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Relationship of grain size and deformation mechanism to the fracture behavior in high strength–high ductility nanostructured austenitic stainless steel
Materials Science & Engineering A 626 (2015) 41–50
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Relationship of grain size and deformation mechanism to the fracture behavior in high strength–high ductility nanostructured austenitic stainless steel R.D.K. Misra a,n, X.L. Wan a, V.S.A. Challa a, M.C. Somani b, L.E. Murr a a Center for Structural and Functional Materials Research and Innovation and Department of Metallurgical and Materials Engineering, University of Texas at El Paso, 500W University Avenue, El Paso, TX 79968, USA b Materials Engineering Laboratory, Center for Advanced Steels Research, The University of Oulu, P.O. Box 4200, 90014 Oulu, Finland
art ic l e i nf o
a b s t r a c t
Article history: Received 6 November 2014 Received in revised form 9 December 2014 Accepted 12 December 2014 Available online 19 December 2014
In this study we underscore the dependence of grain structure and deformation mechanism on the fracture behavior in a high strength–high ductility bearing nanograined/ultrafine-grained austenite stainless steel. In high strength nanograined steel, deformation twinning contributed to excellent ductility, while in the low strength coarse-grained steel, the high ductility is attained as a consequence of strain-induced martensite transformation. Interestingly, the differences in deformation mechanism of steels deformation mechanisms of steels with different grain structures but with similar elongations influenced the mode of fracture, a behavior that is governed by the change in austenite stability with grain size. The areal density of voids and their average diameter in the fracture surface also increased with increasing grain size, which ranged from 320 nm to 22 μm. & 2014 Elsevier B.V. All rights reserved.
Keywords: Austenitic stainless steel Grain size Deformation mechanism Fracture Austenite stability
1. Introduction The continued interest in advanced high-strength steels, including stainless steels, has led to the consideration of innovative processing routes. While grain refinement [1,2], microalloying addition [3–7], and severe plastic deformation [7,8] continue to represent a pragmatic approach to enhance the strength of existing metals and alloys, it is clear and widely agreed that the limitation of the mean path of gliding dislocation by the nanocrystalline structure constitutes the origin of limited ductility in high strength nanostructured alloys. There is also a significant interest in increasing the stability of austenite phase to delay the onset of necking and benefit from the strain-induced transformation of austenite to martensite to obtain high ductility. In order to increase the strength through grain refinement without compromising the ductility, we have recently developed an ingenious concept of phase reversion annealing to obtain nanograined/ultrafine-grained (NG/UFG) structures in metastable austenitic stainless steels. The concept involves extensive cold deformation (60–75%) of austenite to obtain strain-induced martensite. In the subsequent step, referred as phase-reversion annealing, martensite transforms back to austenite via diffusional
n
Corresponding author. Tel.: þ 1 915 747 8679; fax: þ 1 915 747 8036. E-mail address: [email protected] (R.D.K. Misra).
http://dx.doi.org/10.1016/j.msea.2014.12.052 0921-5093/& 2014 Elsevier B.V. All rights reserved.
or shear reversion mechanism [9–13]. Using this approach, NG/UFG structure was obtained having high yield strength and elongation of 900–1000 MPa and 30–40%, respectively [9–13]. These properties were superior to that of the coarse-grained (CG) counterpart that was characterized by yield strength typically in the range of 350– 450 MPa and elongation of the order of 40% [9–13]. In 1995, Christian and Mahajan [14], critically assessed the relationship between deformation twinning and fracture. In bcc metals and alloys, high stress concentration induced by deformation twins was recognized as the potential reason for initiation of fracture at twin–twin intersections. The fcc metals and alloys are ductile at room temperature. But, at sub-zero temperatures, significant amount of deformation occurred by twinning in austenitic stainless steels having low stacking fault energy (SFE), and as a consequence micro-cracking was observed at twin–twin intersections [14]. It was proposed that the twinning and fracture were independent phenomena. However, the above analysis by Christian and Mahajan dealt with conventional coarse-grained structure. To the best of our understanding there is no report on the fracture behavior in a single material processed using identical processing parameters that exhibits a distinct transition in deformation mechanism from strain-induced martensite formation to twinning, when the grain size changes from CG to NG/UFG. It is in this regard that the study described here is unique and provides new knowledge in nanocrystalline materials. In high strength NG/ UFG steel, deformation twinning contributed to the excellent
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ductility and high strain hardening rate, while in the low strength CG steel, the high ductility and strain hardening ability were associated with strain-induced martensite. Interestingly, the differences in the deformation mechanism of CG and NG/UFG steels influenced the fracture behavior. Thus, the objective of the study described here is to understand the interplay between grain size and deformation mechanism as they relate to the fracture behavior in austenitic stainless steel from the CG to NG regime.
2. Experimental procedure The experimental steel was a commercial Type 301LN austenitic stainless steel of 1.5 mm thickness with a nominal composition (in wt%) of Fe–0.017C–0.52Si–1.3Mn–17.3Cr–6.5Ni–0.15Mo–0.15N. Samples of stainless steel strips were cold-rolled in a laboratory rolling mill to 62% reduction ( 0.6 mm thick) via a number of passes and subsequently reversion-annealed in the temperature range of 700–900 1C for 10–100 s in a Gleeble 1500 thermomechanical simulator to obtain different grain sizes from NG to CG regime. The reversion annealing experiments were carried out on specimens of dimensions 120 mm 25 mm cut from the cold rolled samples. The experimental details are given elsewhere [9–13]. The grain structure was examined in a transmission electron microscope (TEM) operated at 120 kV. Keeping in view the grain size distribution, the weighted average grain size dw was determined [15]. Here, about 100 grains
were distributed in bins of 250 nm (0.25 μm) in size. A bin of 250 nm was so selected in order to optimize the statistical data. A small bin size is expected to result in poor statistical accuracy, while a large bin size may mask the effect of small grains. Thus, an optimum bin size of 250 nm (0.25 μm) was selected, keeping in view the grain size range of samples. Denoting the number of grains in the ith bin as ni and dividing it by the total number of grains, N, the weight of the ith bin is [15]: wi ¼
ni N
ð1Þ
Table 1 Tensile properties of phase reversion-induced austenitic stainless steel with different grain size and average distance between striations measured from the scanning electron fractograph. Striations were absent in the CG structure. Weighted average
Average yield Average strength (MPa) elongation (%)
Distance between striations (μm)
768 722 667 350
3.2 6.1 8.2 –
grain size, dw
NG/UFG SMG FG CG
320 nm 757 nm 2132 nm 22 mm
34 38 41 40
Fig. 1. (a–c) TEM micrographs of phase reversion annealed 301LN type austenite stainless steel with varying grain size from NG/UFG regime to fine-grained (FG) regime and (d) light micrographs of CG steel. The average weighted grain size dw was determined from a number of micrographs and is indicated on each of the micrographs. NG/UFG: nanograined/ultrafinegrained, SMG: sub-micron-grained, FG: fine-grained, and CG: coarse-grained steels (adapted from Ref. [13]).
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Fig. 2. Representative bright field transmission electron micrographs of (a, b) NG/UFG, (c, d) SMG, (e, f) FG and (g, h) CG structures illustrating tensile strain-induced deformation structure.
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Moreover, the square root of the areal mean of ni grains in the ith bin gives the average grain size, di , for the ith bin. Knowing di and wi, the weighted average grain size of the sample is calculated by [15] N
dw ¼ ∑ w i di i¼1
ð2Þ
The mechanical properties of reversion-annealed austenitic stainless steel were determined by tensile testing samples machined to a profile of 25 mm 25 mm with 20 mm gage length. They were tested at a cross-head speed of 0.016 mm/s up to strain of 0.03, beyond which it was increased to 0.062 mm/s. The corresponding average engineering strain rates were 0.00075/s and 0.003/s, respectively. Deformation-induced structure was examined by preparing TEM foils from samples deformed to different levels of tensile strain (2%, 10%, and 20%), prior to fracture. The sample area close to the highly stressed region within the gage length was used for the preparation of electron transparent foils. The specimens were examined in a TEM (Hitachi H7600) operated at 120 kV. Thin foils were prepared by twin-jet
electropolishing of 3 mm disks, punched from the specimens, using a solution of 10% perchloric acid in acetic acid as electrolyte. A number of foils were examined for each experimental condition. On the other hand, the fractographic features of the samples tensile tested until fracture was examined in a scanning electron microscope (JEOL-6300FV SEM). The voids in the digital images of the fracture surface were selected and painted black using Adobe Photoshops software, and then the diameter of voids were estimated using a commercial image processing software. The software had provision for quantitative analysis, such as average diameter of voids, frequency of voids of a particular size and average number density of voids. A number of fractographs were analyzed to arrive at an average value of the above parameters.
3. Results Optical and transmission electron (TEM) micrographs describing the grain structure obtained via different temperature–time combination are revisited in Fig. 1 [13]. The different grain sizes are referred to as nanograined/ultrafine-grained (NG/UFG), submicron grained (SMG), fine-grained (FG) and coarse-grained (CG).
Fig. 3. (a–c, e) Scanning electron fractographs at different magnifications showing fracture surface of tensile specimen of NG/UFG steel tested to fracture. The river-like markings and striations are marked by arrows. Note interconnected voids just beneath the striations (d, f). Line-up of voids are more apparent after image processing of figures (c, e) using a commercial software.
R.D.K. Misra et al. / Materials Science & Engineering A 626 (2015) 41–50
Their mechanical properties are summarized in Table 1. The weighted average grain size of CG steel was 22 mm, while that of the smallest grain size NG/UFG steel (cold rolled to 62% reduction and annealed at 800 1C for 10 s) comprised of predominantly nanograins (dia 100 to 200 nm) and ultrafine grains (dia 200 to 500 nm), with the weighted average grain size dw of 320 nm. The NG/UFG material showed a considerable increase in yield strength (more than twice that of the CG sample), without any significant decrease in tensile elongation. 3.1. Microstructural evolution during tensile deformation It is important to first briefly describe the structural evolution during tensile straining, prior to describing the fractographic features. Representative TEM micrographs illustrating microstructural evolution as a function of selected strain for different grain sizes are presented in Fig. 2. In the NG/UFG structure, there were already numerous stacking faults (SF) at low strain (ε ¼0.02, figure not shown here) and extended stacking faults in two systems intersected one another, and dislocations were inhibited by stacking faults. With increase in strain (ε ¼0.1), mechanical twins of nanoscale thickness were present. In some grains, twins grew in
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different directions and mutually intersected one another (Fig. 2a). Dislocation glide during plastic deformation is also inhibited by twin boundaries. At appreciably higher strain (ε ¼0.2), there was an increase in twin density such that the twins organized in bundles (Fig. 2b). The bundles in some cases were 300 nm large. The diffraction pattern confirmed the presence of deformation twins. These deformation twins were envisaged to be formed by the successive emission of Shockley partial dislocations from the same grain boundary on (111) plane [16]. A detailed discussion on the interplay between grain structure and deformation mechanisms is discussed elsewhere in recent publications [11,12]. Fig. 2c and d summarizes the representative TEM micrographs of the deformation processes associated with tensile straining of SMG steel. The main microstructural features were formation of twins with different growth directions which mutually intersected each other (ε ¼0.1), (Fig. 2c). At high strain (ε ¼ 0.2), twins intersected each other, separating a typical grain into many small regions (Fig. 2d). Some of the twins were organized in bundles. We now describe the behavior of phase reversion annealed FG steel in comparison to NG/UFG and SMG structures. In FG steel, with an average grain size of 2.1 μm, besides SF, dislocations and twins, nucleation of strain-induced bcc α0 -martensite was
Fig. 4. (a–c, e) Scanning electron fractographs at different magnifications showing fracture surface of tensile specimen of SMG steel tested to fracture. The river-like markings and striations are marked by arrows. Note interconnected voids just beneath the striations (d, f). Line-up of voids are more apparent after image processing of Figures (c, e) using a commercial software.
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detected. At ε ¼ 0.1, twins and strain-induced α0 -martensite at shear bands were present simultaneously (Fig. 2e and f). The deformation mechanism in the FG structure was a combination of both twinning and strain-induced martensite. The deformation structures for the CG structure are presented in Fig. 2g and h. A large number of straight martensite laths nucleated at shear bands and grew in different directions at high strain (ε ¼0.2) (Fig. 2g). Martensite laths intersected each other and separated a typical grain into many small regions of quadrilateral shape. The diffraction pattern analysis (Fig. 2g) indicated bcc martensite (α0 -martensite). The α0 -martensite laths are barriers to dislocation motion. Meanwhile, the martensite transformation occurred by repeated nucleation of new α0 -lath-like embryos and coalescence of such embryos resulting in the formation of a wider lath, such that the thickness of the packet increased to as high as 400 nm. Thus, there was a distinct transition in the deformation mechanism from twinning in the NG/UFG structure to straininduced martensitic transformation in the CG structure. The transition occurred in FG steel, when combinations of both twinning and strain-induced martensite were observed. In conclusion, both twinning and strain-induced α0 -martensite are effective strain hardening mechanisms that inhibit strain
localization and are responsible for the observed high ductility. Twinning was a major factor that contributed to excellent ductility in ‘high strength’ NG/UFG structure, where as in the ‘low strength’ CG structure, the high ductility resulted from the strain-induced martensite formation. This change in the deformation mechanism is attributed to an increase in the stability of austenite with decrease in grain size (Section 4). 3.2. Fracture characteristics We now describe the fractographic features of the tensile tested specimens elucidating the fracture characteristics of the steel with different grain sizes. There were striking differences in the nature of fracture (Figs. 3–6) associated with steel specimens of different grain sizes, in particular for NG/UFG and CG steels, even though they were all characterized by a nearly similar tensile elongation-to-fracture (Table 1). Two kinds of typical fracture patterns were observed as a consequence of the variation in grain size. The fracture surface of NG/UFG steel (Fig. 3a) appeared relatively flat, but at higher magnification river-like markings or striations (marked by white arrows in Figs. 3b and c) that were nearly parallel to one another were observed. High magnification
Fig. 5. (a–c, e) Scanning electron fractographs at different magnifications showing fracture surface of tensile specimen of FG steel tested to fracture. The river-like markings and striations are marked by arrows. Note interconnected voids just beneath the striations and also the presence of microvoid coalescence type of fracture (c, e). Image processing of Figures (c, e) using a commercial software is presented in (d, f).
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Fig. 6. (a–c, e) Scanning electron fractographs at different magnification showing fracture surface of tensile specimen of CG steel tested to fracture. (d, f) Voids are more apparent after image processing of figures (c, e) using a commercial software.
fractographs indicated line-up of voids (Figs. 3c and e) interconnected side by side just beneath the striations and represented a unique fracture surface that does not appear to have been documented in the literature. The line-up of voids was more apparent after image processing of SEM fractographs, using a commercial image processing software, and is presented in Fig. 3d and f. Figs. 4 and 5 summarize the representative SEM micrographs of the fracture surface of SMG and FG steels tensile tested to fracture. The characteristics of SMG steel were similar to NG/UFG steel. But in FG steel, besides river-like markings or striations, microvoid coalescence-type of fracture typical of dimple rupture was also present. This is not surprising because FG steel was characterized by two deformation mechanisms, twinning and strain-induced martensite (Fig. 2e and f). In contrast to the NG/UFG steel, the fracture surface of CG steel that experienced strain-induced martensitic transformation during tensile deformation was microvoid coalescence-type of fracture (Fig. 6), which is typically observed in ductile metals and alloys. The areal density of voids increased from 0.32 μm 2, 0.40 μm 2, 0.51 μm 2 and 0.75 μm 2 with increase in grain size from NG/UFG, SMG, FG and CG, respectively (Fig. 7a). The size of
voids was measured from several SEM micrographs for each sample. The size distribution of voids with different grain sizes is presented in Fig. 7c, which depicts that the distribution of void size became uniform with decreasing grain size. The average diameter of the voids increased with an increase in grain size from NG/UFG regime to CG regime (Fig. 7b). Similarly, from the SEM micrographs, the average distance between the striations was measured and is presented in Table 1. It may be seen from Table 1 that the spacing between striations increased with increase in grain size from NG/UFG to FG structure. This is attributed to a decrease in twin density with the increase in grain size. In the quest to understand the aforementioned characteristics, the broken tensile specimens of the NG/UFG and CG steels were lightly polished, etched, and the microstructure just below the fracture surface was examined in an SEM. It was concluded that in NG/UFG steel, the voids in the austenite matrix nucleated preferentially along the twin boundaries (Fig. 8). We envisage the following fracture mechanism or process associated with twinning-induced ductile fracture in the NG/UFG austenitic steel. During plastic deformation beyond the necking stage, microvoids grew longitudinally along the twin boundaries with increase in strain. This was accompanied by deformation of the region
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Fig. 7. Void size distribution of phase reversion-annealed austenitic stainless steels processed to obtain different grain size from NG/UFG to CG regime. (a) Areal density of the voids, (b) mean size of voids, (c) void size distribution, and (d) spacing between the striations (striations were absent in CG steel).
Fig. 8. Low and high magnification scanning electron micrographs illustrating voids just beneath the fracture surface in NG/UFG steel. The voids are marked by arrows.
surrounding the twins and microvoids resulting in the growth and coalescence of voids that apparently led to ductile fracture. Microvoid nucleation and growth in the NG/UFG steel is governed by the plastic strain, which in turn is dictated by the density of twins, and their interactions with dislocations, given that the twin boundaries are barriers to movement of dislocations. The aforementioned process governs the ultimate mechanical properties of NG/UFG steels, such that there is a relationship between the mechanical properties and the distribution and nature of voids in the twinning-induced ductile fracture surface. In a manner similar to NG/UFG steel, the microstructural examination just below the fracture surface of CG steel in SEM
after polishing and etching of the fracture surface indicated fine platelets of strain-induced martensite that acted as potential nucleating sites for voids (Fig. 9).
4. Discussion Combining the microstructural evolution during tensile deformation and mode of fracture, it is concluded that the intriguing differences between twinning-induced deformation mechanism and associated striated fracture behavior with line-up of voids beneath the striations in the NG/UFG steel and strain-induced
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Fig. 9. Scanning electron micrographs (a, b) of the surface just beneath the fracture surface illustrating nucleation of voids at martensite laths and (c, d) post-deformation microstructure showing tensile deformation-induced martensite in CG steel.
martensite formation associated with microvoid coalescence-type fracture in the CG steel, are related to the grain size effect. This is a significant and new finding. Based on the observations presented in Figs. 2–6, the deformation clearly influenced the fracture behavior of the respective steels and there was a clear distinction between the deformation structure and fractographic features in NG/UFG and CG steels. Deformation twinning is an effective and active deformation mechanism in NG/UFG steel and strain-induced α0 -martensite in the CG austenitic stainless steel. Both these mechanisms are effective strain hardening mechanisms and prevent strain localization and thereby enhance ductility. This behavior can be described in terms of the interplay between grain size and austenite stability. The observation that fracture behavior is governed by the deformation mechanism as a function of grain size is interesting because deformation twinning in the NG/UFG structure and strain-induced martensite in the CG structure are somewhat similar microstructurally, i.e., both of them involve diffusionless shear of a constrained plate-shaped region in the parent crystals. The deformation mechanism must be related to the enhanced contribution of high density of grain boundaries leading to increased strength of NG/UFG austenite that inhibits martensite formation. Grain size governs the thermal stability of austenite [17–19], but the influence on the mechanical stability of austenite is unclear. It is accepted that the transformation of fcc austenite to bcc martensite introduces anisotropic strain in adjacent untransformed austenite. The near uniform distribution of transformation strain requires several multi-variant transformations to occur simultaneously within an austenite grain for minimization of total strain energy [19]. However, in the event that the austenite grain is smaller than the martensite lath, as applicable in our case, then the probability of several variants of martensite to participate simultaneously within an austenite grain is significantly minimized because of reduced space. Furthermore, a single variant is preferred for deformation-induced martensite transformation in
NG/UFG structure because in a tensile test the deformed specimen has a texture where 〈101〉α0 direction is parallel to the tensile direction [19]. Thus, austenite can be anticipated to transform via the single variant mode but the reduction in the strain energy due to martensitic transformation in NG/UFG austenite cannot be attained, as outlined below. The mechanism of grain refinement-induced austenite stabilization can be explained in terms of the physical energy associated with austenite-to-martensitic transformation, involving Eqs. 3 and 4 [17]. If austenite transforms to martensite via single variant mode, the increase in elastic strain energy is given by [17,20]: ΔEv ¼ 0:5E1 ε21 x=d
2
þ ð0:5E2 ε22 þ 0:5E3 ε23 Þ x=d
ð3Þ
where E and ε are Young's modulus and elastic strain in each lattice plane, x is the thickness of martensite plate and lattice strain is elastically accommodated over the space of austenite grain (grain size: d). Inserting Young's modulus and strain in Eq. (3), the increase in elastic strain energy is given by ΔEv ¼ 1276:1 x=d
2
þ 562:6 x=d
ð4Þ
Thus, from Eq. (4), for average CG size of 22 mm, ΔEv is 6 MJ/m3 and for NG/UFG structure, ΔEv increases significantly to 850 MJ/m3, which decreases the ability to nucleate martensite with a decrease in grain size. We conclude that in the NG/UFG structure, multi-variant transformation is difficult and the transformation of austenite to strain-induced martensite transformation is largely suppressed, leading to an increase in the propensity for twinning with decrease in the grain size. Under these circumstances, the twinning-induced deformation mechanism and corresponding fracture behavior exhibited typical characteristics of striations or river-markings with line-ups of connected voids, which provided the observed high ductility in the NG/UFG austenitic stainless steel.
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5. Conclusions We have elucidated here the interplay between grain size and deformation mechanisms as they relate to the fracture behavior in 301LN Type austenitic steel from the NG/UFG to CG regime. This was accomplished through a combination of post-mortem TEM analysis of tensile deformed samples and SEM observations of the fracture surface. The differences in microstructural evolution during tensile deformation strongly influenced the fracture mechanism. Thus, in contrast to the conventionally wellestablished strain-induced martensite transformation contributing to the high ductility in the low-strength CG austenitic stainless steel, deformation twinning has played a vital role in contributing the corresponding excellent ductility to the NG/UFG version of the steel, and hence is characterized with a significantly new fracture mechanism. Interestingly, the difference in the deformation behavior of NG/UFG and CG steels with similar elongation-to-fracture was reflected in the mode and mechanism of fracture. In the low strength CG steel, the fracture occurred through traditional microvoid-coalescence, while in the high strength NG/UFG steel the fracture was characterized by line-up of small voids just beneath the striations or river markings. The differences in deformation mechanism that influenced the mode of fracture as a function of grain size from NG/UFG to CG regime is attributed to a change in austenite stability with grain size. Acknowledgments The authors (X.L. Wan, V.S.A. Challa and R.D.K. Misra) gratefully acknowledge support from National Science Foundation, USA through Grant number DMR #261883 (Program Manager, Dr. Eric Taleff). Discussion with Professor P. Rama Rao (ARC International,
India) and Professor Warren Garrison (CMU, USA) are gratefully acknowledged. References [1] E. Ma, Scr. Mater. 49 (2003) 663–668. [2] C.C. Koch, Scr. Mater. 49 (2003) 657–662. [3] R.D.K. Misra, S.W. Thompson, T.A. Hylton, A.J. Boucek, Metall. Mater. Trans. A 32 (2001) 745–760. [4] R.D.K. Misra, K.K. Tenneti, G.C. Weartherly, G. Tither, Metall. Mater. Trans. A 34 (2003) 2341–2351. [5] R.D.K. Misra, H. Nathani, J.E. Hartmann, F. Siciliano, Mater. Sci. Eng. A 394 (2005) 339–352. [6] S. Shanmugam, R.D.K. Misra, J.E. Hartmann, S. Jansto, Mater. Sci. Eng. A 441 (2006) 215–229. [7] R. Song, D. Ponge, D. Rabbe, R. Kasper, Acta Mater. 53 (2005) 4881–4892. [8] F.J. Humphreys, P.B. Prangnell, J.R. Bowen, A. Gholina, C. Harris, Philos. Trans. R. Soc. Lond Ser. A 357 (1999) 1663–1680. [9] R.D.K. Misra, S. Nayak, S. Mali, J.S. Shah, M.C. Somani, L.P. Karjalainen, Metall. Mater. Trans. A 41 (2010) 2162–2174. [10] M.C. Somani, P. Juntunen, L.P. Karjalainen, R.D.K. Misra, A. Kyrolainen, Metall. Mater. Trans. A 40 (2009) 729–744. [11] V.S.A. Challa, X.L. Wan, M.C. Somani, L.P. Karjalainen, R.D.K. Misra, Mater. Sci. Eng. A 613 (2014) 60–70. [12] R.D.K. Misra, V.S.A. Challa, P.K.C. Venkatasurya, Y.F. Shen, M.C. Somani, L. P. Karjalainen, Acta Mater. 84 (2015) 339–348. [13] R.D.K. Misra, P.K.C. Venkatsurya, M. Somani, L.P. Karjalainen, Metall. Mater. Trans. A 43A (2012) 5286–5297. [14] J.W. Christian, S. Mahajan, Prog. Mater. Sci. 39 (1995) 1–157. [15] S. Rajasekhara, P.J. Ferreira, L.P. Karjalainen, A. Kyröläinen, Metall. Mater. Trans. A 38A (2007) 1202–1210. [16] S. Mahajan, Scripta Mater. 68 (2013) 95–98. [17] S. Takaki, K. Fukunaga, J. Syarif, T. Tsuchiyama, Mater. Trans. 45 (2004) 2245–2251. [18] E. Jimenez-Melero, N.H. van Dijk, L. Zhao, J. Sietsma, S.E. Offerman, J.P. Wright, S. van der Zwaag, Scr, Mater. 56 (2007) 421–424. [19] Y. Matsuoka, T. Iwasaki, N. Nakada, T. Tsuchiyama, S. Takaki, ISIJ Int. 53 (2013) 1224. [20] S. Yamamoto, K. Asabe, M. Nishiguchi, Y. Maebara, Tetsu-to-Hagané 82 (1996) 771–776.
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Relationship of grain size and deformation mechanism to the fracture behavior in high strength–high ductility nanostructured austenitic stainless steel R.D.K. Misra a,n, X.L. Wan a, V.S.A. Challa a, M.C. Somani b, L.E. Murr a a Center for Structural and Functional Materials Research and Innovation and Department of Metallurgical and Materials Engineering, University of Texas at El Paso, 500W University Avenue, El Paso, TX 79968, USA b Materials Engineering Laboratory, Center for Advanced Steels Research, The University of Oulu, P.O. Box 4200, 90014 Oulu, Finland
art ic l e i nf o
a b s t r a c t
Article history: Received 6 November 2014 Received in revised form 9 December 2014 Accepted 12 December 2014 Available online 19 December 2014
In this study we underscore the dependence of grain structure and deformation mechanism on the fracture behavior in a high strength–high ductility bearing nanograined/ultrafine-grained austenite stainless steel. In high strength nanograined steel, deformation twinning contributed to excellent ductility, while in the low strength coarse-grained steel, the high ductility is attained as a consequence of strain-induced martensite transformation. Interestingly, the differences in deformation mechanism of steels deformation mechanisms of steels with different grain structures but with similar elongations influenced the mode of fracture, a behavior that is governed by the change in austenite stability with grain size. The areal density of voids and their average diameter in the fracture surface also increased with increasing grain size, which ranged from 320 nm to 22 μm. & 2014 Elsevier B.V. All rights reserved.
Keywords: Austenitic stainless steel Grain size Deformation mechanism Fracture Austenite stability
1. Introduction The continued interest in advanced high-strength steels, including stainless steels, has led to the consideration of innovative processing routes. While grain refinement [1,2], microalloying addition [3–7], and severe plastic deformation [7,8] continue to represent a pragmatic approach to enhance the strength of existing metals and alloys, it is clear and widely agreed that the limitation of the mean path of gliding dislocation by the nanocrystalline structure constitutes the origin of limited ductility in high strength nanostructured alloys. There is also a significant interest in increasing the stability of austenite phase to delay the onset of necking and benefit from the strain-induced transformation of austenite to martensite to obtain high ductility. In order to increase the strength through grain refinement without compromising the ductility, we have recently developed an ingenious concept of phase reversion annealing to obtain nanograined/ultrafine-grained (NG/UFG) structures in metastable austenitic stainless steels. The concept involves extensive cold deformation (60–75%) of austenite to obtain strain-induced martensite. In the subsequent step, referred as phase-reversion annealing, martensite transforms back to austenite via diffusional
n
Corresponding author. Tel.: þ 1 915 747 8679; fax: þ 1 915 747 8036. E-mail address: [email protected] (R.D.K. Misra).
http://dx.doi.org/10.1016/j.msea.2014.12.052 0921-5093/& 2014 Elsevier B.V. All rights reserved.
or shear reversion mechanism [9–13]. Using this approach, NG/UFG structure was obtained having high yield strength and elongation of 900–1000 MPa and 30–40%, respectively [9–13]. These properties were superior to that of the coarse-grained (CG) counterpart that was characterized by yield strength typically in the range of 350– 450 MPa and elongation of the order of 40% [9–13]. In 1995, Christian and Mahajan [14], critically assessed the relationship between deformation twinning and fracture. In bcc metals and alloys, high stress concentration induced by deformation twins was recognized as the potential reason for initiation of fracture at twin–twin intersections. The fcc metals and alloys are ductile at room temperature. But, at sub-zero temperatures, significant amount of deformation occurred by twinning in austenitic stainless steels having low stacking fault energy (SFE), and as a consequence micro-cracking was observed at twin–twin intersections [14]. It was proposed that the twinning and fracture were independent phenomena. However, the above analysis by Christian and Mahajan dealt with conventional coarse-grained structure. To the best of our understanding there is no report on the fracture behavior in a single material processed using identical processing parameters that exhibits a distinct transition in deformation mechanism from strain-induced martensite formation to twinning, when the grain size changes from CG to NG/UFG. It is in this regard that the study described here is unique and provides new knowledge in nanocrystalline materials. In high strength NG/ UFG steel, deformation twinning contributed to the excellent
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ductility and high strain hardening rate, while in the low strength CG steel, the high ductility and strain hardening ability were associated with strain-induced martensite. Interestingly, the differences in the deformation mechanism of CG and NG/UFG steels influenced the fracture behavior. Thus, the objective of the study described here is to understand the interplay between grain size and deformation mechanism as they relate to the fracture behavior in austenitic stainless steel from the CG to NG regime.
2. Experimental procedure The experimental steel was a commercial Type 301LN austenitic stainless steel of 1.5 mm thickness with a nominal composition (in wt%) of Fe–0.017C–0.52Si–1.3Mn–17.3Cr–6.5Ni–0.15Mo–0.15N. Samples of stainless steel strips were cold-rolled in a laboratory rolling mill to 62% reduction ( 0.6 mm thick) via a number of passes and subsequently reversion-annealed in the temperature range of 700–900 1C for 10–100 s in a Gleeble 1500 thermomechanical simulator to obtain different grain sizes from NG to CG regime. The reversion annealing experiments were carried out on specimens of dimensions 120 mm 25 mm cut from the cold rolled samples. The experimental details are given elsewhere [9–13]. The grain structure was examined in a transmission electron microscope (TEM) operated at 120 kV. Keeping in view the grain size distribution, the weighted average grain size dw was determined [15]. Here, about 100 grains
were distributed in bins of 250 nm (0.25 μm) in size. A bin of 250 nm was so selected in order to optimize the statistical data. A small bin size is expected to result in poor statistical accuracy, while a large bin size may mask the effect of small grains. Thus, an optimum bin size of 250 nm (0.25 μm) was selected, keeping in view the grain size range of samples. Denoting the number of grains in the ith bin as ni and dividing it by the total number of grains, N, the weight of the ith bin is [15]: wi ¼
ni N
ð1Þ
Table 1 Tensile properties of phase reversion-induced austenitic stainless steel with different grain size and average distance between striations measured from the scanning electron fractograph. Striations were absent in the CG structure. Weighted average
Average yield Average strength (MPa) elongation (%)
Distance between striations (μm)
768 722 667 350
3.2 6.1 8.2 –
grain size, dw
NG/UFG SMG FG CG
320 nm 757 nm 2132 nm 22 mm
34 38 41 40
Fig. 1. (a–c) TEM micrographs of phase reversion annealed 301LN type austenite stainless steel with varying grain size from NG/UFG regime to fine-grained (FG) regime and (d) light micrographs of CG steel. The average weighted grain size dw was determined from a number of micrographs and is indicated on each of the micrographs. NG/UFG: nanograined/ultrafinegrained, SMG: sub-micron-grained, FG: fine-grained, and CG: coarse-grained steels (adapted from Ref. [13]).
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Fig. 2. Representative bright field transmission electron micrographs of (a, b) NG/UFG, (c, d) SMG, (e, f) FG and (g, h) CG structures illustrating tensile strain-induced deformation structure.
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Moreover, the square root of the areal mean of ni grains in the ith bin gives the average grain size, di , for the ith bin. Knowing di and wi, the weighted average grain size of the sample is calculated by [15] N
dw ¼ ∑ w i di i¼1
ð2Þ
The mechanical properties of reversion-annealed austenitic stainless steel were determined by tensile testing samples machined to a profile of 25 mm 25 mm with 20 mm gage length. They were tested at a cross-head speed of 0.016 mm/s up to strain of 0.03, beyond which it was increased to 0.062 mm/s. The corresponding average engineering strain rates were 0.00075/s and 0.003/s, respectively. Deformation-induced structure was examined by preparing TEM foils from samples deformed to different levels of tensile strain (2%, 10%, and 20%), prior to fracture. The sample area close to the highly stressed region within the gage length was used for the preparation of electron transparent foils. The specimens were examined in a TEM (Hitachi H7600) operated at 120 kV. Thin foils were prepared by twin-jet
electropolishing of 3 mm disks, punched from the specimens, using a solution of 10% perchloric acid in acetic acid as electrolyte. A number of foils were examined for each experimental condition. On the other hand, the fractographic features of the samples tensile tested until fracture was examined in a scanning electron microscope (JEOL-6300FV SEM). The voids in the digital images of the fracture surface were selected and painted black using Adobe Photoshops software, and then the diameter of voids were estimated using a commercial image processing software. The software had provision for quantitative analysis, such as average diameter of voids, frequency of voids of a particular size and average number density of voids. A number of fractographs were analyzed to arrive at an average value of the above parameters.
3. Results Optical and transmission electron (TEM) micrographs describing the grain structure obtained via different temperature–time combination are revisited in Fig. 1 [13]. The different grain sizes are referred to as nanograined/ultrafine-grained (NG/UFG), submicron grained (SMG), fine-grained (FG) and coarse-grained (CG).
Fig. 3. (a–c, e) Scanning electron fractographs at different magnifications showing fracture surface of tensile specimen of NG/UFG steel tested to fracture. The river-like markings and striations are marked by arrows. Note interconnected voids just beneath the striations (d, f). Line-up of voids are more apparent after image processing of figures (c, e) using a commercial software.
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Their mechanical properties are summarized in Table 1. The weighted average grain size of CG steel was 22 mm, while that of the smallest grain size NG/UFG steel (cold rolled to 62% reduction and annealed at 800 1C for 10 s) comprised of predominantly nanograins (dia 100 to 200 nm) and ultrafine grains (dia 200 to 500 nm), with the weighted average grain size dw of 320 nm. The NG/UFG material showed a considerable increase in yield strength (more than twice that of the CG sample), without any significant decrease in tensile elongation. 3.1. Microstructural evolution during tensile deformation It is important to first briefly describe the structural evolution during tensile straining, prior to describing the fractographic features. Representative TEM micrographs illustrating microstructural evolution as a function of selected strain for different grain sizes are presented in Fig. 2. In the NG/UFG structure, there were already numerous stacking faults (SF) at low strain (ε ¼0.02, figure not shown here) and extended stacking faults in two systems intersected one another, and dislocations were inhibited by stacking faults. With increase in strain (ε ¼0.1), mechanical twins of nanoscale thickness were present. In some grains, twins grew in
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different directions and mutually intersected one another (Fig. 2a). Dislocation glide during plastic deformation is also inhibited by twin boundaries. At appreciably higher strain (ε ¼0.2), there was an increase in twin density such that the twins organized in bundles (Fig. 2b). The bundles in some cases were 300 nm large. The diffraction pattern confirmed the presence of deformation twins. These deformation twins were envisaged to be formed by the successive emission of Shockley partial dislocations from the same grain boundary on (111) plane [16]. A detailed discussion on the interplay between grain structure and deformation mechanisms is discussed elsewhere in recent publications [11,12]. Fig. 2c and d summarizes the representative TEM micrographs of the deformation processes associated with tensile straining of SMG steel. The main microstructural features were formation of twins with different growth directions which mutually intersected each other (ε ¼0.1), (Fig. 2c). At high strain (ε ¼ 0.2), twins intersected each other, separating a typical grain into many small regions (Fig. 2d). Some of the twins were organized in bundles. We now describe the behavior of phase reversion annealed FG steel in comparison to NG/UFG and SMG structures. In FG steel, with an average grain size of 2.1 μm, besides SF, dislocations and twins, nucleation of strain-induced bcc α0 -martensite was
Fig. 4. (a–c, e) Scanning electron fractographs at different magnifications showing fracture surface of tensile specimen of SMG steel tested to fracture. The river-like markings and striations are marked by arrows. Note interconnected voids just beneath the striations (d, f). Line-up of voids are more apparent after image processing of Figures (c, e) using a commercial software.
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detected. At ε ¼ 0.1, twins and strain-induced α0 -martensite at shear bands were present simultaneously (Fig. 2e and f). The deformation mechanism in the FG structure was a combination of both twinning and strain-induced martensite. The deformation structures for the CG structure are presented in Fig. 2g and h. A large number of straight martensite laths nucleated at shear bands and grew in different directions at high strain (ε ¼0.2) (Fig. 2g). Martensite laths intersected each other and separated a typical grain into many small regions of quadrilateral shape. The diffraction pattern analysis (Fig. 2g) indicated bcc martensite (α0 -martensite). The α0 -martensite laths are barriers to dislocation motion. Meanwhile, the martensite transformation occurred by repeated nucleation of new α0 -lath-like embryos and coalescence of such embryos resulting in the formation of a wider lath, such that the thickness of the packet increased to as high as 400 nm. Thus, there was a distinct transition in the deformation mechanism from twinning in the NG/UFG structure to straininduced martensitic transformation in the CG structure. The transition occurred in FG steel, when combinations of both twinning and strain-induced martensite were observed. In conclusion, both twinning and strain-induced α0 -martensite are effective strain hardening mechanisms that inhibit strain
localization and are responsible for the observed high ductility. Twinning was a major factor that contributed to excellent ductility in ‘high strength’ NG/UFG structure, where as in the ‘low strength’ CG structure, the high ductility resulted from the strain-induced martensite formation. This change in the deformation mechanism is attributed to an increase in the stability of austenite with decrease in grain size (Section 4). 3.2. Fracture characteristics We now describe the fractographic features of the tensile tested specimens elucidating the fracture characteristics of the steel with different grain sizes. There were striking differences in the nature of fracture (Figs. 3–6) associated with steel specimens of different grain sizes, in particular for NG/UFG and CG steels, even though they were all characterized by a nearly similar tensile elongation-to-fracture (Table 1). Two kinds of typical fracture patterns were observed as a consequence of the variation in grain size. The fracture surface of NG/UFG steel (Fig. 3a) appeared relatively flat, but at higher magnification river-like markings or striations (marked by white arrows in Figs. 3b and c) that were nearly parallel to one another were observed. High magnification
Fig. 5. (a–c, e) Scanning electron fractographs at different magnifications showing fracture surface of tensile specimen of FG steel tested to fracture. The river-like markings and striations are marked by arrows. Note interconnected voids just beneath the striations and also the presence of microvoid coalescence type of fracture (c, e). Image processing of Figures (c, e) using a commercial software is presented in (d, f).
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Fig. 6. (a–c, e) Scanning electron fractographs at different magnification showing fracture surface of tensile specimen of CG steel tested to fracture. (d, f) Voids are more apparent after image processing of figures (c, e) using a commercial software.
fractographs indicated line-up of voids (Figs. 3c and e) interconnected side by side just beneath the striations and represented a unique fracture surface that does not appear to have been documented in the literature. The line-up of voids was more apparent after image processing of SEM fractographs, using a commercial image processing software, and is presented in Fig. 3d and f. Figs. 4 and 5 summarize the representative SEM micrographs of the fracture surface of SMG and FG steels tensile tested to fracture. The characteristics of SMG steel were similar to NG/UFG steel. But in FG steel, besides river-like markings or striations, microvoid coalescence-type of fracture typical of dimple rupture was also present. This is not surprising because FG steel was characterized by two deformation mechanisms, twinning and strain-induced martensite (Fig. 2e and f). In contrast to the NG/UFG steel, the fracture surface of CG steel that experienced strain-induced martensitic transformation during tensile deformation was microvoid coalescence-type of fracture (Fig. 6), which is typically observed in ductile metals and alloys. The areal density of voids increased from 0.32 μm 2, 0.40 μm 2, 0.51 μm 2 and 0.75 μm 2 with increase in grain size from NG/UFG, SMG, FG and CG, respectively (Fig. 7a). The size of
voids was measured from several SEM micrographs for each sample. The size distribution of voids with different grain sizes is presented in Fig. 7c, which depicts that the distribution of void size became uniform with decreasing grain size. The average diameter of the voids increased with an increase in grain size from NG/UFG regime to CG regime (Fig. 7b). Similarly, from the SEM micrographs, the average distance between the striations was measured and is presented in Table 1. It may be seen from Table 1 that the spacing between striations increased with increase in grain size from NG/UFG to FG structure. This is attributed to a decrease in twin density with the increase in grain size. In the quest to understand the aforementioned characteristics, the broken tensile specimens of the NG/UFG and CG steels were lightly polished, etched, and the microstructure just below the fracture surface was examined in an SEM. It was concluded that in NG/UFG steel, the voids in the austenite matrix nucleated preferentially along the twin boundaries (Fig. 8). We envisage the following fracture mechanism or process associated with twinning-induced ductile fracture in the NG/UFG austenitic steel. During plastic deformation beyond the necking stage, microvoids grew longitudinally along the twin boundaries with increase in strain. This was accompanied by deformation of the region
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Fig. 7. Void size distribution of phase reversion-annealed austenitic stainless steels processed to obtain different grain size from NG/UFG to CG regime. (a) Areal density of the voids, (b) mean size of voids, (c) void size distribution, and (d) spacing between the striations (striations were absent in CG steel).
Fig. 8. Low and high magnification scanning electron micrographs illustrating voids just beneath the fracture surface in NG/UFG steel. The voids are marked by arrows.
surrounding the twins and microvoids resulting in the growth and coalescence of voids that apparently led to ductile fracture. Microvoid nucleation and growth in the NG/UFG steel is governed by the plastic strain, which in turn is dictated by the density of twins, and their interactions with dislocations, given that the twin boundaries are barriers to movement of dislocations. The aforementioned process governs the ultimate mechanical properties of NG/UFG steels, such that there is a relationship between the mechanical properties and the distribution and nature of voids in the twinning-induced ductile fracture surface. In a manner similar to NG/UFG steel, the microstructural examination just below the fracture surface of CG steel in SEM
after polishing and etching of the fracture surface indicated fine platelets of strain-induced martensite that acted as potential nucleating sites for voids (Fig. 9).
4. Discussion Combining the microstructural evolution during tensile deformation and mode of fracture, it is concluded that the intriguing differences between twinning-induced deformation mechanism and associated striated fracture behavior with line-up of voids beneath the striations in the NG/UFG steel and strain-induced
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Fig. 9. Scanning electron micrographs (a, b) of the surface just beneath the fracture surface illustrating nucleation of voids at martensite laths and (c, d) post-deformation microstructure showing tensile deformation-induced martensite in CG steel.
martensite formation associated with microvoid coalescence-type fracture in the CG steel, are related to the grain size effect. This is a significant and new finding. Based on the observations presented in Figs. 2–6, the deformation clearly influenced the fracture behavior of the respective steels and there was a clear distinction between the deformation structure and fractographic features in NG/UFG and CG steels. Deformation twinning is an effective and active deformation mechanism in NG/UFG steel and strain-induced α0 -martensite in the CG austenitic stainless steel. Both these mechanisms are effective strain hardening mechanisms and prevent strain localization and thereby enhance ductility. This behavior can be described in terms of the interplay between grain size and austenite stability. The observation that fracture behavior is governed by the deformation mechanism as a function of grain size is interesting because deformation twinning in the NG/UFG structure and strain-induced martensite in the CG structure are somewhat similar microstructurally, i.e., both of them involve diffusionless shear of a constrained plate-shaped region in the parent crystals. The deformation mechanism must be related to the enhanced contribution of high density of grain boundaries leading to increased strength of NG/UFG austenite that inhibits martensite formation. Grain size governs the thermal stability of austenite [17–19], but the influence on the mechanical stability of austenite is unclear. It is accepted that the transformation of fcc austenite to bcc martensite introduces anisotropic strain in adjacent untransformed austenite. The near uniform distribution of transformation strain requires several multi-variant transformations to occur simultaneously within an austenite grain for minimization of total strain energy [19]. However, in the event that the austenite grain is smaller than the martensite lath, as applicable in our case, then the probability of several variants of martensite to participate simultaneously within an austenite grain is significantly minimized because of reduced space. Furthermore, a single variant is preferred for deformation-induced martensite transformation in
NG/UFG structure because in a tensile test the deformed specimen has a texture where 〈101〉α0 direction is parallel to the tensile direction [19]. Thus, austenite can be anticipated to transform via the single variant mode but the reduction in the strain energy due to martensitic transformation in NG/UFG austenite cannot be attained, as outlined below. The mechanism of grain refinement-induced austenite stabilization can be explained in terms of the physical energy associated with austenite-to-martensitic transformation, involving Eqs. 3 and 4 [17]. If austenite transforms to martensite via single variant mode, the increase in elastic strain energy is given by [17,20]: ΔEv ¼ 0:5E1 ε21 x=d
2
þ ð0:5E2 ε22 þ 0:5E3 ε23 Þ x=d
ð3Þ
where E and ε are Young's modulus and elastic strain in each lattice plane, x is the thickness of martensite plate and lattice strain is elastically accommodated over the space of austenite grain (grain size: d). Inserting Young's modulus and strain in Eq. (3), the increase in elastic strain energy is given by ΔEv ¼ 1276:1 x=d
2
þ 562:6 x=d
ð4Þ
Thus, from Eq. (4), for average CG size of 22 mm, ΔEv is 6 MJ/m3 and for NG/UFG structure, ΔEv increases significantly to 850 MJ/m3, which decreases the ability to nucleate martensite with a decrease in grain size. We conclude that in the NG/UFG structure, multi-variant transformation is difficult and the transformation of austenite to strain-induced martensite transformation is largely suppressed, leading to an increase in the propensity for twinning with decrease in the grain size. Under these circumstances, the twinning-induced deformation mechanism and corresponding fracture behavior exhibited typical characteristics of striations or river-markings with line-ups of connected voids, which provided the observed high ductility in the NG/UFG austenitic stainless steel.
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5. Conclusions We have elucidated here the interplay between grain size and deformation mechanisms as they relate to the fracture behavior in 301LN Type austenitic steel from the NG/UFG to CG regime. This was accomplished through a combination of post-mortem TEM analysis of tensile deformed samples and SEM observations of the fracture surface. The differences in microstructural evolution during tensile deformation strongly influenced the fracture mechanism. Thus, in contrast to the conventionally wellestablished strain-induced martensite transformation contributing to the high ductility in the low-strength CG austenitic stainless steel, deformation twinning has played a vital role in contributing the corresponding excellent ductility to the NG/UFG version of the steel, and hence is characterized with a significantly new fracture mechanism. Interestingly, the difference in the deformation behavior of NG/UFG and CG steels with similar elongation-to-fracture was reflected in the mode and mechanism of fracture. In the low strength CG steel, the fracture occurred through traditional microvoid-coalescence, while in the high strength NG/UFG steel the fracture was characterized by line-up of small voids just beneath the striations or river markings. The differences in deformation mechanism that influenced the mode of fracture as a function of grain size from NG/UFG to CG regime is attributed to a change in austenite stability with grain size. Acknowledgments The authors (X.L. Wan, V.S.A. Challa and R.D.K. Misra) gratefully acknowledge support from National Science Foundation, USA through Grant number DMR #261883 (Program Manager, Dr. Eric Taleff). Discussion with Professor P. Rama Rao (ARC International,
India) and Professor Warren Garrison (CMU, USA) are gratefully acknowledged. References [1] E. Ma, Scr. Mater. 49 (2003) 663–668. [2] C.C. Koch, Scr. Mater. 49 (2003) 657–662. [3] R.D.K. Misra, S.W. Thompson, T.A. Hylton, A.J. Boucek, Metall. Mater. Trans. A 32 (2001) 745–760. [4] R.D.K. Misra, K.K. Tenneti, G.C. Weartherly, G. Tither, Metall. Mater. Trans. A 34 (2003) 2341–2351. [5] R.D.K. Misra, H. Nathani, J.E. Hartmann, F. Siciliano, Mater. Sci. Eng. A 394 (2005) 339–352. [6] S. Shanmugam, R.D.K. Misra, J.E. Hartmann, S. Jansto, Mater. Sci. Eng. A 441 (2006) 215–229. [7] R. Song, D. Ponge, D. Rabbe, R. Kasper, Acta Mater. 53 (2005) 4881–4892. [8] F.J. Humphreys, P.B. Prangnell, J.R. Bowen, A. Gholina, C. Harris, Philos. Trans. R. Soc. Lond Ser. A 357 (1999) 1663–1680. [9] R.D.K. Misra, S. Nayak, S. Mali, J.S. Shah, M.C. Somani, L.P. Karjalainen, Metall. Mater. Trans. A 41 (2010) 2162–2174. [10] M.C. Somani, P. Juntunen, L.P. Karjalainen, R.D.K. Misra, A. Kyrolainen, Metall. Mater. Trans. A 40 (2009) 729–744. [11] V.S.A. Challa, X.L. Wan, M.C. Somani, L.P. Karjalainen, R.D.K. Misra, Mater. Sci. Eng. A 613 (2014) 60–70. [12] R.D.K. Misra, V.S.A. Challa, P.K.C. Venkatasurya, Y.F. Shen, M.C. Somani, L. P. Karjalainen, Acta Mater. 84 (2015) 339–348. [13] R.D.K. Misra, P.K.C. Venkatsurya, M. Somani, L.P. Karjalainen, Metall. Mater. Trans. A 43A (2012) 5286–5297. [14] J.W. Christian, S. Mahajan, Prog. Mater. Sci. 39 (1995) 1–157. [15] S. Rajasekhara, P.J. Ferreira, L.P. Karjalainen, A. Kyröläinen, Metall. Mater. Trans. A 38A (2007) 1202–1210. [16] S. Mahajan, Scripta Mater. 68 (2013) 95–98. [17] S. Takaki, K. Fukunaga, J. Syarif, T. Tsuchiyama, Mater. Trans. 45 (2004) 2245–2251. [18] E. Jimenez-Melero, N.H. van Dijk, L. Zhao, J. Sietsma, S.E. Offerman, J.P. Wright, S. van der Zwaag, Scr, Mater. 56 (2007) 421–424. [19] Y. Matsuoka, T. Iwasaki, N. Nakada, T. Tsuchiyama, S. Takaki, ISIJ Int. 53 (2013) 1224. [20] S. Yamamoto, K. Asabe, M. Nishiguchi, Y. Maebara, Tetsu-to-Hagané 82 (1996) 771–776.