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Mechanical behavior and microstructure evolution during steady-state dynamic recrystallization in the austenitic steel 800H
Materials Science and Engineering A 506 (2009) 101–110
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Mechanical behavior and microstructure evolution during steady-state dynamic recrystallization in the austenitic steel 800H M. Frommert a , G. Gottstein b,∗ a b
Max-Planck-Institut für Eisenforschung GmbH, Max-Planck-Str. 1, 40237 Düsseldorf, Germany Institut für Metallkunde und Metallphysik, RWTH Aachen, 52056 Aachen, Germany
a r t i c l e
i n f o
Article history: Received 20 June 2008 Received in revised form 11 November 2008 Accepted 16 November 2008 Keywords: Steady-state dynamic recrystallization Austenitic steel Microstructure development Texture evolution Transient deformation conditions
a b s t r a c t Investigations of steady-state dynamic recrystallization (DRX) were carried out on an austenitic steel alloy 800H. The influence of strain rate and temperature on the mechanical behavior, microstructure development and texture evolution were analyzed. Strain rate and temperature change experiments during steady-state deformation revealed characteristic interdependencies of flow stress, hardening rate, and grain size. The grain size sensitivity of the flow stress was found to scale with the characteristic length scale of the deformed structure. Based on these observations a new model is proposed that relates the process of DRX to an interaction of mobile grain boundaries with deformation-induced subboundaries. © 2008 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental procedure
Despite extensive research during the past decades the physical mechanisms of dynamic recrystallization (DRX) are not yet fully understood. The subject is not only of academic interest but also of immense importance for industrial processing, e.g. hot rolling: DRX offers a powerful tool for microstructure control and, therefore, a useful way for the optimization of the sheet properties. Furthermore, advances in through-process computer simulation require precise experimental data and physics-based models of the material behavior for each step of the complex process chain (hot rolling, cold rolling, annealing, . . .) for reliable predictions of microstructure and texture evolution. Early models of DRX were based on concepts assuming a simple superposition of deformation and (static) recrystallization [1–3]. While the essential features of microstructure and flow behavior could be reproduced, e.g. the development of grain size, the apparent differences to static recrystallization – like the nucleation mechanisms and the steady-state behavior – could not be accounted for. The current study focused on the steady-state regime of the flow curve. Particular attention was paid to the microstructure and texture development as well as to the transient behavior during strain path changes.
The material used in this investigation was the austenitic steel X10NiCrAlTi3220, also referred to as alloy 800H. Its exact chemical composition is given in Table 1. Cylindrical samples of 5 mm diameter and 7.7 mm height were machined from the statically recrystallized material using Rastegaev geometry [4] with BN as lubricant. Hot Compression tests were performed with true strain rates of 10−4 s−1 ≤ ε˙ ≤ 10−1 s−1 at temperatures of 1000 ◦ C ≤ T ≤ 1200 ◦ C. For texture and microstructure analysis the samples were quenched with cold helium gas immediately after deformation. Details are given elsewhere [5]. The influence of the deformation parameters on the flow stress, dynamically recrystallized grain size, and texture evolution was investigated. Electron backscatter diffraction (EBSD) measurements using a field emission gun scanning electron microscope (FEGSEM) served for the analysis of the local orientation arrangement and for the reconstruction of the microstructural features. The main focus was on the examination of the grain size evolution and the texture development during steady-state DRX.
3. Results 3.1. Plastic flow behavior
∗ Corresponding author. Fax: +49 241 8022608. E-mail addresses: [email protected] (M. Frommert), [email protected] (G. Gottstein). 0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2008.11.035
The characteristic stress–strain curve of a material undergoing DRX exhibits either a single maximum (single-peak behavior) or an oscillating shape (multiple-peak behavior) depending on the deformation parameters, i.e. temperature and strain rate [6]. Fig. 1
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M. Frommert, G. Gottstein / Materials Science and Engineering A 506 (2009) 101–110 Table 1 Chemical composition of the austenitic steel Alloy 800H. Cr Ni Mn Si Ti Cu S P Al Co C Fe
20.35 30.20 0.70 0.42 0.34 0.12 0.002 0.013 0.30 0.05 0.071 bal.
3.2. Microstructure development Fig. 1. Typical flow curves of the austenitic steel Alloy 800H during high temperature deformation at different strain rates and temperatures.
shows the typical flow curves of the austenitic steel 800H in the temperature range 1000 ◦ C ≤ T ≤ 1200 ◦ C and at true strain rates of 10−4 s−1 ≤ ε˙ ≤ 10−1 s−1 . With increasing temperature T or decreasing strain rate ε˙ the flow curves are shifted to lower stress levels. Furthermore, a transition from single-peak to multiple-peak behavior is observed. The slight increase of the stress in the steady-state regime at higher strains (ε > 60%) which is discernible in Fig. 1 is the result of friction due to the increasing contact area between the sample and the compression platens.
The microstructural features were determined from orientation maps measured by EBSD. The initial grain size of the statically recrystallized material (Fig. 2a) was 27.1 m and contained a large fraction of recrystallization twins. During DRX at 1100 ◦ C and strain rates of 1 × 10−2 s−1 (Fig. 2b and c) and 1 × 10−3 s−1 (Fig. 2d), grain refinement was observed. In Fig. 3 the microstructure evolution is shown for constant (triangular symbols) and transient deformation conditions. The full lines indicate the average dynamically recrystallized grain size in the steady-state regime at constant strain rates giving values of 14.9 m (1100 ◦ C; 1 × 10−2 s−1 ) and 21.2 m (1100 ◦ C; 1 × 10−3 s−1 ). Since the steady-state regime was attained at higher strains in case of higher strain rates (see Fig. 1), the grain −2 size at ε ∼ = 40% and ε˙ = 1 × 10 s−1 was not considered for the calculation of the average grain size.
Fig. 2. Microstructure development at 1100 ◦ C: (a) initial microstructure; (b) and (c) deformed at 1 × 10−2 s−1 to true strains of 38% and 96%; (d) deformed at 1 × 10−3 s−1 to 96%; (e) strain rate change from 1 × 10−3 s−1 to 1 × 10−2 s−1 at 56% and further deformation to a total strain of 96%; (f) strain rate change from 1 × 10−2 s−1 to 1 × 10−3 s−1 at 57%, total strain 96%; the compression axis is perpendicular to the sheet plane.
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3.3. Texture evolution The microtextures were obtained from EBSD mappings which contain the full orientation data of each point of the scanned sample surface. Due to the uniaxial compression geometry, the texture is presented in form of inverse pole figures of the compression axis. Fig. 4 shows the texture development for samples deformed at 1100 ◦ C at different true strains. The initial, statically recrystallized texture (Fig. 4a) is rather weak with a maximum intensity of 1.4. At a strain rate of 1 × 10−2 s−1 and a true strain of 38% (Fig. 4b) a strong <1 1 0>-component has developed. With further straining (Fig. 4c–e) the <1 1 0>-component becomes weaker and finally disappears, and the (low) maximum intensity arises at <1 0 0>. In case of the lower strain rate of 1 × 10−3 s−1 (Fig. 4f), after 38% of true strain only the <1 0 0>-component exists which is in agreement with the earlier attainment of the steady-state regime under these conditions (see Fig. 1). Similar textures were found for all testing conditions with minor variations of the maximum intensities which were in the range of 2–3. The texture did not significantly change in the steady-state regime of DRX, even for transient deformation conditions.
4. Discussion 4.1. Constant deformation conditions
Fig. 3. Development of grain size during constant and transient deformation conditions for (a) strain rate changes from 1 × 10−3 s−1 to 1 × 10−2 s−1 and (b) vice versa. The triangular symbols represent the grain size under constant parameters; the square and circular symbols give the values of strain rate changes after true strains of 36% and 56%, respectively.
Early investigations of DRX already showed that the average grain size in the steady-state regime, usually referred to as the dynamically recrystallized grain size dR , does not change with further straining and is supposed to be constant (e.g. [1–3]). Furthermore, for a large variety of materials the DRX grain size dR can be related to the steady-state flow stress s by a power law: s = K · dR
−n
(1)
with K, n: empirical constants and 0.4 ≤ n ≤ 0.8 (e.g. [7]). In this study, a grain size exponent of n = 0.77 was found for the austenitic steel 800H at the given deformation parameters.
The most prominent point of the curve is the maximum which is characterized by the peak stress p and the peak strain εp as a result of deformation-induced hardening superimposed by softening due to DRX. The maximum of the flow curves – and likewise the onset of DRX – is shifted to lower stress and strain values with increasing temperature and decreasing strain rate (Fig. 1). However, the onset of DRX in a polycrystalline material cannot be directly extracted from the flow curve. In the microstructure the nucleation of DRX can be more easily traced. In Fig. 2b at 1100 ◦ C and 1 × 10−2 s−1 , two fractions of grains are discernible after a true strain of 38%: the larger grains are mostly of green color indicating orientations close to the <1 1 0>-fiber axis and belong to the initial structure, whereas the smaller grains developed during DRX. The nucleation mechanisms of DRX are not of concern in this work but were investigated for the same material by Brünger et al. [5] and Wang et al. [8]. After a total strain of 58% the steady-state flow stress regime is attained in the flow curve (Fig. 1), and the microstructure consists of small grains with a single grain size distribution and a constant, average grain size of 14.9 m
Fig. 4. Texture evolution at 1100 ◦ C: (a) initial texture; (b–e) 1 × 10−2 s−1 after true strains of 38%, 58%, 76% and 96%; (f) 1 × 10−3 s−1 and 38% true strain; the maximum intensity of the pole figure is indicated as “max”; note: in this figure, the color code represents the intensity, not the orientation.
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superplastic behavior, which is accompanied by a steady-state grain size. In order to rule out the occurrence of superplastic deformation at the imposed testing conditions, strain rate changes were performed before the attainment of the maximum in the flow curve (Fig. 5). The strain rate sensitivity was calculated according to m=
Fig. 5. Detail from a flow curve at 1100 ◦ C with a strain rate change before the attainment of the peak stress used for the calculation of the strain rate sensitivity.
(Fig. 3a and b). For comparison, at a strain rate of 1 × 10−3 s−1 , the steady-state regime had been already attained after 38%, as can be seen from the flow curve (Fig. 1) and the grain size development (Fig. 3a and b). 4.2. Transient deformation conditions Strain rate changes are often used to determine the strain rate sensitivity m of a material which is defined as m=
d ln d lnε˙
ln(2 /1 ) ln(ε˙ 2 /ε˙ 1 ) ε
(3)
where 1 , 2 , ε˙ 1 and ε˙ 2 are the flow stresses and strain rates prior to and subsequent to the strain rate change. The experiments rendered 0.14 ≤ m ≤ 0.15. In case of strain rate changes at larger strains, i.e. in the steady-state regime, the m-values were slightly higher 0.15 ≤ m ≤ 0.17. In both cases, superplastic deformation can be ruled out and the observed deformation behavior must be attributed to crystallographic glide and DRX only. In case of transient deformation conditions, i.e. a change of the strain rate or temperature, an adjustment of the flow stress according to the actual parameters occurs as already shown by Sakai et al. for a microalloyed steel [9]. In Fig. 6a and b the flow curves of two experiments at 1100 ◦ C are shown with instantaneous changes of the strain rate from 1 × 10−2 s−1 to 1 × 10−3 s−1 and vice versa; the corresponding strain rate versus strain schedule is given in Fig. 6c and d. For comparison, the flow curves at constant strain rates are added to the diagrams as gray curves. The flow stress change following a strain rate change is composed of three regimes:
(2)
corresponding to a power law dependency of the flow stress ˙ At low homologous temperatures, the value on the strain rate ε. of m in fcc metals is usually small (m ∼ = 0.01), and the flow stress is essentially independent of the strain rate. At high homologous temperatures, however, the strain rate sensitivity increases and under certain conditions can even reach values of m ≥ 0.3 in finegrained materials. In the latter case, the deformation mechanisms change from dislocation glide to grain boundary sliding and cause
c to t . (i) Instantaneous change of the flow stress from s,1
(ii) A continuous flow stress change from t to the steady-state c flow s,2 for the new deformation conditions. This includes an overshooting or undershooting of the flow curve without strain rate change, depending on whether the strain rate was increased or decreased. (iii) Attainment of the steady-state flow stress for the new deformation condition.
Fig. 6. Flow curves (a and b) at 1100 ◦ C with strain rate changes from 1 × 10−2 s−1 to 1 × 10−3 s−1 and vice versa (black curves, for comparison flow curves with constant strain rates of 1 × 10−2 s−1 and 1 × 10−3 s−1 are plotted as gray curves) and corresponding true strain rates (c and d) for transient flow curves shown in (a) and (b), respectively.
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we obtain 1 from Fig. 6a and b as
c − t ≡ 1 1 (dR1 ) − 1 (dR2 ) = S,2
(5)
where dR1 and dR2 denote the steady-state grain size before and after the strain rate change, t is the flow stress immediately after c is the corresponding flow stress of a monothe change and s,2 tonic test with the new strain rate at the strain where the change occurs. The same holds for temperature changes (Fig. 7), except that the temperature change does not occur instantaneously but with c and t can also be some delay. Nevertheless, the magnitude of s,2 assessed in this case. Since 1 represents the grain size sensitivity of the flow stress, it is of interest, whether it scales with the dynamic length scale of the deformed crystal, i.e. the dislocation spacing, or equivalently the subgrain size ds . It has been shown frequently that the flow stress inversely scales with ds b =ς· ds
(6)
where is the shear modulus, b is the Burgers vector and ς is a scaling constant, typically 15 for metals. Corresponding to Eq. (6) the subgrain size sensitivity of is
Fig. 7. Flow curves (a) at 1 × 10−3 s−1 with temperature changes from 1100 ◦ C to 1150 ◦ C (black curve, for comparison flow curves at constant temperatures of 1100 ◦ C and 1150 ◦ C are plotted as gray curves) and corresponding temperature (b) for transient flow curve shown in (a).
In case of a change of the strain rate, the grain size adjusted to adapt to the new testing conditions. In Fig. 2e and f two examples are shown of the microstructure after strain rate changes from 1 × 10−3 s−1 to 1 × 10−2 s−1 and vice versa where the new dynamic equilibrium under the current deformation conditions is already attained. Fig. 3a displays the grain size development after strain rate changes from 1 × 10−3 s−1 to 1 × 10−2 s−1 . The different symbols denote the strain at which the strain rate change was performed. For example, the strain rate was altered at ε = 36%; at that point of the flow curve a grain size of about 21.2 m was already obtained. The experiment was continued up to a total strain of ε = 58% (square symbol at ε = 58%). In this case, an average grain size of d = 14.7 m was measured which matches the steady-state grain size of d = 14.9 m at constant parameters. As expected, the grain size does not significantly vary upon further straining since the steady-state regime is then reached. The same observations as described for the strain rate changes from 1 × 10−3 s−1 to 1 × 10−2 s−1 apply to the reverse case, i.e. strain rate changes from 1 × 10−2 s−1 to 1 × 10−3 s−1 under grain coarsening conditions as shown in Fig. 3b: after the transient the grain size changes, and the equilibrium grain size according to the strain rate ε˙ 2 is reached after an additional strain of about 20%. Regime (i) of the instantaneous change reflects the dependency of the flow stress on the deformation conditions (strain rate) for the microstructure prior to the change. Consequently, the flow stress change in regime (ii) reflects the change of the flow stress for constant deformation conditions but different grain size. This allows us to consider the flow stress as the sum of two contributions, the microstructure and the deformation parameters ε˙ and T. The microstructure is in this case represented by the recrystallized grain size dR = 1 (dR ) + 2 (ε˙ i T )
(4)
d ln = −1 d(ln ds )
(7)
In Fig. 8 we have investigated the dependency of 1 on dR , i.e. the DRX grain size sensitivity of the flow stress. Obviously the data follow the dependency ln
= A − 2 ln(dR ) dR
or
=
C dR
(8)
with C = exp(A) ≈ 30 MPa m Evidently, the DRX grain size change scales inversely with the change of the flow stress, i.e. with the same functional dependency as the subgrain size, i.e. the DRX grain size and the subgrain size are related. This remarkable result sheds a new light on our theoretical concepts of DRX, in fact it paves the way to a deeper physical understanding. In contrast to the classical engineering approach which relates the flow stress to a non-rational power law of the DRX grain size (Eq. (1)) which cannot be rationalized in terms of microstructural mechanisms, Eqs. (4) and (8) reflect a more sensible dependency which can be interpreted in terms of physical state variables.
Fig. 8. Dependency of the DRX grain size sensitivity on the grain size. The relation follows a power law with an exponent of about 2.
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Fig. 9. Proposed microstructure evolution during DRX. (a) Dislocations are generated during deformation; (b) the dislocation arrange in subgrain boundaries; (c) the surface tension of unbalanced subgrain boundaries create a bulge on a prior high angle boundary; (d) the dislocation in the bulge arrange in subboundaries and drag the moving boundary; (e) only the unbalanced segment of the bulge will continue to move; (f) new dislocations are generated in the second bulge; (g) stages (a–f) correspond to the formation of the 1st and 2nd necklace.
4.3. A new concept of DRX 4.3.1. Microstructure evolution The association of the DRX grain size with the subgrain size does not only allow another view on the dependence of the flow stress on DRX grain size but also on the processes underlying DRX as such. Previous models of DRX [1–3,7,10,11] attribute the initiation and steady-state development of DRX to the energy stored during deformation in terms of dislocations and assume that there is a critical value of strain, or better stress, to set off nucleation and growth of dynamically recrystallizing grains. In essence, DRX is considered as a superposition of deformation and static recrystallization. Other proposals associate DRX with continuous subgrain rotation (also referred to as continuous DRX) until mobile high angle grain boundaries are generated [12]; this may apply to ceramics or minerals, but in metals the misorientation usually does not exceed a few degrees, which makes such an approach less realistic. However, current theories fail to rationalize the microstructure evolution in the course of DRX, the attainment of a steadystate,
and the relation of flow stress and steady-state DRX grain size in terms of physical mechanisms. In fact, a power law ∝ dR−n with non-rational n is only an empirical approximation for a monotonic dependency without any physical meaning. Attempts to explain the odd exponent by a mixture between Hall-Petch law: ∼ d−1/2 (grain size hardening) and subgrain hardening: ∼ d−1 are misleading since both relations consider very different physics, namely a stress concentration for a Hall-Petch relation and dislocation patterning for the subgrain size dependency. We have shown recently, that the initiation of DRX can be associated with the generation of mobile subboundaries from immobile cell walls by dynamic recovery [13]. This transformation has two effects:
(i) the subboundary can move and, therefore, react to forces imposed on it, e.g. internal stresses; (ii) the subboundary acquires a surface tension which exerts forces on connected high and low angle boundaries.
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Fig. 10. (a) Dislocation substructure in dynamically recrystallized grains (1100 ◦ C, 10−2 s−1 , 97.4% strain); (b) misorientation distribution formation of the specimen shown in (a).
We will show that on this basis one can understand not only the initiation of DRX but also the steady-state flow behavior and microstructural evolution towards a steady-state DRX grain size. From the analysis of the strain rate change tests we have learned that the dynamically recrystallized grain size scales with the subgrain size. On this basis we propose a new approach to the microstructure evolution during (discontinuous or generic) DRX. A physical model of DRX has to account for the following observations: (i) There is a critical condition to set off DRX. This is usually described in terms of a critical strain, but, since the strain is not a state parameter of deformation, it is more appropriately associated with a critical stress. (ii) The recrystallization microstructure develops as a necklace structure originating at the prior grain boundaries and progressively consuming the interior of the deformed grains. (iii) The necklace grains have already essentially the steady-state grain size. (iv) The steady-state recrystallized grain size scales with the steady-state flow stress. (v) The dynamically recrystallizing microstructure is characterized by curved boundaries and dislocations inside the new grains. (vi) The flow stress reveals a single or multiple-peak behavior depending on the Zener-Hollomon-parameter Z = ε˙ exp(Q /kT ). We propose the following concept to account for these features (Fig. 9): (a) The critical condition for DRX is associated with the development of mobile subboundaries which causes bulging of the prior high angle boundaries.
(b) During growth of the recrystallized grains dislocations are generated within the grains which readily arrange in subgrain boundaries. The attachment of subgrain boundaries to the moving grain boundaries will exert a drag on the boundary that causes boundary motion to stagnate. (c) A new bulging process of the arrested boundary will set off the next necklace generations. (d) During motion of a boundary – even at the state of bulging – (annealing) twinning can occur which will change the grain boundary character and the orientation of the growing grain. The model differs from previous models of DRX in particular by the introduction of subboundary drag instead of boundarydislocation interactions. Most previous models of steady-state DRX are based on the assumption that during concurrent deformation a dislocation density is accumulated in a virgin recrystallized grain which eventually will cause arrest of the boundary when critical conditions are attained. This is very unlikely to occur, however, since a boundary will always continue moving, since the driving force on the boundary is the specific free energy gain of the swept volume, i.e. in front of the boundary irrespective of the dislocation density behind the boundary. The dislocations behind the boundary do not exert a drag on the boundary if they are not dragged along by the boundary, irrespective of their geometry. We recently proposed a model for the critical conditions to set off DRX. An essential assumption of that model is the conversion of immobile cell boundaries to mobile subgrain boundaries. The associated change in character from a tangled dislocation arrangement to a low angle grain boundary structure engenders an equilibrium of surface tensions at grain boundary junctions, in particular at the junctions of the subboundaries with the prior grain boundaries. An unbalanced junction distribution on both sides of a prior grain boundary will give rise to bulging owing to the unbalanced surface tension (Fig. 9c). The frequency of such arrangements was
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Fig. 11. Hardening rate calculated from the flow curves (a) at a constant strain rate of 1 × 10−2 s−1 (black curve) and after strain rate changes from 1 × 10−3 s−1 to 1 × 10−2 s−1 (gray curves) and (b) at a constant strain rate of 1 × 10−3 s−1 (black curve) and after strain rate changes from 1 × 10−2 s−1 to 1 × 10−3 s−1 (gray curves).
calculated by Derby and Ashby [14] in an attempt to predict the dynamically recrystallized grain size. The development of subboundaries is considered essential within the proposed model. In contrast to individual dislocations, the junctions of subboundaries with a moving grain boundary will exert a drag on the moving boundary owing to the surface tension of the subboundary. This is because a motion of the boundary has to extend the subboundary and, therefore, to provide the energy to generate this subboundary. This corresponds to a back driving force pR = 3 S /dS where S is the subboundary energy, and ds is the average subboundary spacing or subgrain size. Part of the boundary will again undergo bulging and continue the DRX process with the next necklace generation (Fig. 9f). This process is repeated until the grain volume is completely consumed by necklace grains and naturally explains, why already the first necklace grains assume already the steady-state DRX grain size, simply because the necklace grain size scales with the subgrain size. When the complete volume is filled with necklace grains bulging continues because grains having suffered higher strains will become invaded by their boundaries to less deformed grains. A quantitative theoretical treatment of the problem is given elsewhere [15]. The existence of low angle grain boundaries during steady-state DRX with a frequency very much in excess of a random misorientation is corroborated by orientation imaging analysis (Fig. 10).
4.3.2. The flow curve It is textbook knowledge that the flow curve of a material undergoing DRX reveals a single flow stress peak prior to steady-state for high Z conditions, with Z = ε˙ exp (Q /kT ) the Zener-Hollomonparameter, i.e. for high strain rates and low temperatures. For low Z conditions (high temperature, low strain rate) the flow curve oscillates and, eventually, assumes a steadystate. Sakai and Jonas [10] have shown that this behavior can also be associated with grain refinement (high Z) or grain coarsening (low Z) during DRX. The proposed new model outlined above, applies to both grain refinement and coarsening during DRX. It is most obvious for grain refinement during DRX which manifests itself by a necklace structure. The progressive consumption of the deformed microstructure causes a continuous decrease of the flow stress until a steadystate is attained when the whole original structure is replaced by a DRX structure, and steady-state is characterized by a continuous deletion of deformed grains by their less deformed neighbor grains. Low Z behavior, respectively grain coarsening, will also be set off by bulging, but owing to the higher recovery rate at lower Z the subgrain size remains large, hence fewer nuclei will be developed and nucleation may be delayed. Consequently, the existing nuclei grow into a volume that contains prior grain bound-
aries besides a dislocation structure, and the growth rate will be high. Correspondingly, the flow stress will strongly decrease. Further hardening will set off a new wave of DRX and eventually steady-state conditions are established with an equilibrium between growth rate and hardening rate for a constant number of nuclei. Grain coarsening occurs when at constant strain rate and temperature the grain size will fall below two times the subgrain size for the given deformation conditions, no subgrain boundaries can form in the DRX grains and no drag can be exerted by a subboundary on a moving grain boundary. Therefore, the boundaries will move until a grain size of at least two times the subgrain size is reached to have subboundaries affect boundary motion. Hence, the boundaries move rapidly and soften the material. This way the grain size will coarsen, and only after the grain size is large enough, a steadystate behaviour will be attained. This is reflected by a flow curve with damped oscillations to attain a steady-state.
4.3.3. Transient steady-state For a more refined analysis of the transient behavior, the hardening rate = ∂/∂ε is plotted versus the flow stress in Fig. 11 (Kocks-Mecking-plot [10]). Recently, Poliak and Jonas [11] proposed that DRX is initiated at the point of reflection of this area, i.e. at the transition from stage IV to stage V of the hardening curve, and we identified this point with the generation of mobile subboundaries since this will change the deformation mechanisms, increase dynamic recovery, and cause the initiation of DRX [13]. The hardening curves for experiments without (black curves) and with (gray curves) strain rate changes for true stain rates of 1 × 10−3 s−1 and 1 × 10−2 s−1 , respectively, reveal that at constant strain rates, the curves display a characteristic shape with a point of inflection in stage IV on the verge of stage V, where the hardening rate drops to zero. The broken line extrapolates the stage IV behavior, i.e. indicates the development of the hardening rate if only stage IV behavior would govern the flow stress. Correspondingly, a steady-state flow stress would be reached for = 0. Compared to a constant strain path, the hardening rates under transient strain rate conditions display a steeper decrease and more akin to stage V behavior. This substantiates that a new DRX cycle is set off immediately after the change to accommodate the new deformation conditions by grain refinement or grain coarsening, respectively. The shift in the stress range is due to the fact that the flow stress behavior after the change is considered up to the first maximum only. Close to the flow stress maximum, i.e. for → 0, the slope of both types of hardening curves (at constant and transient parameters) is approximately the same, implicating that the microstructural evolution and thus, mechanisms in the approach of steadystate are identical.
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Fig. 12. Simulation of texture changes after a true strain of 100% during high temperature deformation of two different initial texture components: (a) <1 1 1>-fiber; (b) <1 0 0>-fiber.
The flow behavior of dynamically recrystallizing materials can be calculated from physics-based concept in terms of dislocation theory of work hardening [16]. For DRX to occur in this model, subboundary motion has to be allowed for in the transition to stage V. The similarity of the approach of steady-state for constant and transient deformation conditions suggests within this model that the microstructural rearrangement after the strain rate change is also associated with the motion of boundaries. This hypothesis is supported by the result that the grain size sensitivity 1 /(dR ) scales with the grain size (∼dR −2 ) rather than with ∼dR −3/2 , which would indicate Hall-Petch-behavior driven by stress concentrations. 4.3.4. Crystallographic texture The texture evolution complements the mechanical behavior and microstructure development. For a strain rate of 1 × 10−2 s−1 , a distinct <1 1 0>-fiber texture is found after a true strain of 38% (Fig. 4b). This component is typical for uniaxial compression of fcc metals [17] and associated with the deformed initial grains in the microstructure with an orientation close to the <1 1 0>-direction parallel to the compression axis (Fig. 2b). The flow curve (Fig. 1) reveals that the steady-state regime has not yet been attained at that strain. With further straining DRX continues towards the steady-state regime, and the <1 1 0>-component disappears. However, the texture does not completely randomize, rather a weak <1 0 0>-fiber develops at high strains as already observed by Bocher [18] and Tsuji et al. [19] in austenitic steels. At a strain rate of 1 × 10−3 s−1 where the steady-state is attained at lower strains the <1 1 0>-component has already vanished at a strain of 38% (Fig. 4f) and given way to a weak <1 0 0>-fiber. The origin of the <1 0 0> texture component is not yet understood. In fact, most studies of texture development during DRX report a texture randomization. An analysis of the texture contributions of different fractions of grain sizes of the dynamically recrystallized microstructure reveals that small grains in the range ≤20 m exhibit maximum intensities at <1 1 0> and <1 0 0> whereas larger grains ≥20 m predominantly show orientations around <1 0 0>. In order to trace the behavior of distinct texture components during deformation, computer simulations were performed with the deformation texture model “GIA” (“grain interaction model” [20]). As expected from the deformation geometry for compression tests of fcc crystals, the model predicts the emergence of a <1 1 0>-fiber after a true strain of 100% for a specimen with an initial <1 1 1>-fiber texture (Fig. 12a). By contrast, an initially <1 0 0> textured polycrystal shows after the same amount of strain still an orientation distribution along the <1 0 0>-<1 1 0> symmetry line (Fig. 12b). The lattice rotation of the <1 0 0>-fiber is obviously slow compared to other orientations. These results are supported by
experiments on nickel single crystals by Tsuij et al. who observed that the <1 0 0>-orientation is relatively stable during high temperature deformation up to strains of 60% [19]. It is unlikely, however, that the sluggish orientation change of <1 0 0> grains fully accounts for the observed texture development. For the same reason one would expect a <1 1 0> component to appear, which is a stable orientation and therefore, likely to be retained. We surmise that also the observation of a larger grain size of <1 0 0> grains plays a role, maybe due to a larger growth rate of <1 0 0> oriented grains as observed for the cube orientation in rolled fcc materials [21]. It is finally stressed, however, that the strength of the <1 0 0>fiber component is rather low and amplified by the high symmetry of the <1 0 0> axis. Hence, we expect this observation not to be of major significance for the DRX process. On the other hand, a texture randomization is easily understood from the random movement and arrest of boundaries during steady-state DRX, further assisted by annealing twinning which also tends to randomize the texture [22]. 5. Summary and conclusions Dynamic recrystallization was investigated under constant and transient deformation conditions in the austenitic steel 800H. Microstructure and texture development were studied to elucidate the physical mechanisms underlying the evolution and maintenance of the steady state regime. 1. Depending on deformation conditions single-peak and multiplepeak flow curves were observed, but invariably grain refinement occurred. With increasing temperature and decreasing strain rate the flow stress maximum as well as the steady-state regime were attained at lower values of stress and strain. 2. Based on EBSD measurements the microtexture was calculated. At low strains a <1 1 0>-fiber texture developed as typical for fcc metals subjected to deformation in uniaxial compression. With increasing volume fraction of dynamically recrystallized grains towards the steady-state regime, the <1 1 0>-texture component vanished and a weak <1 0 0>-fiber appeared. The origin of this component is uncertain but likely due to the stability of the <1 0 0>-fiber during deformation and a growth advantage of respective grains. 3. Transient deformation conditions were applied to analyze the steady state behavior in more detail. During an instantaneous change of the strain rate, a sharp step of the flow stress was followed by a gradual approach of a new dynamic equilibrium according to the current deformation parameters with regard to the flow stress and the dynamically recrystallized grain size. The same holds for temperature changes except that the
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transition was less rapid owing to a non-instantaneous temperature change. 4. The grain size sensitivity of the flow stress scales with dR −2 , where dR is the change of the steady-state dynamically recrystallized grain size. This dependency associates the steady-state flow stress development with the subgrain size and thus, with the characteristic length scale of the deformed structure. 5. On this basis a new concept of DRX is proposed which relates the formation of the DRX microstructure to the bulging of grain boundaries and their arrest by junctions with subboundaries. The model can qualitatively account for the essential microstructural and mechanical features indicative of DRX and supports a previously proposed model for the onset of DRX by the conversion of deformation-induced cell walls to mobile subboundaries. References [1] M.J. Luton, C.M. Sellars, Acta Metall. 17 (1969) 1033. [2] R. Sandström, R. Lagneborg, Acta Metall. 23 (1975) 387. [3] H.P. Stüwe, B. Ortner, Metal Sci. 13 (1974) 161.
[4] W. Reiss, K. Pöhlandt, Exp. Techn. 10 (1986) 20. [5] E. Brünger, et al., Scripta Mater. 38 (1998) 1843. [6] H.J. McQueen, J.J. Jonas, Treatise on Materials Science and Technology, vol. 6, Academic Press, San Francisco, 1975. [7] W. Roberts, B. Ahlblom, Acta Metall. 26 (1978) 801. [8] X. Wang, et al., Scripta Mater. 46 (2002) 875. [9] T. Sakai, et al., Acta Metall. 31 (1983) 631. [10] T. Sakai, J.J. Jonas, Acta Metall. 32 (1984) 189. [11] E.I. Poliak, J.J. Jonas, Acta Mater. 44 (1996) 127. [12] S. Gourdet, F. Montheillet, Acta Mater. 51 (2003) 2685. [13] G. Gottstein, et al., Mater. Sci. Eng. A 387–389 (2004) 604. [14] B. Derby, M.F. Ashby, Scripta Metall. 21 (1987) 879. [15] G. Gottstein, M. Frommert, M. Goerdeler, M. Zeng, Z. Metallk. 94 (2003) 628. [16] H. Mecking, U.F. Kocks, Acta Metall. Vol.29 (1981) 1865. [17] G. Wassermann, Texturen Metallischer Werkstoffe, Springer Verlag, Berlin, 1962. [18] Ph. Bocher, Ph.D. Thesis, McGill University, Montreal, Canada, 1998. [19] N. Tsuji et al. Presented at the J.J. Jonas Symposium on Thermomechanical Processing, Texture and Formability of Steel, Ottawa, Canada (2000), unpublished. [20] M. Crumbach, et al., in: G. Gottstein, D. Molodov (Eds.), Proceedings of the First Joint Int. Conf. on Recrystallization and Grain Growth, Springer Verlag, 2001, p. 1053. [21] D. Juul Jensen, Scripta Metall. Mater. 27 (1992) 553. [22] G. Gottstein, Acta Metall. 32 (1984) 1117.
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Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Mechanical behavior and microstructure evolution during steady-state dynamic recrystallization in the austenitic steel 800H M. Frommert a , G. Gottstein b,∗ a b
Max-Planck-Institut für Eisenforschung GmbH, Max-Planck-Str. 1, 40237 Düsseldorf, Germany Institut für Metallkunde und Metallphysik, RWTH Aachen, 52056 Aachen, Germany
a r t i c l e
i n f o
Article history: Received 20 June 2008 Received in revised form 11 November 2008 Accepted 16 November 2008 Keywords: Steady-state dynamic recrystallization Austenitic steel Microstructure development Texture evolution Transient deformation conditions
a b s t r a c t Investigations of steady-state dynamic recrystallization (DRX) were carried out on an austenitic steel alloy 800H. The influence of strain rate and temperature on the mechanical behavior, microstructure development and texture evolution were analyzed. Strain rate and temperature change experiments during steady-state deformation revealed characteristic interdependencies of flow stress, hardening rate, and grain size. The grain size sensitivity of the flow stress was found to scale with the characteristic length scale of the deformed structure. Based on these observations a new model is proposed that relates the process of DRX to an interaction of mobile grain boundaries with deformation-induced subboundaries. © 2008 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental procedure
Despite extensive research during the past decades the physical mechanisms of dynamic recrystallization (DRX) are not yet fully understood. The subject is not only of academic interest but also of immense importance for industrial processing, e.g. hot rolling: DRX offers a powerful tool for microstructure control and, therefore, a useful way for the optimization of the sheet properties. Furthermore, advances in through-process computer simulation require precise experimental data and physics-based models of the material behavior for each step of the complex process chain (hot rolling, cold rolling, annealing, . . .) for reliable predictions of microstructure and texture evolution. Early models of DRX were based on concepts assuming a simple superposition of deformation and (static) recrystallization [1–3]. While the essential features of microstructure and flow behavior could be reproduced, e.g. the development of grain size, the apparent differences to static recrystallization – like the nucleation mechanisms and the steady-state behavior – could not be accounted for. The current study focused on the steady-state regime of the flow curve. Particular attention was paid to the microstructure and texture development as well as to the transient behavior during strain path changes.
The material used in this investigation was the austenitic steel X10NiCrAlTi3220, also referred to as alloy 800H. Its exact chemical composition is given in Table 1. Cylindrical samples of 5 mm diameter and 7.7 mm height were machined from the statically recrystallized material using Rastegaev geometry [4] with BN as lubricant. Hot Compression tests were performed with true strain rates of 10−4 s−1 ≤ ε˙ ≤ 10−1 s−1 at temperatures of 1000 ◦ C ≤ T ≤ 1200 ◦ C. For texture and microstructure analysis the samples were quenched with cold helium gas immediately after deformation. Details are given elsewhere [5]. The influence of the deformation parameters on the flow stress, dynamically recrystallized grain size, and texture evolution was investigated. Electron backscatter diffraction (EBSD) measurements using a field emission gun scanning electron microscope (FEGSEM) served for the analysis of the local orientation arrangement and for the reconstruction of the microstructural features. The main focus was on the examination of the grain size evolution and the texture development during steady-state DRX.
3. Results 3.1. Plastic flow behavior
∗ Corresponding author. Fax: +49 241 8022608. E-mail addresses: [email protected] (M. Frommert), [email protected] (G. Gottstein). 0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2008.11.035
The characteristic stress–strain curve of a material undergoing DRX exhibits either a single maximum (single-peak behavior) or an oscillating shape (multiple-peak behavior) depending on the deformation parameters, i.e. temperature and strain rate [6]. Fig. 1
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20.35 30.20 0.70 0.42 0.34 0.12 0.002 0.013 0.30 0.05 0.071 bal.
3.2. Microstructure development Fig. 1. Typical flow curves of the austenitic steel Alloy 800H during high temperature deformation at different strain rates and temperatures.
shows the typical flow curves of the austenitic steel 800H in the temperature range 1000 ◦ C ≤ T ≤ 1200 ◦ C and at true strain rates of 10−4 s−1 ≤ ε˙ ≤ 10−1 s−1 . With increasing temperature T or decreasing strain rate ε˙ the flow curves are shifted to lower stress levels. Furthermore, a transition from single-peak to multiple-peak behavior is observed. The slight increase of the stress in the steady-state regime at higher strains (ε > 60%) which is discernible in Fig. 1 is the result of friction due to the increasing contact area between the sample and the compression platens.
The microstructural features were determined from orientation maps measured by EBSD. The initial grain size of the statically recrystallized material (Fig. 2a) was 27.1 m and contained a large fraction of recrystallization twins. During DRX at 1100 ◦ C and strain rates of 1 × 10−2 s−1 (Fig. 2b and c) and 1 × 10−3 s−1 (Fig. 2d), grain refinement was observed. In Fig. 3 the microstructure evolution is shown for constant (triangular symbols) and transient deformation conditions. The full lines indicate the average dynamically recrystallized grain size in the steady-state regime at constant strain rates giving values of 14.9 m (1100 ◦ C; 1 × 10−2 s−1 ) and 21.2 m (1100 ◦ C; 1 × 10−3 s−1 ). Since the steady-state regime was attained at higher strains in case of higher strain rates (see Fig. 1), the grain −2 size at ε ∼ = 40% and ε˙ = 1 × 10 s−1 was not considered for the calculation of the average grain size.
Fig. 2. Microstructure development at 1100 ◦ C: (a) initial microstructure; (b) and (c) deformed at 1 × 10−2 s−1 to true strains of 38% and 96%; (d) deformed at 1 × 10−3 s−1 to 96%; (e) strain rate change from 1 × 10−3 s−1 to 1 × 10−2 s−1 at 56% and further deformation to a total strain of 96%; (f) strain rate change from 1 × 10−2 s−1 to 1 × 10−3 s−1 at 57%, total strain 96%; the compression axis is perpendicular to the sheet plane.
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3.3. Texture evolution The microtextures were obtained from EBSD mappings which contain the full orientation data of each point of the scanned sample surface. Due to the uniaxial compression geometry, the texture is presented in form of inverse pole figures of the compression axis. Fig. 4 shows the texture development for samples deformed at 1100 ◦ C at different true strains. The initial, statically recrystallized texture (Fig. 4a) is rather weak with a maximum intensity of 1.4. At a strain rate of 1 × 10−2 s−1 and a true strain of 38% (Fig. 4b) a strong <1 1 0>-component has developed. With further straining (Fig. 4c–e) the <1 1 0>-component becomes weaker and finally disappears, and the (low) maximum intensity arises at <1 0 0>. In case of the lower strain rate of 1 × 10−3 s−1 (Fig. 4f), after 38% of true strain only the <1 0 0>-component exists which is in agreement with the earlier attainment of the steady-state regime under these conditions (see Fig. 1). Similar textures were found for all testing conditions with minor variations of the maximum intensities which were in the range of 2–3. The texture did not significantly change in the steady-state regime of DRX, even for transient deformation conditions.
4. Discussion 4.1. Constant deformation conditions
Fig. 3. Development of grain size during constant and transient deformation conditions for (a) strain rate changes from 1 × 10−3 s−1 to 1 × 10−2 s−1 and (b) vice versa. The triangular symbols represent the grain size under constant parameters; the square and circular symbols give the values of strain rate changes after true strains of 36% and 56%, respectively.
Early investigations of DRX already showed that the average grain size in the steady-state regime, usually referred to as the dynamically recrystallized grain size dR , does not change with further straining and is supposed to be constant (e.g. [1–3]). Furthermore, for a large variety of materials the DRX grain size dR can be related to the steady-state flow stress s by a power law: s = K · dR
−n
(1)
with K, n: empirical constants and 0.4 ≤ n ≤ 0.8 (e.g. [7]). In this study, a grain size exponent of n = 0.77 was found for the austenitic steel 800H at the given deformation parameters.
The most prominent point of the curve is the maximum which is characterized by the peak stress p and the peak strain εp as a result of deformation-induced hardening superimposed by softening due to DRX. The maximum of the flow curves – and likewise the onset of DRX – is shifted to lower stress and strain values with increasing temperature and decreasing strain rate (Fig. 1). However, the onset of DRX in a polycrystalline material cannot be directly extracted from the flow curve. In the microstructure the nucleation of DRX can be more easily traced. In Fig. 2b at 1100 ◦ C and 1 × 10−2 s−1 , two fractions of grains are discernible after a true strain of 38%: the larger grains are mostly of green color indicating orientations close to the <1 1 0>-fiber axis and belong to the initial structure, whereas the smaller grains developed during DRX. The nucleation mechanisms of DRX are not of concern in this work but were investigated for the same material by Brünger et al. [5] and Wang et al. [8]. After a total strain of 58% the steady-state flow stress regime is attained in the flow curve (Fig. 1), and the microstructure consists of small grains with a single grain size distribution and a constant, average grain size of 14.9 m
Fig. 4. Texture evolution at 1100 ◦ C: (a) initial texture; (b–e) 1 × 10−2 s−1 after true strains of 38%, 58%, 76% and 96%; (f) 1 × 10−3 s−1 and 38% true strain; the maximum intensity of the pole figure is indicated as “max”; note: in this figure, the color code represents the intensity, not the orientation.
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superplastic behavior, which is accompanied by a steady-state grain size. In order to rule out the occurrence of superplastic deformation at the imposed testing conditions, strain rate changes were performed before the attainment of the maximum in the flow curve (Fig. 5). The strain rate sensitivity was calculated according to m=
Fig. 5. Detail from a flow curve at 1100 ◦ C with a strain rate change before the attainment of the peak stress used for the calculation of the strain rate sensitivity.
(Fig. 3a and b). For comparison, at a strain rate of 1 × 10−3 s−1 , the steady-state regime had been already attained after 38%, as can be seen from the flow curve (Fig. 1) and the grain size development (Fig. 3a and b). 4.2. Transient deformation conditions Strain rate changes are often used to determine the strain rate sensitivity m of a material which is defined as m=
d ln d lnε˙
ln(2 /1 ) ln(ε˙ 2 /ε˙ 1 ) ε
(3)
where 1 , 2 , ε˙ 1 and ε˙ 2 are the flow stresses and strain rates prior to and subsequent to the strain rate change. The experiments rendered 0.14 ≤ m ≤ 0.15. In case of strain rate changes at larger strains, i.e. in the steady-state regime, the m-values were slightly higher 0.15 ≤ m ≤ 0.17. In both cases, superplastic deformation can be ruled out and the observed deformation behavior must be attributed to crystallographic glide and DRX only. In case of transient deformation conditions, i.e. a change of the strain rate or temperature, an adjustment of the flow stress according to the actual parameters occurs as already shown by Sakai et al. for a microalloyed steel [9]. In Fig. 6a and b the flow curves of two experiments at 1100 ◦ C are shown with instantaneous changes of the strain rate from 1 × 10−2 s−1 to 1 × 10−3 s−1 and vice versa; the corresponding strain rate versus strain schedule is given in Fig. 6c and d. For comparison, the flow curves at constant strain rates are added to the diagrams as gray curves. The flow stress change following a strain rate change is composed of three regimes:
(2)
corresponding to a power law dependency of the flow stress ˙ At low homologous temperatures, the value on the strain rate ε. of m in fcc metals is usually small (m ∼ = 0.01), and the flow stress is essentially independent of the strain rate. At high homologous temperatures, however, the strain rate sensitivity increases and under certain conditions can even reach values of m ≥ 0.3 in finegrained materials. In the latter case, the deformation mechanisms change from dislocation glide to grain boundary sliding and cause
c to t . (i) Instantaneous change of the flow stress from s,1
(ii) A continuous flow stress change from t to the steady-state c flow s,2 for the new deformation conditions. This includes an overshooting or undershooting of the flow curve without strain rate change, depending on whether the strain rate was increased or decreased. (iii) Attainment of the steady-state flow stress for the new deformation condition.
Fig. 6. Flow curves (a and b) at 1100 ◦ C with strain rate changes from 1 × 10−2 s−1 to 1 × 10−3 s−1 and vice versa (black curves, for comparison flow curves with constant strain rates of 1 × 10−2 s−1 and 1 × 10−3 s−1 are plotted as gray curves) and corresponding true strain rates (c and d) for transient flow curves shown in (a) and (b), respectively.
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we obtain 1 from Fig. 6a and b as
c − t ≡ 1 1 (dR1 ) − 1 (dR2 ) = S,2
(5)
where dR1 and dR2 denote the steady-state grain size before and after the strain rate change, t is the flow stress immediately after c is the corresponding flow stress of a monothe change and s,2 tonic test with the new strain rate at the strain where the change occurs. The same holds for temperature changes (Fig. 7), except that the temperature change does not occur instantaneously but with c and t can also be some delay. Nevertheless, the magnitude of s,2 assessed in this case. Since 1 represents the grain size sensitivity of the flow stress, it is of interest, whether it scales with the dynamic length scale of the deformed crystal, i.e. the dislocation spacing, or equivalently the subgrain size ds . It has been shown frequently that the flow stress inversely scales with ds b =ς· ds
(6)
where is the shear modulus, b is the Burgers vector and ς is a scaling constant, typically 15 for metals. Corresponding to Eq. (6) the subgrain size sensitivity of is
Fig. 7. Flow curves (a) at 1 × 10−3 s−1 with temperature changes from 1100 ◦ C to 1150 ◦ C (black curve, for comparison flow curves at constant temperatures of 1100 ◦ C and 1150 ◦ C are plotted as gray curves) and corresponding temperature (b) for transient flow curve shown in (a).
In case of a change of the strain rate, the grain size adjusted to adapt to the new testing conditions. In Fig. 2e and f two examples are shown of the microstructure after strain rate changes from 1 × 10−3 s−1 to 1 × 10−2 s−1 and vice versa where the new dynamic equilibrium under the current deformation conditions is already attained. Fig. 3a displays the grain size development after strain rate changes from 1 × 10−3 s−1 to 1 × 10−2 s−1 . The different symbols denote the strain at which the strain rate change was performed. For example, the strain rate was altered at ε = 36%; at that point of the flow curve a grain size of about 21.2 m was already obtained. The experiment was continued up to a total strain of ε = 58% (square symbol at ε = 58%). In this case, an average grain size of d = 14.7 m was measured which matches the steady-state grain size of d = 14.9 m at constant parameters. As expected, the grain size does not significantly vary upon further straining since the steady-state regime is then reached. The same observations as described for the strain rate changes from 1 × 10−3 s−1 to 1 × 10−2 s−1 apply to the reverse case, i.e. strain rate changes from 1 × 10−2 s−1 to 1 × 10−3 s−1 under grain coarsening conditions as shown in Fig. 3b: after the transient the grain size changes, and the equilibrium grain size according to the strain rate ε˙ 2 is reached after an additional strain of about 20%. Regime (i) of the instantaneous change reflects the dependency of the flow stress on the deformation conditions (strain rate) for the microstructure prior to the change. Consequently, the flow stress change in regime (ii) reflects the change of the flow stress for constant deformation conditions but different grain size. This allows us to consider the flow stress as the sum of two contributions, the microstructure and the deformation parameters ε˙ and T. The microstructure is in this case represented by the recrystallized grain size dR = 1 (dR ) + 2 (ε˙ i T )
(4)
d ln = −1 d(ln ds )
(7)
In Fig. 8 we have investigated the dependency of 1 on dR , i.e. the DRX grain size sensitivity of the flow stress. Obviously the data follow the dependency ln
= A − 2 ln(dR ) dR
or
=
C dR
(8)
with C = exp(A) ≈ 30 MPa m Evidently, the DRX grain size change scales inversely with the change of the flow stress, i.e. with the same functional dependency as the subgrain size, i.e. the DRX grain size and the subgrain size are related. This remarkable result sheds a new light on our theoretical concepts of DRX, in fact it paves the way to a deeper physical understanding. In contrast to the classical engineering approach which relates the flow stress to a non-rational power law of the DRX grain size (Eq. (1)) which cannot be rationalized in terms of microstructural mechanisms, Eqs. (4) and (8) reflect a more sensible dependency which can be interpreted in terms of physical state variables.
Fig. 8. Dependency of the DRX grain size sensitivity on the grain size. The relation follows a power law with an exponent of about 2.
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Fig. 9. Proposed microstructure evolution during DRX. (a) Dislocations are generated during deformation; (b) the dislocation arrange in subgrain boundaries; (c) the surface tension of unbalanced subgrain boundaries create a bulge on a prior high angle boundary; (d) the dislocation in the bulge arrange in subboundaries and drag the moving boundary; (e) only the unbalanced segment of the bulge will continue to move; (f) new dislocations are generated in the second bulge; (g) stages (a–f) correspond to the formation of the 1st and 2nd necklace.
4.3. A new concept of DRX 4.3.1. Microstructure evolution The association of the DRX grain size with the subgrain size does not only allow another view on the dependence of the flow stress on DRX grain size but also on the processes underlying DRX as such. Previous models of DRX [1–3,7,10,11] attribute the initiation and steady-state development of DRX to the energy stored during deformation in terms of dislocations and assume that there is a critical value of strain, or better stress, to set off nucleation and growth of dynamically recrystallizing grains. In essence, DRX is considered as a superposition of deformation and static recrystallization. Other proposals associate DRX with continuous subgrain rotation (also referred to as continuous DRX) until mobile high angle grain boundaries are generated [12]; this may apply to ceramics or minerals, but in metals the misorientation usually does not exceed a few degrees, which makes such an approach less realistic. However, current theories fail to rationalize the microstructure evolution in the course of DRX, the attainment of a steadystate,
and the relation of flow stress and steady-state DRX grain size in terms of physical mechanisms. In fact, a power law ∝ dR−n with non-rational n is only an empirical approximation for a monotonic dependency without any physical meaning. Attempts to explain the odd exponent by a mixture between Hall-Petch law: ∼ d−1/2 (grain size hardening) and subgrain hardening: ∼ d−1 are misleading since both relations consider very different physics, namely a stress concentration for a Hall-Petch relation and dislocation patterning for the subgrain size dependency. We have shown recently, that the initiation of DRX can be associated with the generation of mobile subboundaries from immobile cell walls by dynamic recovery [13]. This transformation has two effects:
(i) the subboundary can move and, therefore, react to forces imposed on it, e.g. internal stresses; (ii) the subboundary acquires a surface tension which exerts forces on connected high and low angle boundaries.
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Fig. 10. (a) Dislocation substructure in dynamically recrystallized grains (1100 ◦ C, 10−2 s−1 , 97.4% strain); (b) misorientation distribution formation of the specimen shown in (a).
We will show that on this basis one can understand not only the initiation of DRX but also the steady-state flow behavior and microstructural evolution towards a steady-state DRX grain size. From the analysis of the strain rate change tests we have learned that the dynamically recrystallized grain size scales with the subgrain size. On this basis we propose a new approach to the microstructure evolution during (discontinuous or generic) DRX. A physical model of DRX has to account for the following observations: (i) There is a critical condition to set off DRX. This is usually described in terms of a critical strain, but, since the strain is not a state parameter of deformation, it is more appropriately associated with a critical stress. (ii) The recrystallization microstructure develops as a necklace structure originating at the prior grain boundaries and progressively consuming the interior of the deformed grains. (iii) The necklace grains have already essentially the steady-state grain size. (iv) The steady-state recrystallized grain size scales with the steady-state flow stress. (v) The dynamically recrystallizing microstructure is characterized by curved boundaries and dislocations inside the new grains. (vi) The flow stress reveals a single or multiple-peak behavior depending on the Zener-Hollomon-parameter Z = ε˙ exp(Q /kT ). We propose the following concept to account for these features (Fig. 9): (a) The critical condition for DRX is associated with the development of mobile subboundaries which causes bulging of the prior high angle boundaries.
(b) During growth of the recrystallized grains dislocations are generated within the grains which readily arrange in subgrain boundaries. The attachment of subgrain boundaries to the moving grain boundaries will exert a drag on the boundary that causes boundary motion to stagnate. (c) A new bulging process of the arrested boundary will set off the next necklace generations. (d) During motion of a boundary – even at the state of bulging – (annealing) twinning can occur which will change the grain boundary character and the orientation of the growing grain. The model differs from previous models of DRX in particular by the introduction of subboundary drag instead of boundarydislocation interactions. Most previous models of steady-state DRX are based on the assumption that during concurrent deformation a dislocation density is accumulated in a virgin recrystallized grain which eventually will cause arrest of the boundary when critical conditions are attained. This is very unlikely to occur, however, since a boundary will always continue moving, since the driving force on the boundary is the specific free energy gain of the swept volume, i.e. in front of the boundary irrespective of the dislocation density behind the boundary. The dislocations behind the boundary do not exert a drag on the boundary if they are not dragged along by the boundary, irrespective of their geometry. We recently proposed a model for the critical conditions to set off DRX. An essential assumption of that model is the conversion of immobile cell boundaries to mobile subgrain boundaries. The associated change in character from a tangled dislocation arrangement to a low angle grain boundary structure engenders an equilibrium of surface tensions at grain boundary junctions, in particular at the junctions of the subboundaries with the prior grain boundaries. An unbalanced junction distribution on both sides of a prior grain boundary will give rise to bulging owing to the unbalanced surface tension (Fig. 9c). The frequency of such arrangements was
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Fig. 11. Hardening rate calculated from the flow curves (a) at a constant strain rate of 1 × 10−2 s−1 (black curve) and after strain rate changes from 1 × 10−3 s−1 to 1 × 10−2 s−1 (gray curves) and (b) at a constant strain rate of 1 × 10−3 s−1 (black curve) and after strain rate changes from 1 × 10−2 s−1 to 1 × 10−3 s−1 (gray curves).
calculated by Derby and Ashby [14] in an attempt to predict the dynamically recrystallized grain size. The development of subboundaries is considered essential within the proposed model. In contrast to individual dislocations, the junctions of subboundaries with a moving grain boundary will exert a drag on the moving boundary owing to the surface tension of the subboundary. This is because a motion of the boundary has to extend the subboundary and, therefore, to provide the energy to generate this subboundary. This corresponds to a back driving force pR = 3 S /dS where S is the subboundary energy, and ds is the average subboundary spacing or subgrain size. Part of the boundary will again undergo bulging and continue the DRX process with the next necklace generation (Fig. 9f). This process is repeated until the grain volume is completely consumed by necklace grains and naturally explains, why already the first necklace grains assume already the steady-state DRX grain size, simply because the necklace grain size scales with the subgrain size. When the complete volume is filled with necklace grains bulging continues because grains having suffered higher strains will become invaded by their boundaries to less deformed grains. A quantitative theoretical treatment of the problem is given elsewhere [15]. The existence of low angle grain boundaries during steady-state DRX with a frequency very much in excess of a random misorientation is corroborated by orientation imaging analysis (Fig. 10).
4.3.2. The flow curve It is textbook knowledge that the flow curve of a material undergoing DRX reveals a single flow stress peak prior to steady-state for high Z conditions, with Z = ε˙ exp (Q /kT ) the Zener-Hollomonparameter, i.e. for high strain rates and low temperatures. For low Z conditions (high temperature, low strain rate) the flow curve oscillates and, eventually, assumes a steadystate. Sakai and Jonas [10] have shown that this behavior can also be associated with grain refinement (high Z) or grain coarsening (low Z) during DRX. The proposed new model outlined above, applies to both grain refinement and coarsening during DRX. It is most obvious for grain refinement during DRX which manifests itself by a necklace structure. The progressive consumption of the deformed microstructure causes a continuous decrease of the flow stress until a steadystate is attained when the whole original structure is replaced by a DRX structure, and steady-state is characterized by a continuous deletion of deformed grains by their less deformed neighbor grains. Low Z behavior, respectively grain coarsening, will also be set off by bulging, but owing to the higher recovery rate at lower Z the subgrain size remains large, hence fewer nuclei will be developed and nucleation may be delayed. Consequently, the existing nuclei grow into a volume that contains prior grain bound-
aries besides a dislocation structure, and the growth rate will be high. Correspondingly, the flow stress will strongly decrease. Further hardening will set off a new wave of DRX and eventually steady-state conditions are established with an equilibrium between growth rate and hardening rate for a constant number of nuclei. Grain coarsening occurs when at constant strain rate and temperature the grain size will fall below two times the subgrain size for the given deformation conditions, no subgrain boundaries can form in the DRX grains and no drag can be exerted by a subboundary on a moving grain boundary. Therefore, the boundaries will move until a grain size of at least two times the subgrain size is reached to have subboundaries affect boundary motion. Hence, the boundaries move rapidly and soften the material. This way the grain size will coarsen, and only after the grain size is large enough, a steadystate behaviour will be attained. This is reflected by a flow curve with damped oscillations to attain a steady-state.
4.3.3. Transient steady-state For a more refined analysis of the transient behavior, the hardening rate = ∂/∂ε is plotted versus the flow stress in Fig. 11 (Kocks-Mecking-plot [10]). Recently, Poliak and Jonas [11] proposed that DRX is initiated at the point of reflection of this area, i.e. at the transition from stage IV to stage V of the hardening curve, and we identified this point with the generation of mobile subboundaries since this will change the deformation mechanisms, increase dynamic recovery, and cause the initiation of DRX [13]. The hardening curves for experiments without (black curves) and with (gray curves) strain rate changes for true stain rates of 1 × 10−3 s−1 and 1 × 10−2 s−1 , respectively, reveal that at constant strain rates, the curves display a characteristic shape with a point of inflection in stage IV on the verge of stage V, where the hardening rate drops to zero. The broken line extrapolates the stage IV behavior, i.e. indicates the development of the hardening rate if only stage IV behavior would govern the flow stress. Correspondingly, a steady-state flow stress would be reached for = 0. Compared to a constant strain path, the hardening rates under transient strain rate conditions display a steeper decrease and more akin to stage V behavior. This substantiates that a new DRX cycle is set off immediately after the change to accommodate the new deformation conditions by grain refinement or grain coarsening, respectively. The shift in the stress range is due to the fact that the flow stress behavior after the change is considered up to the first maximum only. Close to the flow stress maximum, i.e. for → 0, the slope of both types of hardening curves (at constant and transient parameters) is approximately the same, implicating that the microstructural evolution and thus, mechanisms in the approach of steadystate are identical.
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Fig. 12. Simulation of texture changes after a true strain of 100% during high temperature deformation of two different initial texture components: (a) <1 1 1>-fiber; (b) <1 0 0>-fiber.
The flow behavior of dynamically recrystallizing materials can be calculated from physics-based concept in terms of dislocation theory of work hardening [16]. For DRX to occur in this model, subboundary motion has to be allowed for in the transition to stage V. The similarity of the approach of steady-state for constant and transient deformation conditions suggests within this model that the microstructural rearrangement after the strain rate change is also associated with the motion of boundaries. This hypothesis is supported by the result that the grain size sensitivity 1 /(dR ) scales with the grain size (∼dR −2 ) rather than with ∼dR −3/2 , which would indicate Hall-Petch-behavior driven by stress concentrations. 4.3.4. Crystallographic texture The texture evolution complements the mechanical behavior and microstructure development. For a strain rate of 1 × 10−2 s−1 , a distinct <1 1 0>-fiber texture is found after a true strain of 38% (Fig. 4b). This component is typical for uniaxial compression of fcc metals [17] and associated with the deformed initial grains in the microstructure with an orientation close to the <1 1 0>-direction parallel to the compression axis (Fig. 2b). The flow curve (Fig. 1) reveals that the steady-state regime has not yet been attained at that strain. With further straining DRX continues towards the steady-state regime, and the <1 1 0>-component disappears. However, the texture does not completely randomize, rather a weak <1 0 0>-fiber develops at high strains as already observed by Bocher [18] and Tsuji et al. [19] in austenitic steels. At a strain rate of 1 × 10−3 s−1 where the steady-state is attained at lower strains the <1 1 0>-component has already vanished at a strain of 38% (Fig. 4f) and given way to a weak <1 0 0>-fiber. The origin of the <1 0 0> texture component is not yet understood. In fact, most studies of texture development during DRX report a texture randomization. An analysis of the texture contributions of different fractions of grain sizes of the dynamically recrystallized microstructure reveals that small grains in the range ≤20 m exhibit maximum intensities at <1 1 0> and <1 0 0> whereas larger grains ≥20 m predominantly show orientations around <1 0 0>. In order to trace the behavior of distinct texture components during deformation, computer simulations were performed with the deformation texture model “GIA” (“grain interaction model” [20]). As expected from the deformation geometry for compression tests of fcc crystals, the model predicts the emergence of a <1 1 0>-fiber after a true strain of 100% for a specimen with an initial <1 1 1>-fiber texture (Fig. 12a). By contrast, an initially <1 0 0> textured polycrystal shows after the same amount of strain still an orientation distribution along the <1 0 0>-<1 1 0> symmetry line (Fig. 12b). The lattice rotation of the <1 0 0>-fiber is obviously slow compared to other orientations. These results are supported by
experiments on nickel single crystals by Tsuij et al. who observed that the <1 0 0>-orientation is relatively stable during high temperature deformation up to strains of 60% [19]. It is unlikely, however, that the sluggish orientation change of <1 0 0> grains fully accounts for the observed texture development. For the same reason one would expect a <1 1 0> component to appear, which is a stable orientation and therefore, likely to be retained. We surmise that also the observation of a larger grain size of <1 0 0> grains plays a role, maybe due to a larger growth rate of <1 0 0> oriented grains as observed for the cube orientation in rolled fcc materials [21]. It is finally stressed, however, that the strength of the <1 0 0>fiber component is rather low and amplified by the high symmetry of the <1 0 0> axis. Hence, we expect this observation not to be of major significance for the DRX process. On the other hand, a texture randomization is easily understood from the random movement and arrest of boundaries during steady-state DRX, further assisted by annealing twinning which also tends to randomize the texture [22]. 5. Summary and conclusions Dynamic recrystallization was investigated under constant and transient deformation conditions in the austenitic steel 800H. Microstructure and texture development were studied to elucidate the physical mechanisms underlying the evolution and maintenance of the steady state regime. 1. Depending on deformation conditions single-peak and multiplepeak flow curves were observed, but invariably grain refinement occurred. With increasing temperature and decreasing strain rate the flow stress maximum as well as the steady-state regime were attained at lower values of stress and strain. 2. Based on EBSD measurements the microtexture was calculated. At low strains a <1 1 0>-fiber texture developed as typical for fcc metals subjected to deformation in uniaxial compression. With increasing volume fraction of dynamically recrystallized grains towards the steady-state regime, the <1 1 0>-texture component vanished and a weak <1 0 0>-fiber appeared. The origin of this component is uncertain but likely due to the stability of the <1 0 0>-fiber during deformation and a growth advantage of respective grains. 3. Transient deformation conditions were applied to analyze the steady state behavior in more detail. During an instantaneous change of the strain rate, a sharp step of the flow stress was followed by a gradual approach of a new dynamic equilibrium according to the current deformation parameters with regard to the flow stress and the dynamically recrystallized grain size. The same holds for temperature changes except that the
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transition was less rapid owing to a non-instantaneous temperature change. 4. The grain size sensitivity of the flow stress scales with dR −2 , where dR is the change of the steady-state dynamically recrystallized grain size. This dependency associates the steady-state flow stress development with the subgrain size and thus, with the characteristic length scale of the deformed structure. 5. On this basis a new concept of DRX is proposed which relates the formation of the DRX microstructure to the bulging of grain boundaries and their arrest by junctions with subboundaries. The model can qualitatively account for the essential microstructural and mechanical features indicative of DRX and supports a previously proposed model for the onset of DRX by the conversion of deformation-induced cell walls to mobile subboundaries. References [1] M.J. Luton, C.M. Sellars, Acta Metall. 17 (1969) 1033. [2] R. Sandström, R. Lagneborg, Acta Metall. 23 (1975) 387. [3] H.P. Stüwe, B. Ortner, Metal Sci. 13 (1974) 161.
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