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A study of the surface deformation behaviour at grain boundaries in an ultra-low-carbon steel
Acta Materialia 51 (2003) 5375–5384 www.actamat-journals.com
A study of the surface deformation behaviour at grain boundaries in an ultra-low-carbon steel Dilip Chandrasekaran a,∗, Mikael Nyga˚rds b a
Department of Materials Science and Engineering, Royal Institute of Technology, Brinellv 23, SE-100 44, Stockholm, Sweden b Department of Solid Mechanics, Royal Institute of Technology, SE-100 44, Stockholm, Sweden Received 1 April 2003; received in revised form 1 April 2003; accepted 12 July 2003
Abstract Tensile specimens of ultra-low-carbon ferritic steel with two different grain sizes were studied by atomic force microscopy (AFM) and electron backscatter diffraction (EBSD) after different plastic strains up to 10%. Different parameters, such as the change in surface roughness and the change in misorientation with strain, were evaluated. There was good agreement between the AFM and EBSD results. Both the surface roughness and the misorientation measurements on the surface showed a linear increase with the overall strain, an obvious consequence being that both AFM and EBSD are suitable for characterising the surface deformation behaviour. The results are discussed with respect to the difference in grain size in the samples and the implication on the strain hardening behaviour. 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Atomic force microscopy; EBSD; IF steels
1. Introduction Grain boundaries play an important role in the deformation behaviour of polycrystals. Although the literature on the topic is extensive, the effect of grain boundaries on the propagation of plastic deformation is still not fully understood. This is of particular interest in light of the many attempts to include physically based length scales into crystal plasticity models. Recently, continuum models that account for the existence of strain gradients in
Corresponding author. Tel.: +46-8-790-8289; fax: +46-8203107. E-mail address: [email protected] (D. Chandrasekaran). ∗
microstructure have increased in popularity [1–4]. One of the main difficulties in the development of these types of models is the lack of experimental measurements of gradients and other inhomogenities at the grain level. A great deal of experimental work in the past has been concentrated towards the characterisation of dislocation cell structures, with X-ray and TEM, at comparatively large strains [5]. At present, there are a number of techniques available that may be used, at least indirectly, to study local strain fields e.g. atomic force microscopy (AFM) [6–11], digital speckle methods [12] and electron backscatter diffraction (EBSD) [13–15]. All these are surface techniques, in contrast to bulk methods such as TEM and X-ray, and consequently they reveal the deformation behaviour of
1359-6454/$30.00 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/S1359-6454(03)00394-X
D. Chandrasekaran, M. Nyga˚rds / Acta Materialia 51 (2003) 5375–5384
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Table 1 Composition of the ultra-low-carbon steel in wt% C
Mn
N
Ni
P
S
Ti
V
Al
Cr
Cu
Mo
Fe
0.002
0.14
0.002
0.04
0.008
0.005
0.09
0.004
0.039
0.02
0.01
0.001
Bal.
a free surface. By combining several different techniques, it is possible to get a more complete picture of the deformation behaviour. In this work, AFM measurements have been combined with EBSD measurements to collect information on both surface topology and crystal rotations. AFM has been used on numerous occasions to study deformation characteristics qualitatively and quantitatively; this includes the study of slip lines, extrusions and general surface roughness. The advantages of the technique are several, for instance sample preparation is straightforward and
fairly large areas can be covered, in comparison with, for example, TEM. As has been shown in earlier work [16], AFM is a good tool to follow the deformation characteristics at the grain level. It is also well suited for in situ studies of tensile deformation [8,10]. Moreover, AFM studies also show that the surface roughness increases with increasing strain, which can be seen as an indication of the increase in dislocation activity. One key point is to understand if the roughness increase as measured with AFM is due to significant outof-plane displacement or if there is instead a large
Fig. 1. ODFs describing the global texture for the fine-grained (a) and the coarse-grained (b) sample with the ⬍1 1 1⬎//ND. The γ-fibre is seen in the f2 = 45° cross-section.
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this paper. Lately, there has been an interest in using EBSD measurements to follow changes in misorientations at relatively small strains, and this is also the focus of the present work. Earlier work shows that the average misorientation increases with strain [14,17], indicating that the change in misorientation is proportional to change in the total dislocation density. In this study, we will characterise the evolution of plastic deformation in an ultra-low-carbon steel, at relatively small strains, with AFM and EBSD. The main objective is to understand the role of grain boundaries in the propagation of plastic deformation, in materials showing homogenous yielding on a macroscopic scale. Fig. 2. Stress–strain curves for the two samples: CG (coarse grained), FG (fine grained).
amount of grain rotation associated with deformation. Another important issue is how well AFM measurements correlate with EBSD measurements. EBSD is today a well-established tool for quantitative and qualitative characterisation of deformed and recrystallised microstructures and is often applied to improve the understanding of recrystallisation and deformation characteristics. The orientation imaging maps produced from such measurements provide a wealth of information. The technique is useful not only to study the change of average orientations globally, but also to follow orientation changes within individual grains. Intra-grain misorientations are of interest because they can be used to understand and quantify the storage of dislocations and the inhomogeneous straining occurring within grains. This parameter will be discussed in more detail later in Table 2 Settings used in the EBSD measurements Name
Sample
EBSD step size (µm)
Average grain size (µm)
CG CG CG FG FG
Coarse grained Coarse grained Coarse grained Fine grained Fine grained
2.5 2.5 2.5 1 and 0.5 1 and 0.5
60 60 60 14 14
1 2 3 2 3
2. Experimental 2.1. Material characterisation The material used in this study was a titanium alloyed ultra-low-carbon (ULC) steel with the composition as presented in Table 1. The delivered samples were taken from sheet cold rolled to 10 different degrees of deformation, up to 2.3 in effective plastic strain. Tensile coupons were prepared from the cold rolled samples and subsequently annealed, in order to obtain material with different recrystallised grain sizes. The samples used in this study had been deformed to an effective plastic strain of 27% and 210%, respectively, followed by subsequent annealing, for 30 min, at 740 and 660 °C, respectively. Average grain sizes in the samples were evaluated from the EBSD measurements with the sample denoted as CG (coarsegrained) having a grain size of 60 µm and the sample denoted as FG (fine-grained) having a grain size of 14 µm. This corresponded reasonably well with line intercept measurements. The microstructure of the material revealed a fully recrystallised ferritic structure. Global textures were evaluated from the EBSD results and showed a typical recrystallisation texture, with the ⬍1 1 1⬎ direction parallel to the normal direction, as shown in the ODFs in Fig. 1. Titanium alloyed IF steels are known to exhibit a strong γ-fibre (seen in the f2 = 45° cross-section in Fig. 1) texture after recrystallisation, causing an increase in the planar ani-
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sotropy (usually described by the Lankford coefficient or r-value) [18]. The texture was comparatively strong for the fine-grained specimen and relatively weak for the coarse-grained one. From the above result, one can expect the finegrained specimen to show a more anisotropic mechanical behaviour. 2.2. Experimental set-up After various polishing stages, where the finest was with 1 µm diamond paste, the samples were electro-polished in a mixture of perchloric acid and acetic acid at 10 V for 2–3 min. This final step
was to remove all traces of surface deformation from the earlier polishing stages. The electro-polishing also resulted in a slight etching of the samples. The dimensions of the flat tensile specimens were 30 × 6 mm, with a thickness of 0.75 mm for the fine-grained sample and 3.65 mm for the coarse-grained sample. A number of different areas were then marked with micro-indents in each sample, in order to be able to identify and follow the grains after each deformation step. The samples were then characterised in contact mode AFM (D3000 Nanoscope from Digital Instruments with an silicon nitride tip) and in a LEO Gemini 1530 FEG-EBSD before the tensile testing.
Fig. 3. Change in orientation with strain, colour coding defined by Euler angles, for (a) CG 3 (after 0.2%), (b) FG 3 (after 0.2%), (c) CG 3 (after 10%), (d) FG 1 (after 10%). Misorientation maps after 10% strain of (e) CG 3, (f) FG 1.
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local and global information were evaluated. Local information included, for example, the change in surface profile and crystal orientation near specific grain boundaries. Global information included, for example, the standard deviation in surface roughness and change in mean intra-grain misorientation, with strain, for a larger number of grains. Two different regions were studied in sample FG, while three different regions were studied in sample CG. 3.1. EBSD results Fig. 4. Change in average intra-grain misorientation with strain for the different regions in the two samples (attention should be paid to the relative change in average intra-grain misorientation, not absolute values, as there is a certain spread in the individual orientation measurements).
The experimental procedure was the following: the samples were tensile tested at a constant strain rate of 3 × 10⫺3 s⫺1, whereupon the testing was interrupted at three different strain levels, as shown in Fig. 2. After unloading, marked areas were identified and scanned with AFM and EBSD and this was repeated for each strain level. The resolution of the scans was adapted to the grain size in the samples, with larger areas scanned in the case of the coarse-grained specimen. In the AFM study, initially relatively large areas1 (75 × 75 µm) were scanned, followed by scans of smaller areas (down to 20 × 20 µm), in order to obtain a high enough resolution in the measurements. The step size in the EBSD scans was varied between 0.5, 1 and 2.5 µm depending on the grain size, in order to cover a large enough number of grains in each area. The settings used in the EBSD measurements are presented in Table 2.
3. Results The results from the AFM and EBSD measurements provide both quantitative and qualitative information. For the specific areas studied, both 1 75 × 75 µm is a large scan size for the AFM, but not a large area compared to the grain size.
The EBSD scans covered a comparatively large number of grains in the fine-grained sample and a fewer number in the coarse-grained sample. The EBSD data were analysed by the HKL Channel 5 software, which was also used to evaluate the different parameters presented in this paper. More on the possibilities and limitations of the EBSD technique can be found in the excellent review by Humphreys [19]. From the EBSD measurements, crystal orientations at each point, represented by the three Euler angles, were evaluated. With suitable definitions, the microstructure can be represented by a colour coding system. The different colours of the grains represent different combinations of Euler angles, as illustrated in Figs. 3a–d. In these figures, the Euler angles for one region in each sample (CG 3 and FG 1) have been plotted, after 0.2% strain and 10%, respectively, thus giving a picture of the absolute crystal orientations at each strain level. In the evaluation, neighbouring points showing a difference in orientation larger than 10° were defined as grain boundaries and coloured black, and similarly neighbouring points with a difference in orientation larger than 2° were defined as sub-grain boundaries and coloured white. It can be observed in Fig. 3 that after 0.2% strain, orientations within grains are almost uniform. After 10% strain, however, there is an increase in the occurrence of other orientations (colours) within grains. This is especially visible near certain grain boundaries, indicating rotations within grains. Also, a large increase in the number of sub-grain boundaries can be seen at the highest strain. This indicates an increased rotation within grains, leading to
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inhomogeneous deformation. These do not, however, cover entire grains but instead are predominantly present in the vicinity of grain boundaries and triple junctions, in other words, in regions that are strongly stressed and where the generation of dislocations can be expected to be larger. Another interesting parameter that was evaluated from the EBSD measurements was intra-grain misorientations. This was defined as the deviation from the average orientation within a grain. Thus, the intra-grain misorientation can be seen as a stat-
istical measure of the reorientation occurring within grains. This parameter was evaluated after each strain level, and the change in intra-grain misorientation can be seen as a measure of dislocation storage. Thus, it should be a good measure of the local deformation behaviour. This is illustrated in Fig. 3e and f, where intra-grain misorientation maps, of the same regions as earlier, are shown after 10% strain. The grains have been colour coded according to the average intra-grain misorientation value within each grain, giving each
Fig. 5. Typical AFM scan of regions in the different samples after different strains: (a) CG 3 (after 0.2%), (b) CG 3 (after 4%), (c) CG 3 (after 10%), (d) FG 1 (after 4%).
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grain a uniform colour. It can be observed that a number of grains in the fine-grained sample show intra-grain misorientations larger than 5° and are thus coloured grey. The average intra-grain misorientation for each region in the respective sample was also evaluated quantitatively at each strain level. This is shown in Fig. 4, where the average intra-grain misorientation shows a linear increase with macroscopic strain. This further emphasises that the intra-grain misorientation can be seen as a measure of local deformation. 3.2. AFM results The same areas as in the EBSD study were identified and scanned in the AFM measurements. In the case of the coarse-grained sample, CG, exactly the same grains could easily be identified and in this case, e.g. individual grains could be analyzed both with AFM and EBSD. In the case of the fine-grained sample, FG, there was a difficulty in identifying the same grains although the same regions were scanned. This was partly because of the electro-polishing, which affected the two specimens differently, and partly because the number of grains in sample FG was much larger, thus making it more difficult to identify individual grain features. A typical example of the information available from AFM measurements is shown in Fig. 5. Areas in the fine-grained and coarse-grained samples are shown here before and after different amounts of strain. In Fig. 6, roughness profile measurements over the lines shown in the figure are also displayed. As can be observed, most changes occur in the last deformation step, as illustrated by slip lines at grain boundaries after 10% strain (Fig. 5c). The roughness profiles (Fig. 6a and b) show an increase with strain and also a smoothening of gradients with increasing strain. The different areas examined by AFM were analysed and different parameters, such as the overall roughness change with strain, were evaluated. The roughness profiles over grains in the different areas were analysed and compared with corresponding EBSD measurements. One measure of the roughness is the standard deviation of all height measurements within a region. This is shown in Fig. 7, where the variation of out-of-plane dis-
Fig. 6. Variation of surface profiles, at different strains, over the corresponding lines shown in previous AFM scans: (a) CG 3 and (b) FG 1.
Fig. 7. Change in overall roughness with strain, represented by the standard deviation, sz, for the different regions in the two samples.
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placements, for different regions in the two samples, has been plotted. The standard deviation, sz, increases fairly linearly with strain. Other features that can be visualised with AFM are individual slip lines, which can be measured quite accurately. In Fig. 8a, an overview of a deformed region in the sample FG is shown after 10% plastic strain, where slip lines can clearly be seen. At higher magnifications, as shown in Fig. 8b, the individual slip lines can be resolved and measured. The height of the individual slip lines can be assumed to correspond to the number of dislocations slipping on the slip plane. In this case, a step height of 50 nm (see Fig. 8c) corresponds
to roughly 200 individual dislocations, which can be seen as a measure of the accumulated strain.
4. Discussion Clearly, the EBSD and AFM observations give quite a consistent picture on misorientation and out-of-plane displacements. This seems to hold both on a global scale, as seen from a comparison of the standard deviation of the average intra-grain misorientation, sq, with the standard deviation of surface roughness, sz, shown in Fig. 10, and on a local scale, relative to an individual grain boundary, as
Fig. 8. AFM scan of region in the fine-grained (FG) sample showing the existence and evolution of slip lines after 10% strain. (a) Overview of deformed region, (b) magnification of slip lines seen in previous scan, (c) measurement of surface profile over slip lines as shown in (b).
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Fig. 9. Comparison between roughness profile and misorientation profile measured relative to a grain boundary. Grain boundary in CG 3: (a) after 4% strain, (b) after 10% strain, (c) Surface roughness profile measured with AFM along line in (a). (d) Misorientation measurement relative to grain boundary along line in (a).
shown in Fig. 9. In this figure, the misorientation profile is compared with the corresponding out-of-plane displacement. Both the misorientation and the surface roughness show a linear increase with strain (compare e.g. Figs. 4 and 7). The results indicate that there is a significant rotation within grains, with plastic deformation, which causes an increased surface roughness. Since both the misorientation and the surface roughness increase with strain, it is also an indication that out-of-plane rotation is the dominating feature. The results also indicate a good correlation between the surface behaviour and the bulk deformation behaviour. It should be noted though that all our measurements concern deformation of a free sur-
face and should therefore be interpreted with some caution, as the grains in the interior can be expected to behave differently. This point will be addressed in a separate study. The average intra-grain misorientation is quite sensitive to the minimum size of “allowed grains” from the EBSD measurements. For example, one single EBSD measurement point can hardly be accepted as a grain and has to be removed. In a statistical analysis of the EBSD data at 10% strain, all grains smaller than five pixel points were removed, and two interesting features appeared. First, both the average intra-grain misorientation and the standard deviation of the misorientation
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mation behaviour. Inhomogeneous features are more predominant in large grains although there are more grains in the fine-grained sample, with large intra-grain misorientations. This latter effect is perhaps due to the larger strain hardening in the fine-grained sample. It can also be concluded that significant out-of-plane rotation is consistent with plastic deformation at small strains. Acknowledgements
Fig. 10. Comparison of the overall surface roughness represented by sz, with the standard deviation of the average intragrain misorientation sq, for different strain levels.
measurements were larger for the fine-grained sample. This is consistent with the results presented in Fig. 3e and f, where only grains in the fine-grained sample showed intra-grain misorientations greater than 5°. Second, within each sample, the intra-grain misorientation was larger for large grains, compared to small ones. The latter observation is partly an artefact of the misorientation measurements but also indicates a greater tendency for intra-grain rotation and inhomogeneous yielding to occur within large grains in a sample. One possible explanation for larger misorientations in the fine-grained sample could be due to the extra strain hardening contribution from grain boundaries, in line with Ashby’s model [20] involving geometrically necessary dislocations. A consequence of this can be observed in the stress– strain curves, where the fine-grained sample initially, i.e. at strains lower than 1%, shows a steeper increase in stress.
5. Conclusions There is good agreement, both on a global and a local scale, between the AFM and EBSD measurements. Both the surface roughness and the misorientation increase linearly with strain. The surface behaviour thus reflects the bulk defor-
Financial support from the Swedish research foundation, SSF, through the Brinell Centre and from Gerhard von Hofstein foundation, to one of the authors, is gratefully acknowledged. Ms. Lena Ryde and Dr. L. Belova are thanked for their assistance with the EBSD and AFM measurements. Dr. B. Hutchinson is also thanked for valuable comments in the interpretation of the EBSD data. References [1] Nyga˚ rds M. Technical report, Department of Solid Mechanics, KTH, 2002. [2] Bassani JL. J Mech Phys Solids 2001;49:1983–96. [3] Needleman A. Acta Mater 2000;48:105–24. [4] Hutchinson JW. Int J Solids Struct 2000;37:225–38. [5] Ungar T, Mughrabi H, Ro¨ nnpagel D, Wilkens M. Acta Met 1984;32:333–42. [6] Harvey SE, Marsh PG, Gerberich WW. Acta Mater 1994;42:3493–502. [7] Brinck A, Engelke C, Kopmann W, Neuha¨ user H. Mater Sci Eng A 1997;239-240:180–7. [8] Tong W, Hector Jr LG, Weiland H, Wieserman LF. Scr Mater 1997;36:1339–44. [9] Cretegny L, Saxena A. Acta Mater 2001;49:3755–65. [10] Vinogradov A, Hashimoto S, Patlan V, Kitagawa K. Mater Sci Eng A 2001;319-321:862–6. [11] Man J, Orbrtlik K, Blochwitz C, Polak J. Acta Mater 2002;50:3767–80. [12] Wang YY, Chen DJ. Chiang, FP. Exp Tech 1993;17:30–2. [13] Zhu G, Mao W, Yu Y. Scr Mater 2000;42:37–41. [14] Fukoka C, Morishima K, Yoshizawa H, Mino K. Scr Mater 2002;46:61–6. [15] Balke P, Hosson JTMD. Scr Mater 2001;44:461–6. [16] Chandrasekaran D, Nyga˚ rds M. Mater Sci Eng A [submitted for publication]. [17] Wilkinson AJ. Scr Mater 2001;44:2379–85. [18] Hutchinson B, Artymowicz D. ISIJ Int 2001;41:533–41. [19] Humphreys FJ. J Mater Sci 2001;36:3833–54. [20] Ashby MF. Philos Mag 1970;21:399–424.
A study of the surface deformation behaviour at grain boundaries in an ultra-low-carbon steel Dilip Chandrasekaran a,∗, Mikael Nyga˚rds b a
Department of Materials Science and Engineering, Royal Institute of Technology, Brinellv 23, SE-100 44, Stockholm, Sweden b Department of Solid Mechanics, Royal Institute of Technology, SE-100 44, Stockholm, Sweden Received 1 April 2003; received in revised form 1 April 2003; accepted 12 July 2003
Abstract Tensile specimens of ultra-low-carbon ferritic steel with two different grain sizes were studied by atomic force microscopy (AFM) and electron backscatter diffraction (EBSD) after different plastic strains up to 10%. Different parameters, such as the change in surface roughness and the change in misorientation with strain, were evaluated. There was good agreement between the AFM and EBSD results. Both the surface roughness and the misorientation measurements on the surface showed a linear increase with the overall strain, an obvious consequence being that both AFM and EBSD are suitable for characterising the surface deformation behaviour. The results are discussed with respect to the difference in grain size in the samples and the implication on the strain hardening behaviour. 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Atomic force microscopy; EBSD; IF steels
1. Introduction Grain boundaries play an important role in the deformation behaviour of polycrystals. Although the literature on the topic is extensive, the effect of grain boundaries on the propagation of plastic deformation is still not fully understood. This is of particular interest in light of the many attempts to include physically based length scales into crystal plasticity models. Recently, continuum models that account for the existence of strain gradients in
Corresponding author. Tel.: +46-8-790-8289; fax: +46-8203107. E-mail address: [email protected] (D. Chandrasekaran). ∗
microstructure have increased in popularity [1–4]. One of the main difficulties in the development of these types of models is the lack of experimental measurements of gradients and other inhomogenities at the grain level. A great deal of experimental work in the past has been concentrated towards the characterisation of dislocation cell structures, with X-ray and TEM, at comparatively large strains [5]. At present, there are a number of techniques available that may be used, at least indirectly, to study local strain fields e.g. atomic force microscopy (AFM) [6–11], digital speckle methods [12] and electron backscatter diffraction (EBSD) [13–15]. All these are surface techniques, in contrast to bulk methods such as TEM and X-ray, and consequently they reveal the deformation behaviour of
1359-6454/$30.00 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/S1359-6454(03)00394-X
D. Chandrasekaran, M. Nyga˚rds / Acta Materialia 51 (2003) 5375–5384
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Table 1 Composition of the ultra-low-carbon steel in wt% C
Mn
N
Ni
P
S
Ti
V
Al
Cr
Cu
Mo
Fe
0.002
0.14
0.002
0.04
0.008
0.005
0.09
0.004
0.039
0.02
0.01
0.001
Bal.
a free surface. By combining several different techniques, it is possible to get a more complete picture of the deformation behaviour. In this work, AFM measurements have been combined with EBSD measurements to collect information on both surface topology and crystal rotations. AFM has been used on numerous occasions to study deformation characteristics qualitatively and quantitatively; this includes the study of slip lines, extrusions and general surface roughness. The advantages of the technique are several, for instance sample preparation is straightforward and
fairly large areas can be covered, in comparison with, for example, TEM. As has been shown in earlier work [16], AFM is a good tool to follow the deformation characteristics at the grain level. It is also well suited for in situ studies of tensile deformation [8,10]. Moreover, AFM studies also show that the surface roughness increases with increasing strain, which can be seen as an indication of the increase in dislocation activity. One key point is to understand if the roughness increase as measured with AFM is due to significant outof-plane displacement or if there is instead a large
Fig. 1. ODFs describing the global texture for the fine-grained (a) and the coarse-grained (b) sample with the ⬍1 1 1⬎//ND. The γ-fibre is seen in the f2 = 45° cross-section.
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this paper. Lately, there has been an interest in using EBSD measurements to follow changes in misorientations at relatively small strains, and this is also the focus of the present work. Earlier work shows that the average misorientation increases with strain [14,17], indicating that the change in misorientation is proportional to change in the total dislocation density. In this study, we will characterise the evolution of plastic deformation in an ultra-low-carbon steel, at relatively small strains, with AFM and EBSD. The main objective is to understand the role of grain boundaries in the propagation of plastic deformation, in materials showing homogenous yielding on a macroscopic scale. Fig. 2. Stress–strain curves for the two samples: CG (coarse grained), FG (fine grained).
amount of grain rotation associated with deformation. Another important issue is how well AFM measurements correlate with EBSD measurements. EBSD is today a well-established tool for quantitative and qualitative characterisation of deformed and recrystallised microstructures and is often applied to improve the understanding of recrystallisation and deformation characteristics. The orientation imaging maps produced from such measurements provide a wealth of information. The technique is useful not only to study the change of average orientations globally, but also to follow orientation changes within individual grains. Intra-grain misorientations are of interest because they can be used to understand and quantify the storage of dislocations and the inhomogeneous straining occurring within grains. This parameter will be discussed in more detail later in Table 2 Settings used in the EBSD measurements Name
Sample
EBSD step size (µm)
Average grain size (µm)
CG CG CG FG FG
Coarse grained Coarse grained Coarse grained Fine grained Fine grained
2.5 2.5 2.5 1 and 0.5 1 and 0.5
60 60 60 14 14
1 2 3 2 3
2. Experimental 2.1. Material characterisation The material used in this study was a titanium alloyed ultra-low-carbon (ULC) steel with the composition as presented in Table 1. The delivered samples were taken from sheet cold rolled to 10 different degrees of deformation, up to 2.3 in effective plastic strain. Tensile coupons were prepared from the cold rolled samples and subsequently annealed, in order to obtain material with different recrystallised grain sizes. The samples used in this study had been deformed to an effective plastic strain of 27% and 210%, respectively, followed by subsequent annealing, for 30 min, at 740 and 660 °C, respectively. Average grain sizes in the samples were evaluated from the EBSD measurements with the sample denoted as CG (coarsegrained) having a grain size of 60 µm and the sample denoted as FG (fine-grained) having a grain size of 14 µm. This corresponded reasonably well with line intercept measurements. The microstructure of the material revealed a fully recrystallised ferritic structure. Global textures were evaluated from the EBSD results and showed a typical recrystallisation texture, with the ⬍1 1 1⬎ direction parallel to the normal direction, as shown in the ODFs in Fig. 1. Titanium alloyed IF steels are known to exhibit a strong γ-fibre (seen in the f2 = 45° cross-section in Fig. 1) texture after recrystallisation, causing an increase in the planar ani-
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sotropy (usually described by the Lankford coefficient or r-value) [18]. The texture was comparatively strong for the fine-grained specimen and relatively weak for the coarse-grained one. From the above result, one can expect the finegrained specimen to show a more anisotropic mechanical behaviour. 2.2. Experimental set-up After various polishing stages, where the finest was with 1 µm diamond paste, the samples were electro-polished in a mixture of perchloric acid and acetic acid at 10 V for 2–3 min. This final step
was to remove all traces of surface deformation from the earlier polishing stages. The electro-polishing also resulted in a slight etching of the samples. The dimensions of the flat tensile specimens were 30 × 6 mm, with a thickness of 0.75 mm for the fine-grained sample and 3.65 mm for the coarse-grained sample. A number of different areas were then marked with micro-indents in each sample, in order to be able to identify and follow the grains after each deformation step. The samples were then characterised in contact mode AFM (D3000 Nanoscope from Digital Instruments with an silicon nitride tip) and in a LEO Gemini 1530 FEG-EBSD before the tensile testing.
Fig. 3. Change in orientation with strain, colour coding defined by Euler angles, for (a) CG 3 (after 0.2%), (b) FG 3 (after 0.2%), (c) CG 3 (after 10%), (d) FG 1 (after 10%). Misorientation maps after 10% strain of (e) CG 3, (f) FG 1.
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local and global information were evaluated. Local information included, for example, the change in surface profile and crystal orientation near specific grain boundaries. Global information included, for example, the standard deviation in surface roughness and change in mean intra-grain misorientation, with strain, for a larger number of grains. Two different regions were studied in sample FG, while three different regions were studied in sample CG. 3.1. EBSD results Fig. 4. Change in average intra-grain misorientation with strain for the different regions in the two samples (attention should be paid to the relative change in average intra-grain misorientation, not absolute values, as there is a certain spread in the individual orientation measurements).
The experimental procedure was the following: the samples were tensile tested at a constant strain rate of 3 × 10⫺3 s⫺1, whereupon the testing was interrupted at three different strain levels, as shown in Fig. 2. After unloading, marked areas were identified and scanned with AFM and EBSD and this was repeated for each strain level. The resolution of the scans was adapted to the grain size in the samples, with larger areas scanned in the case of the coarse-grained specimen. In the AFM study, initially relatively large areas1 (75 × 75 µm) were scanned, followed by scans of smaller areas (down to 20 × 20 µm), in order to obtain a high enough resolution in the measurements. The step size in the EBSD scans was varied between 0.5, 1 and 2.5 µm depending on the grain size, in order to cover a large enough number of grains in each area. The settings used in the EBSD measurements are presented in Table 2.
3. Results The results from the AFM and EBSD measurements provide both quantitative and qualitative information. For the specific areas studied, both 1 75 × 75 µm is a large scan size for the AFM, but not a large area compared to the grain size.
The EBSD scans covered a comparatively large number of grains in the fine-grained sample and a fewer number in the coarse-grained sample. The EBSD data were analysed by the HKL Channel 5 software, which was also used to evaluate the different parameters presented in this paper. More on the possibilities and limitations of the EBSD technique can be found in the excellent review by Humphreys [19]. From the EBSD measurements, crystal orientations at each point, represented by the three Euler angles, were evaluated. With suitable definitions, the microstructure can be represented by a colour coding system. The different colours of the grains represent different combinations of Euler angles, as illustrated in Figs. 3a–d. In these figures, the Euler angles for one region in each sample (CG 3 and FG 1) have been plotted, after 0.2% strain and 10%, respectively, thus giving a picture of the absolute crystal orientations at each strain level. In the evaluation, neighbouring points showing a difference in orientation larger than 10° were defined as grain boundaries and coloured black, and similarly neighbouring points with a difference in orientation larger than 2° were defined as sub-grain boundaries and coloured white. It can be observed in Fig. 3 that after 0.2% strain, orientations within grains are almost uniform. After 10% strain, however, there is an increase in the occurrence of other orientations (colours) within grains. This is especially visible near certain grain boundaries, indicating rotations within grains. Also, a large increase in the number of sub-grain boundaries can be seen at the highest strain. This indicates an increased rotation within grains, leading to
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inhomogeneous deformation. These do not, however, cover entire grains but instead are predominantly present in the vicinity of grain boundaries and triple junctions, in other words, in regions that are strongly stressed and where the generation of dislocations can be expected to be larger. Another interesting parameter that was evaluated from the EBSD measurements was intra-grain misorientations. This was defined as the deviation from the average orientation within a grain. Thus, the intra-grain misorientation can be seen as a stat-
istical measure of the reorientation occurring within grains. This parameter was evaluated after each strain level, and the change in intra-grain misorientation can be seen as a measure of dislocation storage. Thus, it should be a good measure of the local deformation behaviour. This is illustrated in Fig. 3e and f, where intra-grain misorientation maps, of the same regions as earlier, are shown after 10% strain. The grains have been colour coded according to the average intra-grain misorientation value within each grain, giving each
Fig. 5. Typical AFM scan of regions in the different samples after different strains: (a) CG 3 (after 0.2%), (b) CG 3 (after 4%), (c) CG 3 (after 10%), (d) FG 1 (after 4%).
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grain a uniform colour. It can be observed that a number of grains in the fine-grained sample show intra-grain misorientations larger than 5° and are thus coloured grey. The average intra-grain misorientation for each region in the respective sample was also evaluated quantitatively at each strain level. This is shown in Fig. 4, where the average intra-grain misorientation shows a linear increase with macroscopic strain. This further emphasises that the intra-grain misorientation can be seen as a measure of local deformation. 3.2. AFM results The same areas as in the EBSD study were identified and scanned in the AFM measurements. In the case of the coarse-grained sample, CG, exactly the same grains could easily be identified and in this case, e.g. individual grains could be analyzed both with AFM and EBSD. In the case of the fine-grained sample, FG, there was a difficulty in identifying the same grains although the same regions were scanned. This was partly because of the electro-polishing, which affected the two specimens differently, and partly because the number of grains in sample FG was much larger, thus making it more difficult to identify individual grain features. A typical example of the information available from AFM measurements is shown in Fig. 5. Areas in the fine-grained and coarse-grained samples are shown here before and after different amounts of strain. In Fig. 6, roughness profile measurements over the lines shown in the figure are also displayed. As can be observed, most changes occur in the last deformation step, as illustrated by slip lines at grain boundaries after 10% strain (Fig. 5c). The roughness profiles (Fig. 6a and b) show an increase with strain and also a smoothening of gradients with increasing strain. The different areas examined by AFM were analysed and different parameters, such as the overall roughness change with strain, were evaluated. The roughness profiles over grains in the different areas were analysed and compared with corresponding EBSD measurements. One measure of the roughness is the standard deviation of all height measurements within a region. This is shown in Fig. 7, where the variation of out-of-plane dis-
Fig. 6. Variation of surface profiles, at different strains, over the corresponding lines shown in previous AFM scans: (a) CG 3 and (b) FG 1.
Fig. 7. Change in overall roughness with strain, represented by the standard deviation, sz, for the different regions in the two samples.
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placements, for different regions in the two samples, has been plotted. The standard deviation, sz, increases fairly linearly with strain. Other features that can be visualised with AFM are individual slip lines, which can be measured quite accurately. In Fig. 8a, an overview of a deformed region in the sample FG is shown after 10% plastic strain, where slip lines can clearly be seen. At higher magnifications, as shown in Fig. 8b, the individual slip lines can be resolved and measured. The height of the individual slip lines can be assumed to correspond to the number of dislocations slipping on the slip plane. In this case, a step height of 50 nm (see Fig. 8c) corresponds
to roughly 200 individual dislocations, which can be seen as a measure of the accumulated strain.
4. Discussion Clearly, the EBSD and AFM observations give quite a consistent picture on misorientation and out-of-plane displacements. This seems to hold both on a global scale, as seen from a comparison of the standard deviation of the average intra-grain misorientation, sq, with the standard deviation of surface roughness, sz, shown in Fig. 10, and on a local scale, relative to an individual grain boundary, as
Fig. 8. AFM scan of region in the fine-grained (FG) sample showing the existence and evolution of slip lines after 10% strain. (a) Overview of deformed region, (b) magnification of slip lines seen in previous scan, (c) measurement of surface profile over slip lines as shown in (b).
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Fig. 9. Comparison between roughness profile and misorientation profile measured relative to a grain boundary. Grain boundary in CG 3: (a) after 4% strain, (b) after 10% strain, (c) Surface roughness profile measured with AFM along line in (a). (d) Misorientation measurement relative to grain boundary along line in (a).
shown in Fig. 9. In this figure, the misorientation profile is compared with the corresponding out-of-plane displacement. Both the misorientation and the surface roughness show a linear increase with strain (compare e.g. Figs. 4 and 7). The results indicate that there is a significant rotation within grains, with plastic deformation, which causes an increased surface roughness. Since both the misorientation and the surface roughness increase with strain, it is also an indication that out-of-plane rotation is the dominating feature. The results also indicate a good correlation between the surface behaviour and the bulk deformation behaviour. It should be noted though that all our measurements concern deformation of a free sur-
face and should therefore be interpreted with some caution, as the grains in the interior can be expected to behave differently. This point will be addressed in a separate study. The average intra-grain misorientation is quite sensitive to the minimum size of “allowed grains” from the EBSD measurements. For example, one single EBSD measurement point can hardly be accepted as a grain and has to be removed. In a statistical analysis of the EBSD data at 10% strain, all grains smaller than five pixel points were removed, and two interesting features appeared. First, both the average intra-grain misorientation and the standard deviation of the misorientation
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mation behaviour. Inhomogeneous features are more predominant in large grains although there are more grains in the fine-grained sample, with large intra-grain misorientations. This latter effect is perhaps due to the larger strain hardening in the fine-grained sample. It can also be concluded that significant out-of-plane rotation is consistent with plastic deformation at small strains. Acknowledgements
Fig. 10. Comparison of the overall surface roughness represented by sz, with the standard deviation of the average intragrain misorientation sq, for different strain levels.
measurements were larger for the fine-grained sample. This is consistent with the results presented in Fig. 3e and f, where only grains in the fine-grained sample showed intra-grain misorientations greater than 5°. Second, within each sample, the intra-grain misorientation was larger for large grains, compared to small ones. The latter observation is partly an artefact of the misorientation measurements but also indicates a greater tendency for intra-grain rotation and inhomogeneous yielding to occur within large grains in a sample. One possible explanation for larger misorientations in the fine-grained sample could be due to the extra strain hardening contribution from grain boundaries, in line with Ashby’s model [20] involving geometrically necessary dislocations. A consequence of this can be observed in the stress– strain curves, where the fine-grained sample initially, i.e. at strains lower than 1%, shows a steeper increase in stress.
5. Conclusions There is good agreement, both on a global and a local scale, between the AFM and EBSD measurements. Both the surface roughness and the misorientation increase linearly with strain. The surface behaviour thus reflects the bulk defor-
Financial support from the Swedish research foundation, SSF, through the Brinell Centre and from Gerhard von Hofstein foundation, to one of the authors, is gratefully acknowledged. Ms. Lena Ryde and Dr. L. Belova are thanked for their assistance with the EBSD and AFM measurements. Dr. B. Hutchinson is also thanked for valuable comments in the interpretation of the EBSD data. References [1] Nyga˚ rds M. Technical report, Department of Solid Mechanics, KTH, 2002. [2] Bassani JL. J Mech Phys Solids 2001;49:1983–96. [3] Needleman A. Acta Mater 2000;48:105–24. [4] Hutchinson JW. Int J Solids Struct 2000;37:225–38. [5] Ungar T, Mughrabi H, Ro¨ nnpagel D, Wilkens M. Acta Met 1984;32:333–42. [6] Harvey SE, Marsh PG, Gerberich WW. Acta Mater 1994;42:3493–502. [7] Brinck A, Engelke C, Kopmann W, Neuha¨ user H. Mater Sci Eng A 1997;239-240:180–7. [8] Tong W, Hector Jr LG, Weiland H, Wieserman LF. Scr Mater 1997;36:1339–44. [9] Cretegny L, Saxena A. Acta Mater 2001;49:3755–65. [10] Vinogradov A, Hashimoto S, Patlan V, Kitagawa K. Mater Sci Eng A 2001;319-321:862–6. [11] Man J, Orbrtlik K, Blochwitz C, Polak J. Acta Mater 2002;50:3767–80. [12] Wang YY, Chen DJ. Chiang, FP. Exp Tech 1993;17:30–2. [13] Zhu G, Mao W, Yu Y. Scr Mater 2000;42:37–41. [14] Fukoka C, Morishima K, Yoshizawa H, Mino K. Scr Mater 2002;46:61–6. [15] Balke P, Hosson JTMD. Scr Mater 2001;44:461–6. [16] Chandrasekaran D, Nyga˚ rds M. Mater Sci Eng A [submitted for publication]. [17] Wilkinson AJ. Scr Mater 2001;44:2379–85. [18] Hutchinson B, Artymowicz D. ISIJ Int 2001;41:533–41. [19] Humphreys FJ. J Mater Sci 2001;36:3833–54. [20] Ashby MF. Philos Mag 1970;21:399–424.