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Strength of AISI 316L in torsion at high temperature
Materials Science and Engineering A 475 (2008) 257–267
Strength of AISI 316L in torsion at high temperature G. Angella b,∗ , B.P. Wynne a , W.M. Rainforth a , J.H. Beynon c a
IMMPETUS, Department of Engineering Materials, The University of Sheffield, Sheffield, UK b Istituto IENI-CNR, via R. Cozzi 53, 20125 Milano, Italy c Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Hawthorn, Vic. 3122, Australia Received 15 December 2006; received in revised form 11 April 2007; accepted 19 May 2007
Abstract Hot torsion flow behaviour of 30 m grained AISI 316L stainless steel was investigated in the range of temperatures 850–1100 ◦ C with equivalent strain rates 0.0001–0.006 s−1 . For temperatures higher than 900 ◦ C the material presented an unusual linear relationship at low strains between equivalent stress, σ Eq , and equivalent strain, εEq , whilst at 850 ◦ C a parabolic σ Eq –εEq relationship was observed. The flow behaviour of 100 m grained AISI 316L stainless steel torsionally deformed at 1000 ◦ C with equivalent strain rate of 0.006 s−1 was reported to follow the expected parabolic σ Eq –εEq relationship and produced a significantly higher flow stress than the 30 m grained material (about 40% higher at 0.5 equivalent strain). In both materials an unusual grain shape evolution from pre-deformation equiaxed to rhomboidal was observed during torsion, which was rationalised [G. Angella, B.P. Wynne, W.M. Rainforth, J.H. Beynon, Acta Mater. 53 (2005) 1263] in terms of strain induced grain boundary migration (SIGBM) combined with the torsion stress field. A qualitative model is proposed to describe the flow behaviour of the AISI 316L stainless steel based on the unusual grain structure evolution and, in turn, on SIGBM. © 2007 Elsevier B.V. All rights reserved. Keywords: Stainless steel; Torsion; High-temperature deformation; Work hardening; Strain-induced grain boundary migration
1. Introduction A number of mechanisms occurs during high-temperature deformation of metals, and which are the most prominent depends on material factors such as stacking fault energy and the presence of second phase particles, and extrinsic factors such as temperature, strain rate and strain. At lower values of strain rate grain boundary mobility is enhanced in polycrystalline metals at high-temperature. Under such conditions, strain induced grain boundary migration (SIGBM) has been introduced to explain the bulging of the grain boundaries and the direction of migration of the grain boundary [2–4]. SIGBM has been widely investigated in static recrystallisation studies [5–8] and the generally accepted model proposed by Bailey and Hirsch [6] is based on the experimental evidence that GBM through bulging is triggered by a driving force differential across grain boundaries arising from the difference in stored energy in the neighbouring grains. Grain boundaries are, in fact, sites of inhomogeneous deformation because of the incompatibility strain that occurs in
∗
Corresponding author. Tel.: +39 02 66173327; fax: +39 02 66173321. E-mail address: [email protected] (G. Angella).
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grains at their common grain boundaries. Recently SIGBM has also received attention in dynamic recrystallisation investigations [9,10], where it has been reported that extensive SIGBM occurs before nuclei of recrystallised material appear at bulged grain boundaries. Although significant dislocation activity has been observed in the regions left behind by the migrated grain boundaries, particularly in bi-crystal experiments [3,10], investigations have been mainly focused on microstructure and no exploration of the effects that such localised deformation has on flow stress has been carried out. The present paper aims to link the unusual flow behaviour of a fine-grained AISI 316L stainless steel with the unusual microstructure evolved during torsion at hightemperature that was rationalised in terms of SIGBM [1]. 2. Experimental The stainless steel AISI 316L was investigated in hot torsion with different equivalent strain rates in the range of temperatures 850–1100 ◦ C. The chemical composition of the tested material is reported in Table 1. The material has a low carbon content, such that no strain-induced precipitation would have been expected during deformation, which would have made the correlation
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Table 1 AISI 316L chemical composition (wt.%) C Cr Ni Si Mn P S Mo Fe
0.020 17.1 11.2 0.37 1.78 0.048 0.009 2.12 67.4
between microstructure evolution and flow stress more complex. Solid bars 3 m long and 60 mm in diameter were machined into tubular specimens with internal and external gauge radii of 8 and 11 mm, respectively. The tubular specimens had gauge lengths of 11 mm and fillet radii of 25 mm. Tubular specimens were deformed in a bi-axial testing rig [11] designed to carry out complex deformation paths at high temperatures that could be achieved by using an induction heating system capable of rapid heating. The rig was equipped with a quenching system to as far as possible retain the material microstructure evolved during deformation and an average quenching rate of about 90 ◦ C/s from 1000 to 800 ◦ C was typically achieved. The torsion tests were carried out in fixed-end conditions and the presence of any axial load, indicating axial dimension variations because of the torsional deformation, was monitored. Under the deformation conditions of the current investigation, the tubular specimens shortened, inducing axial loads increasing with strain but always smaller than 2 MPa, which was low when compared with the typical equivalent stresses due to the torsion deformation of about 100 MPa for these test conditions. Torque and twist data were transformed into shear stress and shear strain by using the method of the critical radius proposed by Barraclough et al. [12]. According to this method, at a particular radius R* of the round torsion specimen, called the critical radius, the shear stress τR∗ is given by τR∗ =
3T 2π(R3o − R3i )
(1)
where Ro and Ri are the external and the internal radii of the tubular specimen at the test temperature, respectively; i.e. the data were corrected for the thermal expansion of the specimen. For the geometry of the tubular specimen used in the current research, R* could be approximated to 0.90 of the external radius [12,13]. The shear strain at the critical radius is given by γR∗ =
R∗ ϑ Leff
(2)
where Leff is the effective gauge length that was used rather than the nominal gauge length L because of the contribution to the overall deformation of the material in the tubular specimen fillets. A straight scratch parallel to the longitudinal axis of the tube was made on the surface of each tubular specimen in order to detect the region where homogeneous torsional deformation occurred, i.e. the region where the scratch was still straight after deformation. The length of the homogeneous region was
Fig. 1. Representation of a tubular specimen and the observation plane (θ, Z) at the critical radius R* , i.e. 0.90Ro . The maximum shear directions in torsion are reported on the section plane.
assumed to be the effective length. The method of the critical radius is simple to apply and it is accurate [14]. Another benefit is that at the critical radius the stress–strain data appear to be insensitive to the notch effect [13,15] that could be expected because of the tubular specimen fillet and, hence, the data should be more representative of the material behaviour regardless the specimen geometry. Furthermore, microstructure observations could be directly related to the flow curve through observing the microstructure on planes tangent to the tube that were far away from the longitudinal tube axis, i.e. at distance equal to the critical radius, as indicated in Fig. 1. Finally the shear stress and strain were reported as von Mises equivalent values according to the equations: √ γR∗ σEq = 3τR∗ and εEq = √ (3) 3 Conventional metallographic observations were carried out on the stainless steel to measure the average grain size using the mean intercept method. To determine the starting grain size, a tubular specimen was heated up to 1000 ◦ C with the induction heating system according to the soaking procedure that was carried out before each high-temperature test and subsequent quenching. The grain size was the result of measurements on 20 different fields, giving a value of 29.2 ± 1.6 m (hereafter referred to as ‘30 m’). AISI 316L with a larger grain size of 97.4 ± 4.6 m (hereafter referred to as ‘100 m’) was tested in similar conditions to investigate the effects of grain size on the alloy microstructure evolution and flow stress behaviour. This material was obtained by simply heating the finer grained AISI 316L in a controlled nitrogen atmosphere furnace at 1100 ◦ C for 25 min and air cooled to room temperature before being re-heated for testing. Conventional X-ray techniques [16,17] for measuring bulk crystallographic texture were performed to investigate the crys-
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tallographic evolution during torsion with a modified Shultz reflection goniometer by Siemens equipped with Philips X-ray source using a Co target. Four experimental incomplete pole figures were measured corresponding to the crystallographic planes (1 1 1), (2 0 0), (2 2 0) and (3 1 1). The incompleteness of the pole figures was because of the inability of the system to detect reflections corresponding to X-rays incident at almost a tangent to the flat surface of the sample. Orientation distribution functions (ODF) were calculated using the software NTNTAY [18], from which the pole figures were produced. The material microstructure evolution during deformation was analysed through conventional metallographic techniques and more detailed investigations of the microstructure were performed using transmission electron microscopy (TEM) with a JEM 2000FXII by Jeol with an accelerating voltage of 200 kV. Slices of material tangential to the tubular specimens were carefully taken in such a way that the thin foils for TEM observations corresponded to the material at the critical radius. A Struers–Tenupol twin jet electro-polishing unit was used operating at a voltage to have a current of about 0.9 mA and using an electrolyte of chemical composition 23% perchloric acid in ethanol. The electro polishing was undertaken at an electrolyte temperature of about −25 ◦ C. 3. Results 3.1. AISI 316L flow curves Fig. 2(a) and (b) reports the equivalent stress–strain curves from torsion tests on 30 m grained AISI 316L at different deformation conditions. In Fig. 2(a) the flow curve at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 has well defined different regions. The first is a transitional region at small equivalent strain, soon after yielding and generally smaller than 0.05 under these deformation conditions, where a sharp elbow can be detected. This was followed by an unusual, almost linear region, i.e. with almost constant strain hardening rate ΘEq ≡ dσ Eq /dεEq , that was found in the strain range about 0.05–0.20. After this linear region, the work hardening decreased progressively until a stress plateau was achieved at an equivalent strain of about 0.50. Beyond this plateau the flow stress increased until deformation instabilities occurred in the specimen gauge section and the curve was no longer representative of the material behaviour. The decrease of strain rate to 0.001 and 0.0001 s−1 did not alter the flow curve shape observed at the strain rate of 0.006 s−1 , whilst the stress plateaus occurred at lower strains. Fig. 2(b) shows the material behaviour at different temperatures, when the deformation rate at the critical radius was held constant at a value of 0.006 s−1 . It was possible to detect a trend of the material behaviour with changing temperatures: above 1000 ◦ C the flow curves presented the same peculiarities observed at 1000 ◦ C, whilst below 1000 ◦ C the material behaviour diverged from the one detected at higher temperatures. The elbow that characterised the transitional region at small strains became less sharp at 900 ◦ C and disappeared completely at 850 ◦ C. Furthermore, with decreasing temperature the almost constant work hardening region vanished progressively in such a
Fig. 2. Equivalent stress–strain curves of 30 m AISI 316L deformed: (a) at 1000 ◦ C with equivalent strain rates at the critical radius of 0.006, 0.001 and 0.0001 s−1 and (b) at different temperatures with an equivalent strain rate at the critical radius of 0.006 s−1 . (c) Comparison between 30 and 100 m grained materials deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 .
way that at 850 ◦ C a flow curve with a familiar parabolic shape was observed. In Fig. 2(c) the flow curves of 30 and 100 m grained AISI 316L deformed at similar conditions of 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 are compared. The flow stress for the coarser grained material
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Fig. 3. (a) Work hardening ΘEq vs. σ Eq of 30 m grained AISI 316L deformed at different temperatures with equivalent strain rate at the critical radius of 0.006 s−1 and (b) work hardening ΘEq vs. σ Eq of 30 and 100 m grained materials deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 .
was significantly higher than that for the material with an average grain size of 30 m, about 40% at 0.5 equivalent strain. In addition, the shape of the flow curve changed notably, since a parabolic stress–strain curve was observed for the material with the larger grain size. 3.2. Flow stress curves analysis The work hardening behaviour of the 30 m grained material with changing temperature and an equivalent strain rate at the critical radius of 0.006 s−1 , was investigated by plotting the work hardening rate ΘEq against σ Eq , as reported in Fig. 3(a). At 850 ◦ C, where the stress–strain curve was parabolic, the ΘEq versus σ Eq curve could be fitted over a quite large data range with the linear equation ΘEq = Θo (1 − (σ Eq /σ V )), resulting in a value of Θo equal to E850 /N with N = 54.8 ± 2.0, where E850 is the Young’s modulus at the test temperature of 850 ◦ C. The value of Θo was consistent with the results reported in the literature [19], where Θo is commonly about ET /50 and ET is the Young modulus at the test temperature. The linear data range represents what is conventionally called Stage III of the strain hardening and is
well fitted by the Voce equation, which results in a line in the plot ΘEq versus σ Eq . The deviation of the experimental data from the Voce equation at small stresses is attributed to effect of the grain boundaries on dislocation storage in well annealed materials, whilst at higher stresses the deviation is conventionally known as Stage IV, which anticipates dynamic recrystallisation in low stacking fault materials like AISI 316L. Dynamic recrystallisation commonly appears with an abrupt deviation from the Stage IV trend to achieve rapidly the condition ΘEq = 0, such deviation being conventionally defined as Stage V of strain hardening [19–21]. The Voce lines at higher temperatures than 850 ◦ C were artificially drawn, by imposing an athermal work hardening equal to ET /54.8. The range of experimental ΘEq versus σ Eq data that could be well fitted by the Voce equation at 900 ◦ C was appreciably reduced. At higher temperatures, where linear stress–strain curves were found at low strains, no Voce equation fitting was possible, i.e. Stage III could not be detected. The ΘEq versus σ Eq curve for the 100 m grained material deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 , having a parabolic flow curve, was well described by the Voce equation using an athermal strain hardening Θo = E1000 /54.8, as reported in Fig. 3(b), where the 30 m material data are also reported for comparison. Therefore, when a parabolic stress–strain curve was found, the Stage III of strain hardening was established, as would normally be expected. The beginning of the Stage IV in the ΘEq versus σ Eq curves where Stage III was found, occurred at a nearly constant value of the ratio ΘEq /σ Eq of about 1.0 in Fig. 3(a) and (b) the line ΘEq = mσ Eq with m = 1.0 is reported. The constancy of the ratio ΘEq /σ Eq at the beginning of the presumed Stage IV matched results reported in literature on Stage IV investigations on several austenitic stainless steels deformed in torsion and compression under similar temperature and deformation rate conditions [20,21]. However, the line ΘEq = mσ Eq with m = 1.0 seemed to intercept closely also the beginning of the flat regions for the higher temperatures, i.e. 1000 and 1100 ◦ C, with the exception of 900 ◦ C, where some discrepancy could be observed. 3.3. Determination of dynamic recrystallisation: Stage V There is no general agreement concerning the best functional fitting of Stage IV in the plot ΘEq versus σ Eq and, in addition, at high temperatures the deviation of Stage IV from Stage III is usually quite smooth and does not show any unambiguous trend [19]. Nevertheless, Stage IV has been modelled by some researchers [20,21] with linear behaviour in the ΘEq versus σ Eq plot by the necessity of calculation of the asymptotic stress value of Stage IV. The same linear assumption was adopted in the present work. The linear behaviour in the ΘEq versus σ Eq plot results in a Voce-type equation for the stress–strain curves as σEq = σA + (σo − σA ) e−αεEq
(4)
where σ o is the extrapolated stress value for εEq = 0, σ A the asymptotic stress for εEq going to infinity, i.e. ΘEq = 0, and α is
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Fig. 4. (a) Experimental equivalent stress–strain curve and the best Voce-type equation fitting at 850 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 for the 30 m grained alloy and (b) ΘEq vs. σ Eq plot of the experimental equivalent stress–strain curve in (a). The negative slope line is the best Voce-type fitting to the experimental data, whilst σ D (194.5 MPa) and σ A (210.0 MPa) are the deviation stress and the asymptotic stress, respectively. σ Pl (197.5 MPa) is the stress at which the work hardening rate is first zero and matches well the stress plateau in Fig. 4(a).
the parameter controlling the rate to achieve σ A . In the present work, rather than fitting Stage IV in the ΘEq versus σ Eq plot, which could be quite difficult for the data scattering of the work hardening ΘEq because of the low values, the Voce-type equation (4) was interpolated to the stress–strain curves in the almost linear region. In Fig. 4(a) the result of the flow curve interpolation for the 30 m grained materials deformed at 850 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 is reported. With the exception of the region at the beginning of the curve, where Stage III was found, the curve is well fitted in the intermediate region, whilst at high stress a deviation of the interpolation curve from the experimental one is evident. In Fig. 4(b), the interpolation result in Fig. 4(a) is reported in the ΘEq versus σ Eq plot. The negative slope line is the best Vocetype fitting line and σ A is the asymptotic stress of the Voce-type equation. Consistent results were found for the 100 m grained material deformed at 1000 ◦ C with an equivalent strain rate of
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0.006 s−1 . The authors defined σ D as the deviation stress, i.e. as the minimum experimental stress after the well fitted region for which the curve difference between the experimental stress and the Voce-type fitting stress was bigger than 1%. After the calculation of σ D , the values of the work hardening ΘD corresponding to the deviation stress σ D were used to calculate the ratios Γ D = ΘD /σ D . The values of Γ D were found to be 0.20 for the 30 m grained AISI 316L deformed at 850 ◦ C and 0.006 s−1 , and 0.21 for the 100 m grained AISI 316L deformed at 1000 ◦ C and 0.006 s−1 . The results are quite consistent and are comparable with data reported in literature [20,21] where Γ D has been reported to be 0.27 for various austenitic stainless steels deformed in torsion at deformation conditions similar to the present tests. σ Pl is the stress at which the work hardening rate was first zero and matches well the stress plateau observed in the flow stress curve reported in Fig. 4(a). The increased hardening beyond σ Pl was caused by geometrical instabilities typical of tubular specimens deformed at deformation conditions when dynamic recrystallisation occurs so that it was not representative of the material behaviour. The same procedure used for the parabolic curves was implemented for the anomalous flow curves obtained at high temperatures, through interpolating the almost linear regions of the flow curves. In Fig. 5(a) the result of the flow curve interpolation for the 30 m grained materials deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 is reported. With the exception of the transitional region at the beginning of the curve, where there was no attempt to fit the Voce-type equation, and the region at high strains, the Vocetype equation fitted quite well the intermediate experimental data, also over a wide data range beyond the almost linear region. In Fig. 5(b), the interpolation result of the flow stress analysis for the 30 m grained materials is reported in the ΘEq versus σ Eq plot. The values of the ratios Γ D were consistent to those from the parabolic flow curves: 0.20 at 900 ◦ C and 0.18 at 1000 and 1100 ◦ C. Also in these cases the values of σ Pl correspond to the stress plateaus observed in the flow curves. Even if at 0.1 equivalent strain no steady state was achieved, the minor difference in work hardening rate allowed the procedure of computing the stress exponent n by assuming a power law relationship between strain rate and stress. The Norton exponent n appeared to be in the range 6.6–6.9. The apparent activation energy of deformation QApp could be found by assuming an Arrhenius-type relationship between strain rate and temperature in the range of temperatures 1000–1100 ◦ C with equivalent strain rates 0.006–0.0001 s−1 at an equivalent strain of 0.1. QApp was determined as 350 kJ mol−1 . 3.4. Texture analysis Texture measurements were conducted on the plane (θ, Z) at a distance from the tubular axis equal to the critical radius in a AISI 316L tubular specimen in pre-test conditions, i.e. heated to 1000 ◦ C according to the procedure before any high-temperature torsion test and then quenched. No significant texture was
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not provide any additional information, and were therefore not included. 3.5. Microstructure evolution
Fig. 5. (a) Experimental equivalent stress–strain curve and the best Voce-type equation fitting at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 for the 30 m grained alloy and (b) ΘEq vs. σ Eq plot of the experimental equivalent stress–strain curve in (a). The negative slope line is the best Voce-type fitting to the experimental data, whilst σ D (93.5 MPa) and σ A (119.5 MPa) are the deviation stress and the asymptotic stress, respectively. σ Pl (95.0 MPa) is the stress at which the work hardening rate is first zero and matches well the stress plateau in Fig. 5(a).
present before testing. The texture evolutions of the 30 and the 100 m grain sized materials were investigated after the same deformation conditions of 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 . In Fig. 6 the crystallographic textures of the two different grained materials evolved after similar equivalent strain at the critical radius of 0.36 are reported. The texture of the 30 m grain size material in Fig. 6(a) was extremely weak. A weak torsion texture seemed to be observable in the 100 m grained material, see Fig. 6(b), as reported in literature [22,23] with easy slip planes ({1 1 1}in FCC materials as AISI 316L) parallel to the principal shear directions. However, the weakness of texture was such that the difference between the textures of 30 and 100 m grained materials may not be significant. EBSD measurements were also used [11] to determine local lattice curvature, particularly at the grain boundaries, to complement the optical and TEM microstructural studies, described below. However, the EBSD measurements did
Under some of the current deformation conditions the stainless steel exhibited an uncommon microstructure evolution, resulting in the formation of a rhomboidal grain structure with horizontal grain boundaries regularly aligned along the horizontal directions of maximum shear stresses during monotonic torsion. The structure evolution was complete already at the first stage deformation, i.e. at the beginning of the linear region. The adopted grain shape, reported in Fig. 7 for the 30 m grained material deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 to a final equivalent strain of 0.18, was such that dihedral angles at the triple junctions and 90◦ elbow grain boundaries were observed, which is not expected from the minimisation of grain boundary energy. The rhomboidal grain structure occurred only on the tangential plane of the tubular specimen, i.e. on the observation plane (θ, Z) in Fig. 1, whilst on the planes along through the tubular specimen thickness, i.e. the planes (R, Z) and (R, θ), the grain structure maintained an equiaxed structure. The detailed description and rationalisation of the microstructure evolution is reported elsewhere [1], where it was concluded that the evolution from equiaxed to rhomboidal grain shape in monotonic torsion occurred through strain induced grain boundary migration (SIGBM) combined with the torsion stress field. Metallographic samples from specimens deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 to different final equivalent strains were observed with Nomarski contrast to emphasise any surface specimen irregularity brought out by a slight electro-etching. A typical observation at high magnification is reported in Fig. 7(b), which shows that a significant proportion of the grain boundaries were highly irregular surfaces. Twin boundaries were slightly bent in the grain core, whilst in the vicinity of the grain boundaries the twin boundaries appeared irregular and fuzzy. These etching irregularities revealed some dislocation microstructure heterogeneity at the grain boundaries. However, at strains beyond the flow stress plateau the rhomboidal grain structure disappeared and the deformed microstructure appeared partly consumed by a new, fine grain structure, as reported in Fig. 8, in such a way that grains with regular shapes could no longer be found. This microstructure was typical of dynamic recrystallisation, confirming the stress analysis results that identified the occurrence of Stage V. At temperatures above 900 ◦ C, the uncommon microstructure evolution reported at 1000 ◦ C was also observed, while at 850 ◦ C no sign of a rhomboidal grain structure was found and the grains maintained an elongated shape after deformation from equiaxed structure. It was possible to correlate the microstructure evolution at different temperatures to the shape of the flow curves of the 30 m grained material: when the microstructure did not evolve into rhomboidal grain structure, i.e. at 850 ◦ C, the flow curve shape was parabolic, whilst, when the rhomboidal grain structure was formed at high temperatures, the flow curves
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Fig. 6. {1 1 1} Pole figures on the planes (θ, Z) at the critical radii of AISI 316L tubular specimens deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 to a final equivalent strain at the critical radius of 0.36 with an average grain size of (a) 30 m and (b) 100 m. The horizontal shear direction is reported in the figure.
presented a region of almost constant work hardening at small strains. The temperature appeared to be a critical parameter in affecting the grain structure evolution. However, metallographic observations for the 100 m grained stainless steel deformed at 1000 ◦ C with an equivalent strain rate of 0.006 s−1 revealed a grain microstructure that exhibited rhomboidal shape, as seen in the 30 m grained material, but the flow curve was parabolic and higher with respect to the 30 m AISI 316L for the same test conditions. Therefore, the mechanism leading to the aligned grain boundary evolution was linked to the deformation conditions, i.e. temperature, strain rate, torsion and the grain boundaries themselves, regardless of the grain size, but the larger grain size conferred strength to the material and the expected parabolic flow curve shape. Table 2 summarises the grain evolution and the flow stress curve shapes during torsion at different temperatures and grain sizes with similar equivalent strain rate at the critical radius of 0.006 s−1 .
Fig. 7. (a) Grain structure of AISI 316L deformed at 1000 ◦ C with equivalent strain rate at the critical radius of 0.006 s−1 , evolved after an equivalent strain of 0.18 and (b) at higher magnifications with Nomarski contrast. The horizontal direction of maximum shear is reported in the figure.
Fig. 8. Grain structure of AISI 316L deformed at 1000 ◦ C with equivalent strain rate at the critical radius of 0.006 s−1 to a final equivalent strain at the critical radius of 1.10. The horizontal direction of maximum shear is reported in the figure.
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Table 2 Grain evolution and flow stress curve shapes during torsion at different temperatures and grain sizes with similar equivalent strain rate at the critical radius of 0.006 s−1 Temperature (◦ C)
Grain size (m)
Rhomboidal grains
Flow stress curve shape
850 900 1000 1100 1000
30 30 30 30 100
No Yes Yes Yes Yes
Parabolic Parabolic/linear Linear Linear Parabolic
3.6. Microstructure observation with TEM The microstructure of the 30 m grained material deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 was investigated through TEM at different strains. In Fig. 9 the grain core dislocation structure at an equivalent strain of 0.09 is reported. The dislocation cells appeared quite regular in shape, in accordance with structure reported in the literature for materials deformed in torsion and conventionally called a “checkerboard” structure. The dislocation cell interiors were quite clear of dislocations, the cell walls appeared to be sharp and bi-dimensional, and the crystallographic misorientation among different cells was quantified through the analysis of
the selected area diffraction patterns to be about 2◦ . The dislocation structure was typical of materials deformed in conditions conventionally defined as Stage IV [19,24]. Not all grains presented such a structure, although it was significantly present, and dislocation structures with thick walls and numerous dislocations in the cells were also observed. However, this could be rationalised because of the small strains and different grain orientations with respect to the external stress axes. The microstructure at the grain boundaries of the same material reported in Fig. 9 is shown in Fig. 10(a), and was significantly different to that at the grain cores. The dislocation structures also consisted of low angle dislocation boundaries, but they were elongated with major axes parallel to the grain boundaries themselves and the crystallographic misorientations were quantified through Kikuchi diffraction pattern analysis to be about 1–1.5◦ with respect to the parent grain. On increasing the strain, the dislocation structure at the grain boundaries increased in complexity as reported in Fig. 10(b) for the 30 m grained material deformed at 1000 ◦ C to an equivalent strain of 0.18. Such complexity of the dislocation structure seemed to be consistent with the microstructure details observed with Nomarsky contrast in Fig. 7(b). In the proximity of a double elbow grain boundary, consistent with the grain boundary shape observed in Fig. 7(a) and (b), the dislocation structure was square-shaped, similar to the elbow shape, whilst towards the core of the parent grain it was elongated, analogous to the structure reported Fig. 10(a), and in the grain core the dislocation structure was “checkerboard”. The crystallographic misorientation, analysed using the Kikuchi diffraction technique, increased from 1.5◦ between the grain core (point A in the Fig. 10(b)) and the middle of the elongated structure (point B in the figure), to a final value of about 2◦ between point A and point C, close to the elbow grain boundary. Such dislocation structures seemed to be traces of successive grain boundary migrations, for which the final result was the formation of the grain boundary elbow, i.e. the rhomboidal grain boundary structure. 4. Discussion
Fig. 9. Grain core dislocation structure of AISI 316L deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 to a final equivalent strain of 0.09: “checkerboard” structure with dislocation cells with low angle dislocation walls and crystallographic misorientation of about 2◦ .
The analysis of the parabolic flow curves revealed that the experimental data fell into the typical Stages of strain hardening, i.e. the Stages III, IV and V, which was confirmed by the distinctive values of ΘC /σ C ∼ 1.0 for the beginning of Stage IV, and ΘD /σ D ∼ 0.2 for the beginning of Stage V, i.e. the end of Stage IV. The values ΘD /σ D were smaller than those reported in literature [20,21], where ΘD /σ D ∼ 0.27 was found; however, the consistency of the ratios ΘD /σ D in the present work, for any deformation conditions, indicated that the same strain hardening stage was beginning, i.e. Stage V. The lower value of ΘD /σ D could be attributed to the different experimental procedure used. Consistent values of ΘC /σ C and ΘD /σ D were also found for the anomalous flow curves, even if the ΘEq versus σ Eq data curves appeared flat and of completely different shape to the parabolic flow curves data, which indicated that such flat regions were Stage IV. The TEM observations reported in Fig. 9 confirmed that the dislocation structure in the grain cores was typical
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Fig. 10. Dislocation structure at grain boundaries in AISI 316L deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 (a) to a final equivalent strain of 0.09: dislocation structures elongated consistently to the grain boundary with crystallographic misorientation with respect to the parent grain of about 1–1.5◦ and (b) to a final equivalent strain of 0.18. The crystallographic misorientation from the core of the parent grain to the elbows increased from 1.5◦ between points A and B, to 2◦ between A and C.
of Stage IV [19,24], and the micrograph of the alloy at high strains reported in Fig. 8 showed the consumed structure, typical of recrystallised materials. Therefore, all experimental findings indicated that Stage IV took place, dominating the whole deformation, whilst Stage III did not manifest itself. To the authors’ knowledge such behaviour has not previously been reported in literature. The wide Stage IV of strain hardening observed in the ΘEq versus σ Eq curves for AISI 316L, regardless of the deformation conditions, confirmed that the deformation was intrinsically due to bulk dislocation activity, as indicated by the Norton exponent around 6.6–6.9 and the apparent activation energy of deformation of 350 kJ mol−1 [25,26]. Furthermore, there was no measurable difference in the texture evolution in the 30 and 100 m grained materials, which excludes the hypothesis of any crystallographic texture effect. It has been reported [1] that the alloy exhibited an uncommon grain boundary evolution from an equiaxed structure in pre-test conditions to a rhomboidal shape during torsion at high temperatures, which was found to be linked to the flow stress behaviour. The link between grain structure evolution and flow stress indicated that the microstructure evolution mechanism that affected the grain structure also affected the flow stress. The qualitative model proposed by the authors to describe the anomalous AISI 316L behaviour under the current deformation conditions is based on SIGBM, i.e. the microstructural mechanism by which the grain evolution was rationalised [1]. The SIGBM events at the grain boundaries were triggered by gradients of stored energy and occurred to minimise dislocation accumulation at the grain boundaries. According to the mechanistic interpretation by Kocks and Mecking [19,27] Stage III
can be described by the Voce equation: ΘVoce = Θo − D(T, ε˙ )σ
(5)
where Θo has the usual meaning and D(T, ε˙ ) is the dynamic recovery term. According to the model proposed by the authors, the work hardening in Eq. (5) deviated from the common Voce behaviour through a softening term, arising from SIGBM, i.e. SSIGBM , in such a way that the Voce equation resulted in Θ = ΘVoce − SSIGBM = Θo − (D(T, ε˙ )σ + SSIGBM )
(6)
At small deformation after yielding, dislocation density did not increase as expected from Voce behaviour because of local reductions in dislocation density in the grain boundary regions due to the SIGBM events that transformed the pre-test equiaxed grain structure into the rhomboidal structure, which came into low stress and abruptly reduction of the work hardening rate. In this way the material was prevented from entering Stage III. The softening occurred in the 30 m grained material because of the relatively small grain size, whilst in the 100 m grained material the ratio of the grain boundary area to the volume decreased by about 30% with respect to the smaller grained material in such a way that the term SSIGBM in Eq. (6) was no longer significant. The grain boundary migrations left behind regions of low dislocation density that were more easily deformed than the bulk, which could have produced localised deformation at the grain boundaries and could explain the small difference in the texture evolutions of the two differently grained materials. The reason of why Stage IV survived rather than also being by-passed was found in the microstructural evolution of Stage
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IV. If typical work hardening behaviour is considered, i.e. when Stage III is followed by Stage IV (in the present work this occurred for 30 m grained AISI 316L deformed at 850 ◦ C and 100 m grained material at 1000 ◦ C), the increase of hardening in Stage IV with respect to Stage III has been explained in the literature [9,19,28–30] as being caused by the transformation of the dislocation structures with thick walls typical of Stage III into dislocation subgrains, i.e. tilted and twisted dislocation cells with sharp and bi-dimensional walls. The latter should be more effective obstacles to dislocation motion than the former, which gives additional hardening, or the hardening may arise because the cells are tilted and slip transfer is more difficult [29]. A modified Hall–Petch relation has been proposed [28–30] to link this microstructure evolution with Stage IV: σ = σ ∗ + kd −1
(7)
where σ * is the friction stress, k the “locking parameter” and the cell size d (with the exponent of −1 rather than −0.5) has replaced the typical grain size D. Therefore, in the present work, the grain boundaries represented the main obstacles to dislocation motion prior to the onset of Stage IV and dislocation accumulation was sufficient for the accumulated stored energy to trigger significant SIGBM events. With the occurrence of Stage IV, i.e. at ΘC /σ C ∼ 1.0, the “harder” dislocation structure typical of this deformation stage reduced the effectiveness of the dislocation accumulation at the grain boundaries, since the dislocation motion was retained in the grain core. In this way Stage IV became evident and only when the work hardening and stress conditions for Stage V occurred, did Stage IV end and new grains of recrystallised material consume the original structure, as reported in Fig. 7.
flow stress behaviour was observed. A model also based on SIGBM was proposed to describe qualitatively the AISI 316L flow stress behaviour: • At small deformation after yielding, the dislocation density did not increase because of local reduction near the grain boundaries due to the SIGBM events that transformed the pre-test equiaxed grain structure into the rhomboidal structure, which abruptly reduced the work hardening rate. In this way the 30 m grained material was prevented from entering Stage III. In the larger grained material the ratio of grain boundary area to volume decreased with respect to the 30 m grain size material in such a way that SIGBM was no longer significant and the material exhibited the expected Stage III and the common parabolic flow curve. • Stage IV was not by-passed because of its dislocation microstructure. The dislocation cells typical of this deformation stage were effective obstacles to the dislocation motion such that the dislocations were retained in the grain core, and the effectiveness of the dislocation accumulation at the grain boundaries was reduced. SIGBM also became insignificant in the 30 m grain size material. • When the work hardening and stress conditions for Stage V occurred, dynamic recrystallisation took place, consuming the original deformation grain structure. Acknowledgements The financial support of The University of Sheffield is gratefully acknowledged, as is the funding for the experimental facility provided by the Engineering and Physical Sciences Research Council, UK.
5. Conclusions References The stainless steel AISI 316L with an average grain size of about 30 m was investigated in hot torsion in the temperature range 850–1100 ◦ C with equivalent strain rates of 0.006–0.0001 s−1 . The alloy showed unusual flow stress curves at high temperatures with almost linear work hardening behaviour at low strains, and presented a significant reduction of flow stress with respect to the 100 m grained material deformed under similar conditions. No measurable difference between the texture evolution of the 30 and 100 m grained materials was observed. This and the presence of a dominant Stage IV of strain hardening, the values found for the stress exponent, and the apparent activation energy of deformation were typical of bulk dislocation deformation. The AISI 316L microstructure evolution during deformation appeared to be quite unusual, since a rhomboidal grain shape was adopted with dihedral angles at triple junctions and 90◦ elbow boundaries consistent with the torsion stress field, which was clearly not expected from minimisation of grain boundary energy. The microstructure evolution was rationalised on the basis of the SIGBM mechanism and minimisation of stored energy at the grain boundaries combined with the torsion stress field. A relationship between the unusual microstructure and
[1] G. Angella, B.P. Wynne, W.M. Rainforth, J.H. Beynon, Acta Mater. 53 (2005) 1263. [2] R.L. Bell, N.B.W. Thompson, P.A. Turner, J. Mater. Sci. 3 (1968) 524. [3] S. Hashimoto, B. Baudelet, Scripta. Metall. 23 (1989) 1855. [4] H. Miura, M. Ozama, R. Mogawa, T. Sakai, Scripta. Mater. 48 (2003) 1501. [5] P.A. Beck, P.R. Sperry, J. Appl. Phys. 21 (1950) 150. [6] J.E. Bailey, P.B. Hirsch, Proc. Roy. Soc. London, Ser. A 267 (1961) 11. [7] F.J. Humphreys, M. Hatherley, Recrystallisation and Related Phenomena, Pergamon Press, Oxford, UK, 1996. [8] C. Escher, G. Gottstein, Acta Mater. 46 (1998) 525. [9] G. Gottstein, E. Br¨unger, M. Frommert, M. Goerdeler, M. Zeng, Z. Metallkd. 94 (2003) 628. [10] H. Miura, T. Sakai, R. Mogawa, G. Gottstein, Scripta. Mater. 51 (2004) 671. [11] G. Angella, Strain path, flow stress and microstructure evolution of an austenitic stainless steel at high temperature, Ph.D. Thesis, Department of Mechanical Engineering, The University of Sheffield, Sheffield, UK, 2002. [12] D.R. Barraclough, H.J. Whittaker, K.D. Nair, C.M. Sellars, J. Test. Eval. 1 (1973) 220. [13] K. P¨ohlandt, A.E. Tekkaya, E. Lach, Arch. Eisenh¨uttenwes. 55 (1984) 149. [14] G.J. Richardson, D.N. Hawkins, C.M. Sellars, Worked Examples in Metalworking, The Institute of Metals, London, UK, 1985. [15] K. P¨ohlandt, A.E. Tekkaya, Mater. Sci. Technol. 1 (1985) 972.
G. Angella et al. / Materials Science and Engineering A 475 (2008) 257–267 [16] M. Hatherley, W.B. Hutchinson, An Introduction to Textures in Metals (Monograph No. 5), The Institute of Metals, London, UK, 1979. [17] U.F. Kocks, C.N. Tom´e, H.R. Wenk, Texture and Anisotropy, Cambridge University Press, Cambridge, UK, 1998. [18] P. Van Houtte, The “MTM-FHM” Software System, Version 2. Manual, Department of Metallurgy and Materials Engineering, Katholieke Universiteit, Leuven, Belgium, 2000. [19] U.F. Kocks, H. Mecking, Prog. Mater. Sci. 48 (2003) 171. [20] N.D. Ryan, H.J. McQueen, Can. Metall. Quart. 29 (1990) 147. [21] E.I. Poliak, J.J. Jonas, Acta Mater. 44 (1996) 127. [22] G.R. Canova, U.F. Kocks, J.J. Jonas, Acta Metall. 32 (1984) 211.
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[23] A.D. Rollett, T. Lower, U.F. Kocks, M.G. Stout, Proceedings of the 8th International Conference on Textures of Materials (ICOTOM 8), TSMAIME, Santa Fe, USA, 1987. [24] J.G. Sevillano, A.E. Aernoudt, Mater. Sci. Eng. A 86 (1987) 35. [25] H.J. Frost, M.F. Ashby, Deformation Mechanism Maps, Pergamon Press, Oxford, UK, 1982. [26] D.G. Morris, D.R. Harries, Met. Sci. J. (1978) 525. [27] H. Mecking, U.F. Kocks, Acta Metall. Mater. 29 (1981) 1865. [28] J.G. Sevillano, P. Van Houtte, E. Aernoudt, Prog. Mater. Sci. 25 (1981) 69. [29] A.S. Argon, P. Haasen, Acta Metall. Mater. 41 (1993) 3289. [30] T. Ung´ar, M. Zehetbauer, Scripta. Mater. 35 (1996) 1467.
Strength of AISI 316L in torsion at high temperature G. Angella b,∗ , B.P. Wynne a , W.M. Rainforth a , J.H. Beynon c a
IMMPETUS, Department of Engineering Materials, The University of Sheffield, Sheffield, UK b Istituto IENI-CNR, via R. Cozzi 53, 20125 Milano, Italy c Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Hawthorn, Vic. 3122, Australia Received 15 December 2006; received in revised form 11 April 2007; accepted 19 May 2007
Abstract Hot torsion flow behaviour of 30 m grained AISI 316L stainless steel was investigated in the range of temperatures 850–1100 ◦ C with equivalent strain rates 0.0001–0.006 s−1 . For temperatures higher than 900 ◦ C the material presented an unusual linear relationship at low strains between equivalent stress, σ Eq , and equivalent strain, εEq , whilst at 850 ◦ C a parabolic σ Eq –εEq relationship was observed. The flow behaviour of 100 m grained AISI 316L stainless steel torsionally deformed at 1000 ◦ C with equivalent strain rate of 0.006 s−1 was reported to follow the expected parabolic σ Eq –εEq relationship and produced a significantly higher flow stress than the 30 m grained material (about 40% higher at 0.5 equivalent strain). In both materials an unusual grain shape evolution from pre-deformation equiaxed to rhomboidal was observed during torsion, which was rationalised [G. Angella, B.P. Wynne, W.M. Rainforth, J.H. Beynon, Acta Mater. 53 (2005) 1263] in terms of strain induced grain boundary migration (SIGBM) combined with the torsion stress field. A qualitative model is proposed to describe the flow behaviour of the AISI 316L stainless steel based on the unusual grain structure evolution and, in turn, on SIGBM. © 2007 Elsevier B.V. All rights reserved. Keywords: Stainless steel; Torsion; High-temperature deformation; Work hardening; Strain-induced grain boundary migration
1. Introduction A number of mechanisms occurs during high-temperature deformation of metals, and which are the most prominent depends on material factors such as stacking fault energy and the presence of second phase particles, and extrinsic factors such as temperature, strain rate and strain. At lower values of strain rate grain boundary mobility is enhanced in polycrystalline metals at high-temperature. Under such conditions, strain induced grain boundary migration (SIGBM) has been introduced to explain the bulging of the grain boundaries and the direction of migration of the grain boundary [2–4]. SIGBM has been widely investigated in static recrystallisation studies [5–8] and the generally accepted model proposed by Bailey and Hirsch [6] is based on the experimental evidence that GBM through bulging is triggered by a driving force differential across grain boundaries arising from the difference in stored energy in the neighbouring grains. Grain boundaries are, in fact, sites of inhomogeneous deformation because of the incompatibility strain that occurs in
∗
Corresponding author. Tel.: +39 02 66173327; fax: +39 02 66173321. E-mail address: [email protected] (G. Angella).
0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2007.05.089
grains at their common grain boundaries. Recently SIGBM has also received attention in dynamic recrystallisation investigations [9,10], where it has been reported that extensive SIGBM occurs before nuclei of recrystallised material appear at bulged grain boundaries. Although significant dislocation activity has been observed in the regions left behind by the migrated grain boundaries, particularly in bi-crystal experiments [3,10], investigations have been mainly focused on microstructure and no exploration of the effects that such localised deformation has on flow stress has been carried out. The present paper aims to link the unusual flow behaviour of a fine-grained AISI 316L stainless steel with the unusual microstructure evolved during torsion at hightemperature that was rationalised in terms of SIGBM [1]. 2. Experimental The stainless steel AISI 316L was investigated in hot torsion with different equivalent strain rates in the range of temperatures 850–1100 ◦ C. The chemical composition of the tested material is reported in Table 1. The material has a low carbon content, such that no strain-induced precipitation would have been expected during deformation, which would have made the correlation
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Table 1 AISI 316L chemical composition (wt.%) C Cr Ni Si Mn P S Mo Fe
0.020 17.1 11.2 0.37 1.78 0.048 0.009 2.12 67.4
between microstructure evolution and flow stress more complex. Solid bars 3 m long and 60 mm in diameter were machined into tubular specimens with internal and external gauge radii of 8 and 11 mm, respectively. The tubular specimens had gauge lengths of 11 mm and fillet radii of 25 mm. Tubular specimens were deformed in a bi-axial testing rig [11] designed to carry out complex deformation paths at high temperatures that could be achieved by using an induction heating system capable of rapid heating. The rig was equipped with a quenching system to as far as possible retain the material microstructure evolved during deformation and an average quenching rate of about 90 ◦ C/s from 1000 to 800 ◦ C was typically achieved. The torsion tests were carried out in fixed-end conditions and the presence of any axial load, indicating axial dimension variations because of the torsional deformation, was monitored. Under the deformation conditions of the current investigation, the tubular specimens shortened, inducing axial loads increasing with strain but always smaller than 2 MPa, which was low when compared with the typical equivalent stresses due to the torsion deformation of about 100 MPa for these test conditions. Torque and twist data were transformed into shear stress and shear strain by using the method of the critical radius proposed by Barraclough et al. [12]. According to this method, at a particular radius R* of the round torsion specimen, called the critical radius, the shear stress τR∗ is given by τR∗ =
3T 2π(R3o − R3i )
(1)
where Ro and Ri are the external and the internal radii of the tubular specimen at the test temperature, respectively; i.e. the data were corrected for the thermal expansion of the specimen. For the geometry of the tubular specimen used in the current research, R* could be approximated to 0.90 of the external radius [12,13]. The shear strain at the critical radius is given by γR∗ =
R∗ ϑ Leff
(2)
where Leff is the effective gauge length that was used rather than the nominal gauge length L because of the contribution to the overall deformation of the material in the tubular specimen fillets. A straight scratch parallel to the longitudinal axis of the tube was made on the surface of each tubular specimen in order to detect the region where homogeneous torsional deformation occurred, i.e. the region where the scratch was still straight after deformation. The length of the homogeneous region was
Fig. 1. Representation of a tubular specimen and the observation plane (θ, Z) at the critical radius R* , i.e. 0.90Ro . The maximum shear directions in torsion are reported on the section plane.
assumed to be the effective length. The method of the critical radius is simple to apply and it is accurate [14]. Another benefit is that at the critical radius the stress–strain data appear to be insensitive to the notch effect [13,15] that could be expected because of the tubular specimen fillet and, hence, the data should be more representative of the material behaviour regardless the specimen geometry. Furthermore, microstructure observations could be directly related to the flow curve through observing the microstructure on planes tangent to the tube that were far away from the longitudinal tube axis, i.e. at distance equal to the critical radius, as indicated in Fig. 1. Finally the shear stress and strain were reported as von Mises equivalent values according to the equations: √ γR∗ σEq = 3τR∗ and εEq = √ (3) 3 Conventional metallographic observations were carried out on the stainless steel to measure the average grain size using the mean intercept method. To determine the starting grain size, a tubular specimen was heated up to 1000 ◦ C with the induction heating system according to the soaking procedure that was carried out before each high-temperature test and subsequent quenching. The grain size was the result of measurements on 20 different fields, giving a value of 29.2 ± 1.6 m (hereafter referred to as ‘30 m’). AISI 316L with a larger grain size of 97.4 ± 4.6 m (hereafter referred to as ‘100 m’) was tested in similar conditions to investigate the effects of grain size on the alloy microstructure evolution and flow stress behaviour. This material was obtained by simply heating the finer grained AISI 316L in a controlled nitrogen atmosphere furnace at 1100 ◦ C for 25 min and air cooled to room temperature before being re-heated for testing. Conventional X-ray techniques [16,17] for measuring bulk crystallographic texture were performed to investigate the crys-
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tallographic evolution during torsion with a modified Shultz reflection goniometer by Siemens equipped with Philips X-ray source using a Co target. Four experimental incomplete pole figures were measured corresponding to the crystallographic planes (1 1 1), (2 0 0), (2 2 0) and (3 1 1). The incompleteness of the pole figures was because of the inability of the system to detect reflections corresponding to X-rays incident at almost a tangent to the flat surface of the sample. Orientation distribution functions (ODF) were calculated using the software NTNTAY [18], from which the pole figures were produced. The material microstructure evolution during deformation was analysed through conventional metallographic techniques and more detailed investigations of the microstructure were performed using transmission electron microscopy (TEM) with a JEM 2000FXII by Jeol with an accelerating voltage of 200 kV. Slices of material tangential to the tubular specimens were carefully taken in such a way that the thin foils for TEM observations corresponded to the material at the critical radius. A Struers–Tenupol twin jet electro-polishing unit was used operating at a voltage to have a current of about 0.9 mA and using an electrolyte of chemical composition 23% perchloric acid in ethanol. The electro polishing was undertaken at an electrolyte temperature of about −25 ◦ C. 3. Results 3.1. AISI 316L flow curves Fig. 2(a) and (b) reports the equivalent stress–strain curves from torsion tests on 30 m grained AISI 316L at different deformation conditions. In Fig. 2(a) the flow curve at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 has well defined different regions. The first is a transitional region at small equivalent strain, soon after yielding and generally smaller than 0.05 under these deformation conditions, where a sharp elbow can be detected. This was followed by an unusual, almost linear region, i.e. with almost constant strain hardening rate ΘEq ≡ dσ Eq /dεEq , that was found in the strain range about 0.05–0.20. After this linear region, the work hardening decreased progressively until a stress plateau was achieved at an equivalent strain of about 0.50. Beyond this plateau the flow stress increased until deformation instabilities occurred in the specimen gauge section and the curve was no longer representative of the material behaviour. The decrease of strain rate to 0.001 and 0.0001 s−1 did not alter the flow curve shape observed at the strain rate of 0.006 s−1 , whilst the stress plateaus occurred at lower strains. Fig. 2(b) shows the material behaviour at different temperatures, when the deformation rate at the critical radius was held constant at a value of 0.006 s−1 . It was possible to detect a trend of the material behaviour with changing temperatures: above 1000 ◦ C the flow curves presented the same peculiarities observed at 1000 ◦ C, whilst below 1000 ◦ C the material behaviour diverged from the one detected at higher temperatures. The elbow that characterised the transitional region at small strains became less sharp at 900 ◦ C and disappeared completely at 850 ◦ C. Furthermore, with decreasing temperature the almost constant work hardening region vanished progressively in such a
Fig. 2. Equivalent stress–strain curves of 30 m AISI 316L deformed: (a) at 1000 ◦ C with equivalent strain rates at the critical radius of 0.006, 0.001 and 0.0001 s−1 and (b) at different temperatures with an equivalent strain rate at the critical radius of 0.006 s−1 . (c) Comparison between 30 and 100 m grained materials deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 .
way that at 850 ◦ C a flow curve with a familiar parabolic shape was observed. In Fig. 2(c) the flow curves of 30 and 100 m grained AISI 316L deformed at similar conditions of 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 are compared. The flow stress for the coarser grained material
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Fig. 3. (a) Work hardening ΘEq vs. σ Eq of 30 m grained AISI 316L deformed at different temperatures with equivalent strain rate at the critical radius of 0.006 s−1 and (b) work hardening ΘEq vs. σ Eq of 30 and 100 m grained materials deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 .
was significantly higher than that for the material with an average grain size of 30 m, about 40% at 0.5 equivalent strain. In addition, the shape of the flow curve changed notably, since a parabolic stress–strain curve was observed for the material with the larger grain size. 3.2. Flow stress curves analysis The work hardening behaviour of the 30 m grained material with changing temperature and an equivalent strain rate at the critical radius of 0.006 s−1 , was investigated by plotting the work hardening rate ΘEq against σ Eq , as reported in Fig. 3(a). At 850 ◦ C, where the stress–strain curve was parabolic, the ΘEq versus σ Eq curve could be fitted over a quite large data range with the linear equation ΘEq = Θo (1 − (σ Eq /σ V )), resulting in a value of Θo equal to E850 /N with N = 54.8 ± 2.0, where E850 is the Young’s modulus at the test temperature of 850 ◦ C. The value of Θo was consistent with the results reported in the literature [19], where Θo is commonly about ET /50 and ET is the Young modulus at the test temperature. The linear data range represents what is conventionally called Stage III of the strain hardening and is
well fitted by the Voce equation, which results in a line in the plot ΘEq versus σ Eq . The deviation of the experimental data from the Voce equation at small stresses is attributed to effect of the grain boundaries on dislocation storage in well annealed materials, whilst at higher stresses the deviation is conventionally known as Stage IV, which anticipates dynamic recrystallisation in low stacking fault materials like AISI 316L. Dynamic recrystallisation commonly appears with an abrupt deviation from the Stage IV trend to achieve rapidly the condition ΘEq = 0, such deviation being conventionally defined as Stage V of strain hardening [19–21]. The Voce lines at higher temperatures than 850 ◦ C were artificially drawn, by imposing an athermal work hardening equal to ET /54.8. The range of experimental ΘEq versus σ Eq data that could be well fitted by the Voce equation at 900 ◦ C was appreciably reduced. At higher temperatures, where linear stress–strain curves were found at low strains, no Voce equation fitting was possible, i.e. Stage III could not be detected. The ΘEq versus σ Eq curve for the 100 m grained material deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 , having a parabolic flow curve, was well described by the Voce equation using an athermal strain hardening Θo = E1000 /54.8, as reported in Fig. 3(b), where the 30 m material data are also reported for comparison. Therefore, when a parabolic stress–strain curve was found, the Stage III of strain hardening was established, as would normally be expected. The beginning of the Stage IV in the ΘEq versus σ Eq curves where Stage III was found, occurred at a nearly constant value of the ratio ΘEq /σ Eq of about 1.0 in Fig. 3(a) and (b) the line ΘEq = mσ Eq with m = 1.0 is reported. The constancy of the ratio ΘEq /σ Eq at the beginning of the presumed Stage IV matched results reported in literature on Stage IV investigations on several austenitic stainless steels deformed in torsion and compression under similar temperature and deformation rate conditions [20,21]. However, the line ΘEq = mσ Eq with m = 1.0 seemed to intercept closely also the beginning of the flat regions for the higher temperatures, i.e. 1000 and 1100 ◦ C, with the exception of 900 ◦ C, where some discrepancy could be observed. 3.3. Determination of dynamic recrystallisation: Stage V There is no general agreement concerning the best functional fitting of Stage IV in the plot ΘEq versus σ Eq and, in addition, at high temperatures the deviation of Stage IV from Stage III is usually quite smooth and does not show any unambiguous trend [19]. Nevertheless, Stage IV has been modelled by some researchers [20,21] with linear behaviour in the ΘEq versus σ Eq plot by the necessity of calculation of the asymptotic stress value of Stage IV. The same linear assumption was adopted in the present work. The linear behaviour in the ΘEq versus σ Eq plot results in a Voce-type equation for the stress–strain curves as σEq = σA + (σo − σA ) e−αεEq
(4)
where σ o is the extrapolated stress value for εEq = 0, σ A the asymptotic stress for εEq going to infinity, i.e. ΘEq = 0, and α is
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Fig. 4. (a) Experimental equivalent stress–strain curve and the best Voce-type equation fitting at 850 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 for the 30 m grained alloy and (b) ΘEq vs. σ Eq plot of the experimental equivalent stress–strain curve in (a). The negative slope line is the best Voce-type fitting to the experimental data, whilst σ D (194.5 MPa) and σ A (210.0 MPa) are the deviation stress and the asymptotic stress, respectively. σ Pl (197.5 MPa) is the stress at which the work hardening rate is first zero and matches well the stress plateau in Fig. 4(a).
the parameter controlling the rate to achieve σ A . In the present work, rather than fitting Stage IV in the ΘEq versus σ Eq plot, which could be quite difficult for the data scattering of the work hardening ΘEq because of the low values, the Voce-type equation (4) was interpolated to the stress–strain curves in the almost linear region. In Fig. 4(a) the result of the flow curve interpolation for the 30 m grained materials deformed at 850 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 is reported. With the exception of the region at the beginning of the curve, where Stage III was found, the curve is well fitted in the intermediate region, whilst at high stress a deviation of the interpolation curve from the experimental one is evident. In Fig. 4(b), the interpolation result in Fig. 4(a) is reported in the ΘEq versus σ Eq plot. The negative slope line is the best Vocetype fitting line and σ A is the asymptotic stress of the Voce-type equation. Consistent results were found for the 100 m grained material deformed at 1000 ◦ C with an equivalent strain rate of
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0.006 s−1 . The authors defined σ D as the deviation stress, i.e. as the minimum experimental stress after the well fitted region for which the curve difference between the experimental stress and the Voce-type fitting stress was bigger than 1%. After the calculation of σ D , the values of the work hardening ΘD corresponding to the deviation stress σ D were used to calculate the ratios Γ D = ΘD /σ D . The values of Γ D were found to be 0.20 for the 30 m grained AISI 316L deformed at 850 ◦ C and 0.006 s−1 , and 0.21 for the 100 m grained AISI 316L deformed at 1000 ◦ C and 0.006 s−1 . The results are quite consistent and are comparable with data reported in literature [20,21] where Γ D has been reported to be 0.27 for various austenitic stainless steels deformed in torsion at deformation conditions similar to the present tests. σ Pl is the stress at which the work hardening rate was first zero and matches well the stress plateau observed in the flow stress curve reported in Fig. 4(a). The increased hardening beyond σ Pl was caused by geometrical instabilities typical of tubular specimens deformed at deformation conditions when dynamic recrystallisation occurs so that it was not representative of the material behaviour. The same procedure used for the parabolic curves was implemented for the anomalous flow curves obtained at high temperatures, through interpolating the almost linear regions of the flow curves. In Fig. 5(a) the result of the flow curve interpolation for the 30 m grained materials deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 is reported. With the exception of the transitional region at the beginning of the curve, where there was no attempt to fit the Voce-type equation, and the region at high strains, the Vocetype equation fitted quite well the intermediate experimental data, also over a wide data range beyond the almost linear region. In Fig. 5(b), the interpolation result of the flow stress analysis for the 30 m grained materials is reported in the ΘEq versus σ Eq plot. The values of the ratios Γ D were consistent to those from the parabolic flow curves: 0.20 at 900 ◦ C and 0.18 at 1000 and 1100 ◦ C. Also in these cases the values of σ Pl correspond to the stress plateaus observed in the flow curves. Even if at 0.1 equivalent strain no steady state was achieved, the minor difference in work hardening rate allowed the procedure of computing the stress exponent n by assuming a power law relationship between strain rate and stress. The Norton exponent n appeared to be in the range 6.6–6.9. The apparent activation energy of deformation QApp could be found by assuming an Arrhenius-type relationship between strain rate and temperature in the range of temperatures 1000–1100 ◦ C with equivalent strain rates 0.006–0.0001 s−1 at an equivalent strain of 0.1. QApp was determined as 350 kJ mol−1 . 3.4. Texture analysis Texture measurements were conducted on the plane (θ, Z) at a distance from the tubular axis equal to the critical radius in a AISI 316L tubular specimen in pre-test conditions, i.e. heated to 1000 ◦ C according to the procedure before any high-temperature torsion test and then quenched. No significant texture was
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not provide any additional information, and were therefore not included. 3.5. Microstructure evolution
Fig. 5. (a) Experimental equivalent stress–strain curve and the best Voce-type equation fitting at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 for the 30 m grained alloy and (b) ΘEq vs. σ Eq plot of the experimental equivalent stress–strain curve in (a). The negative slope line is the best Voce-type fitting to the experimental data, whilst σ D (93.5 MPa) and σ A (119.5 MPa) are the deviation stress and the asymptotic stress, respectively. σ Pl (95.0 MPa) is the stress at which the work hardening rate is first zero and matches well the stress plateau in Fig. 5(a).
present before testing. The texture evolutions of the 30 and the 100 m grain sized materials were investigated after the same deformation conditions of 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 . In Fig. 6 the crystallographic textures of the two different grained materials evolved after similar equivalent strain at the critical radius of 0.36 are reported. The texture of the 30 m grain size material in Fig. 6(a) was extremely weak. A weak torsion texture seemed to be observable in the 100 m grained material, see Fig. 6(b), as reported in literature [22,23] with easy slip planes ({1 1 1}in FCC materials as AISI 316L) parallel to the principal shear directions. However, the weakness of texture was such that the difference between the textures of 30 and 100 m grained materials may not be significant. EBSD measurements were also used [11] to determine local lattice curvature, particularly at the grain boundaries, to complement the optical and TEM microstructural studies, described below. However, the EBSD measurements did
Under some of the current deformation conditions the stainless steel exhibited an uncommon microstructure evolution, resulting in the formation of a rhomboidal grain structure with horizontal grain boundaries regularly aligned along the horizontal directions of maximum shear stresses during monotonic torsion. The structure evolution was complete already at the first stage deformation, i.e. at the beginning of the linear region. The adopted grain shape, reported in Fig. 7 for the 30 m grained material deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 to a final equivalent strain of 0.18, was such that dihedral angles at the triple junctions and 90◦ elbow grain boundaries were observed, which is not expected from the minimisation of grain boundary energy. The rhomboidal grain structure occurred only on the tangential plane of the tubular specimen, i.e. on the observation plane (θ, Z) in Fig. 1, whilst on the planes along through the tubular specimen thickness, i.e. the planes (R, Z) and (R, θ), the grain structure maintained an equiaxed structure. The detailed description and rationalisation of the microstructure evolution is reported elsewhere [1], where it was concluded that the evolution from equiaxed to rhomboidal grain shape in monotonic torsion occurred through strain induced grain boundary migration (SIGBM) combined with the torsion stress field. Metallographic samples from specimens deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 to different final equivalent strains were observed with Nomarski contrast to emphasise any surface specimen irregularity brought out by a slight electro-etching. A typical observation at high magnification is reported in Fig. 7(b), which shows that a significant proportion of the grain boundaries were highly irregular surfaces. Twin boundaries were slightly bent in the grain core, whilst in the vicinity of the grain boundaries the twin boundaries appeared irregular and fuzzy. These etching irregularities revealed some dislocation microstructure heterogeneity at the grain boundaries. However, at strains beyond the flow stress plateau the rhomboidal grain structure disappeared and the deformed microstructure appeared partly consumed by a new, fine grain structure, as reported in Fig. 8, in such a way that grains with regular shapes could no longer be found. This microstructure was typical of dynamic recrystallisation, confirming the stress analysis results that identified the occurrence of Stage V. At temperatures above 900 ◦ C, the uncommon microstructure evolution reported at 1000 ◦ C was also observed, while at 850 ◦ C no sign of a rhomboidal grain structure was found and the grains maintained an elongated shape after deformation from equiaxed structure. It was possible to correlate the microstructure evolution at different temperatures to the shape of the flow curves of the 30 m grained material: when the microstructure did not evolve into rhomboidal grain structure, i.e. at 850 ◦ C, the flow curve shape was parabolic, whilst, when the rhomboidal grain structure was formed at high temperatures, the flow curves
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Fig. 6. {1 1 1} Pole figures on the planes (θ, Z) at the critical radii of AISI 316L tubular specimens deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 to a final equivalent strain at the critical radius of 0.36 with an average grain size of (a) 30 m and (b) 100 m. The horizontal shear direction is reported in the figure.
presented a region of almost constant work hardening at small strains. The temperature appeared to be a critical parameter in affecting the grain structure evolution. However, metallographic observations for the 100 m grained stainless steel deformed at 1000 ◦ C with an equivalent strain rate of 0.006 s−1 revealed a grain microstructure that exhibited rhomboidal shape, as seen in the 30 m grained material, but the flow curve was parabolic and higher with respect to the 30 m AISI 316L for the same test conditions. Therefore, the mechanism leading to the aligned grain boundary evolution was linked to the deformation conditions, i.e. temperature, strain rate, torsion and the grain boundaries themselves, regardless of the grain size, but the larger grain size conferred strength to the material and the expected parabolic flow curve shape. Table 2 summarises the grain evolution and the flow stress curve shapes during torsion at different temperatures and grain sizes with similar equivalent strain rate at the critical radius of 0.006 s−1 .
Fig. 7. (a) Grain structure of AISI 316L deformed at 1000 ◦ C with equivalent strain rate at the critical radius of 0.006 s−1 , evolved after an equivalent strain of 0.18 and (b) at higher magnifications with Nomarski contrast. The horizontal direction of maximum shear is reported in the figure.
Fig. 8. Grain structure of AISI 316L deformed at 1000 ◦ C with equivalent strain rate at the critical radius of 0.006 s−1 to a final equivalent strain at the critical radius of 1.10. The horizontal direction of maximum shear is reported in the figure.
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Table 2 Grain evolution and flow stress curve shapes during torsion at different temperatures and grain sizes with similar equivalent strain rate at the critical radius of 0.006 s−1 Temperature (◦ C)
Grain size (m)
Rhomboidal grains
Flow stress curve shape
850 900 1000 1100 1000
30 30 30 30 100
No Yes Yes Yes Yes
Parabolic Parabolic/linear Linear Linear Parabolic
3.6. Microstructure observation with TEM The microstructure of the 30 m grained material deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 was investigated through TEM at different strains. In Fig. 9 the grain core dislocation structure at an equivalent strain of 0.09 is reported. The dislocation cells appeared quite regular in shape, in accordance with structure reported in the literature for materials deformed in torsion and conventionally called a “checkerboard” structure. The dislocation cell interiors were quite clear of dislocations, the cell walls appeared to be sharp and bi-dimensional, and the crystallographic misorientation among different cells was quantified through the analysis of
the selected area diffraction patterns to be about 2◦ . The dislocation structure was typical of materials deformed in conditions conventionally defined as Stage IV [19,24]. Not all grains presented such a structure, although it was significantly present, and dislocation structures with thick walls and numerous dislocations in the cells were also observed. However, this could be rationalised because of the small strains and different grain orientations with respect to the external stress axes. The microstructure at the grain boundaries of the same material reported in Fig. 9 is shown in Fig. 10(a), and was significantly different to that at the grain cores. The dislocation structures also consisted of low angle dislocation boundaries, but they were elongated with major axes parallel to the grain boundaries themselves and the crystallographic misorientations were quantified through Kikuchi diffraction pattern analysis to be about 1–1.5◦ with respect to the parent grain. On increasing the strain, the dislocation structure at the grain boundaries increased in complexity as reported in Fig. 10(b) for the 30 m grained material deformed at 1000 ◦ C to an equivalent strain of 0.18. Such complexity of the dislocation structure seemed to be consistent with the microstructure details observed with Nomarsky contrast in Fig. 7(b). In the proximity of a double elbow grain boundary, consistent with the grain boundary shape observed in Fig. 7(a) and (b), the dislocation structure was square-shaped, similar to the elbow shape, whilst towards the core of the parent grain it was elongated, analogous to the structure reported Fig. 10(a), and in the grain core the dislocation structure was “checkerboard”. The crystallographic misorientation, analysed using the Kikuchi diffraction technique, increased from 1.5◦ between the grain core (point A in the Fig. 10(b)) and the middle of the elongated structure (point B in the figure), to a final value of about 2◦ between point A and point C, close to the elbow grain boundary. Such dislocation structures seemed to be traces of successive grain boundary migrations, for which the final result was the formation of the grain boundary elbow, i.e. the rhomboidal grain boundary structure. 4. Discussion
Fig. 9. Grain core dislocation structure of AISI 316L deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 to a final equivalent strain of 0.09: “checkerboard” structure with dislocation cells with low angle dislocation walls and crystallographic misorientation of about 2◦ .
The analysis of the parabolic flow curves revealed that the experimental data fell into the typical Stages of strain hardening, i.e. the Stages III, IV and V, which was confirmed by the distinctive values of ΘC /σ C ∼ 1.0 for the beginning of Stage IV, and ΘD /σ D ∼ 0.2 for the beginning of Stage V, i.e. the end of Stage IV. The values ΘD /σ D were smaller than those reported in literature [20,21], where ΘD /σ D ∼ 0.27 was found; however, the consistency of the ratios ΘD /σ D in the present work, for any deformation conditions, indicated that the same strain hardening stage was beginning, i.e. Stage V. The lower value of ΘD /σ D could be attributed to the different experimental procedure used. Consistent values of ΘC /σ C and ΘD /σ D were also found for the anomalous flow curves, even if the ΘEq versus σ Eq data curves appeared flat and of completely different shape to the parabolic flow curves data, which indicated that such flat regions were Stage IV. The TEM observations reported in Fig. 9 confirmed that the dislocation structure in the grain cores was typical
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Fig. 10. Dislocation structure at grain boundaries in AISI 316L deformed at 1000 ◦ C with an equivalent strain rate at the critical radius of 0.006 s−1 (a) to a final equivalent strain of 0.09: dislocation structures elongated consistently to the grain boundary with crystallographic misorientation with respect to the parent grain of about 1–1.5◦ and (b) to a final equivalent strain of 0.18. The crystallographic misorientation from the core of the parent grain to the elbows increased from 1.5◦ between points A and B, to 2◦ between A and C.
of Stage IV [19,24], and the micrograph of the alloy at high strains reported in Fig. 8 showed the consumed structure, typical of recrystallised materials. Therefore, all experimental findings indicated that Stage IV took place, dominating the whole deformation, whilst Stage III did not manifest itself. To the authors’ knowledge such behaviour has not previously been reported in literature. The wide Stage IV of strain hardening observed in the ΘEq versus σ Eq curves for AISI 316L, regardless of the deformation conditions, confirmed that the deformation was intrinsically due to bulk dislocation activity, as indicated by the Norton exponent around 6.6–6.9 and the apparent activation energy of deformation of 350 kJ mol−1 [25,26]. Furthermore, there was no measurable difference in the texture evolution in the 30 and 100 m grained materials, which excludes the hypothesis of any crystallographic texture effect. It has been reported [1] that the alloy exhibited an uncommon grain boundary evolution from an equiaxed structure in pre-test conditions to a rhomboidal shape during torsion at high temperatures, which was found to be linked to the flow stress behaviour. The link between grain structure evolution and flow stress indicated that the microstructure evolution mechanism that affected the grain structure also affected the flow stress. The qualitative model proposed by the authors to describe the anomalous AISI 316L behaviour under the current deformation conditions is based on SIGBM, i.e. the microstructural mechanism by which the grain evolution was rationalised [1]. The SIGBM events at the grain boundaries were triggered by gradients of stored energy and occurred to minimise dislocation accumulation at the grain boundaries. According to the mechanistic interpretation by Kocks and Mecking [19,27] Stage III
can be described by the Voce equation: ΘVoce = Θo − D(T, ε˙ )σ
(5)
where Θo has the usual meaning and D(T, ε˙ ) is the dynamic recovery term. According to the model proposed by the authors, the work hardening in Eq. (5) deviated from the common Voce behaviour through a softening term, arising from SIGBM, i.e. SSIGBM , in such a way that the Voce equation resulted in Θ = ΘVoce − SSIGBM = Θo − (D(T, ε˙ )σ + SSIGBM )
(6)
At small deformation after yielding, dislocation density did not increase as expected from Voce behaviour because of local reductions in dislocation density in the grain boundary regions due to the SIGBM events that transformed the pre-test equiaxed grain structure into the rhomboidal structure, which came into low stress and abruptly reduction of the work hardening rate. In this way the material was prevented from entering Stage III. The softening occurred in the 30 m grained material because of the relatively small grain size, whilst in the 100 m grained material the ratio of the grain boundary area to the volume decreased by about 30% with respect to the smaller grained material in such a way that the term SSIGBM in Eq. (6) was no longer significant. The grain boundary migrations left behind regions of low dislocation density that were more easily deformed than the bulk, which could have produced localised deformation at the grain boundaries and could explain the small difference in the texture evolutions of the two differently grained materials. The reason of why Stage IV survived rather than also being by-passed was found in the microstructural evolution of Stage
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IV. If typical work hardening behaviour is considered, i.e. when Stage III is followed by Stage IV (in the present work this occurred for 30 m grained AISI 316L deformed at 850 ◦ C and 100 m grained material at 1000 ◦ C), the increase of hardening in Stage IV with respect to Stage III has been explained in the literature [9,19,28–30] as being caused by the transformation of the dislocation structures with thick walls typical of Stage III into dislocation subgrains, i.e. tilted and twisted dislocation cells with sharp and bi-dimensional walls. The latter should be more effective obstacles to dislocation motion than the former, which gives additional hardening, or the hardening may arise because the cells are tilted and slip transfer is more difficult [29]. A modified Hall–Petch relation has been proposed [28–30] to link this microstructure evolution with Stage IV: σ = σ ∗ + kd −1
(7)
where σ * is the friction stress, k the “locking parameter” and the cell size d (with the exponent of −1 rather than −0.5) has replaced the typical grain size D. Therefore, in the present work, the grain boundaries represented the main obstacles to dislocation motion prior to the onset of Stage IV and dislocation accumulation was sufficient for the accumulated stored energy to trigger significant SIGBM events. With the occurrence of Stage IV, i.e. at ΘC /σ C ∼ 1.0, the “harder” dislocation structure typical of this deformation stage reduced the effectiveness of the dislocation accumulation at the grain boundaries, since the dislocation motion was retained in the grain core. In this way Stage IV became evident and only when the work hardening and stress conditions for Stage V occurred, did Stage IV end and new grains of recrystallised material consume the original structure, as reported in Fig. 7.
flow stress behaviour was observed. A model also based on SIGBM was proposed to describe qualitatively the AISI 316L flow stress behaviour: • At small deformation after yielding, the dislocation density did not increase because of local reduction near the grain boundaries due to the SIGBM events that transformed the pre-test equiaxed grain structure into the rhomboidal structure, which abruptly reduced the work hardening rate. In this way the 30 m grained material was prevented from entering Stage III. In the larger grained material the ratio of grain boundary area to volume decreased with respect to the 30 m grain size material in such a way that SIGBM was no longer significant and the material exhibited the expected Stage III and the common parabolic flow curve. • Stage IV was not by-passed because of its dislocation microstructure. The dislocation cells typical of this deformation stage were effective obstacles to the dislocation motion such that the dislocations were retained in the grain core, and the effectiveness of the dislocation accumulation at the grain boundaries was reduced. SIGBM also became insignificant in the 30 m grain size material. • When the work hardening and stress conditions for Stage V occurred, dynamic recrystallisation took place, consuming the original deformation grain structure. Acknowledgements The financial support of The University of Sheffield is gratefully acknowledged, as is the funding for the experimental facility provided by the Engineering and Physical Sciences Research Council, UK.
5. Conclusions References The stainless steel AISI 316L with an average grain size of about 30 m was investigated in hot torsion in the temperature range 850–1100 ◦ C with equivalent strain rates of 0.006–0.0001 s−1 . The alloy showed unusual flow stress curves at high temperatures with almost linear work hardening behaviour at low strains, and presented a significant reduction of flow stress with respect to the 100 m grained material deformed under similar conditions. No measurable difference between the texture evolution of the 30 and 100 m grained materials was observed. This and the presence of a dominant Stage IV of strain hardening, the values found for the stress exponent, and the apparent activation energy of deformation were typical of bulk dislocation deformation. The AISI 316L microstructure evolution during deformation appeared to be quite unusual, since a rhomboidal grain shape was adopted with dihedral angles at triple junctions and 90◦ elbow boundaries consistent with the torsion stress field, which was clearly not expected from minimisation of grain boundary energy. The microstructure evolution was rationalised on the basis of the SIGBM mechanism and minimisation of stored energy at the grain boundaries combined with the torsion stress field. A relationship between the unusual microstructure and
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