Detailed Technical Report by CEIT

Author:D Jorge-Badiola- I Gutierrez
Pages:175-206
SUMMARY

Summary- A2.1 Links with other partners and workpackages- A2.2 WP1: Evaluation of constitutive models- A2.3 WP2: Experimental investigation of constitutive behaviour- A2.4 WP3: Material characterisation- A2.5 WP4. Formulation of constitutive laws- A2.6 Conclusions- A2.7 References

 
CONTENT

Summary

The work carried out by CEIT in the present project has focused on the following topics:

Performing hot torsion tests in order to obtain the flow curves under monotonic and strain reversal conditions for a set of steels: a Nb microalloyed steel, a medium carbon steel and a duplex stainless steel. These steels were provided by other partners.

Modelling the hot working flow curves for the Nb microalloyed steel for monotonic and strain reversal conditions.

Investigating the effect of the reversion of the strain on the recrystallisation for the Nb microalloyed and the medium carbon steels.

Producing strain reversal cycles under pre-determined conditions in order to simulate the reversions of the shear strain taking place under the rolling rolls.

Performing hot torsion reversal tests and sequences on polished and marked as- cast and wrought duplex stainless steel specimens in order to investigate the effect of the reversal on the J- G interface and to connect it with damage formation.

The main results that can be outlined from the present work are listed in the following:

A model previously proposed by other authors has been applied successfully to model the hot torsion curves under monotonic conditions.

The main parameters describing the transient on the flow curve after the reversion have been determined and related to the deformation conditions. The previous model for monotonic tests has been modified in order to describe the entire stress-strain curve (including the transient) when a reversion of the strain takes place during the deformation.

The main characteristics of the effect of the transient after the reversal on the further softening kinetics have been determined. It has been shown that, depending on the magnitude of the reversion, the softening kinetics can be delayed or accelerated. The total absolute strain is not a good parameter to describe the effect of the reversion. The results have been discussed in terms of the stored energy.

Stress and softening data have been produced under conditions specified by different partners, according to the simulations/modeling they were performing.

Successive reversions lead to lower stress levels than those reached with the same total absolute strain applied under monotonic conditions.

In duplex stainless steel, the stress-strain curve is fully reversible during the reversal. This cannot be related to the dissolution of the substructure, but to the internal stresses coming from the two phases. For small forward/reverse strains, the sliding at the interface is the main component and this one is fully reversible. The cracks become evident at the interface (mainly for the as-cast material) for intermediate strains.

A2.1 Links with other partners and workpackages

The work carried out at CEIT has mainly used torsion facilities to perform multi pass deformation sequences involving or not reversions of the strain. The performed activities have been scheduled within the different workpackages in agreement with the work- programme agreed with the rest of the partners. The activities carried out under the different workpackages and the link with other partners is summarized in the following scheme.

[VER GRAFICO EN PDF ADJUNTO]

A2.2 WP1: Evaluation of constitutive models

A2.2.1 Introduction

The aim within this part of the work was to provide a model able to predict the hot working mechanical behaviour of a low carbon Nb microalloyed steel.

A.2.1.2. Description of the model

It is well established that the mechanical behaviour under hot working conditions is strain rate [VER SIMBOLO EN PDF ADJUNTO] and temperature (T) dependent. Austenite has a relatively slow recovery rate, and dynamic recrystallisation activates for strains higher than a critical value, [VER SIMBOLO EN PDF ADJUNTO]. The development of a model aimed to predict the shape of the stress-strain curve needs to consider separately the two strain ranges, [VER FORMULA EN PDF ADJUNTO]

Strain hardening and dynamic recovery.

The model proposed by Laasraoui and Jonas [A2.1] has been applied to predict the flow curves. It is based on the following formulation:

[VER FORMULA EN PDF ADJUNTO]

With [VER SIMBOLO EN PDF ADJUNTO] the dislocation density and [VER SIMBOLO EN PDF ADJUNTO] the shear strain. The substitution of appropriate functions describing the stored energy and recovery terms and the integration of the resulting equation [A2.1] leads to the following expression for the flow stress,[VER SIMBOLO EN PDF ADJUNTO] as a function of the strain:

[VER FORMULA EN PDF ADJUNTO]

The involved parameters are the yield stress [VER SIMBOLO EN PDF ADJUNTO], the saturation stress attributable to the balance between strain hardening and dynamic recovery alone, [VER SIMBOLO EN PDF ADJUNTO] and a term,[VER SIMBOLO EN PDF ADJUNTO],expressing the contribution of dynamic recovery. This term can be expressed as a function of the austenite grain size, do, the strain rate and the temperature:

[VER FORMULA EN PDF ADJUTNO]

With [VER SIMBOLO EN PDF ADJUTNO] the activation energy. The saturation stress,[VER SIMBOLO EN PDF ADJUNTO] can be expressed, as a function of the strain rate and the deformation temperature through the Zener-Hollomon equation:

[VER FORMULA EN PDF ADJUNTO]

Dynamic recrystallisation range

The model for the dynamic recrystallisation part of the curve leads to the following expression:

[VER FORMULA EN PDF ADJUNTO]

Where [VER SIMBOLO EN PDF ADJUNTO] and [VER SIMBOLO EN PDF ADJUNTO] are determined as before,[VER SIMBOLO EN PDF ADJUNTO] ranges between 1.3 and 1.5, [VER SIMBOLO EN PDF ADJUNTO] the strain for 50% softening by dynamic recrystallisation, [VER SIMBOLO EN PDF ADJUNTO] is the steady state stress and [VER SIMBOLO EN PDF ADJUNTO] the peak strain:

A2.2.3 Experimental: monotonic torsion tests

Monotonic torsion tests have been performed on a C-Mn-Nb steel provided by Corus UK Limited with the composition shown in Table A2. 1. The deformation temperatures ranged in the interval 850 to 1200°C and the strain rates between 0.01 s-1 and 1 s-1. Prior to the deformation, the specimens were reheated at 1250°C, held there over 15 min and subsequently cooled down to the deformation temperature. The stress-strain curves were calculated using the method proposed by Fields and Backoffen [A2.2].

A2.2.4 Comparison with experiment

The above mentioned formulation has been applied to the experimental curves obtained from the monotonic torsion tests leading to the following expressions:

[VER FORMULA EN PDF ADJUNTO]

It is to be noted that the values obtained for m (-0.08) and for [VER SIMBOLO EN PDF ADJUNTO]: (-9000 J/mol) are not far from those obtained previously by other authors [A2.1,A2.3]. Additionally:

[VER FORMULA EN PDF ADJUNTO]

This model predicts reasonably well the experimental stress strain curves for [VER SIMBOLO EN PDF ADJUNTO], as can be seen in the examples shown in Fig. A2.1.

A2.3 WP2: Experimental investigation of constitutive behaviour

The main objectives of this part of the work are listed in the following:

To investigate, the effect of the reversion on the stress and the recrystallisation kinetics, using a hot torsion allowing the application of relatively large strains without the instabilities problems usually associated to tension and compression.

To simulate the effect of the shear strain reversion taking place in the roll gap.

To investigate the effect of the shear strain reversion on the damage formation during hot working on a duplex stainless steel.

To provide experimental results to other partners from specially designed torsion tests.

A2.3.1 Experimental: Selection of the materials

The steels used to perform the torsion strain reversal tests are listed in Table A2. 1.

C-Mn-Nb steel

The same C-Mn Nb steel provided by Corus UK Limited has also been used in order to investigate the effect the reversal has on the flow curves and on the recrystallisation kinetics during the transient after a reversion of the strain. The composition of this steel was selected as close as possible to the one used in a previous project [A2.4].

Medium carbon steel

A medium carbon steel provided by CSM has been used to obtain stress-strain curves under specific conditions defined by CSM in order to generate useful data to be used into the FEM modelling. The aim of performing these tests was to get complementary information that could be applied for modelling mechanical behaviour under complex deformation mode. The chemical composition of this steel is given by CSM in Table A3.1 of Appendix 3.

Duplex stainless steel

A duplex stainless steel provided by CSM has been used to perform torsion tests involving different strain paths. This steel belongs to the cast identified as 426877 with a composition shown in Table A2. 1. As-cast and wrought materials have been used to perform the tests. The wrought material corresponds to the one identified as MAT 1 that was industrially hot rolled (ILVA) to a 77% reduction. Previous works carried out at CEIT [A2.5-A2.11] have shown that the as cast and the wrought materials present different microstructures and behave differently when hot deformed. It was aimed in the present work to investigate how these materials behave under strain reversal tests.

A2.3.2 Experimental: Strain reversal tests

The same torsion machine used previously allows to perform multipass torsion tests, including the reversion of the strain between two consecutive passes. The experimental work procedure applied for each material is described in the following.

C-Mn-Nb steel

Strain reversal torsion tests have been carried out with this steel in order to:

Obtain additional information on the effect the reversion has on the mechanical response of the steel under a broad range of conditions.

Investigate the effect the reversion has on the recrystallisation kinetics.

To reach the first of these objectives, two consecutive passes were applied with a reversion of the twist between both. The flow curves were recorded and compared. In order toinvestigate the effect of the reversion on the recrystallisation, the following sequences were applied:

Two pass tests. Two forward passes, separated by a given holding time were applied, according to the schedule shown in Table A2.2. The second pass was used to determine the fractional softening caused by the holding time at the deformation temperature.

Three pass tests. The first pass was applied in the forward and the second and the third ones in the reverse. A holding time was applied between the second and the last pass. The deformation conditions and amount of reversal applied in the second pass are shown in Table A2.2.

The static fractional softening was determined from the stress-strain curves by the 2% offset method:

[VER FORMULA EN PDF ADJUNTO]

Where [VER SIMBOLO EN PDF ADJUNTO] are the 2% offset yield stress in the fully recrystallised steel and after the holding time respectively and Vpre is the pre-stress before unloading for holding. This method provides results that correlate well with the recrystallized fraction obtained by quantitative metallography for microalloyed steels [A2.12].

In all the cases, the material was preheated before deformation to 1250°C, held there during 15 min and cooled to the deformation temperature.

Medium carbon steel

The torsion tests performed on this steel can be classified as follows:

Monotonic tests and reversal tests: carried out in order to obtain constitutive experimental data to feed the FEM programs (pure shear).

Multipass tests to determine the softening taking place during given holding times applied after different strain paths.

Multipass reversal tests: These tests include a sequence of different low strain passes with a series of strain reversals. They are aimed to simulate the sequence of reversions of the shear component that takes place under the rolls. The sequence simulates what happens during the rolling passes, assuming no softening takes place from one pass to the next one.

The tests were carried out according to the conditions predefined by CSM, Table A2.3. The samples were reheated at a temperature of 1050°C and held there for 2 min, cooled to the deformation temperature and held there for 15 s before the start of the deformation sequence.

Multipass torsion sequences involving combinations of pre-strain, reverse strain and interpass holding times were applied, according to the details shown in Table A2.3. The deformation pass applied after the holding period allowed determining the softening fraction according to the 2% offset method. The sequence, see Table A2.4, was scheduled in order to simulate the reversion of the shear that takes place in the roll gap (no holding time) andbetween the passes (holding time after the reversion). Short interpass holding times (0.3- 0.9 s) were applied that have been estimated to be comparable to those in the rolling mill. The sequence in Table A2.5 was repeated four times for every set of multipass conditions and two times for those conditions denoted by * in Table A2.4.

Duplex stainless steel

The material was heated to the deformation temperature and held there for 1 h. The conditions for these tests are shown in Table A2.6. Two strain rates (0.1 and 1 s-1), two deformation temperatures (950 and 1100°C) and different forward and reverse strains were applied.

All along the present work, the absolute strain and absolute stress have been used, for simplicity, to plot the stress-strain curves.

A2.3.3 Results on the C-Mn-Nb steel

Effect of the reversal on the stress-strain curves

The graphs in Fig. A2.2 show the stress strain curves obtained for the reversals carried out after 0.3 and 0.7 pre-strains at 1100 and at 850°C. It can be seen that just after the reversal, the stress increases rapidly to reach a level slightly lower than the pre-stress. This is followed by some stagnation of the stress and defines a plateau that is not so clearly distinguished than on the tests carried out previously at a lower strain rate (0.1 s-1) [4].

For the case of the test carried out at 1100°C with a pre-strain within the dynamic recrystallisation range (+0.7), the curve after the reversal reaches directly the stress corresponding to the steady state, without passing through the peak. This indicates that some interaction between the dynamic recrystallisation and the reversion takes place when the pre-strain in the forward excess Hc. All these results are in agreement with the behaviour previously observed for another steel of similar composition [4,13].

Effect of the strain path on the static softening.

The fractional softening during the holding time after different reversed strains has been determined according to the method explained in Section A2.3.2. In the absence of softening, it is expected that the stress after holding would increase to reach the pre-stress level. In the case of full recrystallisation, the steel would behave independently of the previous strain path. The curves after a partial softening show an intermediate behaviour.

Pre-strain > c

At 1100°C for a pre-strain in the forward of [VER SIMBOLO EN PDF ADJUNTO] which is within the dynamic recrystallisation range, followed by different amounts of reversal, the reversal is interfering with dynamic recrystallisation, as commented before. In this case, the recrystallisation kinetics after the holding time is independent on the reversed strain, probably due to the activation of metadynamic recrystallisation. However, it has to be mentioned that the softening times after the reversals are slightly longer than those corresponding to the monotonic pre-strain of 0.7.

Pre-strain

This is the range that has particularly been investigated in the present work. The experimental results are summarised in Fig. A2.3, for different deformation conditions and strain paths. The following rules are fulfilled:

The full reversion of the strain (+0.3; -0.3), (+0.15; -0.15) produces shorter recrystallisation times than those reached after applying only the pre-strain (+0.3) (+0.15), but longer than expected for a monotonic strain equal to the total absolute strain.

The same is true for some intermediate partial reversion of the strain for example (+0.3, -0.2) for which the softening curve is between those corresponding to the strain path (+0.3;-0.3) and (+0.3) curves.

For small reverse strains, the recrystallisation time is approximately the same than that for the pre-strain. For example, the softening curves for the test (+0.3) and (+0.3;-0.1) approximately overlap.

For even lower pre-strains, (+0.15;-0.06) the recrystallisation times are longer than those for a monotonic pre-strain of 0.15.

This is in agreement with previous results [A2.14-A2.16]. The longest softening times are obtained for reverse strains close to the end of the plateau.

Additional tests

Some additional tests were performed under conditions defined by Corus UK in order to investigate the softening during a short time (5 s) and different strain paths. It was aimed to approach the strains and times involved in industry and in laboratory trials. The obtained results are shown in Table A2.7 and Table A2.8. The time required to get 50% softening and the n value for the Avrami equation are also indicated for certain conditions.

A2.3.4 Results on the medium carbon steel

The medium carbon steel used to perform the torsion tests was the same supplied by CSM also to the University of Oulu for the tension-compression tests. The aim of performing these tests was to get complementary information that could be applied by CSM for the modelling of the mechanical behaviour under the roll gap.

Monotonic tests

The obtained flow curves for the monotonic are shown in Fig. A2.4. The main parameters defining the curves: strain to the peak, [VER SIMBOLO EN PDF ADJUNTO], peak stress, [VER SIMBOLO EN PDF ADJUNTO], the strain for the start of the steady state, [VER SIMBOLO EN PDF ADJUNTO], and the steady state flow stress, [VER SIMBOLO EN PDF ADJUNTO], are shown in Table A2.9.

Strain reversal tests and interpass softening

The obtained stress-strain curves for different strain paths and holding times are shown in Fig. A2.5 for a deformation temperature of 1050°C. The monotonic curves and those corresponding to different strain paths or holding times are superposed on the same graphs. Excepting for the monotonic curves, between the first and the second pass a reversion was applied (no holding time) a holding time took place between the second and the last pass (no reversion). For the deformation sequence, (+0.1, -0.1), none of the applied holding times: 1 s (curve in black) or 10 s (curve in grey) produces a significant softening and the last pass curve approximately superimpose.

When higher forward and reverse strains are applied, some softening is observed, as can be observed in the second graph of the same figure. This last has been obtained for the deformation sequence +0.2, -0.2, leading to 24% and 66% softening after 1 s and 10 s respectively. All the obtained results with this steel are summarised in Table A2.10.

Multipass strain reversal tests

The obtained flow curves with the multipass sequences, carried out at a deformation temperature of 950°C and strain rates of 0.1 s-1 and 1 s-1 are shown in Fig. A2.6. For comparison, monotonic flow curves have also been plotted in the same figure. A sequence of consecutive reversed passes, leads to stress in the passes significantly lower than that for a monotonic test to the same total equivalent strain.

When comparing the flow curve envelope for the multipass test, [VER SIMBOLO EN PDF ADJUNTO] to the monotonic flow curve,[VER SIMBOLO EN PDF ADJUNTO] mono, see Fig. A2.7, it is possible to define a variable [VER SIMBOLO EN PDF ADJUNTO] for the same total absolute strain as:

[VER FORMULA EN PDF ADJUNTO]

The value of [VER SIMBOLO EN PDF ADJUNTO] depends on the pre-strain and on the deformation conditions. High temperatures lead to low values, but high strain rates raise the [VER SIMBOLO EN PDF ADJUNTO]

Main results and conclusions

The sequences involving forward and reverse strains of 0.1 need holding times between passes higher than 10 seconds to initiate static softening. For strains of 0.2, a significant amount of softening is reached for these same holding times.

For small cyclic strains, the stress level in successive passes remains significantly lower than that for a monotonic test to the same total equivalent strain.

A2.3.5 Results on the duplex stainless steel

From previous works carried out at CEIT [A2.5-A2.11], the following characteristics can be outlined that differentiate as cast and wrought duplex stainless steel materials:

As- cast material

Microstructure formed by large primary G-ferrite grains delimited by ridges of austenite. Inside the G-ferrite grains Widmanstätten austenite plates are present. An example of the microstructure is shown in Fig. A2.8.

During the solidification G-ferrite forms from the liquid and the austenite precipitates in solid state during further cooling. As a result, most of the ferrite- austenite interfaces are partially coherent due to the K-S orientation relationship between both phases.

During deformation, the austenite blocks oriented almost at random within the as-cast microstructure, rotate to align according to the imposed deformation conditions. The main deformation mechanisms are: preferential shearing of the ferrite softest phase, interface sliding and austenite block rotation.

Coherence has an important role in hot ductility given that interface sliding is not possible on coherent interfaces and has been observed to concentrate at the incoherent portions, leading to the formation of cracks at these locations.

The torsion curve has the aspect shown in Fig. A2.8. Three regions are observed: elastic region, followed by strain hardening stage to reach a peak, followed by a monotonic decrease of the stress.

The softening is attributed to the formation of damage and no signs of dynamic recrystallisation in the microstructure of the austenite are observed for any of the performed tests.

Wrought material

Microstructure formed by alternate austenite and ferrite parallel bands, Fig. A2.8.

The coherency at the interface between ferrite and austenite has been lost, as a result of the lattice rotations taking place during deformation.

The main deformation mechanism is preferential shearing of the ferrite softest phase and interface sliding.

The sliding at the interface distributes more homogeneously among the different interfaces and damage formation is reduced significantly. The torsion curves present the shape shown in Fig. A2.8: The stress rises to reach a peak, followed by a slight decrease of the stress. This last cannot be attributed to dynamic recrystallisation, since no signs of this last is observed in the microstructure. At the peak, the ferrite has developed subgrains, while the austenite remains nearly undeformed, which is an indication of the strain partitioning taking place between the two phases.

Behaviour of the as-cast material under a reversion of the strain:

The Fig. A2.9(a) shows the stress-strain curve corresponding to a test involving a reversion of the strain after a pre-strain of about 0.06, which is within the range of those taking place within the roll gap during rolling. The test has been carried out at a strain rate of 0.1 s-1. Thecurve after the reversal does not exhibit the plateau commonly observed in single-phase materials. Instead, some parabolic strain hardening is observed to reach the same stress level than before the reversion. The Bauschinger effect manifests as a lower yielding after the reversal than the pre-stress level just before the reversion. A similar behaviour is also observed for higher pre-strains before the reversal, Fig. A2.9(b).

At higher strain rates, no significant changes are observed, due to the reversion of the strain both for small forward and reverse strains, as can be seen for the curves in Fig. A2.10, corresponding to a test carried out following a deformation sequence involving cyclic forward and reverse straining. The same type of behaviour is observed, independently of the reversion and the place of the curve within the cycle. However, for larger pre-strains (>0.2), Fig. A2.9(c), some differences can be outlined: reverse stress after the reversion exhibits a small peak and the stress level is slightly higher than that before the reversion. At pre- strains >0.5, Fig. A2.9(d), some softening is observed after the reversion, probably associated to some damage formation, before fracture.

Behaviour of the wrought material under a reversion of the strain:

In Fig. A2.11(a), the flow curves corresponding to two tests carried out at two different temperatures and the same strain rate of 0.1 s-1 are shown. For the two cases, the reversion of the strain has been applied for a pre-strain of about 0.06. For these small deformations, the obtained curves are not very different from those reached with the as-cast microstructure, Fig. A2.8.

In Fig. A2.11(a-c), the strain reversal curves for higher pre-strains in the forward are shown. It can be seen that for a pre-strain of 0.2, a transient showing a yield stress plateau is observed. After the transient, following the reversion, the strain hardening activates again and, as it happens for the case of single-phase materials, the shape of the curve, after the appropriate shift along the strain axis, becomes similar to that for monotonic tests. For a strain reversal after a higher pre-strain, the plateau does not manifest after the reversal, and there is a complete reversibility of the shape of the curve. The graph in Fig. A2.11(d) shows the flow curves for strain reversal tests carried out at 1000 and 1050°C and a strain rate of 1 s-1. The shape of the curves is very similar to the one obtained for the as-cast material, Fig. A2.9 the same happens for the cyclic tests, Fig. A2.10.

A2.4 WP3: Material characterisation

The work carried out within this work package has mainly concentrated on the investigation of the effect of the reversal on the duplex stainless steels in connection with the damage formation. Some observations have also been done to investigate the interaction between the reversal and the dynamic recrystallisation in the C-Mn-Nb steel.

A2.4.1 Results of the microstructural characterization. Duplex stainless steel

The main characteristics of the as-cast and wrought duplex stainless steel microstructures have been described in the previous section. The main goal of this part of the work has been to analyse the behaviour of the duplex microstructure under a reversion of the strain. For this, some torsion tests have been performed on specimens previously polished and marked with some scratches.

Effect of the reversion on the wrought duplex microstructure

The original alternate elongated ferrite and austenite bands parallel to the torsion axis that are characteristic of the wrought microstructure remain almost unchanged after a small forward and reverse strain, as can be seen in Fig. A2.12. The scratches remain nearly continuous and no damage formation is observed for the strain reversal tests carried out for a pre-strain of 0.06, followed by the full reversion of the strain. The resulting microstructure at the subsurface of the torsion specimen exhibits nearly imperceptible signs of deformation.

The micrographs in Fig. A2.13 show the marked surface of specimens following multipass cyclic reverse torsion tests, for two different strain rates. It can be seen that, after 6 cycles, the scratches maintain the continuity across the ferrite-austenite interface and that there is no signs of damage formation, as was previously observed when a higher degree of reversion was applied [A2.4,A2.17]. The micrograph in Fig. A2.14 shows the duplex microstructure at the subsurface of the torsion specimen without no significant evidence of a substructure development.

Effect of the reversion on the as-cast duplex microstructure:

When small forward-reverse strains are applied to the as-cast material, the scratch remains straight Fig. A2.15. However, large strains lead to the formation of damage. As an example, in Fig. A2.16, the torsion specimen surface is shown for a test deformed in the forward to a strain of 0.56 and in the reverse to fracture, (flow curve in Fig. A2.9). Some displacement of the scratches is clearly evident associated to some sliding at certain G/ J interfaces, probably the incoherent ones that are expected to slide more easily than K-S orientation related ones.

Reversion and damage formation

For the wrought material, the reversibility of the flow curve after the reversal is clearly evident for low and high pre-strains, Fig. A2.17. The austenite blocks act as hard “fibres” into the soft ferrite matrix and rotate to accommodate to the imposed torsion. On reversing the strain, the “fibres” return to the original position, before starting the rotation in the reverse. This rotation is the main responsible for the linear strain hardening in the flow curves of the wrought material, Fig. A2.8. The difference, ’ V, between the stress just after the reversal and the minimum stress during the following transient can be associated to the work required to rotate the “fibres”. This contribution is relatively small for low pre-strains but becomes important for a large deformation, see Fig. A2.18. But for all the conditions, the possible contribution of the dissolution/rebuilding of a dislocation substructure during the transient is masked by the internal stresses coming from the two phases with significantly different mechanical properties.

The consecutive forward and reverse strains around 0.06 are not able to enhance damage formation, at least under pure shear. However, higher strains lead to the early decohesion of the ferrite-austenite interface `in wrought steels. For the as-cast material, the sliding is nearly impossible on the most part of the ferrite-austenite, and concentrates on the incoherent interfaces. This is true for monotonic and also for reverse strains.

A2.4.2 Results of the microstructural characterization. C-Mn-Nb steel:

It has been observed that when the strain reversal takes place within the dynamic recrystallisation range of strains, the behaviour of the flow curve after the reversion is clearly modified. In order to investigate the interaction between DREX and SREV, different tests have been carried at 1050°C and strain rate 0.1 s-1. Two monotonic tests up to H =0.38 (peak strain) and H=0.76 (halfway between the peak and the onset of the steady state), followed by water quenching. Tests involving different reverse strains after the peak strain has been reached have been performed: H =0.38/-0.38, H=0.38/-0.76. The dynamic recrystallisation seems to progress during the reversal that explains the low strain hardening during the second part of the transient observed when the pre-strain is within the dynamic recrystallisation range [A2.13].

A2.5 WP4. Formulation of constitutive laws

After the reversal of the strain for this same steel, a deviation of the flow curve from the behaviour in a monotonic test is observed (Bauschinger effect).

A2.5.1 Modelling the transient after a reversion of the strain for the C-Mn-Nb steel

The mechanical behaviour after the reversal can be analysed by means of the experimental assessment of several parameters. The first one is the relative drop in stress just after changing the direction of twist, [VER SIMBOLO EN PDF ADJUNTO]. The second one refers to the length of the plateau,[VER SIMBOLO EN PDF ADJUNTO](defined as the strain range where [VER SIMBOLO EN PDF ADJUNTO]. Finally, the third selected parameter,[VER SIMBOLO EN PDF ADJUNTO] or Bauschinger strain is the strain required to reach the same stress value than that at pre- strain, [VER SIMBOLO EN PDF ADJUNTO]

For the tests carried out under constant absolute Z, it has been found that the relative drop in stress is approximately independent of the test conditions, excepting the pre-strain, leading to the following relations between [VER SIMBOLO EN PDF ADJUNTO] and the pre-stress,[VER SIMBOLO EN PDF ADJUNTO] see Fig. A2.19(a):

[VER FORMULA EN PDF ADJUNTO]

The [VER SIMBOLO EN PDF ADJUNTO] is mainly dependent on the prestrain,[VER SIMBOLO EN PDF ADJUNTO]. Fig. A2.19(b):

[VER FORMULA EN PDF ADJUNTO]

The Bauschinger strain [VER SIMBOLO EN PDF ADJUNTO] appears to follow the same trend, leading to:

[VER FORMULA EN PDF ADJUNTO]

For the modelling of the flow curve after the reversal,[VER SIMBOLO EN PDF ADJUNTO] the following equation has been used:

[VER FORMULA EN PDF ADJUNTO]

Whith [VER SIMBOLO EN PDF ADJUNTO] and [VER SIMBOLO EN PDF ADJUNTO] determined through Equations (A2.5) and (A2.6), b=4.41 and B being a function of Z and the pre-strain. Two examples of the predictions obtained with the model are shown in Fig. A2.20. Such an equation is very sensitive to the value of B and some of the above Equations (A2.13 to A2.15) need to be used as filters, when using the mentioned formulation in order to avoid incoherent results.

A2.5.2. Strain rate change simultaneous to the reversal

The parameters used to characterise the transient,[VER SIMBOLO EN PDF ADJUNTO] and [VER SIMBOLO EN PDF ADJUNTO] appear as being independent on the deformation conditions. Additional tests in which the strain rate is modified in sign and absolute value at the same time have been carried out.

Drop in strain rate + reversal: Several tests involving a drop in the strain rate of one order of magnitude (0.1 s-1 o0.01 s-1) have been performed. The decrease in the strain rate makes the Bauschinger effect more pronounced and the drop in stress is higher than that at constant absolute strain rate. Additionally, the length of the plateau becomes larger. This length increases as the pre-strain does, but at a faster rate than that stated for constant absolute strain rate tests. These results are not surprising since, at lower strain rate, the excess of mobile dislocation density produced by the decrease in strain rate superimpose to those due to the dilution of the substructure by the reversal.

Rise in strain rate + reversal: Torsion strain reversal tests at 950°C involving an order of magnitude increases in strain rate (0.01 s-1 o0.1 s-1) at the same time the strain is reversed have been performed. The main results obtained from these tests are the near complete disappearance of any plateau and the change of the sign of the variation of stress after the reversion/rate change. Additionally, the transient seems to shorten as the prestrain gets larger. The balance between the need for more mobile dislocation density to sustain the rise in the strain rate and the dissolution due to the reversal could explain the described observation.

A2.5.3 Modelling the relation between the softening kinetics and the strain path

For the monotonic tests the softening times decrease as the pre-strain increases. By reversing the strain, the recrystallisation times depend on the reversed strain, Fig. A2.21. All the softening curves obtained in this work can satisfactorily be fitted by a Johnson-Mehl- Avrami-Kolmogorov equation of the form:

[VER FORMULA EN PDF ADJUNTO]

With X, the fraction softened, t, the holding time, t0.5, the time required for 50% softening and n=1. For monotonic conditions, t0.5 can be estimated, as a function of the strain, the strain rate and the temperature, using the equations available in the literature for Nb microalloyed steels. However, t0.5 depends on the strain path and it is difficult to find a parameter taking into account such effect. It is clear that the total absolute strain is not the appropriate parameter, Fig. A2.21. Lindh et al [A2.18], proposed that the effective strain can be expressed in terms of the permanent and redundant strain in the way:

[VER FORMULA EN PDF ADJUNTO]

This expression is applicable for large reverse strains, but it is unable to predict the observed delay on the softening kinetics during the transient.

The driving pressure for static recrystallisation after hot working [VER SIMBOLO EN PDF ADJUNTO] can be assumed to decrease with time due to the early consumption during recrystallization of the regions with the highest stored energy, the variations in the mobility of the migrating front due to the segregation of the solutes and/or to recovery processes in the non recrystallised areas. Aquite general formula [A2.19-A2.21] relating the decay with time of the driving pressure for recrystallization can be written in the from: FR (t) =

[VER FORMULA EN PDF ADJUNTO]

With [VER SIMBOLO EN PDF ADJUNTO] a relaxation time and 0 u 1. Assuming site saturation, the recrystallised fraction can be expressed as [A2.22]:

[VER SIMBOLO EN PDF ADJUNTO]

Assuming the driving pressure for nucleation and for growth are approximately the same during the early stages of recrystallization and preferential nucleation at grain boundaries [VER FORMULA EN PDF ADJUNTO] being [VER SIMBOLO EN PDF ADJUNTO] a geometric factor and [VER FORMULA EN PDF ADJUNTO] the austenite specific grain boundary area before recrystallization starts. Assuming the temperature dependent mobility, m, remains constant with time, this equation can be rewritten as:

[VER FORMULA EN PDF ADJUNTO]

To make, after integration, the time dependence in this Equation consistent with the one found experimentally (n = 1) when applying Equation (A2.17) to the present steel:

[VER FORMULA EN PDF ADJUNTO] the integration leads to:

[VER FORMULA EN PDF ADJUNTO]

In this equation,[VER SIMBOLO EN PDF ADJUNTO]and [VER FORMULA EN PDF ADJUNTO] depend on the strain and strain path;[VER SIMBOLO EN PDF ADJUNTO] The variation of [VER SIMBOLO EN PDF ADJUNTO] has been determined [A2.23], assuming the full reversibility of the shape of the grains during the reversal [A2.24]. The following expression:

[VER FORMULA EN PDF ADJUNTO] allows making an estimation of the relative driving pressure for recrystallization for different strain paths. The estimation is refereed for each set of experimental results to a particular forward strain [VER SIMBOLO EN PDF ADJUNTO], Fig. A2.22. The plain symbols correspond to the tests involving a reversion of the strain. It can be seen that, in general, during the transient after the reversal a decrease in the estimated relative driving pressure is observed.

The driving pressure for recrystallisation is defined by the stored energy that can be expressed as the sum of two terms the first one takes into account the dislocation density at the cell interiors and the second one the misorientation across the cell boundaries. The reversion of the strain is expected to modify the balance between the two contributions. The stress relates to the total dislocation density, but not to their arrangement. However, if one plots the pre-stress before holding, as a function of the (Svt0.5)-1/5, Fig. A2.23, a linear relation is obtained for each temperature and strain rate that is applicable to both monotonic and strain reversal tests. The use of this type of representation only gives approximate softening times following a reversion but it is not able to predict the maximum in the recrystallisation times observed at the end of the plateau.

A2.6 Conclusions

Strain reversal tests

The tests carried out in the two carbon steels confirm, for a broad range of conditions, the mechanical behaviour previously deduced in a previous ECSC project [A2.4]. The reversion of the strain produces a transient on the flow curves that can be associated to the partial dissolution of the substructure and the rebuilding of a new one compatible with the new deformation conditions.

The transient is characterised by a plateau (no strain hardening) the main parameters defining it: stress and length (strain) depend on the pre-strain and initial and final strain rates.

Modelling. C-Mn-Nb steel

The model proposed in Reference (A2.1) can be successfully applied to predict the monotonic flow curves of the Nb microalloyed steel in the present work. This model can be modified by using an additional term to describe the transient after the reversal for constant absolute strain rate and temperature. In such a case, the transient stress and strain only depend on the pre-stress or the applied pre- strain.

The effect of the reversal on the softening kinetics has clearly been outlined in the present work. The partial dilution of the substructure during the reversion leads to a decrease of the stored energy and a delay in the softening. The longest softening times are observed at the end of the plateau (highest dilution). The accurate modelling of such effect needs the use of physically based models that are not available at this moment. The instantaneous pre-stress before the holding can be used to make a rough estimation of the delay produced by the reversion on the softening kinetics, but this parameter has not enough sensibility to describe with accuracy such an effect.

Duplex stainless steel

The differences between the as-cast and wrought materials in terms of the answer to the reversal are not significant at low strains, but increase with increasing the pre-strain, as a result of the reversibility of the flow curve.

In duplex stainless steel, the most of the cases, there is a lack of the stress stagnation after the reversion commonly observed for single-phase materials. For the wrought material, the reversibility of the flow curve after the reversal is clearly evident for low and high pre-strains. The austenite blocks act as hard “fibres” into the soft ferrite matrix and need to rotate to accommodate to the imposed torsion. On reversing the strain, the “fibres” return to the original position, before starting the rotation in the reverse. This rotation is the main responsible for the linear strain hardening in the flow curves of the wrought material and is the responsible of difference, ’ V , between the stress just after the reversal and the minimum stress during the following transient. This contribution is relatively small (for low pre-strains but becomes important for a large deformation.

In a duplex microstructure, the contribution of the dissolution/rebuilding of a dislocation substructure during the transient is masked by much strong contributions coming from the presence of the two phases with significantly different mechanical properties.

The reversal involving forward and reverse strains around 0.06 is not able to enhance damage formation. However, higher strains were observed to lead to the early decohesion of the ferrite-austenite interface in wrought steels. For the as-cast material, the sliding is nearly impossible on the most part of the ferrite- austenite, as a result of the semi-coherent character they have. The interface sliding, which is an important source of damage in duplex steels, mainly concentrates on the incoherent interfaces. This is true for monotonic and also for reverse strains.

Cyclic forward/reverse torsion tests

The stress level reached in subsequent passes involving the reversion of the strain is significantly lower than that corresponding to a monotonic test to the same total absolute strain.

A2.7 References

A2.1 Laasraoui, A and Jonas, J J: Metallurgical Transactions A, 1991, Vol. 22A, 1545- 1558.

A2.2 Fields, Jr D S and Backoffen, W A: Proc. ASTM, vol. 57, 1957, 1259.

A2.3 Yoshie, A, Morikawa, H and Onoe, Y: Trans. ISIJ, 1987, Vol. 27, 425.

A2.4 Zhou, M, Morris, P F, Husain, Z, Wiklund, O, Terziyski, T, Peura, P, Karjalainen, L P, Bianchi, J H, Gutierrez, I, Bartolomé, R, Piñol-Juez, A and Iza-Mendia, A: The Effect of Strain Reversal and Strain-Time Path on Constitutive Relationships for Metal Rolling/Forming Processes. Technical Steel Research, EUR 19891 EN, Office for the Official Publications of the European Communities, Luxembourg, 2001.

A2.5 Piñol, A, Iza, A, Gutierrez, I and Urcola, J J: CMMC 96, Key Engineering Materials, Vol. 127-131, Ed. M. Fuentes et al., Trans Tech. Publications, Switzerland, 1997, pp1025-1032.

A2.6 Iza, A, Piñol, A, Gutierrez, I and Urcola, J J: CMMC 96, Key Engineering Materials, Vol. 127-131, Ed. M. Fuentes et al., Trans Tech. Publications, Switzerland, 1997, 1033-1040.

A2.7 Iza-Mendia, A, Piñol-Juez, A, Urcola, J J and Gutierrez, I: Metall. Mater. Trans.,1998, Vol. 29A, 2975.

A2.8 Piñol-Juez, A, Iza-Mendia, A and Gutierrez, I: Metall.l Mater. Trans.. A, 2000,Vol. 31A, 1671.

A2.9 Piñol-Juez, A, Iza-Mendia, A and Gutierrez, I: 13th European Conf. on Fracture (ECF 13) Proc. Eds. Fuentes, M, Elices, M, Martin-Meizoso, A and Martinez-Esnaola, J M, Elsevier, 2000, Paper Ref. 11U.293.

A2.10 Piñol-Juez, A, Iza-Mendia, A and Gutierrez, I: International Conf. on “Thermomechanical processing: Mechanics, Microstructure and Control, 23-26 June 2002, the Univ. of Sheffield, England.

A2.11 Piñol-Juez, A, Iza-Mendia, A and Gutiérrez, I: In European Research Conf. on “ Plasticity of Materials. Fundamentals, Modelling and Application” European Science Foundation, 25-30, April, Granada, 1998.

A2.12 Fernández, A I, López, B and Rodríguez-Ibabe, J M: Scripta Mater., 1999;Vol. 40: 543.

A2.13 Bartolomé, R, Astiazarán, J I, Iza-Mendia, A and Gutierrez, I: Proc.Thermomechanical Processing of Steels, IOM Communications, May 2000, London, 221.

A2.14 Bartolomé, R, Jorge-Badiola, D, Astiazarán, J I and Gutiérrez, I: Mat. Sci. and Eng. A, 2003, Vol. 344, 340.

A2.15 Jorge-Badiola, D, Bartolomé, R, Martín, S and Gutiérrez, I: International Conf. on “Thermomechanical processing: Mechanics, Microstructure and Control, 23-26 June 2002, the Univ. of Sheffield, England.

A2.16 Jorge-Badiola, D and Gutiérrez, I: Acta Mater., 2004, Vol. 52, 333.

A2.17 Zhou, M, Gutierrez, I, Bianchi, J H, Wiklund, O, Schmidtchen, M and Karjalainen,P: Constitutive Modelling Complex Loading in Metal Forming Processes, ECSC Project 7210.PR/291. 2002 annual report.

A2.18 Lindh, E, Hutchinson, B and Veyama, S: Scripta Metal and Mater, 1993, Vol. 29, 347.

A2.19 Furu, T, Marthinsen, K and Nes, E: Mat. Sci. Tech., 1990; 6: 1093.

A2.20 Humphreys, F J and Hatherly, M: “Recrystallization and Related annealing Phenomena”, Pergamon, Oxford, 1995. p127.

A2.21 Sellars, C M: 3rd Int. Conf. on “Recrystallization and Related Phenomena”, Ed.McNelley, T R, Monterey Institute of Advanced Studies, Monterey, USA, 1997. p81.

A2.22 Zurob, H S, Hutchinson, C R, Brechet, Y and Purdy, G: Acta mater., 2002; Vol. 50, 3075.

A2.23 Cotrina, E, Iza-Mendia, A, López, B and Gutiérrez, I: Metall Mater. Trans. A, 35, 2004, 93.

A2.24 Farag, M M, Sellars, C M and McG. Tegart, W J: “Deformation under hot working conditions” (Special Rep. Nº 108), Iron Steel Institute, London, 1968. p60.

Table A2.1: Composition (wt. %) of the steels used into the project


C Si Mn P S Al Nb V N Mo Cu Cr Ni
C-Mn-Nb .15 .30 1.42 .012 .002 .037 .033 .011 .007 .003 .012 0.02 0.03


Cr Ni Mo Mn Si P S C N
Duplex 23.1 4.83 0.22 1.30 0.51 0.024 0.001 0.025 0.095

Table A2.2: Test conditions for the multipass sequences applied to the C-Mn-Nb steel


Temperature(°C) Strain rate S-1 Strain path Interpass time (s)1st-2ndpass/2nd-3rd pass
850 1 Monotonic
0.3 0/from 5 to 500
0.7 0/from 3-100
0.3/(0.3,0.4)/1 0/5
0.7/(0.1,0.7)/1 0/5
875 0.1 0.3/1 0
0.55/1 0
900 0.1 Monotonic
0.6/0.6 0
930 0.1 0.4/1 0
0.5/1 0
0.65/1.2 0
950 0.1 0.1/1 0
0.2/1 0
0.01 0.1/1 0
0.15/1 0
1050 0.1 Monotonic
0.4/from 0 to 0.4 0
0.01 From 0.05 to 0.16/0.9 0
1100 0.1 0.12/1 From 6to 300
0.15/1 From 25-400
0.2/1 From 16 to 300
0.25/1 From 8 to 200
0.2/0.06/1 0/from 25 to 400
0.2/0.1/1 0/from 35 to 1000
0.20.15/1 0/from 8to 200
0.2/0.2/1 0/from 8to 3000
1 Monotonic
0.3/1 From 0.4 to 40
0.7/1 From0.4 to 5
0.3/(0.1,0.3)/1 0/from 0.4 to 5
0.7/(0.1,0.7)/1 0/5
1150 0.1 0.1/1 0/from 25 to 200
0.15/1 0/from 8 to 100
0.2/1 0/from 3 to 200
0.15/0.06/1 0/from 3 to 1000
0.15/0.1/1 0/from 3 to 1000
0.15/0.15/1 0/from 3 to 1000
1200 0.01 From 0.03 to 0.12/0.8 0

[VER TABLA EN PDF ADJUNTO]

Table A2. 3: Torsion test conditions for the medium carbon steel



Deformation temperature (°C) Strain rate     S-1 First pass Firsth olding time (s) Second pass Hoding time (s) Third pass
950 0.1 2
950 1 2
1000 1 3
1050 0.1 0.8
1050 1 3
1050 10 10
1050 1 +0.1 0 -0.1 -1 -1
1050 1 +0.1 0 -0.1 -10 -1
1050 1 +0.1 0 -0.9
1050 1 +0.2 0 -0.2 -1 -1
1050 1 +0.2 0 -0.2 -10 -1

Table A2. 4: Test conditions for the multipass sequences. medium carbon steel


Temperature(°C) Strain rate S-1 Strain path
950 0.1 Monotonic
Multipass strain-reversal*
1 Monotonic
Multipass strain-reversal
1000 0.1 Multipass strain-reversal*
1 Monotonic
Multipass strain-reversal
1050 0.01 Multipass strain-reversal
0.1 Monotonic
Multipass strain-revesal
1 Monotonic
Multipass strain-reversal

Table A2.5: Forward (+), reverse (-) strains and interpass holding times applied for the multipass sequences in the previous table

[VER TABLA EN PDF ADJUNTO]

Table A2.6: Conditions of the tests carried out with the duplex stainless steel


Material Deformation temperature (°C)
Strain rate
S-1
Prest rain Reverse strain Sequences of cyclic reversions
Ascast 1000 0.1 0.06 0.06
950 0.1 0.2 to fracture
1000 1 0.06 0.06 6 passes
1000 1 0.56 to fracture
950 1 0.2 to fracture
1050 0.1 0.06 0.06
1000 0.1 0.06 0.06
950 0.1 0.22 to fracture
950 0.1 0.8 to fracture
1100 1* 0.17 0.17 10 passes
1050 1 0.06 0.06
1000 1* 0.06 0.06
Wrought 1000 1 0.06 0.06 6 passes
1000 1 0.12 0.12
1000 1* 0.14 to fracture
1000 1 0.17 0.17 10 passes
1000 1 0.17 to fracture
1000 1 0.19 0.19
1000 1 0.8 to fracture
1000 1 0.87 0.87
900 1* 0.17 0.17 10 passes

The results of the tests marked with * were reported in the final report of a previous project [A2.8].

Table A2. 7: t0.5, n, tp and fractional softening after 5 s. holding for different thermal cycles and monotonic prestrains: [VER FORMULA EN PDF ADJUNTO]


Preheating temperature (°C) Deformation temperature (°C) Pre strain t 0.5 (s) n p(s) Fractional softening
1300 1100 +0.3 2.1 1 0.73
1200 1100 2.0 1 0.81
1300 850 78.7 0.8 98 0.24
1300 1100 +0.7 0.6 1 0.96
1200 1100 0.5 1
1300 850 10.2 0.7 33 0.35

Table A2.8: t0.5, n, tp and fractional softening after 5 s. Holding for different thermal cycles and monotonic prestrains: [VER FORMULA EN PDF ADJUNTO]


Preheating temperatur (°C) Deformation temperature(°C) Strain path t 0.5(s) n Fractional softening
1300 1100 +0.3/-0.1 2.3 1 0.77
+0.3/-0.2 1.5 1 0.90
+0.3/-0.3 1.1 1 0.93
+0.7/(-0.7,-0.1) 1.5* 0.89
850 +0.3/(-0.4,-0.3) 0.21/0.18
+0.7/-0.1 16* 0.24
+0.7/-0.25 7* 0.40
+0.7/-0.7 2* 0.85


* estimated

Table A2. 9: Main parameters obtained from the monotonic flow curves. Medium carbon steel.

[VER TABLA EN PDF ADJUNTO]

Table A2. 10: Reversal test conditions and the obtained softening fraction. Medium carbon steel.


Deformation temperature (°C) Strain rate  s-1  Prestrain Reverse strain Holding time (s) Softening fraction (%)
1050 1 0.1 0.1 1 0
1050 1 0.1 0.1 10 8
1050 1 0.2 0.2 1 24
1050 1 0.2 0.2 10 66

Fig. A2.1: Comparison between the experimental torsion curves and the predictions from the model

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.2(a-d): Stress-strain curves obtained at with different strain paths. Strain rate:1 s-1 and. (a) and (b) 1100°C and (c) and (d) 850°C

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.3: Fractional softening for different strain paths. C-Mn-Nb steel.

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.4: Medium carbon steel monotonic flow curves

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.5(a and b): Strain-stress curves for strain reversal tests. Deformation sequences: (a) H=+0.1,-0.1 (b) H=+0.2,-0.2. Medium carbon steel.

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.6(a and b): multipass reversal curves and monotonic tests at 950°C and strain rate (a) 1 s-1, (b) 0.1 s-1.

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.7: Determination of [VER SIMBOLO EN PDF ADJUNTO] using the monotonic and multipass reversal tests

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.8: As cast and wrought duplex stainless steel microstructures and torsion curves at 1000°C and 1 s-1

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.9(a-d): As-cast duplex stainless steel: Strain reversal torsion curves for different strain rates and pre-strains.

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.10: As-cast duplex stainless steel: stress strain curve for a multipass torsion test including the cyclic reversion of the strain

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.11(a-d): Wrought duplex stainless steel. Strain reversal torsion curves for different deformation temperatures and pre-strains.

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.12(a and b): marked torsion specimen surface. Torsion test at 1000°C and 1 s-1. Pre-strain =0.06, reverse strain = 0.06. (a) directly after deformation and (b) after some additional polishing.

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.13: marked torsion specimen surface. Cyclic 6 pass torsion tests carried out at 1000°C. Pre-strain =0.06, reverse strain = 0.06. (a) 1 s-1 and (b) 0.1s-1.

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.14: SEM micrograph at the subsurface of the torsion specimen after a 6 pass cyclic test at 1000°C and 1 s-1. Forward/reverse strain: 0.06.

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.15: Marked torsion specimen surface. Test at 1000°C and 1 s-1. As-cast material. Pre-strain =0.06, reverse strain = 0.06.

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.16: Marked torsion specimen surface. Test at 1000°C and 1 s-1. As-cast material. Pre-strain =0.56, reverse strain to fracture.

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.17: Comparison between the flow curves obtained for different strain reversal tests

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.18: Stress contribution associated to the rotation of the austenite "fibers" during torsion

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.19: Transient parameters for different Z values

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.20: Predicted curves after the reversion compared to experiment

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.21: Time to 50% softening, as a function of the total absolute strain. Symbols: black for monotonic, plain for strain reversal.

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.22: Estimated relative driving pressure, as a function of the total absolute strain. (symbols like in the previous figure).

[VER GRAFICO EN PDF ADJUNTO]

Fig. A2.23: Instantaneous stress before holding, as a function of the product (Svt0.5)-1/5. Plain symbols correspond to strain reversal tests

[VER GRAFICO EN PDF ADJUNTO]