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Acta Materialia 60 (2012) 6907–6919 www.elsevier.com/locate/actamat
Low strain rate deformation behavior of a Cr–Mn austenitic steel at ??80 °C
P. Sahu a,??, S.K. Shee b, A.S. Hamada c,d, L. Rovatti c, T. Sahu e, B. Mahato f, S. Ghosh Chowdhury f, D.A. Porter c, L.P. Karjalainen c
a Department of Physics, Jadavpur University, Kolkata 700 032, India Department of Physics, Midnapore College, Midnapore 721 101, West Bengal, India c Centre for Advanced Steels Research, University of Oulu, Box 4200, FIN-90014, Finland d Metallurgical and Materials Engineering Department, Faculty of Petroleum & Mining Engineering, Suez Canal University, Box 43721, Suez, Egypt e Department of Physics, Ramananda College, Bishnupur 722 122, West Bengal, India f Materials Science and Technology Division, National Metallurgical Laboratory, Jamshedpur 831 007, India b
Received 6 June 2012; received in revised form 19 July 2012; accepted 19 July 2012 Available online 4 October 2012
Abstract The deformation behavior of a Cr–Mn austenitic steel during interrupted low strain rate uniaxial tensile testing at ??80 °C has been studied using X-ray di??raction (XRD), electron backscatter di??raction and transmission electron microscopy. Continuous c ! e ! a0 martensite transformation was observed until failure. High dislocation densities were estimated in the austenite phase ($1015 m??2), and for the a0 -martensite they were even an order of magnitude higher. Dislocation character analysis indicated that increasing deformation gradually changed the dislocation character in the austenite phase to edge type, whereas the dislocations in a0 -martensite were predominantly screw type. XRD analyses also revealed signi??cant densities of stacking faults and twins in austenite, which were also seen by transmission electron microscopy. At low strains, the deformation mode in P austenite was found to be dislocation glide, with an increasing contribution from twinning, as evidenced by an increasing incidence of 3 boundaries at high strains. The deformation mode in a0 -martensite was dominated by dislocation slip. ?? 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Cr–Mn austenitic steel; Tensile straining; X-ray di??raction analysis; Martensite transformation; Dislocation character
1. Introduction The AISI 200 series of chromium–high manganese (5– 9% Mn) austenitic steels is a potential substitution for the common AISI 300 series of Cr–Ni austenitic stainless steels due to lower cost from the low nickel (<5%) content [1,2]. Certain 200 series alloys also have about 30% higher yield strength than Type 304 has, thereby making the design of lighter structures possible [3]. Cr–Mn stainless steels are metastable, wherein martensite formation takes place either directly or indirectly,
?? Corresponding author. Tel.: +91 33 2414 6666x2840; fax: +91 33 2413 7121. E-mail address: psahu74@gmail.com (P. Sahu).
i.e. c (face-centered cubic (fcc)) ! a0 (body-centered cubic (bcc) or c (fcc) ! e (hexagonal close-packed (hcp)) ! a0 (bcc). The stability of the austenite depends on the chemical composition and the stacking fault energy (SFE), which decreases with decreasing temperature. The SFE is considered to determine the e??ective path of the martensitic transformation thereby governing the presence or absence of e-martensite [4]. For high-Mn twin-induced plasticity steels, Allain et al. [5] suggested that the e-martensite forms while SFE < 18 mJ m??2, and mechanical twinning takes place when 12 mJ m??2 < SFE < 35 mJ m??2. An SFE of 20 mJ m??2 is generally taken as the upper limit for a0 -martensite formation, i.e. the appearance of the transformation induced plasticity (TRIP) e??ect [6]. For a typical 200
1359-6454/$36.00 ?? 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2012.07.055
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series austenitic steel, the reported SFE value at room temperature is $10 mJ m??2 [7]. It is well established that in low SFE metals twinning and slip are competitive deformation processes, and that a low SFE and/or deformation temperature strongly facilitates the formation of shear bands, deformation twins and stacking faults. Therefore, in 200 series austenitic steels, the dominant deformation mechanism at low temperatures is expected to be the formation of stacking faults and twins, and any associated martensite transformation. However, there are only a few published works on the deformation behavior of Cr–Mn austenitic steels [7,8] and knowledge about the plastic accommodation of austenite in these steels is still incomplete. Microstructural parameters, i.e. various line and planar defect parameters, can be estimated from the use of direct methods, such as transmission electron microscopy (TEM) and electron backscatter di??raction (EBSD). TEM provides local information about the microstructure, while the applicability of EBSD is seriously impaired in studying deformed specimens. X-ray di??raction (XRD) experiments provide information about a relatively large volume of the specimen, although indirectly. Hence each method has its own merits as well as demerits. However, these methods can complement each other very well when used in combination, and can provide substantiated information about the microstructure that directly a??ects the mechanical properties. The analysis of the XRD pattern followed either by the phenomenological Warren–Averbach method [9] of X-ray line pro??le analysis or the relatively modern Rietveld method [10] has been a reliable and widely popular tool for interpreting the substructure of various plastically deformed austenitic steels [7,11–13] and other metals and alloys. The dislocation density estimated from the XRD analyses according to the very old Williamson–Smallman formalism [14] very often di??ers from the actual values due to the non-random arrangement of dislocations [15]. It is well documented that the strain ??eld anisotropy and concomitant anisotropic microstrain broadening are due to the contrast factor of dislocations. Hence, these should be taken into account for the accurate estimation of dislocation densities using XRD methods. In this work, we have employed the Rietveld re??nement of the XRD pattern to estimate the structural and microstructural parameters of a Cr–Mn austenitic steel (Type 201) deformed by low strain rate interrupted uniaxial loading at ??80 °C. We have also quanti??ed the evolution of dislocation density and character using a modi??ed Warren–Averbach method, which incorporates the treatment of dislocation contrast factors. Furthermore, for deformed austenite, the classi??cation of the grain boundary misorientations according to the coincidence site lattice (CSL) model was obtained by EBSD. Recently, Pozuelo et al. [7] employed Rietveld analysis and TEM to study the temperature- and strainrate-dependent mechanical properties of a high-nitrogen 200 series austenitic stainless steel. However, they did not report any quantitative estimation of the microstructural
parameters or their in??uence on mechanical properties. To our knowledge, no such comprehensive study has been attempted on the microstructure evolution of this kind of steel to interpret its ??ow behavior. 2. Experimental The 201-type Cr–Mn austenitic stainless steel used in the present work was supplied by Outokumpu Stainless Oy, Tornio Works (Tornio, Finland) as a sheet of 1 mm thickness in the cold rolled, annealed, pickled and skin passed condition. The chemical composition (wt.%) of the investigated steel is shown in Table 1. Interrupted uniaxial tensile tests were carried out in a Zwick Z 100 tensile machine (Zwick Roell, GmbH) at ??80 °C at a low strain rate: 10??4 s??1 to engineering strains of 2%, 5%, 10%, 20% and 30%, and to failure. Corresponding true strains |e| are 0.02, 0.05, 0.09, 0.18, 0.26 and 0.39. The low strain rate was selected to minimize the e??ect of adiabatic heating on the expected martensite transformation. Standard 20 mm wide tensile test specimens with a gauge length of 80 mm were used in all tensile tests. To assess the deformation microstructure under di??erent straining conditions, the gauge regions of deformed tensile specimens were investigated using XRD, EBSD and TEM. XRD data acquisition was carried out using Cu Ka radiation in a powder di??ractometer (Siemens-D500) equipped with a secondary beam monochromator. The step scan mode, with a preset holding time of 5–10 s at each 0.01° step in 2h, was used to improve the counting statistics and yield data suitable for stable re??nement [16]. A ??eld emission gun scanning electron microscope (FEG-SEM Carl Zeiss Ultra plus) operating at 20 kV and equipped with an EBSD device (Oxford HKL) was used to obtain phase maps and band contrast images. The EBSD specimens were obtained by mechanical polishing down to 1 lm using a diamond suspension followed by chemical polishing for about 20 min using a 0.05 lm colloidal suspension of silica. The TEM microstructures were obtained from a Philips CM20 transmission electron microscope operating at 200 kV and the thin foils were prepared using a twin jet TENUPOL-5 electrolytic polisher. The electrolyte contained 10 vol.% perchloric acid and 90% acetic acid. 3. Methods of analysis 3.1. Structure and microstructure re??nement by the Rietveld method The XRD patterns were subjected to Rietveld analyses, using the MAUD program [17] to interpret the structural
Table 1 Chemical composition of the Cr–Mn steel in wt.%. Steel 201 C 0.047 Si 0.32 Mn 6.74 Cr 17.48 Ni 3.71 Mo 0.05 Cu 0.23 N 0.205
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P. Sahu et al. / Acta Materialia 60 (2012) 6907–6919 Table 2 Values of reliability parameters of the Rietveld analysis with di??erent tensile deformation. Tensile strain Rwp (%) Rexp (%) GoF = Rwp/Rexp 0% |e| = 0 9.6 8.0 1.20 10% |e| = 0.09 8.7 8.1 1.07 20% |e| = 0.18 7.6 6.5 1.17 30% |e| = 0.26 7.9 6.8 1.16 Failure |e| = 0.39 7.5 5.9 1.27
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contrast factor and the magnitude of the Burgers vector, respectively. O stands for higher-order terms in K 2 C hkl . By squaring Eq. (1) and neglecting the higher-order terms of K 2 C hkl , we obtain, after rearrangement: ????DK??2 ?? a??=K 2 ?? bC hkl ??2?? where a = (0.9/D)2 and b = pM2b2q/2. ?? Ungar et al. [27] established that, for cubic crystals, the average contrast factor of dislocations, C hkl , corresponding to the Bragg re??ections (h k l), is given by: C hkl ?? C h00 ??1 ?? qH 2 ?? ??3??
and microstructural features of the tensile specimens. Instrumental broadening of the di??ractometer [18] was determined using a specially prepared silicon standard sample assumed to have no size and strain broadening [19]. The crystallite size and the microstrain values were evaluated from the “size-strain” analysis using the Popa model [20], except in the failed austenite microstructure. Stacking fault probability (Psf), which represents the fraction of slip planes a??ected by faults, and the twinning probability (Ptw), representing the twin density, were estimated from the Rietveld re??nement, following Warren’s model [21] of fault analysis. The quality of ??tting and reliability of the structural as well as microstructural parameters are assessed from the criteria of ??t parameters [22], viz. the weighted residual error (Rwp), expected error (Rexp) and goodnes of ??t (GoF), listed in Table 2. The results of all these analyses, relevant to the microstructural information, are shown in the Table 3. 3.2. Dislocation character and density determination according to the dislocation contrast factor The estimation of dislocation character and densities in the di??erent tensile strained specimens requires appropriate determination of the type of dislocations, the Burgers vectors and the average contrast factors (C hkl ) for the di??erent representative Bragg re??ections (h k l). The average contrast factors, C hkl , were further used in a modi??ed Williamson–Hall plot and the modi??ed Warren–Averbach procedure to calculate the dislocation densities (q), the e??ective outer cut-o?? radius (Re) of dislocations, indicating the range over which the distribution of dislocation is ranp?????? dom, and the dimensionless quantity M???? Re q??, representing the dislocation arrangement parameter [23,24]. The full width at half maximum (FWHM) value obtained from the ??tting of the representative Bragg re??ections for each of the crystallographic phases using a pseudo-Voigt function according to Enzo et al. [25] is substituted into the following modi??ed Williamson–Hall equation [24,26,27]: 2 2 1 0:9 pM b 2 1=2 1=2 DK ?? ?? q C hkl ?? O??K 2 C hkl ?? ??1?? D 2 where K ?? 2 sin h=k and DK ?? 2 cos h??Dh??=k, and Dh, h and k represent the FWHM, Bragg angle and wavelength of the X-rays used, respectively. D, q, C hkl and b represent the average crystallite size, dislocation density, the average
where C h00 is the average contrast factor for the h00 type of Bragg re??ection derived from the elastic constants of the crystal. The parameter q determines the screw or edge character of dislocations, and H2 is de??ned as: H 2 ?? ??h2 k 2 ?? k 2 l2 ?? l2 h2 ??=??h2 ?? k 2 ?? l2 ??2 Using Eq. (3) in Eq. (2), we obtain: ????DK?? ?? a??=K 2 ?? bC h00 ??1 ?? qH 2 ??
2
2
??4??
??5??
Hence, the coe??cient of H in Eq. (5) gives the value of the parameter q. The reported values of q in austenite for pure edge and screw dislocations are 1.71 and 2.46, respectively [27], whereas these values for a0 -martensite are 1.2 and 2.8 for pure edge and screw, respectively [27]. The q values of austenite obtained from Eq. (5) are further used to evaluate the fractions of edge and screw dislocations in this microstructure for the present steel according to following equations [28]: fc??edge?? ?? ??2:46 ?? qc ?? ??2:46 ?? 1:71?? ??6?? ??7??
fc??screw?? ?? 1 ?? fc??edge??
where fc(edge) and fc(screw) represent the fraction of the edge and screw dislocations within the austenite microstructure, respectively. Furthermore, the modi??ed Warren–Averbach equation for the real part of the Fourier coe??cients, A(L), is given as [26]: ?? pb2 2 Re ?? 2 s ln A??L?? ?? ln A ??L?? ?? q L ln K C hkl ?? Q??K 4 C 2 ?? hkl 2 L ??8?? where A (L) are the size Fourier coe??cients of the peak pro??le, L is the Fourier variable and Q is the higher-order constant of K 2 C hkl . From Eq. (8), ln A(L) becomes a function of K 2 C hkl . The real part of the Fourier coe??cients can be plotted with various L values, whose gradient can be rearranged to obtain: Y ??L?? qpb2 qpb2 ln Re ?? ln L ?? 2 2 2 L ??9??
s
The dislocation density (q) and the e??ective outer cut-o?? radius (Re) of dislocations can be directly determined from the graphical plot of Eq. (9). The parameters relevant to the dislocation analysis are presented in Table 4.
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Table 3 Results of the Rietveld structure and microstructure re??nement under various tensile deformation conditions at ??80 °C.
e-Martensite (hcp) Psf ?? 103 ± (0.0001– 0.002) ± (0.0007– 0.002) ± (0.0008– 0.002) ± (0.0008– 0.002) – – – – 0 – – – 1.45 (h k l) Crystallite size (nm) ±(3–7) nm r.m.s strain ?? 103 ± (0.0001– 0.0004) – Ptw ?? 103 Psf ?? 103 Ptw ?? 103 a0 -martensite (bcc) Vol. fraction r.m.s strain ?? 103 ± (0.0002– 0.0008) – ±(1–3) % –
Tensile strain
Austenite (fcc)
Lattice ?? parameter (A)
±(0.0002– 0.0003)
(h k l) Crystallite size (nm) ±(3–7) nm
r.m.s strain ?? 103 ± (0.00007– 0.001)
Lattice parameter ?? (A) ±(0.0002– 0.0006)
Vol. Lattice fraction parameter ?? (A) ± ± (0.15– (0.0004– 0.20) % 0.0006)
(h k l) Crystallite size (nm) ± (2–4) nm
As received, |e| = 0
a = 3.6022
V0 = 0.0116 nm3 a = 2.5467 15.70 c = 4.1519 c/a = 1.630 a = 2.5447 28.21 c = 4.1494 c/a = 1.631 a = 2.5378 43.45 c = 4.1559 c/a = 1.637 Indeterminate Indeterminate – – (102) 5 19.66 (002) (101) 44 16 0.98 0.65 3.02 (100) 44 3.31 (102) 6 2.78 Indeterminate Indeterminate 3% 12.40 14.35 (002) (101) 36 18 0.15 0.57 (100) 46 3.52 (102) 14 4.18 8.79 15.33 11.67 (002) (101) 39 18 0.73 1.95 (100) 43 5.87
(111) (200) (220) (311)
87 88 81 86
0.06 0.05 0.04 0.03
Engineering strain: 10%, |e| = 0.09 5%
a = 3.6024
(111)
82
0.48
a = 2.8921
(110) (200) (211) V0 = 0.0121 nm3 a = 2.8885
32 13 19
1.31 2.68 1.69
52%
(200) V0 = 0.0117 nm3 (220)
28 26
1.69 1.28
(311)
18
1.50
Engineering strain: 20%, |e| = 0.18
a = 3.6047
(111)
66
0.61
(110)
34
1.48
59%
(200) V0 = 0.0117 nm3 (220)
36 33
1.21 0.90
13.26
4%
V0 = 0.0121 nm3 a = 2.8861
(200) (211)
12 23
3.29 1.78
(311)
45
1.03
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Engineering strain: 30%, |e| = 0.26
a = 3.6049
(111)
62
0.65
(110) (200) (211) V0 = 0.0120 nm3
35 14 25
1.66 2.82 1.84
81%
(200) V0 = 0.0117 nm3 (220)
32 29
1.52 1.13
(311)
29
0.95
Failure, |e| = 0.39
a = 3.6032 V0 = 0.0117 nm3
98% – – – –
43
1.49
a = 2.8899 V0 = 0.0121 nm3
(110) (200) (211)
31 12 27
1.68 3.21 1.89
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P. Sahu et al. / Acta Materialia 60 (2012) 6907–6919 Table 4 Results of the dislocation character and density analysis with di??erent tensile deformations. Tensile strain Austenite (fcc) 0% (|e| = 0) Dislocation density, q (??1015 m??2) Dislocation character parameter, q Outer cut o?? radius of dislocation, Re (nm) Dislocation arrangement p?????? parameter, M???? Re q?? Distance between 1 dislocations, d ?? p???? q (nm) fc(edge) fc(screw) 0.19 1.92 479 6.64 72.5 10% (|e| = 0.09) 9.57 2.39 67 6.53 10.2 20% (|e| = 0.18) 3.66 1.79 68 4.14 16.5 30% (|e| = 0.26) 8.78 1.75 45 4.30 10.6 Failure (|e| = 0.39) – – – – – a0 -Martensite (bcc) 0% (|e| = 0) – – – – – 10% (|e| = 0.09) 11.87 2.45 49 5.37 9.2 20% (|e| = 0.18) 30.52 2.73 34 6.00 5.7 30% (|e| = 0.26) 19.87 2.75 41 5.77 7.1
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Failure (|e| = 0.39) 22.47 2.47 41 4.30 6.7
0.72 0.28
0.09 0.91
0.89 0.11
0.95 0.05
– –
– –
– –
– –
– –
– –
3.3. Determination of the grain boundary character distribution
True stress (σ)(MPa)
2000
The grain boundaries (GBs) of the deformed specimens were characterized by the HKL CHANNEL5 software of Oxford Instruments integrated with the EBSD system. EBSD maps were obtained with step P sizes of 0.05– frequencies of primary twins ( 3) and higher 0.08 lm. TheP order twins ( 3n, n > 1) were determined by the grain orientation measurements and subsequent calculation of the misorientation relationship. Deviations from the exact twin relations were allowed for within the Brandon criterion [29]. To avoid spurious boundaries, misorientations below 5° were not measured and this limit was used for all specimens to achieve consistently quantitative data. The grain boundary misorientations were determined by classifying the boundaries with misorientations between 5° and 15° as low angle GBs and those of misorientation >15° as high angle GBs. 4. Results 4.1. The stress–strain behavior at ??80°C Fig. 1 shows the true stress–true strain curve for the studied steel at ??80 °C??up to fracture and also the strain ?? hardening rate (SHR), dr true curve. The tensile tests were de interrupted at various terminal strains to study the intermediate microstructure. However, XRD experiments at the low engineering strains of 2% and 5% were not performed, for two primary reasons: ??rst, these low strains might not induce signi??cant di??erences in the microstructure to be studied by XRD in the bulk scale of the specimen compared to the later stages of straining; and secondly, to restrict the XRD analysis to a reasonable number of XRD patterns for the ease of understanding by the reader. However, the low strain microstructures were studied using the EBSD and TEM. Fig. 1 reveals that the ??ow stress
1500
12000
(dσ/dε)true (MPa)
1000
9000
500
6000
3000
0 0.0 0.1 0.2
0 0.0
0.1
True strain (ε)
0.2
0.3
0.4
0.5
0.3
0.4
0.5
True strain (ε)
Fig. 1. True stress–true strain curve at ??80 °C, j_ j = 10??4 s??1. The strain e hardening rate, ??dr ??true , is shown in the inset. de
curve exhibits an in??ection at the approximate engineering strain of 15% (|e| = 0.14). It is also seen that the SHR decreases rapidly at small strains, reaching a minimum at the engineering strain of 11% (|e| = 0.10). The minimum in SHR and the following maximum are typical of metastable stainless steels, where strain-induced martensite is formed [11]. 4.2. The kinetics of martensite transformation and the unit cell parameters Fig. 2 shows the XRD patterns of the di??erently strained specimens. All the important Bragg re??ections present in the X-ray pro??les have been indexed. It can be seen from Fig. 2 that the as-received specimen (i.e. 0% strained) is completely austenitic. Using SEM–EBSD, the grain size of the annealed austenitic structure was measured as 16 lm with the annealing twin boundaries excluded and 8 lm with them included. At the very early stage of straining, i.e. at 2% engineering strain, the EBSD phase maps presented in Fig. 3 reveal that the deformation is accompanied
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(a)
austenite (fcc)
ε-martensite (hcp) α'-martensite (bcc)
(101) (200) (102) (200)
(b)
(211) (103) (311) (112) (201) (222) (004) (220)
(c)
(d)
also revealed that there is continuous progress of the martensitic transformation, and the amount of a0 -martensite is 52% at 10% deformation, which attains almost complete ($98%) a0 -martensite structure at a failure strain of about 48% (|e| = 0.39). In contrast, the presence of e-martensite is low ($5%) after 10% deformation (|e| = 0.09), even lower ($3%) at 30% deformation (|e| = 0.26) and thereafter becomes negligible at failure. According to the Rietveld analysis (Table 3), the austenite lattice parameter increases with increasing deformation up to 30% strain, beyond which it decreases up to failure. In contrast, the lattice parameter of a0 -martensite follows the opposite trend to that of austenite, i.e. it continuously decreases up to 30% strain but then increases at failure. Both lattice parameters (a and c) in e-martensite also gradually decrease with increasing deformation, although with c some exceptions. Interestingly, the a ratios of the e-martensite also increase with increasing deformation. 4.3. Rietveld analysis of the deformation microstructure 4.3.1. “Size-strain” analysis The crystallite size and microstrain values along di??erent hkl directions in various phases during the deformationinduced martensitic transformation are obtained using the size–strain analysis of the Rietveld algorithm in the MAUD program. We also performed the modi??ed Warren–Averbach analysis on the representative Bragg re??ections of the austenite and a0 -martensite and obtained the crystallite size and strain values for the determination of the dislocation density and character (described in Section 4.4 below). These two methods have obvious limitations and advantages. Warren–Averbach analysis is the least-biased phenomenological approach, but may not be preferred in cases of severe peak overlap (as in some cases of the present study) or large strains that do not follow a Gaussian strain distribution. Therefore, we adopted the Rietveld re??nement, comprising structural and microstructural models, and an alternative approach that also encompasses the various anisotropic hkl-dependent linebroadening models. In our several recent studies [30–33],
(111) (002)
(110)
Intensity (A.U.)
(100)
(220) (110)
(e)
40
50
60
70
80
90
100
2θ (Degrees)
Fig. 2. X-ray di??ractograms of di??erently deformed specimens: (a) asreceived, |e| = 0; (b) 10% deformation, |e| = 0.09; (c) 20% deformation, |e| = 0.18; (d) 30% deformation, |e| = 0.26; and (e) at failure, |e| = 0.39. The respective residual drawn to the same scale is plotted at the bottom of the individual pattern.
by the onset of c ! e ! a0 martensitic transformation. The degree of martensite transformation increases as the engineering strain is extended to 5%. According to EBSD measurements, the amount of e-martensite was $10% at 2% strain and $8% at 5% strain. As the straining was continued to 10% and beyond, we can see a signi??cant c ! e ! a0 or maybe direct c ! a0 martensitic transformation, as evident from the continuous variation of the relative intensities of the constituent phases shown in Fig. 2. Rietveld analysis
(a)
5 ??m
(b)
10 ??m
Fig. 3. EBSD phase-maps, e-martensite (yellow color) and a0 -martensite (red color): (a) 2% deformed, |e|=0.02; and (b) 5% deformed, |e|=0.05. (For interpretation of the references to colour in this ??gure legend, the reader is referred to the web version of this article.)
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2.5
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2.0
[(ΔK) -α]/K /10
2
2
1.5
ε ε ε ε
=0 = 0.09 = 0.18 = 0.26
1.0
1/q
0.5
0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
H
2
Fig. 4. Linear ??tting to the variation of ????DK??2 ?? a??=K 2 with H2 in austenite according to Eq. (5).
we have reported that the size and strain values in deformed steel microstructures are seldom isotropic, which is attributable to the anisotropic elastic constants along different hkl. In the present steel, we also observed a very low amount of e-martensite, at most 5%, which decreased with increasing strain. Thus, this very low fraction of e-martensite during tensile straining clearly puts a restriction on the accuracy of the Warren–Averbach method in this phase. The size–strain analysis (Table 3) of the XRD patterns presented in Fig. 2 revealed that the as-received austenite specimen is characterized by relatively large and almost isotropic crystallite sizes of $100 nm and a negligible root mean square strain ($10??4) within the lattice. The crystallite sizes physically correspond to the sizes of the domains that scatter X-rays in a coherent manner. As the tensile straining is continued to 10%, we can see that a signi??cant amount of anisotropy is introduced in both the crystallite size and strain values within the austenite microstructure. The crystallite size values in 10% deformed austenite also decrease signi??cantly compared to the unstrained specimen and the values vary between 18 and 82 nm along di??erent hkl. A very signi??cant observation is that, although the austenite microstrain values are higher and anisotropic in this specimen compared to the as-received specimen, the individual values are strikingly low ($10??4) along some crystallographic directions (Table 3), uncharacteristic of a typical deformed microstructure. On the other hand, the e-martensite and a0 -martensite microstructures are also represented by comparable but relatively lower anisotropic crystallite size values – 14–43 and 19–32 nm, respectively – and are accompanied by higher anisotropic microstrain values ($10??4 ! 10??3) compared to the austenite. Another, very striking, uncharacteristic observation within the austenite microstructure (Table 3) is that, with further straining to 20%, the size and strain values are still anisotropic. However, the individual crystallite size values increase in the range of 33–66 nm and microstrain values decrease (even the order of magnitude changes from 10??3 to 10??4) in comparison to the 10% deformed specimen, in
spite of the higher strain being imparted. As the straining is extended to 30%, the size values (29–62 nm) and microstrain values decrease and increase marginally, respectively, in comparison to the 20% deformed specimen. Thus, it is quite evident that, at higher strains, the uniaxial straining did not have any recognizable e??ect of decreasing and increasing the size and strain values in austenite, respectively. The implication is that, at higher strains, subgrain formation is not the preferred deformation mode in this phase. The size values in the e-martensite and a0 -martensite microstructures do not manifest any signi??cant change with increasing deformation compared to their respective values in the 10% deformed microstructure, although the microstrain values in the a0 -martensite increase slightly with higher deformation. This nature of the variation of the size–strain values in the e-martensite and a0 -martensite microstructures has two implications: ??rst, the e-martensite seems to possess an ideal plastic behavior; and secondly, we expect some strain hardening and subgrain formation within the a0 -martensite, and the dislocation density in this microstructure is expected to increase with increasing tensile strain. 4.3.2. Planar fault analysis A fault analysis (Table 3) was performed on the close packed structures (i.e. austenite and e-martensite) according to Warren’s model [21] of planar defects implemented in MAUD. Signi??cant broadening of the Bragg re??ections accompanied by asymmetry in selected di??raction lines of the tensile deformed specimens is a clear indication of the presence of planar faults, namely stacking faults (SFs) and twins. The as-received microstructure consists of a low incidence of SFs (Psf $ 10??3) and negligible twins. It was revealed that, with increased strain, the Psf values in both the austenite and e-martensite microstructures change by more than an order of magnitude and increase monotonously with increasing deformation. Finally, reasonably high values of Psf % (0.015–0.043) and (0.008–0.012) were obtained for the austenite and e-martensite microstructures, respectively. Wang et al. [34] and Martin et al. [35] also used the XRD methods and obtained even higher values: Psf $ 10??2 for austenite in metastable low SFE austenitic steels. Similarly, very high values of twinning were estimated in the austenite and e-martensite, with Ptw % (0.011–0.019) and (0.013–0.015), respectively. However, the very low abundance ($3%) of e-martensite in the 30% deformed specimen impaired the applicability of the fault analysis, hence it was not attempted in this microstructure. 4.4. Dislocation character and density in the deformation microstructure 4.4.1. Dislocation character analysis As described in Section 3.2, the parameter q in Eq. (3) determines the character of dislocations existing within the austenite and a0 -martensite microstructures. It is
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4.0 3.5 3.0
-2
(111) - austenite
Intensity (A.U.)
Observed intensity austenite (fcc) α'-martensite (bcc) ε-martensite (hcp) Residue Actual fitting
ρ
π b2
2
ln Re
Y(L)/L /10 nm
??ρ
π b2
2
ε ε ε ε
=0 = 0.09 = 0.18 = 0.26
2.5 2.0 1.5 1.0 0.5
40
42
44
46
48 0.0 0 1 2 3 4 5
2θ (Degrees)
Fig. 5. Selected angular range of an X-ray di??ractogram of the 30% deformed specimen showing the deconvolution of the di??raction pattern to extract the (1 1 1) austenite re??ection. The residue of ??tting is drawn to the same scale and is plotted at the bottom of the pattern.
2
-3
ln L
Fig. 6. Linear ??tting to the variation of Y(L)/L2 with ln L in austenite according to Eq. (9).
estimated from a linear ??tting of Eq. (5) and is presented in Fig. 4 for austenite with varying tensile strain. It is worth mentioning that, due to the low intensity in the 30% deformed specimen, the high angle side of the austenite (1 1 1) re??ection was masked by the simultaneous presence of (0 0 2) and (1 1 0) re??ections of e-martensite and a0 -martensite, respectively, in approximately the same 2h range and therefore the determination of the FWHM of this re??ection was not straightforward. In order to address this issue, we therefore deconvoluted the di??raction pattern ??tted according to the Rietveld method to extract the individual overlapped di??raction lines and subsequently applied the modi??ed Williamson–Hall equation (Eq. (1)). The deconvoluted pattern is presented in Fig. 5 for a selected angular range. It should again be mentioned that the present steel had a very low SFE and that, in such steels, numerous SFs are created due to the movement of a h1 1 2i Shockley partial 6 dislocations on the close-packed {1 1 1} planes of austenite. However, the austenite dislocation character and density determination (Section 3.2) was carried out here for the a h1 1 0i perfect dislocations. In the present steel, the value 2 of q for the as-received specimen is 1.92, signifying that the dislocation character is mixed, i.e. a combination of edge and screw type. At 10% deformation, q in austenite increases to 2.39, i.e. dislocations are predominantly screw type, and, with further increasing deformation to 20% and 30%, q decreases to 1.79 and 1.75, respectively (Table 4). In other words, the dislocations type within austenite changes from screw to edge at higher strains. On the other hand, this analysis reveals that the value of q in a0 -martensite remains almost invariant during di??erent interrupted strains varying over the range 2.45–2.75, i.e. the dislocations in this microstructure are essentially screw type (Table 4). This type of variation of q within austenite and a0 -martensite is in good agreement with the observations of Shintani and Murata [12], who also found that the dislocation character of austenite in Type 304 steel gradually
changes from screw to edge type with increasing cold-rolling deformation and that the dislocations in a0 -martensite are screw type. Yin et al. [36] reported that warm-rolled low-carbon ferritic steels also contain screw-type dislocations. 4.4.2. Dislocation density analysis The dislocation density values were derived from the ??L?? gradient of the linear ??tting of the plot between YL2 and Y ??L?? ln L, as described in Eq. (9). The variation of L2 with ln L for di??erent strain levels is presented in Fig. 6 for the austenite. As seen in Table 4, the estimated dislocation density values are particularly high in both the austenite and the a0 martensite phase. However, they are higher ($1016 m??2) by an order of magnitude in the a0 -martensite compared to in the austenite ($1015 m??2). Shintani and Murata [12] also made similar observations on dislocation densities in the austenite and a0 -martensite during deformation of Type 304 steel. An interesting detail in the variation of dislocation density is that the values decrease (Table 4) at some intermediate strains, e.g. in 20% deformed austenite and 30% deformed a0 -martensite, and again increase with subsequent higher strains. In agreement, Dragomir-Cernatescu et al. [37] reported that, during the cold rolling of copper at 77 K, the dislocation densities exhibit a minimum at intermediate rolling reductions. 4.5. TEM observation of the deformation microstructure A limited number of TEM examinations were performed without trying to validate all the observations from the XRD analyses. Typical TEM bright ??eld (BF) images of the microstructures of the few strained specimens are presented in Fig. 7. Fig. 7a and b reveal that, alongside perfect dislocations, extended dislocations were generated within the austenite under the applied tensile stress and subsequent deformation led to overlapping of SFs. The presence of e-martensite is associated with these SFs. As
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(a)
500 nm
(b)
200 nm
(c)
500 nm
(d)
1 ??m
(e)
500 nm
(f)
200 nm
Fig. 7. TEM bright-??eld micrographs with di??erent strains: (a) 2% deformation, |e| = 0.02; (b) 5% deformation, |e| = 0.05; (c) 5% deformation, |e| = 0.05; (d) 20% deformation, |e| = 0.18; (e) 20% deformation, |e| = 0.18; and (f) 30% deformation, |e| = 0.26.
reported by Talonen and Hanninen [11], further deforma¨ tion is expected to lead to the formation of shear bands due to the overlapping of SFs, containing various planar and line defects. Fig. 7c reveals faint development of incomplete dislocation cell structure within the austenite at the tensile strain level of 5%. At these low strain levels, the presence of dislocations was signi??cant, though no prominent deformation twinning could be observed within the microstructures, except some local occurrences. Further, the dark areas of the BF microstructure in Fig. 7c are presumably a0 -martensite and are represented by a high density of dislocations. As the strain is increased to 20% and 30%, the BF micrographs with di??erent magni??cations presented in Fig. 7d–f reveal the presence of numerous deformation bands containing SFs and twins in the austenite matrix. The lowmagni??cation BF image presented in Fig. 7d shows a larger view of the 20% deformed specimen, wherein dislocation structures indicate high heterogeneity and complexity due to the coexistence of planar faults within the austenite
deformation bands and large transformation regions of a0 -martensite, which have comparatively higher density of dislocations than that of untransformed austenite. However, the higher magni??cation microstructures (Fig. 7e and f) distinctly reveal the presence of numerous planar faults within the untransformed austenite, which are arranged in several intersecting slip systems. This heterogeneity due to local variation in the deformed microstructure also highlights the di??culties in overall characterization of such microstructures using TEM – hence the employment of XRD analysis alongside the TEM to interpret the defect type, density and character. 4.6. Twinning analysis P TheP frequencies of primary twins ( 3) and higher order n twins ( 3 , n > 1) with varying tensile strain are presented P in Fig. 8. In the present study, we report GBs with 3– P P 29, which are considered as low (or special boundP aries), whereas random boundaries are those having
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4
CSL Frequency (%)
3
ε ε ε ε
= 0.18 = 0.09 = 0.05 = 0.02
2
1
Onyuna et al. [40] studied the uniaxial tensile loading behavior of Type 304 steel in the temperature range ??80 to 200 °C and they de??ned the M e!a temperature as that d below which the c ! e, c ! e ! a0 and c ! a0 martensitic transformation takes place. They also observed that the a0 martensite volume fractions increase with decreasing temperature and increasing deformation, similar to what we observed here. The Md temperature is dependent on the strain and for the present steel the Md temperature was calculated to be 21 °C. Thus, in the present steel, the observed martensitic transformation at ??80 °C takes place well below the Md temperature. 5.2. In??uence of martensite transformation on the unit cell dimensions As described in Section 4.2, it was observed that the austenite lattice parameter increases with the progress of martensite transformation during tensile straining, whereas the lattice parameter of a0 -martensite decreases monotonously up to 30% deformation. The situation is the exact opposite at failure, i.e. the lattice parameters of austenite and a0 martensite have decreased and increased, respectively. It is well known that the c ! a0 martensitic transformation involves a massive homogeneous transformation strain (Bain strain), which leads to volume expansion of the crystal. On the other hand, the low test temperature of ??80 °C will lead to normal contraction of the crystal due to reduced thermal vibrations of atoms at sub-zero temperatures. These two simultaneous processes that occur during tensile deformation at ??80 °C are competing in nature. The variation of the lattice parameters of austenite and a0 -martensite during the uniaxial loading may be explained as follows: at small strains, the c ! a0 martensitic transformation is still incomplete and a high volume fraction of austenite is left. Thus, before failure, the gradual increase in the austenite lattice parameter allows us to infer that the contraction of the crystal cannot compensate for the volume expansion due to transformation strain, and it is reasonable that the austenite lattice parameter may increase with the progress of martensite transformation. Streicher-Clarke et al. [41] also report that, under uniaxial and biaxial tension and plane straining of an Fe–0.19C– 1.63Si–1.59Mn TRIP steel, the austenite lattice parameter increases gradually with increasing strain. The transformation strain is partly accommodated by the austenite and a0 -martensite. Since the austenite is the softer phase and therefore deforms more easily under the transformation strain, an increase in the austenite lattice parameter is quite reasonable due to the volume expansion associated with the martensite transformation. Consequently, the expanding austenite lattice may also lead to compressive stress in the transformed region, which may slightly o??set the net volume expansion, and the a0 -martensite unit cell can experience a kind of compressive stress. Hence, we can expect a decrease in the lattice parameters of a0 -martensite as long as there is a signi??cant amount of
0 3 5 7 9 11 13 15 17 19 21 23 25 27 29
∑ value
Fig. 8. Frequencies of CSL with increasing R for di??erent strains: (a) 2% deformation, |e| = 0.02; (b) 5% deformation; |e| = 0.05; (c) 10% deformation, |e| = 0.09; and (d) 20% deformation, |e| = 0.18 .
beyond 29 and are omitted. It is evident from P 8 that Fig. during the initial stage of deformation (2%) the 3 boundary is the dominant CSL boundary, though its frequency is very small (0.26%), and with increasing uniaxial loading the nature of variation of CSL boundaries remains invariP ant but the 3 fraction gradually increases signi??cantly: to 0.76, 2.5 and 4.75% in 5%, 10% and 20% deformed austenite microstructures, respectively. In other words, at higher tensile strains, twinning becomes more prominent in austenite and contributes, together with dislocation glide and martensitic transformation, to the deformation. This also corroborates the observations in Section 4.3.2. Another P signi??cant observation in Fig. 8 is the absence of 9 and P 27 boundaries in the CSL distribution of austenite, indicating that the twins within austenite are likely to be coherent twins. 5. Discussion 5.1. Martensite transformation in straining It is well known that many low SFE austenitic steels are metastable and prone to martensite transformation during deformation, especially at low temperatures. In such steels, the expected martensitic transformation is c ! e ! a0 , even though direct transformation from c to a0 has also been reported [38,39]. The present steel has an SFE of $10 mJ m??2, which decreases further at the low deformation temperature of ??80 °C. Consequently, strain-induced martensite forms and at failure the transformation is almost completed (98%). In the present study, e-martensite is recognized up to 30% strain (i.e. up to: |e| = 0.26). In the present steel, the abundance of e-martensite decreases with increasing tensile strain, and is negligible at failure (Table 3). Thus, it is not possible to infer whether e-martensite is an intermediate phase in this steel; besides, direct c ! a0 martensitic transformation might also take place at high strains.
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retained austenite. At failure, when the martensite transformation is almost complete, the a0 -martensite is able to expand freely under tensile strain and the lattice parameter increases. From Table 3, we can see that the average available volume per atom (V0 ) in the austenite lattice is about 0.0117 nm3, compared to 0.0121 nm3 in the a0 -martensite unit cell; this corresponds to an $3.42% volume expansion. It is reported that the volume change during the austenite ! martensite transformation can be calculated as 4.64 ?? 0.53 ?? (%C), i.e. the volume change is dependent on the carbon content of the steel [42]. The present steel had a C content of 0.047%, thus the calculated volume expansion should be about 4.62%, which is signi??cantly higher than the observed volume expansion. This di??erence in the calculated and actual volume expansions may be attributed to the reduced thermal vibrations of the atoms in the crystal and the presence of transformed regions comprising hard a0 -martensite, which signi??cantly o??set the volume expansion due to Bain strain. 5.3. Stacking faults and twins in austenite and e-martensite The primary e??ect of randomly distributed intrinsic SFs in an fcc structure is re??ected in its representative di??raction pattern by a decrease in the maximum intensities of the (1 1 1) and (2 0 0) re??ections compared to the unfaulted fcc structure. Furthermore, according to the Paterson theory [43], in the presence of intrinsic SFs, the fcc (1 1 1) peak is asymmetrically shifted to higher di??raction angles, while the (2 0 0) re??ection shifts to lower di??raction angles. Besides the opposite shifts of the (1 1 1) and (2 0 0) pair of di??raction lines in the XRD pattern, the consequence of the presence of extrinsic SFs within fcc crystals is a characteristic increase in the intensity di??erence between the (1 1 1) and (2 0 0) di??raction lines [21]. The presence of twinning does not contribute to a signi??cant peak shift, but lowers the maximum intensity and increases the broadening of (1 1 1) and (2 0 0) Bragg re??ections. On the other hand, according to Warren’s model of planar defects [21], the prismatic lattice planes of hcp crystals, e.g. (1 0 1), are a??ected whereas the maximum intensity of the di??raction lines (h 0 0), (h k 0) and (0 0 l) are not. The contribution of close-packed microstructure planar faults on the di??raction pattern of 10% deformed specimen is demonstrated in Fig. 9 for a selected angular range, showing the quality of ??tting achieved without the Warren’s model in the re??nement along with the actual ??tting that includes the Warren’s model. A closer look at Fig. 9a enables us to make some important observations that are in agreement with the Warren’s model. First, the (1 0 1) plane, i.e. the representative prismatic plane of the e-martensite, exhibits a recognizable decrease in the intensity, while the (1 0 0) and (0 0 2) planes, i.e. the (h 0 0) and (0 0 l) lines, are not a??ected. Secondly, in the austenite microstructure, we can see that the (2 0 0) re??ection is distinctly shifted to the lower di??raction angle, whereas the shift of the (1 1 1) re??ection to the higher di??raction angle is not
(111) (002)
austenite (fcc)
(101)
(100)
ε-martensite (hcp) α'-martensite (bcc)
(200)
(a)
Intensity (A.U.)
(b)
42
45
48
51
2θ (Degrees)
Fig. 9. Selected angular range of an X-ray di??ractogram of the 10% deformed specimen showing the e??ect of planar faults: (a) Rietveld re??nement without Warren’s model; and (b) Rietveld re??nement with Warren’s model. The respective residual drawn in the same scale is plotted at the bottom of individual pattern.
very pronounced compared to the (2 0 0) line, although the shift cannot be ignored. From Fig. 9b, we can see that, for the present steel, the incorporation of Warren’s model can su??ciently model the contribution of SFs within the e-martensite, though in the case of austenite some intensity mismatch is clearly evident in the (1 1 1) re??ection. This is presumably due to the extrinsic nature of the SFs within austenite, which leads to an intensity di??erence and some limitations of the Warren’s model, which, according to Velterop et al. [44], often underestimates the Psf values. A single isolated SF represents an intrinsic SF, and the presence of hcp e-martensite structure is recognized if the intrinsic SFs are arranged next to each other on every alternate (1 1 1) austenite plane in a non-localized manner. In the present study, the localized nature of SFs at large strains (20% and 30% deformation; see Fig. 7e and f) has the implication of non-existence of signi??cant hcp e-martensite in these specimens. To explain the occurrence of twinning in the austenite of the present steel, we recall that a deformation twin is created in fcc metals by an extrinsic SF that changes the stacking order from ABCABCABC to ABCACBCA. Meyers et al. [45] assumed that, on the onset of twinning in metals, the critical twinning stress is almost temperature independent and indicated that it is strongly dependent on the strain rate, a lower strain rate signi??cantly reducing the twinning stress. In this work, the considered steel had a low SFE and during sub-zero temperature deformation it decreased further. We thus used a very low strain rate (10??4 s??1), so a low critical twinning stress was expected, which should favor the formation of deformation twins in austenite. Also, stress concentrations favoring twin nucleation may be generated by extended dislocation arrays. Meyers et al. [45] further suggested that the number of edge dislocations present in the dislocation pile-up also directly in??uences the interrelation between the local driv-
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ing force for twin formation and externally applied stress. For the present steel, as described in Section 4.4.1, the dislocations in austenite character becomes increasingly of the edge type with increasing deformation, which may favor the occurrence of twinning at intermediate and large strains. Also, the grain boundary misorientations accordP ing to the CSL method revealed that the incidence of 3 boundaries within the austenite’s microstructure gradually increased with increasing strain (Section 4.6), indicating the growing contribution of twinning deformation at higher strains. 5.4. Evolution of dislocation density and its characteristics in austenite and a0 -martensite We estimated very large values (Table 4) of Re, the e??ective outer cut-o?? radius of dislocations, which describes the variation of strain ??eld between the dislocations. The value of Re in the as-received specimen is very large ($479 nm), representing a nearly random distribution of non-interacting dislocations within the undeformed austenite. However, the onset of tensile straining signi??cantly lowers the Re values in this phase compared to the undeformed austenite, and varies from 67 to 45 nm with increasing strain (Table 4). This indicates that the tensile deformation of the present steel had the e??ect of establishing a very weak interaction among the dislocations in the austenite. In contrast, the change in Re in the a0 -martensite microstructure is not very pronounced with increasing strain and the values are somewhat lower than the austenite microstructure, varying between 49 and 34 nm (Table 4). Thus, somewhat stronger interaction among the dislocations exists within the a0 -martensite. It should be mentioned that the Re values in both the austenite and a0 -martensite of the present steel might be misleading, since they are generally larger than the crystallite size values (Table 3) described in Sec?? tion 4.3.1. Ungar et al. [46] also observed such apparent anomalies while studying the dislocation character in electrodeposited nanocrystalline Ni and indicated the absence of any direct correlation of Re with the actual dimensions of the crystal; rather, the parameter M may be related to the actual distribution of dislocations within the coherently scattering domains. p?????? The dislocation arrangement parameter M???? Re q?? is estimated to assess the strength of the dipole character of dislocations [15], i.e. the statistical distribution of dislocations. It is well known that the dislocation arrangement is a strong or weak dipole, depending on whether M is smaller or greater than unity, respectively. We can see from Table 4 that the M value in the as-received and 10% deformed austenite is greater than 6, which reduces to M ?? 4 in 20% and 30% deformed austenite, i.e. the dislocations within the austenite show a very weak, non-interacting dipole character. In general, for most deformed metallic materials having a high SFE, M decreases to around unity because dislocations tend to form a cell structure in strong correlation.
This phenomenon is not always expected in low SFE materials because such materials favor planar slips during deformation. On the other hand, within the a0 -martensite, M ?? 4–6 again indicates that the dipole character of dislocations in this microstructure is similar to that in the austenite. From Table 4, it can be seen that at large strains the fraction of the edge dislocations, fc??edge?? , in the austenite increases at a very rapid rate and approaches the maximum possible value of 1. In order to explain the characters of the dislocations in austenite and a0 -martensite, we recall that the Peierls stress for screw dislocations in bcc crystals is high compared to in fcc and hcp crystals [47]. Thus, at higher strains, the absence of screw dislocations in austenite may be explained by the annihilation of glissile dislocations from cross slip, which leads to dislocations of predominantly edge character. On the other hand, unlike the fate of screw dislocations in austenite, the annihilation of screw dislocations by cross slip within a0 -martensite is quite unlikely. Hence, the dislocation character within a0 -martensite can be expected to be the sessile screw type, and suggests for the increase and/or saturation in the fraction of dislocation type (edge or screw) and dislocation density values in a0 -martensite (Table 4). At failure, the abundance of austenite was very low ($2%), and this hindered the dislocation analysis. Shintani and Murata [12] observed a similar evolution of dislocation types for Type 304 steel with increasing deformation. They attributed the increasing microhardness values to the increase in edge dislocations and suggested that the strain hardening in austenite is derived from the pinning of such dislocations. However, in the present case, the fraction of austenite decreases rapidly with increasing strain so that its contribution decreases towards zero at fracture, and the high ??nal ??ow stress must be the result of a high degree of strain-induced martensite transformation causing strain hardening of the a0 -martensite. 6. Conclusions The X-ray pro??le analysis and scanning and transmission electron microscopy applied to the low strain rate deformation behavior of 201 Cr–Mn austenitic steel during interrupted tensile testing at ??80 °C leads to the following conclusions: (1) Deformation of austenite is accompanied by continuous progress of the strain-induced martensite transformation, which becomes complete at failure. The fraction of e-martensite is very low and becomes negligible at fracture strain. (2) The austenite unit cell expands until the completion of martensite transformation in order to accommodate the transformation strain, and the net volume expansion due to expanding austenite is o??set by
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the lattice contraction at low temperature and the compressive stress in the transformed region, which decrease the lattice parameters of a0 -martensite. (3) Crystallite “size–strain” analysis indicates that, at low strain, the deformation mode in austenite is dislocation glide. At large strains, twinning also contributes to austenite deformation, which increases the inciP dence of high angle 3 boundaries. However, the primary deformation mode in a0 -martensite is slip. (4) High dislocation density values were estimated in the a0 -martensite and austenite phases; these were an order of magnitude higher in the former ($1016 m??2) than in the latter. The dislocation density in austenite revealed a slight minimum at intermediate strains. (5) Dislocation character analysis suggested that the character of perfect dislocations in the austenite phase gradually changes to edge type with increasing strain. The dislocations in the a0 -martensite were found to be screw type throughout the deformation process. Signi??cant densities of stacking faults and twins were estimated to be present in the austenite, which could also be observed by scanning and transmission electron microscopy examinations.
Acknowledgements The ??nancial support from the Finnish Funding Agency for Technology and Innovation (Tekes) in the Light and E??cient Solutions program (project SPR1) of the Finnish Metals and Engineering Competence Cluster (FIMECC Ltd.) is gratefully acknowledged. The authors would also like to thank Outokumpu Oyj for providing experimental material. References
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[11] Talonen J, Hanninen H. Acta Mater 2007;55:6108–18. ¨ [12] Shintani T, Murata Y. Acta Mater 2011;59:4314–22. [13] Dini G, Naja??zadeh A, Monir-Vaghe?? SM, Ueji R. J Mater Sci Technol 2010;26:181–6. [14] Williamson GK, Smallman RE. Philos Mag 1956;1:34–46. [15] Wilkens M. Phys Stat Sol 1970;2:359–70. [16] Hill RJ. In: Young RA, editor. The Rietveld method, IUCr. Oxford: Oxford University Press; 1993 [chapter 5]. [17] Lutterotti L. MAUD, version 2.038; 2006.