly those involving complex loading paths viz. hot rolling of bar, plate and rod. In addition Corus employs at Swinden Technology Centre various experimental processes, as a means of readily providing data either for input to the models or for use in their validation. This equipment includes a Gleeble machine for testing in tension and compression, and laboratory bar and plate mills. Accordingly Corus has been engaged in the following work packages from the list given in the first part of this report and extracted from the Technical Annex.
WP1: Evaluation of Constitutive Models
WP2.2: Strain Reversal in Tension/Compression
WP2.4: Multi-directional Strain Tests
WP2.6: Stock Rotation during Rolling
WP2.7: High Speed Rolling
WP3: Material Characterisation
WP4: Formulation of Constitutive Laws
WP5: Incorporation of Constitutive Laws into FE Models
WP6: Model Validation
The contributions to these tasks are presented and discussed in Sections A1.2 to A1.7.
Models of all the types mentioned in the main section of the report have been used by Corus in the simulation of hot rolling and, in particular, in the analysis of the stock constitutive behaviour and its interaction with the process parameters. The aim of this section is to provide details of the models considered towards fulfilment of the aims of the project. This involves both usefulness of existing models in the various tasks of the project and scope for development in analysing the influence of the strain path.
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These are frequently used to relate bulk or external quantities, such as rolling load and torque, and deformed geometry to the process parameters. Notable models adopted are those of Orowan [A1.1], and Ekelund [A1.2] respectively for prediction of rolling load and torque, and stock width on exit from the pass. Each of these models, being quite sophisticated, is applied via a pc program and instantly gives reasonably accurate predictions which can be used in design of rolling schedules. Orowan's program requires flow stress data for the steels under consideration; these may be experimental data or obtained from an empirical formula in terms of strain, temperature and strain-rate. It is often assumed that such equations derived for bulk conditions apply locally and can be used in FE codes for prediction of internal stress and strain distributions. Such use is questionable, as (a) structural factors such as grain size are not generally included explictly and (b) it is assumed that the flow stress satisfies a mechanical equation of state i.e. that the flow stress responds instantly to deformation. Investigation of such formulae therefore forms a very important part of the project.
It may transpire, however, that use of such analytical flow stress models may give sufficiently accurate predictions under well defined conditions, not involving complex changes in strain path. Moreover improvements in accuracy can sometimes be obtained by adjustment of the formulae following comparison of predictions with experimental results.
Several analytical flow stress models have been used at STC, including the overstress power law and the Johnson Cook exponential law. Both are available in ABAQUS [A1.3] and are suitable for materials undergoing small deformation (i.e. hardening dominant) and subjected to small variations in strain rate and temperature.
The overstress power law model relates the stress and strain-rate viz.
[VER FÓRMULA EN PDF ADJUNTO]
Where [VER SIMBOLO EN PDF ADJUNTO] denotes the overstress i.e. the difference between the stress [VER SIMBOLO EN PDF ADJUNTO] and the static or back stress [VER FÓRMULA EN PDF ADJUNTO]
It is assumed that the shapes of all stress-strain curves are similar to the hardening curve defined by the input table. This assumption is clearly not suitable for materials which undergo large deformation and exhibit softening due to recovery and dynamic recrystallisation over a wide range of strain rate and temperature. Moreover, the power law relationships between strain rate and the flow stress may not apply for some loading conditions where high stress is involved [A1.5].
In the basic Johnson-Cook analytical model, hardening occurs isotropically, the static yield stress is expressed by a power law, equation viz:
[VER FORMULA EN PDF ADJUNTO]
Where [VER SIMBOLO EN PDF ADJUNTO] is the equivalent plastic strain and [VER SIMBOLO EN PDF ADJUNTO] is a dimensionless temperature parameter taking values between 0 and 1 (see [A1.3]) and the strain-rate dependence of flow stress is given by an exponential law.
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Although the model uses a power function to represent the hardening curve, it cannot describe material behaviour exhibiting saturated flow owing to recovery or flow stress drop associated with dynamic recrystallisation at high temperatures. Similar to the power law, the basic Johnson-Cook model assumes that the stress-strain curves have similarity in shapes for different strain rate, which is not true for most experimental data.
The Johnson-Cook model has been extended to include strain-rate the latter varying exponentially with yield stress [A1.3] so that the latter is given by the equation:-
[VER FORMULA EN PDF ADJUNTO]
Where [VER SIMBOLO EN PDF ADJUNTO] is given by Equation (A1.2).
The above Johnson-Cook model and overstress power law are suitable for high and low strain rates respectively. An alternative model shown to be satisfactory over a wide range of strain rates and temperatures [A1.6] is the Garofalo model [A1.7] in which the steady state strain rate is related to the saturated flow stress by the sinh law:
[VER FORMULA EN PDF ADJUNTO]
This law is suitable especially for materials showing a change in predominant deformation mechanisms from low to high stress levels at elevated temperatures. At low stress levels and strain rates, typical of diffusion processes, the relationship is essentially linear. At high stresses and strain rates, the relationship is highly non-linear (approximately exponential), characteristic of processes controlled by dislocation mechanisms and so potentially useful in models of hot rolling. However, it does not model isotropic and kinematic hardening and recrystallisation [A1.8].
To investigate the effects of loading path on the initiation of recrystallisation another analytical flow stress model [A1.9,A1.10] and an alternative definitions of the equivalent strain have therefore been explored by Corus in the previous ECSC project [A1.8] in which a modified sinh law is adopted given by:
[VER FORMULA EN PDF ADJUNTO]
Where R*=Rh (isotropic hardening) prior to dynamic rex and Rh +Rs subsequently and x is a back stress associated with kinematic hardening.
Temperature dependence is not shown explicitly in most of the above equations but is implied, empirical equations being established for the coefficients, e.g. A, satisfying an Arrhenius equation. Also not included is the dependence on grain size e.g. via a Hall –Petch type equation.
Moreover, to predict the effect of deformation on the evolution of metallurgical structure, equations need to be incorporated for the initiation of development of recrystallisarion and of grain growth. Several such formulae have been fitted empirically or derived theoretically based on the assumed grain geometry etc and stated in a previous ECSC project [A1.11], both for Type 316 Stainless steel and CMn steel.
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For Type 316 stainless steel, the following formulae obtained respectively by Barbosa [A1.12] and Jaiswal [A1.13] for grain growth (microns) in terms of the time t (min) and absolute temperature T have been used in the current project.
[VER FORMULA EN PDF ADJUNTO]
Similar formulae have been obtained for CMn steel by Sellars & Whiteman, and Leduc [A1.11]
For recrystallisation kinetics, a model has been used in which dynamic/static recrystallisation occurs according to the attainment or otherwise of a critical strain and evolves according to a JMAK law [A1.14,A1.15]. Generic formulae for the critical strain [VER SIMBOLO EN PDF ADJUNTO] Hand evolution including the time t0.5 for 50% recrystallisation taken from Ref. [A1.11] are reproduced in the equations below.
[VER FORMULA EN PDF ADJUNTO]
The static recrystallised grain size, [VER SIMBOLO EN PDF ADJUNTO] is given by
[VER FORMULA EN PDF ADJUNTO]
Specific values of the constants for Type 316 Stainless steel and CMnNb steel are given in Table A1.1(a-c). Other equations for Type 316 Stainless steel and CMn steel relating to recrystallisation and grain growth and also recovery may be found in [A1.11].
Temperature Equivalent Time for Recrystallisation under non-isothermal conditions
In obtaining the JMAK Equation (A1.7) for Type 316 stainless steel for the fraction recrystallised the Arrhenius rate term z=exp(-Qrex/RT) is integrated with respect to time. Under isothermal conditions this integral is trivial viz. multiplication by the time elapsed. Under non-isothermal conditions however, the time dependence of the temperature T should strictly be taken into account. Consequently the above term is multiplied by an average i.e. temperature equivalent time tequiv given by:
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[VER FORMULA EN PDF ADJUNTO]
Where [VER SIMBOLO EN PDF ADJUNTO] is the initial temperature for cooling (the final temperature for reheating) and T is dependent on the time t'.. (effectively [VER SIMBOLO EN PDF ADJUNTO] is the length of the base of the rectangle corresponding to isothermal temperature T0, which is equal in area to the area beneath the Z vs time curve when the temperature varies.
To estimate [VER SIMBOLO EN PDF ADJUNTO] a linear time dependence is assumed for the temperature i.e. [VER FORMULA EN PDF ADJUNTO]
Where [VER FORMULA EN PDF ADJUNTO] in this case is the temperature at the end of the time interval.
[VER FORMULA EN PDF ADJUNTO]
Using polynomial approximations in [A1.16] it has been shown that this expression can be approximated very closely by the simpler expression
[VER FORMULA EN PDF ADJUNTO]
Where g is the function defined by
[VER FORMULA EN PDF ADJUNTO]
This formula has been incorporated into a Mathcad file for ready implementation.
These are usually employed at the mesoscopic scale e.g. to determine internal distributions of stress, strain and temperature etc. A range of mesoscopic constitutive models are used at Corus and are implementable using the FE package ABAQUS, which is the principal commercial FE software package used at Corus to simulate the hot rolling process and is available in either ABAQUS/Standard and ABAQUS/Explicit [A1.17].
Three main classical plastic flow options within ABAQUS have been used by Corus viz.(a) elasto – plastic (b) viscoplastic and (c) creep with overlap between these options being possible in certain cases.
In elasto–plastic deformation, non-permanent deformation occurs prior to yielding. Although this is not usually significant in hot forming, elasto–plastic models of the latter have been developed. Such models developed at Corus assume the elastic deformation to be isotropic and so expressible only in terms of a Young’s modulus and Poisson’s ratio. Moreover, the metal is not usually taken to be perfectly plastic but to harden progressively with increasing strain. Generally, this hardening is assumed to be isotropic i.e. the increase in the yield stress is dependent on the magnitude of the strain and not its direction.
The default tabular input in ABAQUS [A1.17] has generally been used here because of its simplicity. The stress-strain data at various strain rates and temperatures are enteredPage 54following standard laboratory tests such as performed on a Gleeble thermomechanical simulator either in plane strain or in uniaxial compression mode. The flow stress at a given strain and strain rate is then determined from interpolation within the extreme boundaries of the data. No extrapolation is made for any strain, strain rate or temperature outside the defined conditions. However, during the rolling process, the strain rate varies continuously in the roll bite. Depending on the processing conditions (intermediate, finishing mills), it could be of the order of 102 s-1 or even higher, well above the strain rate conditions tested in most laboratory simulators such as on a Gleeble thermomechanical simulator, where the maximum achievable strain rate is approximately 25 s-1. This could lead to underestimation in the calculation of the flow stress at higher strain rates during rolling. Consequently, the rolling loads and torques could be affected, although the effects on deformation such as spread and shape may be small [A1.18]. The influence on rolling load and torque can be a significant drawback when using these techniques for ‘what-if’ applications and roll design optimisation.
Alternatively, empirical equations defining a functional dependence of yield stress on the field variables can be incorporated into ABAQUS. For the Johnson Cook law (Equation (A1.3)), there is a specific option allowing this in ABAQUS. However, for isotropic hardening, such as described by the exponential law, the user subroutine UHARD must be used [A1.17]. ABAQUS also allows kinematic hardening in which the yield surface is translated or deformed according to both the magnitude and direction of the strain increment. For the metal forming processes considered in the project, kinematic hardening is not believed to be very relevant unless there is excessive strain reversal. It is important however for strain paths involving repeated cyclic loading as in fatigue testing. A kinematic hardening model [A1.19] has been developed at STC in ABAQUS/Explicit using a VUMAT routine [A1.8]; other such models are being developed in conjunction with Birmingham University [A1.20].
In viscoplastic flow, the material deformation is dependent on the strain rate. This dependence can be implemented by selecting the RATE-DEPENDENT option in ABAQUS and by including, in the deck for each selected strain rate value, tabular data relating stresses to strains etc. The model can then integrated through time to give the deformation path and the stress- strain history. Other means are also possible of describing viscoplastic flow e.g. by specifying the ratio of the equivalent stress to the initial stress at various values of the field variables or by means of an equation incorporated using the user subroutine UHARD. Various viscoplasticity constitutive models [A1.18] have been developed at Corus representing the flow of steels at high working temperatures. The temperatures should include the adiabatic contribution from mechanical working and thus represent the flow softening associated with dynamic recrystallisation. This model has been validated for a concast steel Grade 43 and satisfactorily represents the work softening caused by dynamic recrystallisation.
Creep deformation is another means of simulating viscoplastic flow, one of whose key equations, viz. the overstress power law, Equation (A1.1), is formally similar to that for viscoplastic flow but with significantly different coefficients. This law can thus be included by invoking the CREEP option but with coefficients relevant to viscoplastic flow.
All the above models, however, do not explicitly take into account the microstructure. Although microstructural dependence of flow stress etc can be introduced via the coefficients and the local effect of stress, strain and temperature on fraction recrystallised etc. can be determined using equations such as those in Section A1.1 implemented in ABAQUS via a UVARM or the calculator utility, such approaches are likely to give a limited or even inaccurate picture of the influence of loading path on microstructure as they assumePage 55the behaviour at the microscopic level is the same as that observed at the macroscopic level and, more significantly, neglect its interaction with that at the mesoscopic level. Coupling of the mesoscopic and microscopic behaviour requires more sophisticated approaches as discussed below.
More complex constitutive models, with additional 'mesoscopic' variables implicitly containing information of the microscopic behaviour and satisfying a variety of functional relationships can be introduced [A1.9,A1.21]. Examples of such variables are (a) Critical strain for dynamic recrystallisation – initiated as described above (b) Drag stress -softening associated with dynamic recrystallisation (c) Back stress Xij - kinematic hardening described by the developed by dislocation pile-up and retarded by dynamic recovery (d) Isotropic hardening. These satisfy a hyperbolic flow rule typical of dislocation controlled deformation involving the back stress and isotopic hardening and flow softening caused by dynamic recrystallisation. Such models can be constructed in ABAQUS/Standard using the complex user subroutine UMAT [A1.8]. Indeed, the above additional variables were incorporated into a thermo - elasto - viscoplastic model by Dunne [A1.10 ], adopted in the previous project [A1.8]. The equations for this model are given in the final report of the latter. With variables (b-d) set to zero and the critical strain effectively set out of range of the strain predictions, the traditional elasto-plastic model is obtained. It was decided, to explore the viscoplastic constitutive model described above both with and without the options of isotropic and kinematic hardening and softening.
The determination of the coefficients appearing in such models, however, is itself a significant issue in the formulation of constitutive models; It can be achieved in a number of ways. (i) They can be estimated empirically by obtaining a closely fitting equation (using regression or genetic algorithms (GA)) to load data determined experimentally at various strain-rates etc. This approach however suffers from the drawback that the data relate to bulk rather than mesoscopic deformation. (ii) Alternatively, they can be estimated by optimising the fit of FE predictions of these parameters obtained using various sets of the parameters. Although this may generate a model giving accurate predictions of bulk parameters it may not be suitable for predicting the internal stress and strain distributions and structural properties such as grain size which are partially dependent on the latter.
Augmented mesoscopic models such as those above cannot completely represent material behaviour since they do not explicitly contain microscopic variables and so cannot their evolution and interaction. To understand these processes fully, it is necessary to relate directly the mesoscopic variables to the underlying mechanisms of dislocation dynamics and to incorporate these relationships into a phenomenological model [A1.22] containing the relevant internal variables and additional equations.
A significant internal variable in these models is the dislocation density. Dislocation dynamics models use dislocation density as a history dependent internal variable [A1.23,A1.24] to represent the microstructural changes and macroscopic response of flow stress during hot rolling. They take account of the generation, accumulation and interaction of dislocations (both mobile and immobile) and their annihilation through recovery and recrystallisation. Combined use of dislocation density based and viscoplastic models provides a good means for handling complex loading, since they can predict complex history-dependent and time-dependent material behaviour including changes in flow stress and are able to trace the strain path.
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Corus has, accordingly, utilised the dislocation model developed by MEFOS, which takes account also of recrystallisation and the vacancy concentration [A1.8] incorporating it into an ABAQUS FE program for hot rolling of steel by means of a UMAT user subroutine. Problems of numerical stability however, arise when integrating the equations unless extremely small time steps are taken. The method of implementation within ABAQUS v6.3 is also being assessed viz. using the *CREEP card or using the UMAT routines, the former option being the easier. For the latter, studies have been commenced into incorporating the exact Jacobian instead of the elastic D matrix used previously. It is considered that this allows larger, reasonable time steps to be used with good accuracy.
Another key variable is the grain size. The unified constitutive model has been developed by Birmingham University [A1.20] in conjunction with STC. Based on physical mechanisms for evolution of grain size in addition to dislocation dynamics, recovery, dynamic and static recrystallisation and their coupling with viscoplastic metal flow, this model has been explored in the latter stages of the project. It is frequently assumed that the metal prior to rolling has a uniform grain size, the stock having been adequately soaked in the reheating furnace. In practice, this is found not to be the case, metallographic examination revealing grains of various sizes distributed throughout the stock and even locally a statistical distribution occurring of significantly large standard deviation. It is generally assumed that this distribution is lognormal [A1.25]. If the mean and standard deviation of this distribution are denoted by d and s respectively then it can be shown that upper and lower limits for the grain size, with less than 1% significance are given by
[VER FORMULA EN PDF ADJUNTO]
This expression is useful in estimating maximum and minimum grain sizes as in the analysis of experimental results in Section A1.3.3.
Distributions of grain size clearly arise during the process because of the thermomechanical processing. A number of programs exist in-house, and have been used in this project, for estimating the evolution of grain size, both recrystallised and unrecrystallised and the fractions recrystallised etc. and for calculating the effect on load. They are based on simple assumptions regarding strain and temperature distributions and are used only as a guide e.g. in the drawing up of schedules. For a detailed analysis of the metallurgical evolution, phenomenological models should be used instead. Those models mentioned above, however, assume that the initial conditions etc are known and neglect, for example, statistical distributions such as mentioned above. They also neglect the random nature of phenomena such as nucleation of grains, (that of porosity in ABAQUS being an exception). In-house software exists for determining the distribution of a quantity functionally related to a quantity such as grain size for which the distribution is given but not when the relationship is more complex e.g. via a set of algebraic or differential equations. The way forward is to develop probabilistic or stochastic models [A1.26] which examine the influence of randomness in process parameters to the overall response of the system.
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Use of tabular input in ABAQUS of incomprehensive data for flow stress due to strain rate limitations etc. in the test equipment, can, because of the non-extrapolation in ABAQUS, result in its underestimation during hot rolling simulation and so incur discrepancies in load and torque predictions. Moreover, use of comprehensive data, even if available by sophisticated experimentalPage 57techniques, although ideally giving optimal accuracy, would prove cumbersome to use in practice. A suitable constitutive model is therefore preferred.
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The overstress power law model and the Johnson-Cook analytical flow stress models are available in ABAQUS and are suitable for hardening dominant materials subject to small displacements and strain rate and temperature variations, but not for materials undergoing large deformation and exhibiting softening due to recovery and dynamic recrystallisation.
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For complex loading conditions in hot rolling etc such as strain reversal and bidirectional loading and changing metallurgical structures e.g. associated with partial recrystallisation, the above-embedded methods in ABAQUS are insufficient. Better solutions for handling complex loading are provided by the incorporation via a UMAT into ABAQUS of viscoplastic and dislocation density based models since these can predict complex history-dependent and time- dependent material behaviour and so are able to trace the strain path and its effect on flow stress.
The various options available at Corus for constitutive modelling with comments evaluating their feasibility are contained in Table A1.2. At the end of this table, the models selected for use in this project and/or further development are itemised.
Objectives
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To investigate the effect of alternating tension and compression on stress strain behaviour and recrystallisation kinetics
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To compare the results obtained with those in the analogous process of reverse rolling.
(a) Calibration of the test specimen and the true stress/strain calculation method
To investigate material behaviour of CMnNb steel and 316 stainless steel during strain reversal, it was proposed to use fatigue specimens which would allow compression and tension behaviour being tested in the same test piece. However, the conversion of stroke- force data recorded by the Gleeble simulator into the true stress/strain data proved to be challenging because of the unavoidable barrelling effects in the specimen. Various methods were investigated to convert stroke-force data into true stress/strain data, including ‘hot zone’ method in which the conversion of data was based on the hot zone in the specimen, ‘C-gauge’ method in which the variation of specimen diameter was measured directly by a gauge meter, method of extension of gauge length with attempt to reduce the barreling effects, as well as the ‘constant volume’ method.
The results for extension of specimen gauge length showed that there was no significant difference in true stress/strain data compared with those for the original specimen geometry. The hot zone method which reflects the real deformation region indicated that there was no further improvement. The C-gauge method did not give a reliable measurement in the tension part in compression-tension mode because barreling occurs in compression.
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Discussions were held with the University of Oulu on how to minimise the effect. Consequently the fatigue specimens were redesigned, with a more suitable gauge length to diameter ratio. Diagrams and photographs of the specimens employed are shown in Figs. A1.1 and A1.2.
In addition, it was found initially that the resulting true stress/strain curves were significantly different for tension and compression and consequently the results would affect the interpretation of the subsequent stress relaxation data. The problem was solved by imposing an homogenisation treatment on the CMnNb steel plates at 1250°C for 24 hours, which effectively removed segregation existing in the steel plates, from which the fatigue specimens were machined (following scraping of the decarburised material). Consistency of the tension and compression behaviour was then achieved.
(b) Initial strain reversal tests
Tests were carried out to check the suitability of Husain’s method [A1.27] for CMnNb steel specimens deformed, at a temperature of 1100°C and a strain rate of 1 s-1, (a) in compression to a strain of 0.2 followed by a tensile strain of 0.2 and (b) to a total strain of 0.4, without reversal. Graphs, for both these cases, of the stress relaxation, the stress-strain variation and recrystallisation behaviour are shown in Figs. A1.3 – A1.5 respectively.
These confirmed that useful information could be extracted using this technique. They are discussed in more detail in Section A1.4 on material characterisation.
(c) Further tests
Further testing was carried out on specimens pre-heated to 1200°C, and held for 15 minutes to dissolve the Nb particles. The schedule employed was that shown in Fig. A1.6 using temperatures of 1000°C, 1050°C and 1100°C. Following deformation, stress relaxation tests were carried out to investigate the recrystallisation kinetics.
Strain reversal tests using CMnNb steel fatigue specimens on the Gleeble simulator were completed. The deformation conditions included 0.4C (compressed to a strain of 0.4),0.2C+0.2T (compressed to a strain of 0.2 and followed by a tension to a strain of 0.2) and 0.2T+0.2C in each testing temperature 1000°C, 1050°C and 1100°C.
Figures A1.7, A1.8 and A1.9 show the stress-strain curves at the three temperatures for the 0.4 compression tests and strain reversal tests of 0.2T+0.2C and 0.2C+0.2T, respectively. No significant differences in temperature effects were observed but notable Bauschinger effects were evident. Similar conclusions can be drawn from the stress-strain curves shown in for compression followed by tension.
Figures A1.10 and A1.11 compare the results of compression with those of the strain reversal 0.2 C +0.2 T and 0.2 T +0.2 C respectively. Comparison of the first part of the curves demonstrates the repeatability of the test and shows that the compression and tension behaviour is reasonably matched (i.e. corresponding stresses of similar magnitude but opposite in sign).
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Figure A1.12 compares the results of the two cases of strain reversal, viz. 0.2T+0.2C and 0.2C+0.2T. It is noticed that only a strain of 0.16 was achieved in the case of 0.2T+0.2C; this may have been caused by the control of the Gleeble machine. It is also observed that 0.2T and |0.2C| match very well and the final stress level is very similar.
A symmetrical cyclic/reversal test was also carried out in order to quantify the Bauschinger effect. The testing temperature was 1100°C and the straining range 0.3. The cyclic data are shown in Fig. A1.13. The Bauschinger effect is not significant in this case; more noticeably, there exists a difference of about 20 MPa in stress level between the steady state cycles and the first two cycles.
The evolution of recrystallisation curves for the above strain paths are shown in Figures A1.14, A1.15 and A1.16 for temperatures of 1000°C, 1050°C and 1100°C, respectively. It is observed that t50 (the time corresponding to 50% recrystallised volume fraction) is similar for 0.2T+0.2C and 0.2C+0.2T but somewhat different from 0.4C, suggesting that 0.2T+0.2C as well as 0.2C+0.2T have different recrystallisation kinetics from 0.4C despite having the same equivalent plastic strain.
Objectives
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To investigate the effects of multidirectional compression on the recrystallisation kinetics
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To compare with the recrystallisation kinetics of horizontal-vertical (H-V) rolling
Experimental method
Compression testing was carried out on the Gleeble machine at Swinden Technology Centre. Since this model provides compression in a single, fixed, horizontal direction only, deformations could not be applied in different directions simultaneously and so were applied consecutively i.e. by rotating the specimen after the first pass as required. To eliminate effects of specimen geometry, cubic specimens were used because of their symmetry properties. The edge length of the specimens was 10 mm. Compression was carried out on pairs of opposite, horizontal facing faces and the deformed specimen rotated through 90° in a horizontal or principal vertical plane as required, shown schematically in Fig. A1.17. The tests clearly allow several combinations of rotations and non-rotations to be considered, some of these sequences being analogous to those commonly occurring in industrial hot rolling and in particular, horizontal–vertical (H-V) rolling, in which the stock may be turned through 90° in a transverse plane between passes. The aim was thus to establish the differences obtained between turning and not turning the specimen, all other factors including magnitude of the reductions being unchanged.
In order to isolate the effects of strain path pertaining to stock rotation it is important to eliminate extraneous effects particularly those associated with structural heterogeneity and thermal variation. To reduce the effects of the former, the specimens were heated for 30 minutes to coarsen the grain size. In the second case, ideally the specimens should be heated uniformly and constant temperature maintained during testing. To establish complete thermal and mechanical contact after turning barreling should also be minimised. When turning the specimen after the first deformation, this is impossible to achieve on the local model of the Gleeble because of the substantial heat loss from such a small sized test specimen. However, the effects on structure were avoided or, at least, minimised by Page 60quenching the specimen after the first compression. The specimen was then turned, if required, reheated to testing temperature and held at this temperature for 1 minute before carrying out the second compression and requenching. To assess the feasibility of the procedure, the microstructures (respectively quenched after the first compression and reheated for the second compression) were examined and compared.
The above experimental procedure is shown schematically in Fig. A1.18.
Even if steady and uniform temperature distributions are achieved, the magnitude of any effects of strain path on structure may be dependent on the value of the temperature. An experimental design was adopted in which the effect of temperature was first investigated for a few simple strain paths, followed by a study of a number of sets of complex strain paths characterised by different values of equivalent strain but all associated with the same temperature. This experimental procedure was applied to the compression of Type 316 Stainless steel as described below.
(a) Tests at various temperatures
The tests in the Gleeble compression machine were carried out for low and high temperatures of 900°C and 1100°C respectively and deformed unidirectionally or bidirectionally to strains of 0.3, 0.4 and 0.5 and quenched. Barrelling of the cubes was insignificant.
The microstructures of specimens deformed at 900°C before and after a 90° turn are shown in Figs. A1.19(a) and A1.20(a), respectively and appear to be generally similar, and particularly in the values of the grain size (86 µm and 77 µm, respectively). There is slight difference, however, in the morphology of delta ferrite. Similar conclusions can be drawn from the results for the tests at 1200°C shown in Figs. A1.19(b) and A1.20(b) for both of which the mean grain size was 70 µm.
In examining the microstructures, it was believed that, like the grain size and its distribution, the dislocation densities should also be similar. This claim was not confirmed directly because of difficulties in measuring the latter but was supported by the closeness of the hardness (HV30) measurements viz. 186 and 185, and 182 and 179.
The volume fraction recrystallised was obtained from stress relaxation tests. The test temperatures and the strain were carefully chosen so that the two-volume fraction curves for uni-direction and bi-direction compression at the same temperature could be separated and the variation of the curves with temperature and strain identified. Results of the various unidirection and bi-direction compression tests are shown in Fig. A1.21 for the selected temperatures and strain i.e. (1100°C, 0.3e), (1050°C, 0.4e), (1025°C, 0.5e) and (1000°C,0.5e). Differences between the 50% or 95% recrystallisation time are not significant except for the case (1025°C, 0.5e).
(b) Tests for further reductions and sequences of rotations
The next series of multi-directionial compression tests reflected, in the main, the various configurational changes of stock occurring in industrial rolling processes such as: turning of bar in transverse plane, edge rolling and cross rolling of plates. More general changes e.g. turning of the whole stock in more than 1 plane were also considered. The latter tests, although not representative of bulk processes in conventional rolling may nevertheless be applicable locally to regions of the stock undergoing complex deformation e.g. near the web flange interface in beam rolling.
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The tests were planned to obtain maximum information and to optimise comparability between them and so included;
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Double hit tests and comparable single hit compressions of the same overall reduction – in a similar manner to the strain reversal tests reported previously.
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Repeated deformations using different ordered pairs of reductions.
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Repeated deformations on different pairs of faces, the effect of the order also being investigated (as shown schematically).
A deformation temperature of 1000°C, between the temperatures employed for tests (a) was adopted in the main. The reductions employed of 22.5%, 40% and 53% cover the range of rolling reductions employed in practice and the latter two are mechanically equivalent to a combination of the preceding reductions, in line with objective (1) above.
The tests were carried out as listed according to the programme below. The information given shows the % reduction in height, the occurrence of 90° turns denoted by T and the plane of turning shown by subscripts xz for the horizontal plane and xz for the plane normal to the direction of travel of the anvil. SRX in this context denotes stress relaxation, Q water quench, R reheat to temperature (viz. 1000°C unless indicated otherwise) and M metallographic examination.
(1) (Heating to 1100°C) 22.5%-->22.5%->SRX->QM
(2) 22.5%-->22.5%->SRX->QM
(3) 22.5%->Q->Txy->R->22.5%->SRX->QM
(4) 22.5%->Q->Txy->R->22.5%->Q->Txz->R->22.5%->SRX->QM
(5) 40%->SRX-->QM
(6) 40%-->22.5%->SRX->QM
(7) 22.5%-->40%->SRX->QM
(8) 53.5%->SRX->QM
(9) 22.5%->Q->Txz->R->22.5%->SRX->QM
(10) 22.5%->Q->Txy->R->22.5%->Q->Txy->R->22.5%->SRX->QM
(11) 22.5%->Q->Txz->R->22.5%->Q->Txy->R->22.5%->SRX->QM
(12) 22.5%->Q->Txz->R->40%->SRX->QM
(13) 40%->Q->Txz->R->22.5%->SRX->QM
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Comments
Test 1 is similar to a test carried out in stage 1 except that a reduction of 22.5% instead of 20% has been adopted so providing an indication of the sensitivity of the test in terms of reduction. Tests 2 and 3 are also similar to tests in stage 1 except that, in addition, a lower temperature of 1000°C has been employed to show the variation with temperature. Test 5 was set up for comparison with test 2, based on equivalent reductions. Tests 6 and 7 examine the effect of the order of deformation and both are, as above, comparable with test 8. Test 9 along with test 3 investigates the effect of rotation, albeit in different planes, before the second deformation. Test 10 is comparable with Test 4 except that it is a HVH pass. Test 11 is different in that it involves a double hit on the same face and is analogous to cross rolling. Tests 12 and 13, like tests 5 and 6 investigate the effect of the order of deformation, but with a turn in the horizontal plane in between the hits. It can be seen that tests 4, 10 and 11 investigate the effect of 3 hits of equal reduction with turns in different planes applied in the interpasses and the order in which these turns are applied.
Results and discussion
Figure A1.22 shows the decay of load in the stress relaxation test and the corresponding evolution of recrystallisation for the double compression of 22.5% at 1000°C. In this figure the decrease of load and increase in fraction recrystallised with respect to time is shown using both linear and logarithmic time scales, to show respectively, the asymptotic nature of the time variation and the successive stages of primary recovery, dominant recrystallisation and secondary (post) recovery corresponding to the segments of the ‘S’ type curve. The key parameter generally used is the time to 50% recrystallisation (t50) and, in this case, is equal to 2 s, full recrystallisation taking about 100 s. Figure A1.23 compares the results with those for the test carried out at the smaller strain/pass of 0.25. In this case, recrystallisation is slower in the early stages, 50% recrystallisation taking about 11 s but on comparison of the graphs appears to hasten in the later stages, full recrystallisation taking 100 s. Figure A1.24 compares the results obtained for repeated reductions of 22.5% at temperatures of 1000°C and 1100°C. The recrystallisation appears to be slightly faster at 1100°C, the time for 50% recrystallisation being less than 1.5 s. However, there is a degree of fuzziness in the readings making it impossible to obtain a clearly defined curve and incurring some uncertainty especially in the time for full recrystallisation. Better differentiation has been obtained for the load measurements as shown in Fig. A1.24 (b).
Results for a 90° horizontal turn between applications of the above reductions of 22.5% are given in Fig. A1.25. Comparison with Fig. A1.22 indicates a slower variation in load and recrystallisation, t0.5 being equal to 23 s.
When a single compression of 40% is applied, there appears to be little difference in the recrystallisation kinetics from that of the two monotonic reductions of 22.5% as seen on comparison of Figs. A1.22 and A1.26. The kinetics for the single compression is possibly slightly slower with t0.5 being slightly greater than 2 s.
When a compression of 40% was followed by a 22.5% reduction in the same direction, the recrystallisation was retarded in the early stages (see Fig. A1.27), the value of t0.5 being increased to about 10 s. Reversal of the order of these reductions (cf. Fig. A1.28) makes little difference in the early stages but appears to be faster in the later stages ‘full’ recrystallisation being attained in about 70 s as compared with 100 s when the greater reduction is applied first. Both these times, however, are less than the time of at least 200 s for a single compression of 40%. Application of the single compression of magnitude 53.5% equivalent to these two compressions, in this case, produces similar recrystallisationPage 63behaviour in the early stages to 22.5% followed by 40%, (cf. Fig. A1.29 viz. a viz. Fig. A1.30) but slightly faster t0.5 being 8 s. The process however becomes subsequently slower than both, ‘full’ recrystallisation being attained at a later time of about 130 s.
The next two figures show the effect of introducing a horizontal turn of 90 degrees between the hits considered in Figs. A1.27 and A1.28. It can be seen that in the first case when the turn follows the larger reduction t0.5 is significantly reduced to 1.5 s, but is not reduced as much in the second case when the turn precedes the larger reduction in which case t0.5 is equal to 3.5 s. The times for ‘full’ recrystallisation, viz. 2 min and 1 min however, are only slightly dissimilar from the times for the corresponding sequences without the turns.
Chosen tests involving triple hits were limited by the number of samples available as well as the substantial distortion (e.g. for 3 monotonic hits) that may be incurred. Figure A1.32 shows the results obtained for a triple compression of 22.5% with a 90° horizontal turn at both interpasses (i.e. the case considered in Fig. A1.25 followed by a 90° horizontal turn and further 22.5% reduction in height). The straight graph obtained suggests shallow recovery without recrystallisation. Similar effects are shown in the next two figures corresponding to sequences similar to that above in which one horizontal turn is replaced by a 90° turn in the vertical/transverse plane.
For comparison purposes, the results for fraction recrystallised and load for the full range of strain paths at 1000°C are shown collectively on common sets of axes in Fig. A1.35(a and b) respectively. The results, it can be seen, are divided into four groups in which the behaviour is similar.
Conclusions
-
The results are consistent with those of similar tests carried out previously and are qualitatively as expected in terms of changes in strain and testing temperature (minor measurement errors and experimental noise notwithstanding).
-
Increasing the strain (viz. between 22% and 53.5%) reduces the time for ‘full’ recrystallisation.
-
A greater time for full recrystallisation appears frequently to be associated with a smaller time to 50% recrystallisation (and vice versa).
-
Following a hit by a further hit (cf. 40% and 40% followed by 22.5%) appears to retard recrystallisation but overall is faster.
-
Reversing the order of 2 monotonic reductions makes very small absolute differences in the time for 50% recrystallisation and small relative changes in the time for full recrystallisation.
-
Replacing a large single hit by two hits of equivalent magnitude appears to produce slightly slower early recrystallisation kinetics, (cf. 53.5% into 40% and 22.5%) but overall is faster.
-
A 90° turn between 2 passes in conjunction with an increased reduction in either pass (cf. 40% from to 22.5%) tends to hasten early REX but without the large reduction significantly retards recrystallisation.
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-
Triple hits of the magnitudes considered above appear to prevent recrystallisation irrespective of the sequence of the pairs of planes on which they are applied i.e. this arises basically because the reductions of 22.5% are not sufficiently large (cf. points 2,4 and 7).
Objectives
To assess the effects on microstructure (i.e. fraction recrystallised and recrystallised grain size) and load, during the experimental hot rolling of Type 316 Stainless steel bars to reductions typical those employed on plant, of (a) interpass time (b) interpass turn through 90° and (c) the heating (inc. reheating) strategy.
To compare the results with analogous results obtained from bi-compression techniques on the Gleeble.
Associated requirements
In order to meet the above objectives the following criteria need to be met.
(i) Similar specimen thicknesses, and reductions and temperatures common to those used in the compression testing should be employed.
(ii) The thermomechanical conditions should be typical of those employed on the plant. In particular, a key factor for simulation of rolling processes, not included in the compression tests, is the interpass time. A range of times compatible with the other conditions should therefore be used.
(iii) Specimen geometry needs to be carefully controlled throughout the process.
(iv) Operating parameters such as load and torque need to be accurately measured and maintained within the mill limits.
(v) The metallurgical state, in particular, the grain size and the fraction recrystallised needs to be clearly characterised at each stage of the process.
(vi) The temperatures need to be monitored and controlled during heating and cooling.
Methodology for construction of rolling trials
Rolling schedules were drawn up for initial feedstock as supplied i.e. nominally 23 mm square and approximately 20 cm long, the length sometimes being cut to create more specimens. Initial designs were based on experience using moderately large reductions to highlight any significant strain path effects, (of the order of 20% used in the compression test). The schedules were then corrected iteratively as necessary so that they satisfy the criteria above using the various models listed in section A1.2 and the experimental facilities mentioned in section A1.4 Initial stock temperatures in the range 1100°C to 1150°C and interpass times up to 30 s were considered. For detectability, grain sizes in the range 50 – 120 µm were specified.
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Solution of the Ekelund spread Equation (A1.2) implemented using MATHCAD together with application of inhouse software (cf. Section A1.2) suggested that the 23 mm square bar reduced by 20% would have an exit width of at most 24.5 mm and, if then reduced by further 20% without turning, to a width of 25.8 mm. If turned between passes, the corresponding final thickness would be 19.6 mm and the estimated width 21 mm.
Temperature distributions in the specimen were obtained using an ABAQUS FE heat transfer model for initial soak temperatures of 1150°C and 1120°C. Cooling curves at various locations, obtained from the predictions, are shown in Figs. A1.36 and A1.37. From the graphs it could be seen that there would be a rapid decay in temperature at the stock faces, especially for the higher temperature. Orowan’s formula [A1.1] and the inhouse software using an initial grain size of 50 µm predicted loads in the range 75 to 81 kN for pass 1 and 81 to 89 kN for pass 2 without turning; when the stock is turned the load predicted by Orowan’s formula was of the order of 73 kN (no predictions from additional inhouse software were possible in this case since turning option is not included, the loads for partial recrystallisation would be slightly higher). From the predictions, even taking into account adjustments for partial recrystallisation, the load was expected not to exceed the operating limit of 10T for the Cavendish mill. The predicted torque of at most 1.4kNm was also considered not to present any problems.
For grain sizes at the upper end of the range, predictions of fraction recrystallised, using the Barbosa formula, [A1.12] were very small, viz. of the order of 3%. For grain sizes at the lower end, corresponding predictions are of the order of 18% but the recrystallised grain sizes differs little from the initial value and are small. Predictions of the microstructural evolution were also obtained using the inhouse software, with a grain size of 50 µm and employing a low emissivity corresponding to cooling the specimen isothermally i.e. without the effect of radiation, for the 3 interpass times of 10 s, 20 s and 30 s.
After a 10 s interpass time, the predicted temperature decreases from 1097°C at the centre to 1083°C at the surface; the predicted fraction recrystallised ranges from 29.5 to 33.3% and the recrystallised grain size from 42.1 to 42.7 µm. The predicted load in pass 2 for these temperatures and accumulated strains of up to 0.494 together with the above degree of partial recrystallisation, is 74.6 kN. The corresponding torque is 1.2 kN m.
For the 20 s interpass time, the predicted temperature distribution is little different from that for 10 s but the fraction recrystallised and grain size increase and lie in the range 47.2 to 52.4% and 46.7 to 47.9 µm respectively. The predicted load and torque for pass 2 are 75.8 kN and1.2 kN m respectively.
For 30 s interpass time, the fraction recrystallised and recrystallised grain size lie in the ranges 58.1 to 63.7% and 52.0 to 53.8 µm respectively. The predicted load is 77.1 kN and the torque is 1.2 kN m.
All the loads predicted, even for partial recrystallisation, are less than the 10 t operating limit.
Initial specification of trials
From the above analysis, the following schedules were therefore selected for initial experimental investigation:
Dimensions: 23 mm square cross section, approximately 20 cm long
Grain Size: 50 µm
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Reheating temperature: 1115°C
Initial Stock Temperature: 1100°C
No. of Passes: 2
Time for start of first pass: 6 s
Nominal Reductions: 20% per pass
Rolling speed: 50 rev.min-1
Mean strain rate: 5.4-5.9 s-1
Interpass times: 10 s, 20 s
Rolling schedules:
Schedule 1 (horizontal-horizontal rolling):
Pass 1: Draughting from 23 mm to 18.5 mm (actual reduction 19.6%)
Pass 2: Draughting in the same direction to 15 mm (actual reduction 18.9%).
Schedule 2 (horizontal-vertical rolling):
Pass 1: Draughting from 23 mm to 18.5 mm (actual reduction 19.6%).
Turn 90° in tranverse-vertical plane.
Pass 2: Draughting from nominally 24.5 mm (to be checked by measurement between passes 1 and 2) and reduced by 20%.
Experimental Method
As noted in Section A1.4, the average grain size in the unprocessed samples is of the order of 10 µm. To maximise detectability of changes in the microstructure, the samples needed to be heat treated to induce grain growth. To find the holding time required, a graph (shown in Fig. A1.38) of grain size versus time at this temperature of 1100°C, obtained from experimental data by means of the TableCurve2D package was used. A suitable range of grain sizes (viz. 40 – 60 µm) was therefore selected, significantly larger than 10 µm but on a portion of the curve in which the growth rate is low and hence controllable (i.e. the grain size should not change appreciably whilst the stock is about to exit the furnace prior to rolling). From the graph it can be seen that this requires a hold time of 20 min at 1100°C.
For ‘continuous’ measurement of rolling load and torques for both rolls, the mill was instrumented with load cells and the spindles with strain gauges and slip rings. The signals were transmitted at regular small time intervals to a laptop pc, where the data were recorded and from which traces of the variables could be obtained. The traces were used for determining the onset and duration of steady state conditions, and for confirming subsequently the interpass times taken whilst the trial was in progress. In order to capture the metallurgical structure for subsequent examination, the specimen was placed promptly, on exit from the final pass, into a bucket containing water at ambient temperature, which was agitated to optimise the heat lost by the specimen.
The first specimen was removed from the furnace, rolled in a single pass and quenched immediately. Traces of load and torque are shown in Fig A1.39 from which, the start and duration of rolling were estimated viz. at about 0.4s for 0.6 s and steady state conditions were ascertained. The measured thickness was in the range 18.7 to 18.8 mm i.e. slightly higher than set. The steady state exit width was 25.7 mm. Equating this to the subsequent entry thickness in the second pass following an interpass turn of 90°, the final thickness expected after 20% reduction is 20.56 mm.
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On exit from the rolls, the specimen was quenched. Two transverse sections were later taken from the rolled bar and the metallurgical structure observed by quantitative metallography. Photographs of samples taken at the ¼ depth position and in the central region are shown in Fig. A1.40(a and b) and Fig. A1.40(c and d) respectively. Values of the average grain size were equal, to the nearest micron, to 38 µm. However, from inspection of the figures, it can be seen that there is a wide variation in grain size throughout the samples (standard deviations 3 µm and 6 µm), the value tending to be smaller in the central regions. Moreover, the wide variation including low grain size and also the non-equiaxed nature of the grains found in such figures as above made planned determination of the strain distribution infeasible.
A second specimen was removed from the furnace and rolled in two monotonic passes with an interpass time of the order of 10s and quenched on exit from the final pass. Traces of the load and torque for each pass are shown in Fig. A1.41(a and b). To deduce the potential evolution of recrystallisation on exit from the rolls, initially only three 12 mm thick sections, transverse to the rolling direction, were taken upstream from a position 70 mm from the leading end. One section (A) was allocated for observation of the structure on exit from the rolls, the remaining two (B, C) for determination of the structure (i) shortly after exit and (ii) when recrystallisation was almost complete i.e. at the essential end points of the recrystallisation curve. The information from (i) when compared with that obtained from section A was useful in determining the initial gradient of the recrystallisation curve. Times of 5 s and of 60 s were chosen respectively for (i) from practical considerations and for (ii) estimated from theoretical recrystallisation curves. With a view to attaining these states, the specimens were placed beneath the platens of the Gleeble, heated rapidly to 1100°C and then held at temperature respectively for the times specified. Samples were taken at the midwidth positions for metallographic examination and measurement of the fraction recrystallised.
Photographs of the observed microstructure are shown in Fig A1.42 (a-f), and values found for the average grain size, together with the associated standard deviation in Table A1.3.
A third specimen was similarly heated and rolled in two passes with an intermediate 90° turn, and an interpass time of the order of 10 s as above and quenched on exit from the final pass. Traces of the load and torque for each pass are shown in Fig. A1.43(a and b). A similar procedure to that for the second specimen was followed to reveal the potential recrystallisation kinetics, viz. by taking initially three12 mm thick sections, from a position 50 mm from the leading end. Unlike the previous case, these sections were approximately 21 mm square. Following heating to 1100°C and holding for 5 s and 60 s, two samples were taken at the mid-height and mid-width of the section to investigate the symmetry or otherwise of the metallurgical structure. Photographs of the observed microstructure are shown in Fig. A1.44(a-e) and values found for the average grain size, together with the associated standard deviation are given in Table A1.4.
Discussion of results and issues arising
From the results the following observations were made: 1st Specimen:
-
The loads obtained are comfortably within the 10 t operating limit and are reasonably balanced between the open and drive side.
-
There is an asymmetry between the separate roll torques, the value for the bottom roll being greater.
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-
The measured exit thickness is slightly greater (by about 0.2-0.3 mm) than the specified exit thickness. This is probably due to mill spring which was not taken into account in these trials.
-
The measured grain sizes (on average 38 µm but with a wide variation throughout the samples, with respective.standard deviations of 3 µm and 6 µm), are at the lower end or even below the range specified even though it is unlikely that recrystallisation has occurred by this stage.
The low growth of the grains is likely to be related to the temperature distribution within the specimen or its variation throughout the trial. In particular, a sufficiently high grain size may not have been attained either because the region of the stock did not attain the required temperature or, otherwise, was not held at temperature for a sufficiently long period. Temperatures were not measured for this particular trial but predictions at specific locations within the specimen and at selected times prior to rolling were obtained using an ABAQUS FE heat transfer model assuming an initial uniform temperature of 1120°C. From the predictions, cooling curves have been obtained. The graphs indicate a rapid decay in temperature initially at the surface and subsequently in the central region. The short period prior to, and during rolling, of this trial, however, is unlikely to have any significant effect, suggesting that no portion of the stock had maintained, for sufficiently long, the required temperature of 1100°C (or even attained it).
On the basis of these predictions, a further trial was carried out to monitor the specimen temperature during reheating and subsequent cooling on exit. The evolution of the measured temperature at the centre and surface of the stock for these stages is shown in Fig. A1.45(a and b). The absence of a plateau in the first figure confirms the lack of a holding period and the low first recorded temperatures in the second graph tend to confirm that the required temperature may not even have been attained.
2nd Specimen:
The results observed indicate that:
-
For the first pass the loads are balanced and within operating limits and the torques somewhat asymmetric, replicating the observations for the single pass trial above.
-
The required interpass time of 10 s was attained.
-
In the second pass the loads are higher than those in the first pass and approach the operating limit.
-
The longer times for this trial and consequent temperature losses indicated from the predictions in Fig. A1.37 suggest that the trial did not take place under isothermal rolling conditions.
-
This temperature decay, coupled with the low initial temperature and grain size, according to the equations of the recrystallisation kinetics A1.7 –A1.11) [A1.11], would give rise to low fractions recrystallised and recrystallised grain sizes, difficult to detect.
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The high grain size of 61.9 µm in the unreheated sample at the quarter depth position (where the measurements after the single pass were taken) could be taken as a confirmation that grains had grown to the required size This is consistent with the observed grain size of 66.5 µm observed after 5 s. The moderate value of fraction recrystallised (59%) could be due to experimental error. The low grain size of 36.7 µm found after 60 s is difficult to explain.
3rd specimen:
-
The loads and torques are slightly higher than those in the nominally identical pass for the previous case, also unsteady and slightly less balanced, indicative of ‘noise’.
-
The major difference, if path dependence is important, should occur in the second pass following the rotation. Noticeable differences do occur, the loads in this case being smaller and steadier on the drive side but greater and more variable on the open side. The torque for the current case tends to be smaller on the top but greater on the bottom shaft. The asymmetry, occurring mainly in the torques could, in principle, be caused either by different conditions between top and bottom rolls or by inhomogeneities in the specimen. The possibility of significant geometrical inhomogeneity was considered and ruled out; the evidence suggests that the effect is likely arise from initial inhomogeneities in the material or changes in the metallurgical structure associated with the rolling process.
From inspection of Table A1.4 similar qualitative remarks to those above may be made concerning the structural changes incurred by the rolling with the 90° turn viz. recrystallisation is initiated probably resulting in a larger recrystallised grain size which appears to grow with time. The results are however respectively smaller and greater than the corresponding values in Table A1.3. More precisely, the material in location 1, which has been in contact with rolls once following the turn is recrystallised less than the material, which has been in contact with the rolls twice. This is consistent with the observations for bidirectional compression and tensile-compressive tests. For the material in location 2, especially at the centre, the recrystallisation is greater because the material undergoes repeated compressive strains, which from the geometry of the stock are probably greater than those at the surface for the H-H rolling. The lower loads noted above for H-V rolling suggests that the dominant effects are probably those such as in location 2 i.e. that the recrystallisation is greater when turning is introduced. Further tests were recommended to confirm these effects and to investigate also the effects of interpass time and temperature variation.
Issues
Before carrying out further trials, a number of issues arose relating to (a) uniform attainment of the required initial grain size and reheating temperature (b) minimisation of radiative heat loss in specimen in transit between furnace and rolls and between passes (c) setting the correct roll gap (d) extraction/presentation of meaningful data on grain size, strain distribution and REX.
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Addressing the issues
-
Uniform attainment of the required grain size throughout the specimen was problematic because of the presence of secondary phases in the as-supplied sample as noted in Section A1.4. It was decided therefore that two reheatings be carried out viz. (a) a heat treatment prior to the trial, under predetermined and controlled conditions aimed at minimising the heterogeneities in the structure and (b) one to attain the required initial grain size prior to rolling. Measurements would be taken in the region of the specimen containing the primary phase.
-
Attainment of a uniform temperature distribution in a sample has been found to be difficult, if not impossible, to achieve in practice. As predicted in [A1.11] there is a gradient near the boundary during the heating of Gleeble specimens, as also suggested in Figs. A1.36 and A1.37. The heating conditions for attainment of approximately uniform temperature were therefore found experimentally by monitoring the temperature readings from an inserted thermocouple.
-
From theoretical curves of recrystallisation, for larger interpass times around 30 s (cf. Fig. A1.37), it can be seen that in this case there is a large temperature drop so that, unlike the 10 s case, approximately isothermal conditions cannot be assumed. Various methods of insulating the specimen were therefore examined including immersing the specimen or placing in a suitably heated, specially designed, refractory unit. These measures were ruled out as they would probably not reduce the heat loss significantly or would be impractical. It was therefore decided to use, instead, an isothermally based equivalent time theoreticaly determined from the recrystallisation equation as outlined in Section A1.2 in Equations (A1.13-A1.15).
-
To determine the roll gap required, taking into account mill spring, a spring curve for the mill was obtained by rolling a number of specimens to various gauges, reading the steady state load from the trace and determining the deviation from the set gauge. It is shown in Fig. A1.46. The gauge setting for each of the passes has been obtained by subtracting the spring for the loads noted previously without any corrective iteration.
-
To obtain meaningful information on microstructure it is important not only to determine the microstructural evolution after the final pass but also the structure prior to the first pass and that between passes. To fulfil the latter requirement, a specimen was quenched after the first pass and the structure determined.
In order to make optimal use of the specimens, the evolution of fraction recrystallised and recrystallised grain size was not measured by rolling of several specimens, quenched at different times, but by quenching, for each case, a single specimen approximately 2 s after rolling and measuring the REX characteristics in reheated sections of this specimen after various times of cooling. This method assumes that the strain energy trapped in the quenched section will resume the recrystallisation, as uninterrupted, if reheated to the appropriate temperature. The information is presented as curves of REX percentage v log time.
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Series 2 of rolling trials: Effect of interpass time and temperature
Programme
Before rolling, the remaining specimens of Type 316 stainless steel were homogenised by heating them to 1100°C in the heat treatment furnace, holding at temperature for 2 hours and allowing to cool in air. Samples from the ends of the specimen were then examined metallographically and measurements taken of the grain size. Micrographs are shown in Fig. A1.47 and values of the mean grain size and standard deviation are given in Table A1.5, Compared with the small values measured in specimens used in tests previously, the sizes are unexpectedly high at around 90 microns with standard deviations of the order of 10 microns. A moderate degree of heterogeneity therefore still remains as can be seen in Fig. A1.47. It was expected that the heterogeneity would decrease towards the mid-length position of the bar but samples were not taken here as it was thought at this stage of the procedure that there would be a significant deviation from steady state conditions during rolling in specimens of half the length (c. 10 cm) used previously.
To avoid the problems regarding control of temperature during the interpass, it was decided therefore to adopt the approach used in the triaxial compression tests of quenching the specimen immediately after each pass and reheating to the temperature required.
Two alternative scenarios, I and II, were considered in the trials. In scenario I, to generate moderate recrystallisation, a trial was planned in which a bar was rolled in pass one with the same reduction as above, reheated to 1040°C but then held for 60 s only, quenched and reheated to 950°C, before rolling in pass two by a 20% reduction. The two respective heating profiles are shown in Figs. A1.48 and A1.49. As predicted from the model equations, further recrystallisation at this temperature, if quickly attained, should be minimal. In scenario II, to investigate the effect of zero or negligible recrystallisation on subsequent loads and torques and compare the evolved grain structures, a similar schedule but with the omission, after pass one, of the reheating to 1040°C was also drawn up. In both these scenarios, the effect of strain path is examined, according to the remit in the technical annex, in relation to the introduction or otherwise of interpass turns. The bars employed in the two scenarios were labelled respectively 4R1F64A and 4R1F284A, with subcodes 1 and 2 corresponding to no turn or turn as defined in Table A1.6.
The temperature in the trials was also carefully monitored using a thermocouple inserted into the specimen; if the temperature required was not attained the PID controller of furnace temperature was reset. The mill, including the instrumentation, was also checked and the spurious torque oscillations noticed previously eliminated. The spring curve for the mill was employed to determine the deviation from the set gauge. For the first pass a spring of 0.49 mm was noted.
The traces of load and torque are given in Figs. A1.50 and A1.51 for bars 4R1F284A (1 and 2) and in Fig. A1.52 for bar 4R1F64A (1). After rolling the bar was quenched immediately in order to capture the actual recrystallised structure. Samples taken from the end of the bar after the first quench in the schedule were used to investigate the recrystallised structure and the effect on loads and torques on subsequent rolling in which the bar was rolled with a gap setting, allowing for spring back, of 14.0 mm. Further samples were taken in tests to determine the grain sizes at the end of rolling and the subsequent structural evolution. The samples consisted of a 10 mm thick slices, labelled F64A1-1 etc., one cut from each bar at the end furthest from the thermocouple and of a number of 10 mm cube samples, F64A1a, F64A1b. The 10 mm thick slices underwent metallographic examination. The remaining samples were first heated to 950°C beneath the platens of the
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Gleeble and held at temperature generally for 10 s and 60 s respectively, quenched and then examined. Micrographs of the structure at these times for the 4 cases are shown in Figs. A1.53 - A1.56 respectively. In each figure, the structure at the ¼ depth and centre positions is shown for the above times. Average grain sizes with standard deviations were obtained for bars 4R1F284A2, 4R1F64A1 and 4R1F64A2 and are given in Tables A1.7 – A1.9. Grains in samples from bar 4R1F284A1, which did not have the extra reheat, exhibited significant variability, making it impossible to give measurements of their size. Values were therefore in randomly chosen individual grains along the centreline of the sample at positions 1 mm, 6 mm from the edge where the microstructures were predominantly equiaxed, and at 12 mm where the grain size was mixed and sometimes elongated. Measurements in µm, in this case, are expressed as 'feret max.' (the largest dimension regardless of orientation) and 'feret min.' (the maximum dimension perpendicular to 'feret max.') and are shown in (Table A1.10).
Direct measurement of recrystallisation by optical metallography was not attempted as it was considered unreliable for these specimens.
Discussion of results
(a) Effect of temperature
On comparison of Figs. A1. 52(a) with A1.50(a), for rolling with and without the reheat to 1040°C, the entire profiles are very similar suggesting, surprisingly, that recrystallisation, if taken place, does not affect the magnitude of the load. Differences do exist however between the corresponding torque traces. A qualitative assessment of recrystallisation was made using the grain size results obtained by optical metallography. From Fig. A1.55, there is little evidence of widespread recrystallisation in the bar having had the extra reheat to 1040°C, the small changes in average grain size over the time period being observed (viz. to 55, 55.7 and 55.8 microns probably being due to normal grain growth. However, close inspection of the figure reveals a small network of grains at the centre, suggesting recrystallisation was likely to have occurred locally but not quantifiable with reasonable accuracy.
For the bar not having had the extra reheat, the values cannot be used to accurately determine the average grain size, but do provide some indication of the size of the largest grains present viz. 217 to 531 µm in the unreheated sample after rolling and 250 to 441 µm, 204 to 698 µm for the samples heated to 950°C and held for 10 s and 60 s. They can therefore be compared with estimates of the maximum grain sizes for the previous case. Assuming that the grain sizes are lognormally distributed, the maximum grain size can be estimated using equation A1.16, giving results of 71.1, 63.3 and 64.0 µm. (If the grain sizes were normally distributed application of the '3 standard deviations rule' would give grain sizes of 69.4, 62.9 and 63.6 microns.) It is clear that the large difference between the values even for the smallest measurement of 204 µm cannot be explained simply as the difference between recrystallised grains and grown grains; it is more likely to reflect inhomogeneities and present in the material in its initial state and variability between specimens. The large grains at this position also showed some directionality with the elongation tending to lie parallel to the top/bottom surface.
The presence of smaller networks of grains throughout the specimens suggested extensive recrystallisation. The anomaly between the above two sets of results, in which indications of the absence or presence of recrystallisation are contrary to expectation, is difficult to explain. It was decided therefore to discern whether recrystallised structures are present by the use of EBSD techniques for both the above cases, as described in more detail in Section A1.4.
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This work was carried out using TSL EBSD equipment fitted to a Philips XL30 SEM in accordance with Work Instruction CPR SUS 324. Figures A1.57 and A1.58 provide the IQ (Image Quality) Maps for specimens 4R1F64A1B and 4R1F284A1B respectively for the cases with and without the extra reheat. However, the quality of the EBSD patterns obtained was not fine enough to enable indexation, by the software, of sufficient points (the white areas on IPF maps) to detect regions of recrystallisation.
(b) Effect of turning
-
Through 90° in transverse-vertical plane.
To investigate the effect of changes in stock configuration (at constant reduction) on load and recrystallisation, a similar test to that above was carried out except that the stock was turned through 90° in the transverse vertical plane before the second pass. The loads and torques, are shown in Fig. A1.52(a and b), for the bar in the pass after a 90° turn are smaller than those in the previous figure for the specimen without the turn. This result is qualitatively in agreement with predictions obtained using the Orowan load model [A1.1] and is associated with the changes in stock geometry. It also suggests less strain energy than in the previous case for subsequent promotion of recrystallisation. To compare the microstructure, tests analogous to those for the rolling without the interpass turn were carried out. For the specimen rolled with the interpass turn, grain sizes obtained from the micrographs corresponding to the above values of 55, 55.7 and 55.8 microns are respectively 78.2, 76.0 and 82.5 microns suggesting that the joint effect of reducing the reheating temperature and turning the stock increases the grain size which is consistent with absent or possibly retarded recrystallisation or grain growth. It would be useful to factor out the effect of the reheating temperature and consider only the effect of path change. In principle, this could be done by first estimating for this case the maximum grain sizes as above giving values of 108.8, 99.7 and 103.0 microns (104.6, 97,101.1 microns using the normal distribution), and then comparing with the above values of 217, 250 and 204 microns. The differences are more supportive of an effect of rotation on retardation of grain refinement but, are still too large to attach any great significance to the results.
-
Turning in a horizontal plane
Rolling trials have also been carried out for instance to investigate the effect of turning in the horizontal plane (cross-rolling) on the evolution of microstructure. In particular, the stock followed a similar processing history to 4R1F64A1 above viz. was rolled at 1040°C from 23.1 mm to 18 mm, was then quenched, reheated to 1040°C, held at temperature for 60 s, quenched and reheated to 950°C, but then turned through ~ 45° in the horizontal plane before rolling in the second pass to 14 mm. On comparison with the results for specimen 4R1F64A1, the average grain size is smaller for the two subsequent times. However the differences are not sufficiently significant to support the hypothesis that turning retards the grain refinement. Indeed the mixed grain structure shown in Fig. A1.56 of this set does not provide any clear indication of recrystallisation. The results also suggest that the grain size does not evolve significantly as the holding time is increased.
Conclusions
-
Anomalies have been detected concerning the effect of temperature on recrystallisation, indicating the opposite of the outcome generally expected. This may be indicative of the structural variation within and between samples and insufficient control of heating and cooling schedules.
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-
There is slight evidence that changing the strain path through interpass turns retards evolution of recrystallisation and reduces grain refinement. The evidence, from the limited number of trials possible, therefore is not sufficiently significant to establish whether this is a secondary effect or even a real effect for the steel quality studied.
The objectives of this task are: -
-
To investigate the effects of reversal rolling on the recrystallisation kinetics.
-
To use the results for the benchmark exercise
The reversal rolling trials were carried out on the 3 high laboratory plate mill at Corus Swinden Technology Centre. Figure A1.59 shows the mill facilities used in this rolling trial.
Two schedules were used for rolling temperatures of 1020°C and 1050°C consisting of the following steps viz.
Schedule 1
Reheat 1250°C for 30 min to achieve a grain size of about 150 µm and to dissolve the Nb particles.
Soak in the furnace at 1120°C to achieve as uniform as possible grain structure and temperature.
Roll at 1020°C at fixed speed of 78 rev/min
Roll without reversal to following sequence of stock heights:
Pass 1 (Normal direction): 30 mm to 25 mm, interpass time=10 s (manually change rolling direction)
Pass 2: 25 mm to 22 mm, interpass time = 12 s
Pass 3: 22 mm to 19 mm, interpass time = 12 s
Water quench
Roll with reversal to following sequence:
Pass 1(Normal direction): 30 mm to 25 mm, interpass time = 10 s
Pass 2 (Reverse direction): 25 mm to 22 mm, interpass time = 12 s
Pass 3 (Reverse direction): 22 mm to 19 mm, interpass time = 12 s
Water quench
Schedule 2
Reheat at 1250°C for 30 min to achieve a grain size of about 150 µm and to dissolve the Nb particles.
Soak in the furnace at 1140°C to achieve as uniform as possible grain structure and temperature.
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Roll at 1050°C at fixed speed of 78 rev/min.
Roll without reversal to following sequence of stock heights:
Pass 1 (Normal direction): 30 mm to 25 mm, interpass time=10 s (manually change rolling direction)
Pass 2: 25 mm to 22 mm, interpass time = 12 s
Pass 3: 22 mm to 19 mm, interpass time = 20 s
Water quench
Roll with reversal to following sequence:
Pass 1 (Normal direction): 30 mm to 25 mm, interpass time = 10 s
Pass 2 (Reverse direction): 25 mm to 22 mm, interpass time = 12 s
Pass 3 (Reverse direction): 22 mm to 19 mm, interpass time = 20 s
Water quench
Four dummy trials were performed to check the gauge and the roll gap and to get the control and recording system working correctly. The rolled profiles are shown in Fig. A1.60.
Eight formal trials have been carried out with details as follows:-
TRIAL 1: Tre=1250°C, Tsoak=1120°C, Troll=1020°C, 3 passes in which the original thickness of 30 mm was reduced to 25 mm, 22 mm and 19 mm, respectively, without reversal rolling.
TRIAL 2: Tre=1250°C, Tsoak=1120°C, Troll=1020°C, 3 passes in which the original thickness of 30 mm was reduced to 25 mm, 22 mm and 19 mm, respectively, with reversal rolling.
TRIAL 3: Tre=1250°C, Tsoak=1120°C, Troll=1020°C, 3 passes in which the original thickness of 30 mm was reduced to 25 mm, 22 mm and 19 mm, respectively, with reversal rolling. REPEAT of TRIAL2.
TRIAL 4: Tre=1250°C, Tsoak=1120°C, Troll=1020°C, 3 passes in which the original thickness of 30 mm was reduced to 25 mm, 22 mm and 19 mm, respectively, with reversal rolling. REPEAT of TRIAL2.
TRIAL 5: Tre=1250°C, Tsoak=1140°C, Troll T=1050°C, 3 passes in which the original thickness of 30 mm was reduced to 25 mm, 22 mm and 19 mm, respectively, without reversal rolling.
TRIAL 6: Tre=1250°C, Tsoak=1140°C, Troll T=1050°C, 3 passes in which the original thickness of 30 mm was reduced to 25 mm, 22 mm and 19 mm, respectively, with reversal rolling.
TRIAL 7: Tre=1250°C, Tsoak=1140°C, Troll T=1050°C, 2 passes in which the original thickness of 30 mm was reduced to 25 mm and 22 mm, respectively, without reversal rolling.
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TRIAL 8: Tre=1250°C, Tsoak=1140°C, Troll T=1050°C, 2 passes in which the original thickness of 30 mm was reduced to 25 mm and 22 mm, respectively, with reversal rolling.
(Tre in the above represents the reheating temperature, Tsoak the soaking temperature, Troll the rolling temperature),
Experimental results
Operating parameters
Figure A1.61 shows examples of torque and load in Trial 4 and Fig. A1.62 for Trial 1. The averaged values can be obtained in order to compare with those predicted from metallurgical models.
It can be seen that the loads for Trial 1 (without reversal) are approximately 35, 34, and 38 tonnes for the first, second and third pass, and the loads for Trial 4 (with reversal) are approximately 32.5, 34.5, and 38.5 tonnes. However, it is not certain if these differences were caused by the reverse rolling or by other variables such as interpass time, rolling temperature that are difficult to control in the rolling trials.
(See also report of TU Freiberg contribution in Appendix 5)
Objectives
-
To investigate the effects of Horizontal-Vertical rolling on REX kinetics.
-
To investigate the effects of high speed rolling on flow stress data.
-
To examine the effectiveness of extrapolation of the constitutive models with higher strain rates.
This work has involved collaboration between Corus and TU Freiberg, using the high speed rolling mill of the latter. Trials on the four stand mills were scheduled by Corus originally for 900°C, 1050°C and 1200°C at 40 m/s with a conductive heating temperature of 1250°C to achieve an initial grain size of 180 µm. The low speed (5 m/s) rolling was also planned to calibrate the constitutive models. Details of the trials are contained in the contribution of TU Freiberg in Appendix 5.
FE modeling, taking into account cooling, of the Freiberg two stand rolling was carried out by Corus using ABAQUS. Details are given in Section A1.7.
A cooling model was created with a furnace discharge temperature 1250°C. The variation of temperature with time was examined to provide an understanding of the temperature evolution during rolling. The FE model showed that the strain distribution over the cross section of rolled rod was non-uniform, being highest at the centre (0.7) then the middle (0.55) and finally the surface (0.3). So if complete REX occurs in the centre, there may be partial REX at the surface.
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Of the techniques for material characterisation mentioned in the main section of the report and described in Ref. [A1.28], those employed by Corus in this project are optical metallography, electron back scattering diffraction (EBSD), stress relaxation and, occasionally, the double hit technique. Supporting facilities for reheating, sectioning, machining, etching and polishing etc are readily available and have been utilised. For stress relaxation, the local Gleeble has been used to deform and hold the specimen at a given strain. Specimens have also been held and reheated between the anvils of the Gleeble for rapid attainment of high temperatures with minimal recrystallisation,
Of the total set of steel qualities under overall investigation, contained in the template given in Appendix 7, those for which Corus is responsible are CMn, CMnNb steels and Type 316 Stainless Steel.
CMnNb steel was originally planned to be the main material for rolling and laboratory testing since it is widely used in Corus, and is readily available. CMnNb steel was therefore allocated for use, (a) by Corus, in tensile/compression tests on the Gleeble and in laboratory rolling, (b) by CEIT in torsion testing, and (c) by Freiberg in forward-reverse rolling. Eighty CMnNb steel plates (30 mm in thickness, 120 mm in width, 400 mm in length) were acquired by Corus, thirty were sent to Freiberg for use in their high-speed rod mill and five to CEIT for use in their torsion machine. The composition is given in Table A1.11, has a carbon equivalent value of 0.39 and is similar to that for the steel used by the University of Oulu in its tension/compression testing, thus readily generating data for comparison purposes.
Type 316L stainless steel was procured for use in the Gleeble multi-direction tests and the laboratory horizontal-vertical rolling trials. Its composition is given in Table A1.12. Although not as widely used as in the past when stainless strip was rolled by Corus, it is regarded, in common with microalloyed steels, as a material for which strain path effects are important and ample stocks were available.
The CMn and stainless steels are analogous to, i.e. can be compared and contrasted with, the medium C and duplex stainless steels investigated by CSM, the University of Oulu and CEIT.
(a) A brief assessment on the material characterisation of CMn steels is given in Reference [A1.28]. In particular, it has been found that optical metallography is difficult if the material undergoes a phase transformation during quenching and ambiguous results may be obtained if etching is carried out on prior austenite grains. For stress relaxation and double hit techniques, although recrystallisation occurs simultaneously, it occurs at a faster rate in the former. While the EBSD technique is generally regarded as being the most accurate and powerful technique, it is only possible if no phase transformation occurs after recrystallisation.
(b) CMnNb steel recrystallises moderately quickly, the speed being retarded by the presence of Nb. However, since it is transformable, definition of the deformedPage 78austenite grains can prove extremely difficult following transformation to ferrite, pearlite or bainite but is facilitated if martensite is produced. For transformation to martensite a very high cooling rate is required. The transformation behaviour of this steel has been computed from a database at TU Freiberg and it has been found that a cooling time of t 8/5 = 1.3 s is necessary to obtain martensite. Problems in attaining the critical cooling rate have been encountered in the rolling of plates both on the mill at the Technical University at Freiberg and on the Corus 3-high mill at STC. In the first case, martensite is formed if plates no thicker than 7 mm are rolled; in such thin plates the thermal behaviour is unstable and the temperature difficult to control. At STC similar problems have arisen when using plates of too large a gauge without sufficiently rapid quenching. Achievement of this degree of temperature control thus seems very impractical.
(c) Since Type 316 Stainless Steel is one of the slowest materials to recrystallise, the as-deformed structure in a single pass can be captured more readily by rapid quenching. However, even at the rates of 1 - 2 s-1 typically used in the Gleeble machine and in laboratory rolling of a specimen at very high temperature, the time for significant recrystallisation may be less than the handling time required to re-engage in the rolls or quenching and limit the range of interpass times considered. Nevertheless, for moderately high temperatures and interpass times, the speed of recrystallisation is conducive to the detection and measurement of a range of levels of partial recrystallisation. If the temperature is too low, however, the yield stress of Type 316 stainless is high and there is a danger that the rolling load may break the mill even if moderate reductions are used.
(d) The use of alternative materials which do not have the problems of CMnNb steel associated with transformation and recrystallise slowly was briefly considered. One such material is Fe30% Ni, which does not transform for the thermal conditions considered. Several variants have been produced experimentally but all recrystallise faster than Type 316 Stainless Steel. The selection/creation of such materials having analogous properties in relation to stress history but more transparent to experimental scrutiny must, however, remain on the agenda in future developments.
(a) Recrystallisation kinetics of CMn and CMnNb steels
Experiments to test the suitability of Husain’s method [A1.27] for investigating the material behaviour of CMnNb steel specimens deformed uniaxially at 1100°C and at a strain rate of 1 s-1, with or without reversal, to a total strain of 0.4 have been referred to in Section A1.3.1.
Figure A1.3 shows the stress relaxation curves for both cases, showing the typical ‘S’ shape, with the reversal case (triangle symbol) having a higher stress than the non-reversal case (square symbol). Figure A1.4 shows also the well-known Bauschinger effect (a reduction in flow stress on the reversal direction) and a significant delay to the onset of dynamic recrystallisation. Figure A1.4 shows the (static) recrystallisation kinetics, which indicates that the reversal case takes around 45 seconds for full recrystallisation while the non- reversal case takes about 12 seconds.
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The experiments confirm that stress relaxation is a suitable method for characterising the recrystallisation kinetics
The effects of main rolling variables (viz. composition, reduction, grain size, strain rate, temperature, interpass time/distance, etc.) on recrystallisation kinetics were investigated to assist in determining the rolling schedule on Freiberg’s high speed rod rolling mill and laboratory plate rolling.
Metallurgical modelling for CMn, CMnNb and even medium carbon steels was used to express the activation energy, 50% and 95% recrystallisation fraction as a function of the above variables. The case considered was for an initially 20 mm diameter rod, rolled to oval 16 mm x 22 mm after the first pass F1 at the speed of 10 m/s (strain rate 100 1/s), the distance between the first pass F1 and the second pass F2 being 1500 mm (corresponding to an interpass time 0.15 s). The effects of temperature, initial grain size and strain were also investigated.
It was demonstrated that:
(i) coarsening the initial grain size will significantly increase the recrystallisation time, which makes partial recrystallisation possible before entering to the next pass.
(ii) increasing the temperature significantly reduces the recrystallisation time.
(iii) decreasing the strain significantly increases the recrystallisation time. (cf. validation from the University of Oulu and from the assessment of the high speed trials).
Evolution of grain size of a medium carbon steel, soaked at 1200°C and quenched after 20 minutes was also investigated to assist the heat treatment process for the Freiberg high- speed rod rolling in achieving an initial grain size of 200 microns.
(b) Metallographic examination of Type 316 stainless steel
Heavy etching of specimens in ‘Newdip’ reagent revealed a central core of different appearance to that at the quarter depth shown respectively in Figs. A1.63 and A1.64. A light etch showed that a second phase of delta ferrite was also present with some twinning of the grains (as seen in Fig. A1.65). There is also evidence of inclusions secondary phases delta ferrite and, in the interdendritic spacing, of the original as-cast macrostructure and segregation. This may incur difficulties in the initial definition of the grain size and in its measurement as it evolves. The mean grain-size as measured was low at 8.98 µm with a standard deviation of 0.58 µm. (The underlying results are given in Table A1.3.)
In view of the analysis above, it was decided to maintain use of Type 316 stainless steel for H-V rolling and bi-compression tests, but to seek material in more homogeneous initial condition and having a larger average grain size, by growing them if necessary. In view of its hardness, special care is needed not to exceed the operating limits of the mill.
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(a) Strain reversal tests
Stress relaxation was used, for the CMnNb steel specimens, to obtain the volume fraction recrystallisation curves shown in Figs. A1.14–A1.16. From close inspection of these figures, the order in which tension and compression are applied makes little difference to the commencement and subsequent evolution of recrystallisation except for a slightly greater intermediate speed at 1000°C when compression is applied first. Implementation of the total strain without reversal (i.e. compression only) at the lower temperatures significantly delays the start of recrystallisation and may retard the initial speed.
(b) Multidirectional tests
The stress – time curves in Figs. A1.21 – A1.35 for Type 316 stainless steel have been discussed extensively in Section A1.3.2, the most notable results probably being (a) that a turn hastens early recrystallisation for large reductions but for small reductions retards it and
(b) opposite behaviour to the results quoted in the literature in [A1.28] for CMn steels.
(c) H-V Rolling
Comparing the micrographs in Figs. A1.40, A1.42, A1.44, A1.53 – A1.56 and discussed in Section A1.3.3, for Type 316 Stainless steel after deformation, with those in Figs. A1.63– A1.65 discussed above it appears that the metallurgical structure is non-uniform at the outset and ambiguous after completion of the trials despite heat treatment prior to rolling to mimimise heterogeneity. These observations are reflected in results of the EBSD tests shown in Figs. A1.57 and A1.58. Inverse Pole Figure maps were also used to examine the spread of orientations within grains, those having a small spread compared to the average for the grain being probably recrystallised. The maps for specimens with and without the extra reheat are shown in Figs. A1.66 and A1.67. The maps use colour to represent the orientation of solved patterns. Patterns that the software was unable to solve are coloured white. The figures unfortunately show that a large fraction of the patterns were not solved, indicative of poor pattern quality. The poor pattern quality, however, could be an indication of strain in the lattice, indicating that recrystallisation, but very little, has occurred. Because of the high fraction of unsolved patterns, it was considered unreliable to use the parameter (and associated maps) quantifying the grain orientation spread.
The above heterogeneity could have arisen because (a) the material is not homogenisable
(b) the initial structure is not stable with respect to the thermomechanical schedules used (c) the techniques for material characterisation are not sufficiently sensitive for the steel qualities and schedules employed –or some combination of the above. The results however show a marginal tendency for intermediate turns to reduce recrystallisation but there is insufficient evidence that this is a primary effect.
(d) Forward -reverse rolling of plates
Six samples cut from the centre of the CMnNb plates rolled in the forward-reverse trials described in Section A1.3.3.2 were submitted for micro examination, hardness testing, and grain size measurement. After etching all the samples in 2% Nital reagent, examination revealed a wide range of microstructures between samples. Some samples also exhibited a variation in microstructure through the thickness of each individual sample. All samples were decarburised on both surfaces. In order to show the variations in microstructure a micrograph was taken of each sample at positions of 3 mm below the surface to avoid thePage 81decarburisation and at the centre position. The surfaces were randomly marked as 1 and 2 for identification. Photomicrographs corresponding to trials 1, 4 7 and 8 are shown in Figs. A1.68 to A1.71.
The samples were then re-polished and etched in Japanese Etch to try and reveal the prior austenite grain size. This was only successful for 2 samples (viz. for trials 7 and 8) having martensitic type microstructures. Large differences in grain size were observed through the thickness of each sample, and it was concluded that grain size evaluation could not be undertaken to achieve meaningful results. Photomicrographs were again taken to show the variations observed, that for trial 7 is shown in Fig. A1.72.
Vickers hardness tests to BS EN ISO:6507-1:1998 were also carried out on each sample at positions of 3 mm below each surface and the centre. The results in Table A1.14 show the variations in observed microstructure. The effect of reversal on hardness was however inconclusive.
(e) High speed rolling
The experimental aspect of this work for CMn steel rods has been carried out by TU Freiberg and is discussed in Appendix 5. Grain sizes have been examined optically but were sometimes obscured by the presence of segregation. The results show that the increasing the roll speed has marginal, if any, effect on final austenite grain size.
Various strategies available for constitutive modelling have been evaluated and the findings summarised in Table A1.2. From these findings, it has been decided to utilise the unified viscoplastic model, developed by Birmingham University in conjunction with Swinden Technology Centre [A1.20].
The model is based on physical mechanisms for dislocation dynamics, evolution of grain size, recovery, dynamic and static recrystallisation and their coupling with viscoplastic metal flow. The primary variables in the model are therefore the relative dislocation density [VER SIMBOLO EN PDF ADJUNTO],the instantaneous austenitic grain size d, the volume fraction recrystallised S, the isotropic hardening R, the elastic and plastic strain tensors [VER SIMBOLO EN PDF ADJUNTO] and [VER SIMBOLO EN PDF ADJUNTO] and the Cauchy stress [VER SIMBOLO EN PDF ADJUNTO]
Details of the model are contained in Ref. [A1.20]. The model is formulated via the following equations:
[VER FORMULA EN PDF ADJUNTO]
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[VER FORMULA EN PDF ADJUNTO]
Where [VER SIMBOLO EN PDF ADJUNTO] is the effective plastic strain rate and [VER SIMBOLO EN PDF ADJUNTO] are the rates of elastic and plastic deformation respectively, [VER SIMBOLO EN PDF ADJUNTO] is the Jaumann stress rate and Fis the variable controlling the [VER SIMBOLO EN PDF ADJUNTO] onset of recrystallisation satisfying the differential equation.
[VER FORMULA EN PDF ADJUNTO]
[VER SIMBOLO EN PDF ADJUNTO] is the critical dislocation density, G and [VER SIMBOLO EN PDF ADJUNTO] are the Lame elastic constants, k is the yield stress and the other symbols are constants for the material modelled (currently Type 316 stainless steel). These are determined, for using a genetic algorithms program, from flow stress data obtained on the Gleeble machine at Swinden Technology Centre.
The default material model used at Swinden Technology Centre in the ABAQUS FE code is based on an elasto-plastic formulation in which the flow stress changes instantaneously as strain/strain rate changes. This constitutive behaviour is entered either in tabular format or in combination of tables and analytical expressions for rate and/or temperature dependence of the flow stress. More complex constitutive models, e.g. viscoplastic, based on dislocation dynamics etc. are implemented by user defined material subroutines, viz. UMAT in the ABAQUS/Standard variant of the code (so called Implicit formulation) and VUMAT in the ABAQUS/Explicit version.
Flow stress in tabular format
There are two standard ways of incorporating these into the FE package, ABAQUS.
The first method is to generate flow stress-plastic strain tables from the constitutive equations for various constant temperatures and strain rates. This is limited to a uniform distribution of strain and strain rate because of ABAQUS’ requirement of regularisation. The default tabular input is usually used in ABAQUS because of its simplicity. The stress-strain data at various strain rates and temperatures are entered following standard laboratory tests such as performed on a Gleeble thermomechanical simulator either in plane strain or uniaxial compression mode. The flow stress at a given strain and strain rate is then determined from interpolation within the extreme boundaries of the data. No extrapolation is made for any strain, strain rate or temperature outside the defined conditions. This therefore could result in underestimation of flow stress during hot rolling and could therefore result in discrepancies in load and torque predictions.
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The second method is to write the user-defined subroutine UMAT, noting that special techniques of integration and stability are required for different types of constitutive models. A user defined material subroutine UMAT was available for the viscoplasticity constitutive model [A1.8] developed by Corus to represent the flow of steels at high working temperatures including flow softening associated with dynamic recrystallisation.. It has been shown that the ABAQUS-UMAT method gave more reasonable predictions of flow stress than the ABAQUS plasticity model. However, the numerical stability of the integration algorithm in the UMAT depends on deformation and loading condition, which converges quickly in some cases but, in general, converges slowly or even diverges, thus limiting its applicability to cases where detailed and accurate strain and stress distributions are required for the prediction of microstructural development.
The unified model based on dislocation dynamics developed at MEFOS [A1.29,A1.8] has also been implemented by means of a UMAT within ABAQUS/Standard v6.3 to allow simulation of kinematic hardening. Because of its relatively slow implementation in ABAQUS/Standard, it is recommended for simple sections only. Implementation within ABAQUS v6.3 using the *CREEP card was assessed as an easier option in particular, by using the elastic D matrix instead of the exact Jacobian, enabling reasonably large time steps to be made without significant loss in accuracy.
An alternative method considered of incorporating constitutive models into FE code was to use the commercial software Z-mat from NorthWest Numerics/Transvalor [A1.30]. This is a user-extendable material models’ library that provides additional material modeling capabilities to ABAQUS. In particular, it allows the user to incorporate new materials within the standard Z-mat library and to make a permanent customised site library of UMAT routines which can then be combined with the hot rolling material models that have been developed. In addition, the Z-mat library provides an efficient integration scheme for the implicit solver.
Due to the availability of the trial version of the Z-mat software, work was carried out to assess the Z-mat features that could possibly be used in the current project. This was divided into two tasks viz.: -
-
Use of the standard Z-mat materials library by an FE rolling model.
-
Coding of a given material model and integration into the standard Z-mat library for use in ABAQUS simulation of rolling.
The viscoplasticity models in Z-mat were tested with the samples supplied by the software vendor and gave the expected results. An FE rolling model was also created with an attempt to use the Z-mat built-in materials models and to compare the CPU time with the standard tabular input. Work was not carried out, however, beyond the terms of reference of the trial.
An FE rolling model was subsequently created using the dislocation based viscoplasticity model formulated in A1.5 aimed at modelling the 2 pass bar rolling process described in Section A1.3.3.1. Data were therefore obtained from double hit tests, each of 0.43 strain, on Type 316 Stainless Steel specimens at 1000°C, with an interpass delay of 40 s. The stress- time and stress-strain curves are shown in Fig. A1.73. The data were then fed into the GA program to determine the coefficients for the model for this application; the constants obtained are given in Table A1.15.
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Finite element programs have been applied to several of the experimental tests and rolling trials to obtain predictions of the operating parameters and to ascertain the constitutive behaviour.
The ability for modelling strain reversal was assessed using six approaches combining isotropic and kinematic models using tabular input of: (1) Isotropic hardening, (2) Linear kinematic hardening with a constant isotropic elastic domain, (3) Nonlinear kinematic with constant isotropic hardening, (4) Nonlinear kinematic and exponential isotropic hardening,
(5) Nonlinear kinematic constant isotropic hardening, and (6) Nonlinear kinematic parametric input with nonlinear isotropic hardening. It was concluded that isotropic hardening should be re-formulated to accommodate the softening caused by recrystallisation for which a material user subroutine is required.
FE modelling of a simple geometry, cylinder and block, subjected to 'pulled-compressed', 'pulled-pulled' and bi-direction deformation conditions, was carried out using ABAQUS isotropic tabular input and the useful results were obtained to guide the strain reversal and bi-direction tests.
The results show that:
(i) Strain reversal occurs.
(ii) The equivalent plastic strain 'PEEQ', which is used to calculate the recrystallisation kinetics, does not reflect any change in history of strain components. For example, a cylinder subject to 'pulled-compressed' condition would have the same 'PEEQ' as that subjected to 'pulled-pulled' condition, thus resulting the same von Mises stress. However, to consider the Bauschinger effects induced by straining reversal, kinematic modelling methodology should be used.
FE Predictions of the 3 normal and 3 shear strain components have been obtained for the 40% reduction of the 10 mm cube at 1000°C, considered in Section A1.3.2 and are shown in Fig. A1.74(a-f). The normal strains are qualitatively as expected but the significant variability is exhibited in the shear strains.
The FE cooling model of the Freiberg two stands was created with a furnace discharge temperature 1250°C. The variation of temperature with time was examined to provide understanding of the temperature evolution during rolling. The FE model showed that the strain distribution over the cross section of rolled rod was non-uniform, highest in the centre (0.7) then the middle (0.55) then the surface (0.3). So if complete REX occurs in the centres, it may be only partially recrystallised at the surface. Predictions and more detailed information is given by TU Freiberg in Appendix 5.
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FE modelling of the plate rolling described in Section A1.3.3.2 was also carried out. Examples of predictions obtained of spread and equivalent plastic strain are shown in Figs. A1.75-78, namely for the 3 passes of Trial 1. Values of the predicted and experimental spread for these passes are contained in Table A1.16. For the 3 passes of Trial 4, predictions have been obtained using the in-house metallurgical model as shown below
Trial 4
Roll radius=155 mm
Speed=78 rpm
Rolling Temperature=1020°C, 3 passes with reduction from 30 mm to 25 mm, then to 22 mm and then to 19 mm.
Interpass time=10,12,12 s, respectively.
The following results were obtained where T50 and T95 are the times to 50% and 95% recrystallisation respectively.
Strain rate=9.6, 8.7, 10 1/s, respectively, for the three passes Strain=0.21, 0.15, 0.17, respectively, for the three passes T50=7.2, 4.5, 3.7, respectively, for the three passes T95=60.2, 37.7, 31.2, respectively, for the three passes Unrecrystallised fraction=0.42, 0.26, 0.52, respectively, for the three passes Grain size=59, 47, 39 microns respectively, for the three passes 5%_Nb_ppt=24.1, 25.7, 30.6 s, respectively, for the three passes Force=37.2, 31.3, 32.1 tonnes, respectively, for the three passes Torque=10.2, 7.1, 7.2 kN m, respectively, for the three passes
The predicted loads and torques viz. 37.2,31.3 and 32.1 tonnes and10.2,7.1 and 7.2 kN m respectively generally agree moderately well with the corresponding steady state measured values of 35, ~30 and 37.5 tonnes, and 8, 10 and 10 kN m (top roll)
The dislocation based constitutive model formulated in Section A1.6 has been applied to some of the H-V rolling trials described in Section A1.3.3. In particular, it has been used to simulate the rolling, in two monotonic passes, of a 23 mm square bar of Type 316 Stainless Steel to a thickness of 15 mm. The thickness on exit from pass 1 is 18.5 mm and the time between the passes is 10 s. For both passes the rolls are of diameter 154 mm and rotate at a speed of 50 rev/min. A uniform temperature of 1100°C has been assumed throughout.
The model was implemented in ABAQUS v6.4 and predicted distributions of stress and strain components including Mises stress and PEEQ strain, dislocation density, fraction recrystallised and recrystallised grain size. Examples of these distributions viz. for PEEQ strain, Mises stress, dislocation density and grain size in Pass1 when the stock is fully engaged by the rolls are shown for the 2 passes in Fig. A1.79(a-d). These figures indicate, not surprisingly, essential uniformity in the distributions of equivalent strain, grain size and dislocation density, the values of strain being slightly greater towards the surface than at the centreline and higher than the value employed previously in analytical models ofPage 86recrystallisation. The distribution of Mises stress is not uniform, reaching its maximum near mid radial position in the arc of contact.
Similar predictions for Pass 2 are contained in Fig. A1.80 except that Fig A1.80(d) shows the fraction recrystallised. The strain distribution is more non-uniform than in the first pass. The predicted distributions of dislocation density distribution and fraction recrystallised are slightly non-uniform, greatest values occurring towards the surface, the latter demonstrating, in particular, that the material is essentially unrecrystallised as indicated in the results of the H-V rolling trials.
The various complex loading paths assigned in the Technical Annex have been implemented by means of a series of experimental tests and laboratory rolling trials of the allocated steel qualities to assess their effect on operating parameters and evolution of microstructure specifically grain size and recrystallisation, with outcomes as listed below:
-
In strain reversal tests on CMnNb steel specimens, subjected, on the Gleeble, alternately to tensile and compressive strains of equal magnitude (0.2) at temperatures of 1000°C, 1050°C and 1100°C.
Notable Bauschinger effects were observed.
The magnitudes of these effects, and subsequent REX behaviour are independent of the order of application of the strains and marginally dependent on temperature.
The recrystallisation kinetics are delayed if a strain of the same total magnitude is applied without reversal, but, for the lower temperature, are faster overall.
-
In single and multiple compression tests of various magnitude on Type 316 stainless steel, conducted isothermally on the Gleeble at temperatures of 900°C, 1000°C and 1100°C, stress relaxation tests indicate that:
The time for recrystallisation in a single hit decreases more significantly with strain than with temperature.
Recrystallisation behaviour is marginally dependent on the order of the hits.
Multiple hits of the same total magnitude as a single hit give overall slower recrystallisation and may inhibit recrystallisation entirely if, individually they are moderately large (~20%).
An interpass turn of 90° hastens early recrystallisation when one of the reductions is large (~40%) but significantly retards it when both hits are moderate (~20%).
-
In H-H/H-V rolling of Type 316 stainless steel bars rolled on the STC Cavendish mill to successive reductions of 20% at temperatures between 950°C and 1100°C, indications exist that interpass turns and intermediate low reheats retard microstructural evolution but are not strongly supported by the experimental evidence.
Page 87
In bar rolled at ~1100°C and given a turn of 90° in the transverse plane in 10 s interpass, lower recrystallisation is observed at the surface than without the turn but this is not supported by lower loads in the second pass.
In bars rolled first at 1040°C, reheated to 950°C before the second pass, larger grain sizes with an interpass turn are deduced than can be attributed to retarded grain refinement.
No differences in loads in the second pass are observed between bars given or not given an intermediate reheat to 1040°C and grain sizes differ little from those before rolling suggesting that any recrystallisation for either case is insignificant.
-
In the rolling of CMnNb steel specimens on the STC plate mill, loads with or without reversal are very similar suggesting that reversal has no effect on REX and load or that any differences are masked by thermal effects.
-
In the high speed rolling of CMn rods, at TU Freiberg, grain sizes may marginally be increased with increasing roll speeds but effects can be masked by segregation.
-
Difficulties in drawing sound conclusions on the influence of strain path on structural evolution may be related to problems associated with characterisation of the materials allocated for investigation viz.
In CMnNb steels, the austenite grain size may be masked by phases such as bainite but is more detectable if martensite is present; however, the formation of the latter requires very rapid cooling rates which are achievable, e.g. for plates, for thicknesses less than 7 mm in which temperatures are very unstable and difficult to control.
In Type 316 stainless steel, recrystallisation, although slower than most other steel qualities, may, if temperatures or interpass times are large, may give rise to partial but not full recrystallisation, which can be discriminated in trials with or without interpass turns.
In Type 316 stainless steel material inhomogeneity occurs in the original samples, associated with inclusions, delta ferrite etc. which may not be significantly reduced even with heat treatment and may give rise to unpredictable variations in grain size in the rolled samples and make it difficult to establish, either by optical metallography or EBSD, whether or not recrystallisation has occurred.
-
Constitutive models, both analytical and numerical, implementable in the ABAQUS FE code, have been applied in the simulation of some of the above tests with reasonable agreement on the operating parameters. Their scope for further development/application for the efficient and accurate prediction of microstructural evolution has been reviewed. The dislocation based viscoplastic model, developed in conjunction with Birmingham University has accordingly been selected and applied to the H-H/H-V bar rolling trial using constitutive data obtained from results of delayed double hit tests on the Gleeble under similar conditions. Predictions of equivalent strain, dislocation density, fraction recrystallised and recrystallised grain size have been obtained for both passes and confirm that, in the second pass, the material is essentialy unrecrystallised.
Page 88
A range of models has been developed not only providing good agreement with experimental measurements of load and deformation for rolling cases considered, but breaking new ground in generating reasonable predictions of the evolution of microstructural quantities such as dislocation density and fraction recrystallised, and having the potential to analyse this evolution in regions of stock undergoing complex loading paths as in section rolling.
To realise this potential:
-
More experience should be gained in applying the model to, and acquiring constitutive data for, single and multipass operations involving complex loading histories and abrupt changes in local strain paths.
-
More importantly, much attention needs to be paid to refining and advancing the techniques for material characterisation, for selecting appropriate materials for characterisation and for stringently controlling and monitoring the heating/cooling and rolling operations used not only in the laboratory but also in an industrial context.
-
Differences between the results from experimental mechanical tests and rolling trials need to be investigated and explained.
A1.1 Orowan, E: Proc. IME, 1943, Vol. 150(4), 140.
A1.2 Ekelund, S: Steel, (1933), Vol. 93, 8.
A1.3 ABAQUS Theory Manual v6.1, ABAQUS, Pawtucket, USA.
A1.4 Krausz, A S and Krausz, K (eds.): 'Unified Constitutive Laws of Plastic Deformation', Academic Press, 1996.
A1.5 Sherby, O D and Miller, A K: 'Combining Phenomenology and Physics in Describing the High Temperature Mechanical behaviour of Crystalline Solids', ASME J. Eng. Mat. Technol., 1979, Vol. 101, pp387-394.
A1.6 Sellars, C .M and McG. Tegart, W J: 'Hot Workability', Int. Met. Rev., 1972, Vol. 17, pp1-24.
A1.7 Garofalo, F: 'An Empirical Relation defining the Stress Dependence of Minimum Creep Rate in Metals', Trans. American Inst. Mining & Met. Engineers, 1963, Vol. 227, pp351-356.
A1.8 Ingham, P M: 'The Effect of Strain Reversal and Strain-Time Path on Constitutive Relationships for Metal Rolling/Forming Processes', Final Report ECSC Project, 7210.EC/811, 2000.
A1.9 Miller, A K: 'An Inelastic Constitutive Model for Monotonic, Cyclic, and Creep Deformation: Part I- Equations Development and Analytical Procedures; Part II-Page 89Application to Type 304 Stainless Steel', ASME J. Eng. Mat. Technol., 1976, Vol. 98, pp97-113.
A1.10 Dunne, F P E, Nannah, M M and Zhou, M: 'Anisothermal Large Deformation Constitutive Equations and their Application to Modelling Titanium Alloys in Forging', Phil. Mag. A, 1997, Vol. 75, no. 3, pp587 –610.
A1.11 Farrugia, D C J: ‘Finite Element Modelling of Deformation and Microstructural Evolution in Multipass Rolling’, ECSC Project EUR 18398 EN, Final Report, p195 (formulae of S. Jaiswal and R. Barbosa).
A1.12 Barbosa, R and Sellars, C M: 'Recrystallisation '92', p461.
A1.13 Jaiswal, S et al: 'Modelling of Microstructure in Rod Rolling of Alloy and Stainless Steels', ECSC Project7210.EB/807 (D3.1/89) 1992.
A1.14 Humphreys, F J and Hatherly, M: 'Recrystallisation and Related Annealing Phenomena', Pergamon, 1995.
A1.15 Kolmogorov, A N: Izv. Akad.Nauk,USSr-Ser_Maternat 1(3),355, (1937). (also Johnson, W A and Mehl, R F: Trans. Metall. Soc. A.I.M.E 135,416,1939 and Avrami, M: J. Chem. Phys, 7,1103,(1939).).
A1.16 Abramowitz, M and Stegun, I: 'Handbook of Mathematical Functions', Dover Publications, Inc, NY.
A1.17 ABAQUS User Manual v6.1, ABAQUS., Pawtucket, USA.
A1.18 Zhou, M, Ingham, P M and Farrugia, D C J: 'A User Defined Material Model in ABAQUS to Represent the Viscoplastic Deformation and Work Softening during Hot Rolling', SL/M/R/S474/1/98/D, British Steel plc, Swinden Technology Centre, July 1998.
A1.19 Lemaitre, J and Chaboche, J L: 'Mechanics of Solid Materials', CUP,1994, pp253-345.
A1.20 Liu, Y, Lin, J, Farrugia, D C J and Zhou, M: ‘Modelling of Microstructural Evolution in Multipass Rolling’, *School of Manufacturing and Mechanical Engineering, University of Birmingham, to be published.
A1.21 Chaboche, J L and Rousselier, G: 'On the plastic and viscoplastic constitutive equations - Part I: Rules developed with internal concept, Part II: Application of internal variable concepts to the 316 stainless steel', ASME J. of Pressure Vessel Technology, 1983, Vol. 105, pp153-164.
A1.22 Sherby, O D and Miller, A K: 'Combining Phenomenology and Physics in Describing the High Temperature Mechanical behaviour of Crystalline Solids', ASME J. Eng. Mat. Technol., 1979, Vol. 101, pp387-394.
A1.23 Estrin, Y: 'Dislocation-Density-Related Constitutive Modelling', in Unified Constitutive Laws of Plastic Deformation, Academic Press, London, 1996, pp69- 105.
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A 1.24 Kopp, R: 'The Realistic Simulation of Metal Forming Process Chains', Steel Research, 1998, Vol. 69, pp121-127.
A1.25 Kendall, M and Stuart, A: 'The Advanced Theory of Statistics', publ Griffin 1962.
A1.26 'Computational Stochastic Mechanics in a Meta-Computing Perspective'. ed. J Marczyk, publ. CIMNE, 1997.
A1.27 Husain, Z and Howe, A A: 'Use of Thermomechanical Simulation for the Validation of Microstructure Evolution Models', SL/PH/R/S0340/1/92/A, British Steel Technical, Swinden Laboratories, September 1992.
A1.28 Dzubinsky, M: Comparison of recrystallisation kinetics established by stress relaxation, double hit, optical metallography methods and using orientation maps obtained by SEM/EBSD.
A1.29 Wang, X, Siwecki, T and Engberg, G: 'A physical model for prediction of microstructure evolution during thermomechanical processing', Materials Science Forum. 2003, Vol. 426-432, pp3801-3806.
A1.30 'User Manual: Z-mat Version 8.2’, Transvalor/ENSMP and Northwest Numerics,Inc., Fall 2000. http://www.nwnumerics.com.
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Table A1.1(a-c): Constants for Type 316 Stainless Steel in Equations (A1.8 –A1.11) for recrystallisation
(a) Zener- Hollomon and static recrystallisation
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(b) Critical strain for dynamic/static recrystallisation
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(c) Static recrystallised grain size
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Table A1.2: Options for constitutive modelling
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Table A1.3: Evolution and distribution of recrystallisation in specimen 4R1F287 rolled in 2 passes without turn at 1100°C
| Position: | Quarterdepth | Centralposition | |||||
|---|---|---|---|---|---|---|---|
| Sample subcode | Reheat time (s) | Grain size (microns) | Standard Devn. (microns) | Grain size (microns) | Standard Devn. (microns) | REX (%) | Standard Devn. (%) |
| A | 0 | 61.9 | 14.1 | 20.8 | 2.6 | 61.7 | 7.1 |
| B | 5 | 66.5 | 9.9 | 31.9 | 1.1 | 59.1 | 13.8 |
| C | 60 | 36.7 | 3.5 | 31.5 | 0.9 | ||
(Note: blank entry means not possible to measure meaningful value)
Table A1.4(a and b): Evolution and distribution of recrystallisation in specimen 4R1F50 rolled in 2 passes with turn at 1100°C
(a) Location 1
| Position: | Quarterdepth | Centralposition | |||||
|---|---|---|---|---|---|---|---|
| Samplesubcode | Reheat time (s) | Grain size (microns) | Standard Devn. (microns) | Grain size (microns) | Standard Devn. (microns) | REX (%) | Standard Devn. (%) |
| A | 0 | 57.2 | 3.9 | 26.7 | 3 | 43.1 | 16.6 |
| B | 5 | 34.5 | 2.0 | 25.1 | 1.6 | _ | _ |
| C | 60 | 37.6 | 2.9 | 33.6 | 3.2 | _ | _ |
(b) Location 2
| Position: | Quarterdepth | Centralposition | |||||
|---|---|---|---|---|---|---|---|
| SampleSubcode | Reheat time (s) | Grain size (microns) | Standard Devn. (microns) | Grain size (microns) | Standard Devn. (microns) | REX (%) | Standard Devn. (%) |
| A | 0 | 65.1 | 4.4 | 28 | 3.9 | 70.9 | 4.5 |
| B | 5 | 81.5 | 8 | 22.8 | 0.5 | _ | _ |
| C | 60 | 37.7 | 1.4 | 31.9 | 1.1 | _ | |
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Table A1.5: Grain size statistics for homogenised type 316 stainless steel bars
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Table A1.6: Rolling trials carried out with and without interpass reheat to 1040°C and with and without interpass turns
| QA No. | Process history/(results) | |||||
|---|---|---|---|---|---|---|
| Code | Subcode | Preheating/ rolling temperature | Rolling:Pass1 | Interpass details (micrographs, heating profiles) | Turning operation | Rolling: Pass2 (Loads, Torques) |
| 4R1F71 | 1040°C | 23.1 to18mm | Q, Rehea tto1040°C and Hold 2 min, Q (FigA1.5, Fig.A1.7, Fig.A1.6) | |||
| 4R1F64A | 1 | 1040°C | 23.1 to18mm | Q, Reheat to 1040°C and Hold 60s, Q, Reheat to 950°C (Fig.A1.8, Fig.A1.9) | No Turn | 18 to14mm (Fig.A1.10(a and b)) |
| 4R1F284A | 1 | 1040°C | 23.1 to18mm | Q, Reheat to 950°C | No Turn | 18 to14mm (Fig.A1.11 (a and b)) |
| 4R1F284A | 2 | 1040°C | 23.1 to18mm | Q, Reheat to 950°C | 90° Trans Vert. Plane | 25.5 to 20.4mm (Fig.A1.12 (a and b)) |
| 4R1F64A | 2 | 1040°C | 23.1 to18mm | Q, Reheat to 1040°C and Hold 60s, Q, Reheat to 950°C | 48° Trans Horiz. Plane | 18 to14mm |
| 4R1F514 | 1040°C | 22.6 to14.2mm | ||||
Table A1.7: Average and standard deviation of grain size measurements made in specimen 4R1F284A_2, rolled in 2 passes , 1st pass at 1040°C from 23.1 mm to 18 mm, interpass quench, reheat ,90° turn, 2nd pass at 950°C from 25.5 mm to 20.4 mm
| Position: | Quarter depth | ||
|---|---|---|---|
| Sample subcode | Reheat time(s) | Av. grain size (microns) | Standard devn. (microns) |
| 1 | 0 | 78.2 | 8.8 |
| A | 10 | 76.0 | 7.0 |
| B | 60 | 82.5 | 6.2 |
Table A1.8: Average and standard deviation of grain size measurements made in specimen 4R1F64A1, rolled in 2 passes from 23.1 mm to 18 mm, 1st pass at 1040°C, interpass quench, reheat to 1040°C, held for 60 s, reheat to 950°C
| Position: | Quarter depth | ||
|---|---|---|---|
| Sample subcode | Reheat time (s) | Av. grain size (microns) | Standard devn. (microns) |
| 1 | 0 | 55.0 | 4.8 |
| A | 10 | 55.7 | 2.4 |
| B | 60 | 55.8 | 2.6 |
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Table A1.9: Average and standard deviation of grain size measurements made in specimen 4R1F64A2, rolled in 2 passes, 1st pass at 1040°C from 23.1 mm to 18 mm, interpass quench, reheat, 45° turn in horizontal plane, 2nd pass at 950°C from to 18 mm
| Position | Quarter depth | ||
|---|---|---|---|
| Sample subcode | Reheat time (s) | Av. grain size (microns) | Standard deviation (microns) |
| (1) | 10 | 52.6 | 5.5 |
| A | 20 | 56.6 | 3.9 |
| B | 60 | 56.5 | 6.6 |
Table A1.10: Measurements of randomly selected grains in specimen 4R1F284A1_1 rolled in 2 passes from 23.1 mm to 14.0 mm, 1st pass at 1040°C, between passes quench and reheat to 950°C, no turn
| 1 mm from edge (Equiaxed) Feret max .(m) | 6 mm from edge (Equiaxed) Feret max. (m) | 12 mm from edge (Mixed) Feret max. (m) | Feret min. (m) |
|---|---|---|---|
| 110 | 174 | 476 | 204 |
| 247 | 192 | 466 | 217 |
| 155 | 273 | 314 | 156 |
| 154 | 259 | 258 | 127 |
| 95 | 169 | 270 | 98 |
| 209 | 191 | 508 | 159 |
| 146 | 179 | 314 | 145 |
| 99 | 124 | 241 | 58 |
| 95 | 281 | 430 | 192 |
| 89 | 171 | 249 | 93 |
| 92 | 157 | 142 | 56 |
| 114 | 303 | 214 | 118 |
| 119 | 240 | 240 | 98 |
| 150 | 191 | 216 | 70 |
| 158 | 228 | 184 | 56 |
| 112 | 139 | 160 | 77 |
| 130 | 176 | 41 | 14 |
| 113 | 150 | 24 | 13 |
| 132 | 90 | 21 | 14 |
| 104 | 140 | 21 | 11 |
| 120 | 213 | 39 | 19 |
| 117 | 193 | 38 | 14 |
| 95 | 205 | 30 | 14 |
| 91 | 167 | 28 | 12 |
| 70 | 199 | 26 | 14 |
| 114 | 311 | 24 | 11 |
| 200 | 177 | 17 | 13 |
| 85 | 211 | 18 | 12 |
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| 84 | 208 | 20 | 12 |
| 59 | 268 | 16 | 10 |
| 81 | 185 | 36 | 10 |
| 101 | 189 | 21 | 9 |
| 53 | 211 | 174 | 39 |
| 59 | 156 | 17 | 9 |
| 57 | 381 | 23 | 16 |
| 57 | 230 | 31 | 23 |
| 109 | 223 | 40 | 20 |
| 97 | 188 | 46 | 17 |
| 68 | 171 | 29 | 23 |
| 85 | 178 | 36 | 12 |
| 135 | 161 | 18 | 11 |
| 137 | 121 | 27 | 18 |
| 87 | 310 | 51 | 29 |
| 109 | 157 | 46 | 13 |
| 88 | 217 | 33 | 12 |
| 138 | 202 | 31 | 17 |
| 65 | 192 | 28 | 20 |
| 145 | 182 | 26 | 12 |
| 90 | 412 | 27 | 15 |
| 110 | 126 | 15 | 7 |
| 94 | 138 | 56 | 28 |
| 220 | |||
| 176 | |||
| 196 | |||
| 139 | |||
| 188 | |||
| 176 | |||
| 214 | |||
| 266 | |||
| 157 | |||
| 108 | |||
| 133 | |||
| 175 | |||
| 146 | |||
| 133 | |||
| 135 | |||
| 108 |
Table A1.11: Chemical composition of CMnNb steel
| C | Si | Mn | P | S | Cr | Mo | Ni | Al | Cu | Nb | N | Sn | Ti | V |
| 0.15 | 0.37 | 1.40 | 0.016 | 0.009 | 0.017 | 0.002 | 0.02 | 0.033 | 0.007 | 0.03 | 0.006 | 0.002 | 0.001 | 0.003 |
Table A1.12: Chemical composition of type 316 L stainless steel
| Steel | C | Si | Mn | P | S | Cr | Ni | Mo | N | Ti | V |
| 316L | 0.02 | 0.44 | 1.73 | 0.03 | 0.01 | 17.25 | 11.2 | 2.2 | 0.03 | 0.001 |
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Table A1.13: Quantitative metallograph results for type 316 stainless steel specimen (Micro JobK03M00208)
| Traverse no. | Grain size(m | % 2nd phase |
|---|---|---|
| 1 | 9.14 | 4.39 |
| 2 | 9.39 | 5.63 |
| 3 | 8.01 | 6.32 |
| 4 | 9.44 | 5.98 |
| 5 | 8.92 | 5.11 |
| Average | 8.98 | 5.48 |
| Standard deviation | 0.58 | 0.76 |
Table A1.14: Hardness results HV30 for specimens in forward – reverse rolling trials
| Sample | Surface 1 | Centre | Surface 2 |
|---|---|---|---|
| T2Z8T1 Average | 295 | 197 | 191 |
| 307 | 197 | 194 | |
| 263 | 192 | 198 | |
| 288 | 195 | 194 | |
| T2Z8T4 Average | 187 | 189 | 187 |
| 189 | 186 | 186 | |
| 184 | 186 | 187 | |
| 187 | 187 | 187 | |
| T2Z8T5 Average | 191 | 189 | 216 |
| 194 | 191 | 216 | |
| 194 | 196 | 213 | |
| 193 | 192 | 215 | |
| T2Z8T6 Average | 404 | 323 | 375 |
| 385 | 307 | 373 | |
| 383 | 307 | 377 | |
| 391 | 312 | 375 | |
| T2Z8T7 Average | 328 | 287 | 406 |
| 329 | 295 | 396 | |
| 329 | 278 | 415 | |
| 329 | 287 | 406 | |
| T2Z8T8 Average | 196 | 191 | 198 |
| 195 | 189 | 195 | |
| 198 | 192 | 194 | |
| 196 | 191 | 196 |
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Table A1.15: Parameters employed in application of constitutive model to 2 pass rolling of Type 316 Stainless Steel
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Table A1.16: Table A1.2: Plate reversal rolling measurements and FE predictions of spread for passes 1-3 of Trial 1
| Pass | Experimental spread | FEM passspread | Cumulative FEM spread | hm (mm) | L | hm/L |
|---|---|---|---|---|---|---|
| 1 | 0.4 | 1.82 | 121.82 | 27.40 | 28.16 | 0.97 |
| 2 | 1.9 | 0.8 | 122.56 | 23.55 | 19.5 | 1.20 |
| 3 | 3 | 1.17 | 123.68 | 20.9 | 20.66 | 1.01 |
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Fig. A1.1: Fatigue specimen for strain reversal tests
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Fig. A1.2: Strain reversal test specimens subjected to compression and tension
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Fig. A1.3: Stress relaxation tests on CMn-Nb steels
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Fig. A1.4: Stress-strain curves (CMn-Nb steel)
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Fig. A1.5: Recrystallisation kinetics (CMn-Nb steel)
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Fig. A1.6: Testing schedule for strain reversal tests
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Fig. A1.7: Compression tests at different temperatures
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Fig. A1.8: Strain reversal tests 0.2T+0.2C
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Fig. A1.9: Strain reversal tests 0.2C+0.2T
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Fig. A1.10: Comparison of compression and reversal behaviour (1)
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Fig. A1.11: Comparison of compression and reversal behaviour (2)
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Fig. A1.12: Comparison of reversal behaviour: 0.2T+0.2C and 0.2C+0.2T
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Fig. A1.13: Symmetric cyclic test
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Fig. A1.14: Comparison of recrystallisation kinetics at 1000°C
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Fig. A1.15: Comparison of recrystallisation kinetics at 1050°C
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Fig. A1.16: Comparison of recrystallisation kinetics at 1100°C
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Fig. A1.17(a and b): Schematic representation of compression of 1 cm cube specimen in Gleeble (a) Axes convention (b) Example of cube undergoing 3 consecutive deformations of 22.5% reduction with interpass turns of 90° in xz and yz planes respectively
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Fig. A1.18: Testing schedule for bi-direction tests
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Fig. A1.19(a and b): Metallography of specimen quenched after the first compression
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Fig. A1.20(a and b): Metallography of specimen in fig. A1.31 after 90 degree turn, reheated and quenched
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Fig. A1.21(a-d): Comparison of recrystallisation kinetics in H-V compression
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Fig. A1.22: Evolution of load and recrystallisation, obtained by stress relaxation, in specimen having undergone repeated compression of 22.5% at 1000°C.
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Fig. A1.23(a and b): Curves showing evolution of recrystallisation and decay of load for 2 reduction sequences: (1) two consecutive 22.5% compressions, (2) two consecutive 22% compressions
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Fig. A1.24(a and b): Curves showing evolution of recrystallisation and decay of load for repeated compression of 22.5% at temperatures of 1000°C and 1100°C
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Fig. A1.25: Evolution of load and recrystallisation for repeated 22.5% compression at 1000°C with 90 degree interpass turn
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Fig. A1.26: Evolution of load and recrystallisation for single compression of 40% at 1000°C
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Fig. A1.27: Evolution of load and recrystallisation for 40% followed by 22.5% compression at 1000°C
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Fig. A1.28: Evolution of load and recrystallisation for 22.5% followed by 40% compression at 1000°C
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Fig. A1.29: Evolution of load and recrystallisation for single compression of 53.5% at 1000°C
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Fig. A1.30: Evolution of load and recrystallisation at 1000°C for compression of 40% followed by 22.5% with interpass horizontal turn of 90 degrees
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Fig. A1.31: Evolution of load and recrystallisation at 1000°C for compression of 22.5% followed by 40% with interpass horizontal turn of 90 degrees Fig. A1.32: Decay of load for triple hit of 22.5% at 1000° with 90 degree horizontal turn at each interpass
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Fig. A1.33: Decay of load at 1100°C for triple hot of 22.5% with 90 degree turns during 1st and 2nd interpasses in horizontal and transverse/vertical planes respectively
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Fig. A1.34: Decay of load at 1100°C for triple hit of 22.5% with 90 degree turns during 1st and 2nd interpasses in transverse/vertical and horizontal planes respectively
Page 121
Fig. A1.35(a and b): Evolution of recrystallisation and decay of load for range of strain paths at 1000°C
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Fig. A1.36: Predicted cooling curves for selected points in Type 316 Stainless Steel specimen at Initial Uniform Temperature of 1150°C
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Fig. A1.37: Predicted cooling curves for selected points in Type 316 Stainless Steel specimen at Initial Uniform Temperature of 1120°C
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Fig. A1.38: Grain growth curve for type 316 stainless steel specimen held at 1100°C, fitted using TableCurve2D from measurements of grain size in samples held at temperature for times in the range 0 – 15 min
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Fig. A1.39(a and b): Load and torque traces for rolling of type 316 stainless specimen in single pass (23 mm to 18.5 mm)
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Fig. A1.40(a-d): Photographs of microstructure at ¼ depth and centre positions in sample 1 taken from type 316 stainless steel specimen 4R1F285 immediately after rolling in single pass from 23 mm to 18.5 mm thickness at 1100°C
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Fig. A1.41(a and b): Load and torque traces for rolling of stainless specimen in 2 passes (23 mm to 18.5 mm to 15 mm) with a 10 s interpass time and no turning
(a) Load
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(b)Torque for top and bottom rolls
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Page 128
Fig. A1.42(a-f): Photographs of microstructure at ¼ depth and centre positions in samples from transverse sections A, B and C taken from type 316 stainless steel specimen 4R1F287 immediately after rolling in two 20% passes (interpass '10' s, 1100°C, no turn) and reheated respectively for 0, 5 and 60 s (test reports K4M3011, K4M0312)
(a) Unreheated, at ¼ depth
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(b) Unreheated, at centre position
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(c) Reheated for 5 s, at ¼ depth
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(d) Reheated for 5 s, at centre position
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(e) Reheated for 60 s at ¼ depth
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(f) Reheated for 60 s, at centre position
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Fig. A1.43(a and b): Load and torque traces for rolling of type 316 stainless steel specimen in two 20% passes with 90° turning in '10 s' interpass time
(a) Load
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(b) Torque traces
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Page 132
Fig. A1.44(a-l): Photographs of microstructure at ¼ depth and centre positions in samples, at locations (1) perpendicular and (2) parallel to the rolled surface, in transverse sections A, B and C taken from type 316 stainless steel specimen 4R1F287 immediately after rolling in two 20% passes with 90° turn ('10 s' interpass, temperature 1100°C) and reheated respectively for 0, 5 and 60 s (test reports K4M0312
(a) Unreheated, sample from location 1, at ¼ depth
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(b) Unreheated, sample from location 1, at centre position
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(c) Unreheated, sample from location 2, at ¼ depth
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(d) Unreheated, sample from location 2, at centre position
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(e) Reheated for 5 s, sample from location 1, at ¼ depth
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(f) Reheated for 5 s, sample from location 1, at centre position
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(g) Reheated for 5 s, sample from location 2, at ¼ depth
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(h) Reheated for 5 s, sample from location 2, at centre position
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(i) Reheated for 60 s, sample from location 1, at ¼ depth
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(j) Reheated for 60 s, sample from location 1, at centre position
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(k) Reheated for 60 s, sample from location 2, at ¼ depth
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(l) Reheated for 60 s, sample from location 2, at centre position
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Page 138
Fig. A1.45(a and b): Heating and cooling curves for points at centre and surface of specimen obtained from thermocouple readings during residence in and exit from reheating furnace
(a) Reheating
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(b) Cooling
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Page 139
Fig A1.46: Spring curve for Cavendish Rolling Mill (see Tech Report 6)
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Page 140
Fig. A1.47(a-d): Micrographs of homogenised Type 316 Stainless Steel samples 4R1F64B, 4R1F71B, 4R1F284B and 4R1f514B (as in Test Report No. K4M0340)
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Page 141
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Page 142
Fig. A1.48: Temperature profile employed prior to pass 2 when reheating to 1040°C and holding for 60 s
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Fig. A1.49: Temperature Profile employed when reheating to 950°C prior to pass 2 (without turn)
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Fig. A1.50(a and b): Load and torque traces in Pass 2 for specimen between passes given single reheat to 950°C
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Fig. A1.51(a and b): Load and Torque Traces in Pass 2 for specimen between passes given single reheat to 950°C and turn through 90° in transverse – vertical plane
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Fig. A1. 52(a and b): Load and Torque Traces for specimen in interpass given reheat to 1040°C- held for 60 s, followed by quench and further reheat to 950°C but no turn
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Page 146
Fig. 53(a-d): Micrographs of Type 316 Stainless steel sample taken from bar 4R1F284A1 (a) ,(b) held at 950°C for 10 s, resp. at 1/4depth and centre positions (c), (d) held for 60 s at 1/4depth and centre positions
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Fig. 54(a-d): Micrographs of Type 316 Stainless steel sample taken from bar 4R1F284A2 (a) ,(b) held at 950°C for 10 s, resp. at 1/4depth and centre positions (c), (d) held for 60 s at 1/4depth and centre positions
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Page 149
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Fig. 55(a-d): Micrographs of Type 316 Stainless steel sample taken from bar 4R1F64A1 (a), (b) held at 950°C for 10 s, resp. at 1/4depth and centre positions (c), (d) held for 60 s at 1/4depth and centre positions
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Page 151
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Fig. 56(a-d): Micrographs of Type 316 Stainless steel sample taken from bar 4R1F64A2 (a), (b) held at 950°C for 10 s, resp. at 1/4depth and centre positions (c), (d) held for 60 s at 1/4depth and centre positions
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Fig. A1.57. Image Quality map obtained by EBSD for sample 4R1F64A1B (with extra reheat) (400 microns x 413 microns)
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Figure A1.58: Image Quality map obtained by EBSD for sample 4R1F284A1B (without extra reheat)(400 microns x 500 microns)
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Fig. A1.59(a and b): Facilities for plate reversal rolling trials
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Fig. A1.60: Rolled profiles of the samples
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Fig. A1.61(a-f): Load and Torque in Trial 4
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Fig. A1.62(a and b): Load and Torque in Trial 1 Fig. A1.63: Etch of as-supplied Type 316 stainless steel specimen contrasting central core and outer layers (Macro JobK03M00208)
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Fig. A1.65: Microstructure of Type 316 stainless steel specimen showing second phase of delta ferrite
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Fig. A1.64: Microstructure of Type 316 stainless steel specimen at quarter depth position
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Fig. A1.66: IPF map (and key) for sample 4R1F64A1B (400 microns x 413 microns)
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Fig. A1.67: IPF map (and key) for sample 4R1F284A1B (400 microns x 500 microns)
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Fig. A1.68(a-c): Metallography of trial 1 in forward–reverse rolling
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Fig. A1.69(a-c): Metallography of Trial 4 in forward-reverse rolling
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Fig. A1.70: Metallography of Trial 7 in forward-reverse rolling
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Fig. A1.71(a-c): Metallography of Trial 8 in forward-reverse rolling
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Fig. A1.72(a-c): Metallography following repolishing etc. of Trial 7 (exhibiting martensite) in forward-reverse rolling
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Fig. A1.73(a-c): Curves showing, for each hit of double compression test, the stress-time and stress-strain
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Fig. A1.74(a-f): Predicted components of logarithmic strain in 10 mm cube of type 316 stainless steel after 40% reduction in Gleeble machine at 1000°C (predictions a-c in mid-horizontal plane)
(a) Longitudinal normal
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(b) Vertical normal component
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(c) Transverse normal component
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(d) Longitudinal-transverse shear component
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(e) Transverse-vertical shear component
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(f) Longitudinal-vertical shear component
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Fig. A1.75: Transverse profile predicted by FEM for 3 passes of trial (spread values given in Table A1.2)
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Fig. A1.76: Plate reversal rolling: predicted equivalent plastic strain distribution in quarter section of plate in Pass 1 of Trial 1
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Fig. A1.77: Plate reversal rolling: predicted equivalent plastic strain distribution in quarter section of plate in Pass 2 of Trial 1
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Fig. A1.78: Plate reversal rolling: predicted equivalent plastic strain distribution in quarter section of plate in Pass 3 of Trial 1
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Fig. A1.79(a-d): Predictions, for pass 1 of H-H rolling schedule, of PEEQ strain, Mises stress, dislocation density and grain size
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Fig. A1.80(a-d): Predictions, for pass 1 of H-H rolling schedule, of PEEQ strain, Mises stress, dislocation density and fraction recrystallised
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