Correlation of grain boundary connectivity with grain ...
Acta Materialia 54 (2006) 3617–3626 www.actamat-journals.com
Correlation of grain boundary connectivity with grain boundary character distribution in austenitic stainless steel Sadahiro Tsurekawa *, Shinya Nakamichi, Tadao Watanabe Department of Nanomechanics, Graduate School of Engineering, Tohoku University, 6-6-01 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, Japan Received 13 June 2005; received in revised form 13 March 2006; accepted 27 March 2006 Available online 13 June 2006
Abstract The connectivity of grain boundaries can be an important microstructural parameter governing the bulk properties of polycrystalline materials as well as the grain boundary character distribution. On the basis of the percolation theory, the connectivity of random boundaries that are susceptible to percolative phenomena like corrosion in a polycrystal has been quantitatively evaluated and examined in connection with the grain boundary character distribution in austenitic stainless steel. The percolation threshold has been found to occur at a fraction of approximately 70 ± 5% coincident site lattice (CSL) boundaries (30 ± 5% random boundaries). The maximum random boundary cluster length drastically decreases and the frequency of resistant triple junctions increases with increasing frequency of the CSL boundaries near the percolation threshold. An increase in the frequency of resistant triple junctions can enhance corrosion resistance of polycrystalline austenitic stainless steel even if the grain boundary character distribution is the same. 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Grain boundaries; Grain boundary character distribution; Grain boundary connectivity; Microstructure; Percolation
1. Introduction It is well known that many properties of materials are significantly affected by the microstructure. Particularly, grain boundaries often exert a strong influence on both mechanical and functional properties of polycrystalline materials. Percolative phenomena like fracture, corrosion and oxidation preferentially occur along grain boundaries and sometimes cause a serious problem in service [1–8]. From fundamental studies on grain boundary structures and properties since the 1950s, most grain boundary properties have been found to depend strongly on the grain boundary character and structure [9–12]. On the basis of these observations, Watanabe [13] proposed in the early 1980s the concept of ‘‘grain boundary design and control’’ for the development of high-performance polycrystalline materials (nowadays widely accepted as ‘‘grain boundary engineering’’) and introduced a new microstructural *
Corresponding author. Tel./fax: +81 22 795 6904. E-mail address: [email protected] (S. Tsurekawa).
parameter called the ‘‘grain boundary character distribution’’ (GBCD) as a ranking parameter of grain boundary microstructure. Since then, grain boundary engineering through the control of the GBCD has been extensively employed as a powerful tool for achieving enhanced structural [6–8,14–26] and functional [27] properties. For example, it has been revealed by Palumbo et al. [19] and Shimada et al. [24] that intergranular stress corrosion cracking in Ni-based Alloy 800 and intergranular corrosion in austenitic stainless steel can be significantly reduced by increasing the frequency of low-energy coincident site lattice (CSL) boundaries. Furuya et al. [27] have also found that an increase of the frequency of CSL boundaries can enhance the magnetostriction in an Fe–Pd shape memory alloy. So far, much effort has been directed at increasing the frequency of low-energy CSL boundaries of polycrystalline materials in grain boundary engineering. However, grain boundary-related phenomena occur by the percolation process, so that the connectivity of susceptible grain boundaries may affect the percolation of grain boundary-related
1359-6454/$30.00 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2006.03.048
3618
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
phenomena and, as well as GBCD, can be a key for developing enhanced properties. Watanabe [28] has pointed out that the number of interconnected random boundaries (called the grain boundary correlation number) can change according to microstructure even if the GBCD is a constant. On the basis of the random bond percolation theory, Wells et al. [1] have determined the percolation threshold for a three-dimensional (3D) grain boundary network occurring at 77% of inactive bonds (23% of active bonds) using Kelvin’s tetrakaid ecahedron model. They also demonstrated that intergranular failure was significantly pronounced when the frequency of sensitized (active) grain boundaries reached 23% in SUS304 stainless steel; later Gaudett and Scully [2] reported almost the same result as Wells et al. Palumbo et al. [29] have predicted the scale of susceptible grain boundary networks based on random probabilistic analysis and then showed that the penetration of intergranular cracking decreases with decreasing frequency of susceptible grain boundaries. Recently, Wang et al. [30] have studied the influence of the sharpness of texture and grain boundary inclination on the penetration of intergranular cracks. They found that the sharpness of texture and grain boundary inclination both observably affected the intergranular crack propagation. In addition, Nichols and Clarke [31] have studied the current–voltage (I–V) characteristics of polycrystalline superconducting film on the basis of the percolation theory. Recently, Schuh et al. [32] and Frary and Schuh [33] have predicted that crystallographic constraints, taking account of the R-product rule, on two-dimensional (2D) and 3D grain boundary networks, respectively, substantially change the percolation threshold for susceptible grain boundaries and that the percolation threshold is much higher in a constrained lattice than in a randomly assembled network. The constrained lattice leads to a percolation threshold at a frequency of resistant boundaries of more than 50%, while the random percolation for a 2D hexagonal lattice gives the percolation threshold at a frequency of resistant boundaries of 35% [34]. Schuh et al. also experimentally examined the change in the boundary connectivity during sequential cycles of small straining and annealing on the basis of the percolation theory using electron backscattered diffraction (EBSD) data for a Ni-based alloy [35]. Their work demonstrated that the ‘‘length’’ (originally they used the term ‘‘mass’’) of random boundary clusters (the total length of an interconnected random boundary network) was substantially reduced during the cyclic processing, and also reported that the coordination of CSL boundaries at triple junctions reflected the topology of the grain boundary network more accurately than the GBCD. However, these quantitatively evaluated parameters have not yet been assessed in connection with any properties. The purpose of the present work is to evaluate quantitatively the connectivity of grain boundary networks, particularly of random boundaries, on the basis of the percolation theory, and then to assess the interactive effects of the evaluated parameters in connection with the grain
boundary connectivity and the GBCD on corrosion properties. 2. Experimental 2.1. Specimen preparation A 304L austenitic stainless steel (SUS304L) single crystal, which was supplied by the Materials Research Lab. of Hitachi Ltd, was used as the starting material in this study. The single crystal was cut into rectangular-shaped specimens with different orientations (Æ0 0 1æ, Æ1 0 1æ, Æ1 1 1æ and Æ1 2 3æ) for compression tests. The dimensions of these specimens were 3.5 mm · 3.5 mm · 6.0 mm. The surfaces of the specimens were mechanically polished with waterproof SiC papers (grades 320–1500). The specimens were uniaxially deformed to 30% and 40% in strain under compression at room temperature and at a crosshead speed of 4.2 · 10 3 mm/s. Thereafter, the deformed specimens were annealed at temperatures ranging from 1200 to 1500 K for 3.6 ks in a vacuum of 2 · 10 3 Pa. For observations of recrystallized microstructure, the specimens were sectioned perpendicular to the compression axis using a low-speed diamond cutter, and then a cross-sectional plane was mechanically polished with waterproof SiC papers (grades 320–4000) and buff-finished to a mirror surface using both 3 and 1 lm Al2O3 particles. Finally, these specimens were electrically polished in a mixture of acetic acid and perchloric acid (77:23 by volume) at iced-water temperature to remove any surface strained layer to ensure the subsequent field-emission gun scanning electron microscopy (FEG-SEM)/electron backscattered diffraction pattern (EBSD)/orientation imaging microscopy (OIM) observations. 2.2. Microstructure observations The grain boundary microstructures of the prepared specimens were quantitatively examined with a Hitachi S-4200 FEG-SEM instrument equipped with an OIM facility from TSL Inc. The OIM observations were conducted at an accelerating voltage of 30 kV and at an emission current of 10 lA. The electron beam was scanned on the surface using a step size in the range 2–14 lm. In this study, grain boundaries with R 5 29 were defined as CSL boundaries [36] and Brandon’s criterion [37] was used to categorize the grain boundaries. The grain boundary microstructural properties such as grain size, GBCD and grain boundary connectivity were evaluated on the basis of OIM data. The GBCD to be shown in this paper is given by the length fraction. In particular, details of the evaluation of the grain boundary connectivity are discussed in the following section. On the basis of grain boundary microstructure evaluation, the correlations between microstructural parameters, e.g., GBCD vs. grain boundary connectivity, were statistically analyzed using the least squares fitting procedure. The fitted curves and the standard deviations are shown by solid and broken lines, respectively, in the figures.
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
2.3. Analysis of grain boundary connectivity 2.3.1. Quantification of random boundary cluster The 2D network of grain boundaries contains clusters consisting of all the interconnected boundaries of a like type. We paid particular attention to the clusters in which only random boundaries were interconnected, because random boundaries are susceptible to intergranular percolative phenomena. The total length of each random boundary cluster was measured on the basis of OIM data, and was defined as ‘‘the length of cluster’’ by analogy with the percolation theory [34]. On each measurement of the random boundary cluster length, the boundary clusters that cross the edge of the analyzed area were taken out to decrease the experimental error. 2.3.2. Quantification of resistant triple junction We classified triple junctions into four types, 3-CSL, 2-CSL, 1-CSL and 0-CSL, following Fortier et al. [38,39] based on how to connect the grain boundaries with different characters at a triple junction. For example, a 2-CSL triple junction is composed of two CSL boundaries and one random boundary. In order to assess the resistance to percolation degradation, we consider the distribution of only those triple junctions that are composed of at least one random boundary, following Kumar et al. [40]. Therefore, the 3-CSL triple junctions can be taken out of consideration, because they are inactive entities in the process of arresting advancing corrosion on the assumption that the percolative front would never approach them. Kumar et al. [40] have proposed a new parameter based on the triple junction types defined by Fortier et al. [38,39], f2CSL/ (1 f3CSL), for evaluation of continuous percolative paths in the microstructure, where f2CSL refers to the frequency of triple junctions that have two CSL boundaries and are thereby able to arrest intergranular penetration and (1 f3CSL) is the frequency of triple junctions that are active unit entities in the microstructure. Using the method of Kumar et al., we evaluated the frequency of the resistant triple junctions in the microstructure. 2.4. Corrosion tests For corrosion tests, we used commercially available SUS304 stainless steel. The SUS304 specimens of 40 mm · 16 mm · 3.5 mm in dimension were solution treated at 1323 K for 1.8 ks and then water-quenched. After the surface oxide layer was removed using mechanical polishing with waterproof SiC papers, some specimens were subjected to a thermomechanical treatment to control grain boundary microstructures. The conditions of thermomechanical treatment for each sample are shown in Table 1: specimens A and C were as-solution treated, specimen B received 11% cold rolling and was annealed at 1400 K for 5 h, and then received 3% cold rolling and annealed at 1400 K for 1 h, and specimen D received 16% cold rolling and was annealed at 1400 K for 1 h. After the thermomechanical treatment at
3619
Table 1 The annealing conditions for each specimen subjected to intergranular corrosion test Specimen
Reduction rate, F (%)
Annealing temperature, T (K)
Annealing time, t (h)
A B C D
– 17 + 3 – 16
1323 1400 1323 1400
0.5 5+1 0.5 1
1400 K, the samples were water-quenched. The grain boundary microstructures in these samples were observed using the OIM technique and then statistically analyzed. The intergranular corrosion resistance for SUS304 specimens was evaluated using a commonly used ferric sulfate– sulfuric acid test after sensitization at 923 K for 2 h and air cooling. The specimens were boiled in ferric sulfate– 50% sulfuric acid for 24 or 48 h. The tested specimens were observed using SEM. 3. Results and discussion 3.1. Recrystallized grain structures in SUS304L from single crystals with different orientations Recrystallized grain structures are often affected by initial or deformed structures like grain orientation. Kobayashi et al. have reported that the grains in molybdenum polycrystals recrystallized from deformed single crystals develop different grain orientation clusters in which they have similar orientations because of different initial orientation of single crystals [41]. Fig. 1 shows the inverse pole figures for SUS304L polycrystals recrystallized from single crystals with different initial orientations. For comparison, the inverse pole figures for single-crystal specimens deformed to a strain of 40% are also shown in Fig. 1. These inverse pole figures were obtained from the cross-section perpendicular to the loading axis in the compression test. Looking at the pole figures for the specimens recrystallized at 1300, 1400 and 1500 K, the grain orientation tends to be located between Æ0 0 1æ and Æ1 1 1æ except for the specimen with the 001 initial orientation. In contrast, the grain orientation in the 001 specimen is distributed near the center of the stereographic unit triangle. The difference in the grain orientations in the deformed state may cause a difference in the grain orientations in recrystallized specimens. The crystal orientations of deformed 101, 111 and 213 singlecrystal specimens were found to be sharply concentrated near Æ1 0 1æ because of crystal rotation associated with slip deformation by compression, whereas the crystal orientation of deformed 001 single crystal was spread between Æ0 0 1æ and Æ1 1 3æ, which are both consistent with the result predicted by Calnan [42] for the crystal rotation in copper under compression. The recrystallized grains in a singlecrystal specimen were sometimes related to the deformed matrix by a 40 Æ1 1 1æ rotation [43]. However, we could
3620
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
Fig. 1. Inverse pole figures for SUS304L polycrystals recrystallized at different temperatures from single crystals with different orientations. These inverse pole figures were obtained from the cross-sections perpendicular to the compression axis. These specimens were uniaxially compressed to 40% strain before annealing.
not find such a relation between the recrystallized grains and deformed matrix. This is probably because of the introduction of extensive twin-variants in the microstructure due to a low stacking fault energy in SUS304L stainless steel. Furthermore, one can see that the grain orientation in the 101, 111 and 213 specimens annealed at 1200 K is likely to be localized near 101 orientation in contrast to those in other samples annealed at higher temperatures. This is because they predominantly arise from unrecrystallized areas, namely from deformed grains. Accordingly, we excluded the data associated with the unrecrystallized specimens from any analyses discussed in the following section.
tend to be less localized for low stacking fault energy face-centered cubic materials, with decreasing effective grain size. It is evident that the increase of twin (R3) boundaries is predominantly responsible for the increase in the number of CSL boundaries, as in other materials with a lower stacking fault energy [45]. Furthermore, the interaction of twin boundaries with random boundaries often causes segments of random boundaries to change into CSL boundaries, resulting in the random boundary network being broken up [24,40]. These findings show that the grain growth, that is, the grain boundary migration, will be accompanied by the formation of R3 twin boundaries as suggested by Gleiter [46].
3.2. Relation between GBCD and grain size The GBCD is closely related to the grain size. The frequency of CSL boundaries has been found to decrease with increasing grain size for polycrystalline materials with body-centered cubic and face-centered cubic structures having a high stacking fault energy produced by thermomechanical processing [44]. However, in the case of recrystallized SUS304L austenitic stainless steel having a low stacking fault energy, the frequency of CSL boundaries increases with increasing grain size as shown in Fig. 2 because of multiple twinning during grain growth. As the result of multiple twinning, grain orientation distributions
Fig. 2. Changes in the frequencies of low-angle, R3 and CSL boundaries as a function of grain size in SUS304L stainless steel.
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
3.3. Resistant triple junction distribution Following Kumar et al. [40], the frequency of triple junctions resistant to percolation of intergranular degradation, f2CSL/(1 f3CSL), was measured using OIM data for recrystallized SUS304L and will be discussed in connection with both the grain size and the GBCD. Fig. 3(a) shows the frequency of resistant triple junctions as a function of the grain size. The resistant triple junction fraction f2CSL/(1 f3CSL) appears to depend on the grain size in a parabolic manner. As mentioned above, the interaction of twin boundaries with random boundaries often results in the formation of segments of CSL boundaries according to the R-product rule, which causes an increase of the resistant triple junction fraction. The finding in Fig. 3(a) suggests that a larger extent of grain boundary migration is necessary to produce more twin boundaries. Fig. 3(b) presents the relationship between the frequency of resistant triple junctions and the frequency of CSL boundaries. For comparison, data for Inconel 600 [40] and Cu [40] are included in Fig. 3(b). It is evident that the frequency of resistant triple junctions increases with increasing CSL boundary fraction. Kumar et al. suggested that percolative paths in the microstructure will be broken if the resistant triple junction fraction is more than 35% according to the random percolation model [40]. In other words, the percolation threshold based on the triple junction distribution is a frequency of resistant triple junctions of 35%. An extrapolation of the data plotted in Fig. 3(b) gives the frequency of CSL boundaries as approximately
Fig. 3. Changes in the frequency of resistant triple junction as functions of (a) the grain size and (b) the frequency of CSL boundaries.
3621
70% at the resistant triple junction fraction of 35%. Interestingly, the estimated value of CSL boundary fraction is well consistent with the CSL fraction corresponding to the percolation threshold experimentally determined according to the maximum random boundary clusters as mentioned in the following section. 3.4. Random boundary cluster length and percolation threshold Since the character of single triple junctions is a measure for the evaluation of grain boundary connectivity, we need to know how long or how many random boundaries are interconnected in the grain boundary network. Accordingly, we measured the length of each random boundary cluster, i.e., the total length of all interconnected random boundaries in each cluster. Fig. 4 shows an example of a random boundary cluster identification: all grain boundaries (Fig. 4(a)) and only random boundaries (Fig. 4(b)). An interconnection of random boundaries highlighted by a bold black line in Fig. 4(b) is an example of a single random boundary cluster. We especially pay attention to the
Fig. 4. Example of the random boundary cluster identification: (a) showing full networks of grain boundaries and (b) only the random boundaries. The R3 and random boundaries are shown by bold black and thin black lines, respectively, in (a). The interconnected random boundaries highlighted by bold black line in (b) is an example of a single random boundary cluster.
3622
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
maximum cluster of random boundaries because it would essentially relate to percolation length of intergranular phenomena. Fig. 5 shows the maximum (Fig. 5(a)) and the average (Fig. 5(b)) random boundary cluster lengths in SUS304L stainless steel as a function of the grain size. The maximum random boundary cluster length, Smax, is likely to decrease with increasing grain size, although the data scatter is large. In contrast to this experimental observation, according to the percolation theory, the maximum cluster mass (length) of bonds susceptible to percolation depends only on the frequency of susceptible bonds and does not depend on the size of the lattice. As shown in Fig. 2, the frequency of CSL boundaries increases with increasing grain size in SUS304L. In addition, an increase of CSL boundary fraction yields a decrease in the maximum random boundary cluster length as shown in the following section. Thus, the observed grain size dependence of Smax may have resulted from the grain size dependence of the CSL boundary fraction. The average random boundary cluster mass, Save, seems to be less dependent on grain size. Fig. 6(a) and (b) shows Smax and Save, respectively, as a function of the frequency of CSL boundaries. It is found that the maximum random boundary cluster length Smax depends significantly on the CSL boundary fraction. An important finding is that Smax in terms of the random boundary connectivity drastically decreases with increasing CSL boundary fraction in the range of CSL boundary fraction 60–80%. In contrast, Save is less dependent on the CSL boundary fraction as shown in Fig. 6(b).
Fig. 5. Lengths of (a) the maximum and (b) the average random boundary clusters as a function of the grain size.
Fig. 6. Lengths of (a) the maximum and (b) the average random boundary clusters as a function of the frequency of CSL boundaries.
In previous work on grain boundary engineering, the experimental results have been discussed in connection with a percolation threshold (35% resistant (65% susceptible) boundaries) from a randomly assembled network. As mentioned in Section 1, Schuh et al. [32] pointed out that the percolation threshold would shift toward a resistant boundary fraction of 50–75% when the crystallographic constraint is enforced. Thus, the application of the percolation theory based on a randomly assembled network to
Fig. 7. Percolation probability along random boundaries as a function of the frequency of CSL boundaries, which leads to the percolation threshold occurring at approximately 70% of CSL boundaries. The percolation thresholds based on random percolation and on constrained percolation by Schuh et al. are shown for comparison.
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
understand bulk properties related to percolation phenomena can be misleading. However, to our knowledge, the percolation threshold for a random boundary network
Fig. 8. Relationship between the maximum random boundary cluster length and the frequency of resistant triple junctions. Table 2 The frequencies of CSL boundaries and resistant triple junctions, and the maximum length of random boundary clusters in the specimens for corrosion tests Specimen
GBCD, FR
Max. cluster length (lm)
f2CSL/(1
A B C D
0.68 0.80 0.55 0.55
7600 2300 10500 16800
0.11 0.28 0.10 0.19
f3CSL)
3623
has not been experimentally determined on the basis of microstructural observation. It is useful to give the percolation threshold as a critical value for the design and control of the GBCD in grain boundary engineering. According to the percolation theory, the percolation probability along susceptible boundaries can be expressed by the ratio of the maximum cluster length (mass) to the size of the system. The inflection point on a percolation probability curve as a function of the resistant boundary fraction gives a percolation threshold. Fig. 7 shows the percolation probability of SUS304L polycrystals as a function of the frequency of CSL boundaries, where the percolation probability is given by the maximum random cluster length normalized by the total length of full grain boundaries in the area analyzed. The observed percolation probability curve, which was obtained by the least squares fitting procedure using a power law function, gives the percolation threshold occurring at 70 ± 5% CSL boundaries (30 ± 5% random boundaries). The obtained value of percolation threshold is much higher than the theoretical value from the random percolation theory, approximately 35% resistant boundaries (65% susceptible boundaries), but agrees well with the value estimated from the constrained percolation model [34] within experimental error. The present results based on OIM data are limited to 2D microstructure topology. In the light of percolation models [1,33,34,47], the percolation threshold for 3D topology will be further increased to more than 70% CSL boundaries.
Fig. 9. SEM micrographs for specimen A and specimen B with frequencies of CSL boundaries of 68 and 80%, respectively, after the ferric sulfate–sulfuric acid test for 24 h: (a) · 200; (b) · 500.
3624
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
3.5. Relation between random boundary cluster length and resistant triple junction fraction The relation between the maximum random boundary cluster length Smax and the resistant triple junction fraction f2CSL/(1 f3CSL) is shown in Fig. 8. It is found that Smax is a function of f2CSL/(1 f3CSL) though data scatter is relatively large. The maximum random boundary cluster length Smax is likely to decrease with increasing f2CSL/ (1 f3CSL). 3.6. Influence of grain boundary connectivity on intergranular phenomena In previous sections, grain boundary connectivity was qualitatively evaluated on the basis of the percolation analyzed by both the triple junction distribution and the random boundary cluster length, and then examined in terms of the GBCD. In this section, we correlate experimentally measured f2CSL/(1 f3CSL) and Smax with corrosion property of SUS304 polycrystals. For this purpose,
four types of SUS304 specimens with different grain boundary microstructures were subjected to ferric sulfate–sulfuric acid tests. The annealing conditions and the evaluated microstructural parameters for each SUS304 specimen are shown in Tables 1 and 2, respectively. In particular, the comparison of corrosion properties between specimens C and D is particularly interesting because these specimens have the same CSL boundary fraction but different random boundary connectivities. Fig. 9 shows SEM micrographs for specimen A and specimen B after the ferric sulfate–sulfuric acid test for 24 h. As seen in Table 2, the frequencies of CSL boundaries are 68% (below the percolation threshold) and 80% (above the percolation threshold) in specimens A and B, respectively. The SEM micrographs reveal that grain boundaries were heavily corroded in specimen A, while there is no significant sign of heavy intergranular corrosion in specimen B. These observations show that a high frequency of CSL boundaries (more than the percolation threshold) gives rise to a pronounced resistance to intergranular corrosion.
Fig. 10. SEM micrographs of the surfaces and the cross-sections in specimens C and D after the ferric sulfate–sulfuric acid test for 48 h, showing the influence of grain boundary connectivity on corrosion percolation. The frequency of resistant triple junctions is higher in sample D (19%) than in sample C (10%) but both samples have the same frequency of CSL boundaries (55%).
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
Furthermore, it is worth examining how the connectivity of susceptible (random) boundaries can affect intergranular corrosion. It would be expected that intergranular corrosion depends on the connectivity of susceptible boundaries. In the light of this prediction, a question arises: what would be an appropriate ranking parameter to best reflect percolative properties? For this purpose, two specimens (specimens C and D), which had the same CSL boundary fraction (55%) but different random boundary connectivities, were subjected to ferric sulfate– sulfuric acid tests, and the results were compared to the experimentally obtained parameters given in Table 2. Although the grain boundary microstructures were characterized by OIM analyses on the specimen surface, similar microstructure can be expected on the specimen surface and the cross-section parallel to corrosion percolation, because twin-dominated microstructures have essentially a random texture. Fig. 10 shows SEM micrographs of the surfaces and the cross-sections of specimens C and D after the ferric sulfate–sulfuric acid test for 48 h. Of particular importance is the observation that the corrosion in the two samples is quite different because of different random boundary connectivities even though the grain boundary character distribution is the same. Sample C displays extensive intergranular corrosion percolation. In contrast, specimen D is immune from corrosion percolation, although slight intergranular corrosion is observed on the specimen surface. The resistant triple junction fraction is approximately twice as high in specimen D than in specimen C. Conversely, the maximum random boundary cluster length is lower in specimen C than in specimen D. Although there is a tendency for the length of the maximum random boundary cluster to decrease with increasing resistant triple junction fraction, as shown in Fig. 8, we selected these samples (C and D) for corrosion tests from all the SUS304 specimens in order to assess what is the more useful ranking parameter associated with the grain boundary connectivity to reflect percolative phenomena. Judging from the results mentioned above, the resistant triple junction fraction was more reflective of percolative intergranular corrosion than the maximum random boundary cluster length. 4. Conclusions Connectivity and percolation in random grain boundary networks in austenitic stainless steel were studied in connection with the GBCD. The connectivity of random grain boundaries was quantitatively evaluated using both the triple junction distribution and the random boundary cluster length, and then these measured parameters were correlated with intergranular corrosion of SUS304 stainless steel. The main results obtained were as follows. 1. The frequency of percolation-resistant triple junctions, f2CSL/(1 f3CSL), increases with increasing frequency of CSL boundaries.
3625
2. The maximum length of random boundary clusters (the maximum length of interconnected random boundary networks) drastically decreases with increasing frequency of CSL boundaries probably near the percolation threshold, leading to a percolation threshold occurring at approximately 70 ± 5% CSL boundaries (30 ± 5% random boundaries) and at approximately 35% resistant triple junctions. 3. The connectivity of random boundaries, which are susceptible to intergranular degradation, has a strong influence on intergranular corrosion in SUS304 stainless steel polycrystals. The resistant triple junction distribution is a more important ranking parameter than the maximum of random boundary cluster length for susceptibility to percolative intergranular corrosion. The higher the resistant triple junction fraction, the more the SUS304 polycrystals are immune from intergranular corrosion. Acknowledgements The authors would like to express their thanks to Prof. H. Kokawa (Tohoku University) for his arranging the corrosion tests and useful discussions, Profs. T. Soji (Tohoku University) and P. Lejcek (Institute of Physics, Academy of Sciences of the Czech Republic), Drs. R. Ishibashi, T. Horiuchi, J. Kuniya and M. Yamamoto (Hitachi Ltd) for their useful discussions, Mr. T. Matsuzaki (Tohoku University) for his help with experimental works, Mr. M. Michiuchi for his help with corrosion tests and Dr. V. Yardley (Tohoku University) who kindly read and corrected the manuscript. A SUS304L stainless steel single crystal was supplied by Hitach Ltd. This work was partially supported by a Grant-in-Aid for the innovative and viable nuclear energy technology development program from the Institute of Applied Energy (IAE), and a Grant-in-Aid for Basic Research (A) (15201015) from Japan Society for the Promotion of Science (JSPS). These supports are greatly appreciated. References [1] Wells DB, Stewart J, Herbert AW, Scott PM, Williams DE. Corrosion 1989;45:649. [2] Gaudett MA, Scully JR. Metall Mater Trans 1994;25A:775. [3] Procter RPM. Mater Sci Eng 1994;A184:135. [4] Brumm MW, Grabke HJ, Wagemann B. Corros Sci 1994;36:37. [5] Sklenicka V. Mater Sci Eng 1997;A234–236:30. [6] Lehockey EM, Palumbo G, Lin P, Brennenstuhl AM. Scripta Mater 1997;36:1211. [7] Tsurekawa S, Watanabe T. Mater Res Soc Symp Proc 2000;586: 237. [8] Yamaura S, Tsurekawa S, Watanabe T. Mater Trans 2003;44:1494. [9] Gleiter H, Chalmers B. Prog Mater Sci 1972;16:1. [10] Chadwick GA, Smith DA, editors. Grain boundary structure and properties. Academic Press; 1976. [11] Ishida Y, editor. Trans JIM 1986; suppl 27. [12] Sutton AP, Balluffi RW. Interfaces in crystalline materials. Oxford Science Publishers; 1995. [13] Watanabe T. Res Mech 1984;11:47. [14] Watanabe T, Fujii H, Oikawa H, Arai KI. Acta Metall 1989;37:941. [15] Hirano T. Acta Metall Mater 1990;38:2667.
3626
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
[16] Crawford DC, Was GS. Metall Trans 1992;23A:1195. [17] Watanabe T, Hirano T, Ochiai T, Oikawa H. Mater Sci Forum 1994;157–162:1103. [18] Lin P, Palumbo G, Erb U, Aust KT. Scripta Metall Mater 1995;33:1387. [19] Palumbo G, Lehockey EM, Lin P, Erb U, Aust KT. Mater Res Soc Symp Proc 1997;458:273. [20] Lehockey EM, Palumbo G. Mater Sci Eng 1997;A237:168. [21] Thaveeprungsriporn V, Was GS. Metall Mater Trans 1997;28A:2101. [22] Lehockey EM, Palumbo G, Lin P, Brennenstuhl A. Metall Mater Trans 1998;29A:387. [23] Lehockey EM, Limoges D, Palumbo G, Sklarchuk J, Tomantschger K, Vincze A. J Power Sources 1999;78:79. [24] Shimada M, Kokawa H, Wang ZJ, Sato YS, Karibe I. Acta Mater 2002;50:2331. [25] Kobayashi S, Yoshimura T, Tsurekawa S, Watanabe T. Mater Trans 2003;44:1469. [26] Ishibashi R, Horiuchi T, Kuniya J, Yamamoto M, Tsurekawa S, Kokawa H, et al. Mater Sci Forum 2005;475–479:3863. [27] Furuya Y, Hagood NW, Kimura H, Watanabe T. Mater Trans JIM 1998;39:1248. [28] Watanabe T. Mater Sci Eng 1994;A176:39. [29] Palumbo G, King PJ, Aust KT, Erb U, Lichtenberger PC. Scripta Metall Mater 1991;25:1775.
[30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41]
[42] [43] [44] [45] [46] [47]
Wang G, Zuo L, Esling C. Philos Mag A 2002;82:2499. Nichols CS, Clarke DR. Acta Metall Mater 1991;39:995. Schuh CA, Minich RW, Kumar M. Philos Mag 2003;83:711. Frary M, Schuh CA. Philos Mag 2005;85:1123. Stauffer D, Aharony A. Introduction to percolation theory. London: Taylor and Francis; 1992. Schuh CA, Kumar M, King WE. Acta Mater 2003;51:687. Watanabe T. J Phys 1985;46:C4–C555. Brandon DG. Acta Metall 1966;14:1479. Fortier P, Aust KT, Miller WA. Acta Metall Mater 1995;43:339. Fortier P, Miller WA, Aust KT. Acta Mater 1997;45:3459. Kumar M, King WE, Schwartz AJ. Acta Mater 2000;48:2081. Kobayashi S, Kobylansky A, Nagano T, Tsurekawa S, Watanabe T. In: Sakai T, Suzuki HG, editors. Proc. 4th Int. Conf. on Recrystallization and Related Phenomena. Japan Institute of Metals; 1999. p. 167. Calnan EA. Acta Metall 1954;2:865. Humphreys FJ, Hatherly M. Recrystallization and related annealing phenomena. Pergamon; 1995. Watanabe T. Textures Microstruct 1993;20:195. Lin P, Palumbo G, Aust KT. Scripta Mater 1997;36:1145. Gleiter H. Acta Metall 1969;17:1421. McGarrity ES, Duxbury PM, Holm EA. Phys Rev E 2005; 71:026102.
Correlation of grain boundary connectivity with grain boundary character distribution in austenitic stainless steel Sadahiro Tsurekawa *, Shinya Nakamichi, Tadao Watanabe Department of Nanomechanics, Graduate School of Engineering, Tohoku University, 6-6-01 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, Japan Received 13 June 2005; received in revised form 13 March 2006; accepted 27 March 2006 Available online 13 June 2006
Abstract The connectivity of grain boundaries can be an important microstructural parameter governing the bulk properties of polycrystalline materials as well as the grain boundary character distribution. On the basis of the percolation theory, the connectivity of random boundaries that are susceptible to percolative phenomena like corrosion in a polycrystal has been quantitatively evaluated and examined in connection with the grain boundary character distribution in austenitic stainless steel. The percolation threshold has been found to occur at a fraction of approximately 70 ± 5% coincident site lattice (CSL) boundaries (30 ± 5% random boundaries). The maximum random boundary cluster length drastically decreases and the frequency of resistant triple junctions increases with increasing frequency of the CSL boundaries near the percolation threshold. An increase in the frequency of resistant triple junctions can enhance corrosion resistance of polycrystalline austenitic stainless steel even if the grain boundary character distribution is the same. 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Grain boundaries; Grain boundary character distribution; Grain boundary connectivity; Microstructure; Percolation
1. Introduction It is well known that many properties of materials are significantly affected by the microstructure. Particularly, grain boundaries often exert a strong influence on both mechanical and functional properties of polycrystalline materials. Percolative phenomena like fracture, corrosion and oxidation preferentially occur along grain boundaries and sometimes cause a serious problem in service [1–8]. From fundamental studies on grain boundary structures and properties since the 1950s, most grain boundary properties have been found to depend strongly on the grain boundary character and structure [9–12]. On the basis of these observations, Watanabe [13] proposed in the early 1980s the concept of ‘‘grain boundary design and control’’ for the development of high-performance polycrystalline materials (nowadays widely accepted as ‘‘grain boundary engineering’’) and introduced a new microstructural *
Corresponding author. Tel./fax: +81 22 795 6904. E-mail address: [email protected] (S. Tsurekawa).
parameter called the ‘‘grain boundary character distribution’’ (GBCD) as a ranking parameter of grain boundary microstructure. Since then, grain boundary engineering through the control of the GBCD has been extensively employed as a powerful tool for achieving enhanced structural [6–8,14–26] and functional [27] properties. For example, it has been revealed by Palumbo et al. [19] and Shimada et al. [24] that intergranular stress corrosion cracking in Ni-based Alloy 800 and intergranular corrosion in austenitic stainless steel can be significantly reduced by increasing the frequency of low-energy coincident site lattice (CSL) boundaries. Furuya et al. [27] have also found that an increase of the frequency of CSL boundaries can enhance the magnetostriction in an Fe–Pd shape memory alloy. So far, much effort has been directed at increasing the frequency of low-energy CSL boundaries of polycrystalline materials in grain boundary engineering. However, grain boundary-related phenomena occur by the percolation process, so that the connectivity of susceptible grain boundaries may affect the percolation of grain boundary-related
1359-6454/$30.00 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2006.03.048
3618
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
phenomena and, as well as GBCD, can be a key for developing enhanced properties. Watanabe [28] has pointed out that the number of interconnected random boundaries (called the grain boundary correlation number) can change according to microstructure even if the GBCD is a constant. On the basis of the random bond percolation theory, Wells et al. [1] have determined the percolation threshold for a three-dimensional (3D) grain boundary network occurring at 77% of inactive bonds (23% of active bonds) using Kelvin’s tetrakaid ecahedron model. They also demonstrated that intergranular failure was significantly pronounced when the frequency of sensitized (active) grain boundaries reached 23% in SUS304 stainless steel; later Gaudett and Scully [2] reported almost the same result as Wells et al. Palumbo et al. [29] have predicted the scale of susceptible grain boundary networks based on random probabilistic analysis and then showed that the penetration of intergranular cracking decreases with decreasing frequency of susceptible grain boundaries. Recently, Wang et al. [30] have studied the influence of the sharpness of texture and grain boundary inclination on the penetration of intergranular cracks. They found that the sharpness of texture and grain boundary inclination both observably affected the intergranular crack propagation. In addition, Nichols and Clarke [31] have studied the current–voltage (I–V) characteristics of polycrystalline superconducting film on the basis of the percolation theory. Recently, Schuh et al. [32] and Frary and Schuh [33] have predicted that crystallographic constraints, taking account of the R-product rule, on two-dimensional (2D) and 3D grain boundary networks, respectively, substantially change the percolation threshold for susceptible grain boundaries and that the percolation threshold is much higher in a constrained lattice than in a randomly assembled network. The constrained lattice leads to a percolation threshold at a frequency of resistant boundaries of more than 50%, while the random percolation for a 2D hexagonal lattice gives the percolation threshold at a frequency of resistant boundaries of 35% [34]. Schuh et al. also experimentally examined the change in the boundary connectivity during sequential cycles of small straining and annealing on the basis of the percolation theory using electron backscattered diffraction (EBSD) data for a Ni-based alloy [35]. Their work demonstrated that the ‘‘length’’ (originally they used the term ‘‘mass’’) of random boundary clusters (the total length of an interconnected random boundary network) was substantially reduced during the cyclic processing, and also reported that the coordination of CSL boundaries at triple junctions reflected the topology of the grain boundary network more accurately than the GBCD. However, these quantitatively evaluated parameters have not yet been assessed in connection with any properties. The purpose of the present work is to evaluate quantitatively the connectivity of grain boundary networks, particularly of random boundaries, on the basis of the percolation theory, and then to assess the interactive effects of the evaluated parameters in connection with the grain
boundary connectivity and the GBCD on corrosion properties. 2. Experimental 2.1. Specimen preparation A 304L austenitic stainless steel (SUS304L) single crystal, which was supplied by the Materials Research Lab. of Hitachi Ltd, was used as the starting material in this study. The single crystal was cut into rectangular-shaped specimens with different orientations (Æ0 0 1æ, Æ1 0 1æ, Æ1 1 1æ and Æ1 2 3æ) for compression tests. The dimensions of these specimens were 3.5 mm · 3.5 mm · 6.0 mm. The surfaces of the specimens were mechanically polished with waterproof SiC papers (grades 320–1500). The specimens were uniaxially deformed to 30% and 40% in strain under compression at room temperature and at a crosshead speed of 4.2 · 10 3 mm/s. Thereafter, the deformed specimens were annealed at temperatures ranging from 1200 to 1500 K for 3.6 ks in a vacuum of 2 · 10 3 Pa. For observations of recrystallized microstructure, the specimens were sectioned perpendicular to the compression axis using a low-speed diamond cutter, and then a cross-sectional plane was mechanically polished with waterproof SiC papers (grades 320–4000) and buff-finished to a mirror surface using both 3 and 1 lm Al2O3 particles. Finally, these specimens were electrically polished in a mixture of acetic acid and perchloric acid (77:23 by volume) at iced-water temperature to remove any surface strained layer to ensure the subsequent field-emission gun scanning electron microscopy (FEG-SEM)/electron backscattered diffraction pattern (EBSD)/orientation imaging microscopy (OIM) observations. 2.2. Microstructure observations The grain boundary microstructures of the prepared specimens were quantitatively examined with a Hitachi S-4200 FEG-SEM instrument equipped with an OIM facility from TSL Inc. The OIM observations were conducted at an accelerating voltage of 30 kV and at an emission current of 10 lA. The electron beam was scanned on the surface using a step size in the range 2–14 lm. In this study, grain boundaries with R 5 29 were defined as CSL boundaries [36] and Brandon’s criterion [37] was used to categorize the grain boundaries. The grain boundary microstructural properties such as grain size, GBCD and grain boundary connectivity were evaluated on the basis of OIM data. The GBCD to be shown in this paper is given by the length fraction. In particular, details of the evaluation of the grain boundary connectivity are discussed in the following section. On the basis of grain boundary microstructure evaluation, the correlations between microstructural parameters, e.g., GBCD vs. grain boundary connectivity, were statistically analyzed using the least squares fitting procedure. The fitted curves and the standard deviations are shown by solid and broken lines, respectively, in the figures.
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
2.3. Analysis of grain boundary connectivity 2.3.1. Quantification of random boundary cluster The 2D network of grain boundaries contains clusters consisting of all the interconnected boundaries of a like type. We paid particular attention to the clusters in which only random boundaries were interconnected, because random boundaries are susceptible to intergranular percolative phenomena. The total length of each random boundary cluster was measured on the basis of OIM data, and was defined as ‘‘the length of cluster’’ by analogy with the percolation theory [34]. On each measurement of the random boundary cluster length, the boundary clusters that cross the edge of the analyzed area were taken out to decrease the experimental error. 2.3.2. Quantification of resistant triple junction We classified triple junctions into four types, 3-CSL, 2-CSL, 1-CSL and 0-CSL, following Fortier et al. [38,39] based on how to connect the grain boundaries with different characters at a triple junction. For example, a 2-CSL triple junction is composed of two CSL boundaries and one random boundary. In order to assess the resistance to percolation degradation, we consider the distribution of only those triple junctions that are composed of at least one random boundary, following Kumar et al. [40]. Therefore, the 3-CSL triple junctions can be taken out of consideration, because they are inactive entities in the process of arresting advancing corrosion on the assumption that the percolative front would never approach them. Kumar et al. [40] have proposed a new parameter based on the triple junction types defined by Fortier et al. [38,39], f2CSL/ (1 f3CSL), for evaluation of continuous percolative paths in the microstructure, where f2CSL refers to the frequency of triple junctions that have two CSL boundaries and are thereby able to arrest intergranular penetration and (1 f3CSL) is the frequency of triple junctions that are active unit entities in the microstructure. Using the method of Kumar et al., we evaluated the frequency of the resistant triple junctions in the microstructure. 2.4. Corrosion tests For corrosion tests, we used commercially available SUS304 stainless steel. The SUS304 specimens of 40 mm · 16 mm · 3.5 mm in dimension were solution treated at 1323 K for 1.8 ks and then water-quenched. After the surface oxide layer was removed using mechanical polishing with waterproof SiC papers, some specimens were subjected to a thermomechanical treatment to control grain boundary microstructures. The conditions of thermomechanical treatment for each sample are shown in Table 1: specimens A and C were as-solution treated, specimen B received 11% cold rolling and was annealed at 1400 K for 5 h, and then received 3% cold rolling and annealed at 1400 K for 1 h, and specimen D received 16% cold rolling and was annealed at 1400 K for 1 h. After the thermomechanical treatment at
3619
Table 1 The annealing conditions for each specimen subjected to intergranular corrosion test Specimen
Reduction rate, F (%)
Annealing temperature, T (K)
Annealing time, t (h)
A B C D
– 17 + 3 – 16
1323 1400 1323 1400
0.5 5+1 0.5 1
1400 K, the samples were water-quenched. The grain boundary microstructures in these samples were observed using the OIM technique and then statistically analyzed. The intergranular corrosion resistance for SUS304 specimens was evaluated using a commonly used ferric sulfate– sulfuric acid test after sensitization at 923 K for 2 h and air cooling. The specimens were boiled in ferric sulfate– 50% sulfuric acid for 24 or 48 h. The tested specimens were observed using SEM. 3. Results and discussion 3.1. Recrystallized grain structures in SUS304L from single crystals with different orientations Recrystallized grain structures are often affected by initial or deformed structures like grain orientation. Kobayashi et al. have reported that the grains in molybdenum polycrystals recrystallized from deformed single crystals develop different grain orientation clusters in which they have similar orientations because of different initial orientation of single crystals [41]. Fig. 1 shows the inverse pole figures for SUS304L polycrystals recrystallized from single crystals with different initial orientations. For comparison, the inverse pole figures for single-crystal specimens deformed to a strain of 40% are also shown in Fig. 1. These inverse pole figures were obtained from the cross-section perpendicular to the loading axis in the compression test. Looking at the pole figures for the specimens recrystallized at 1300, 1400 and 1500 K, the grain orientation tends to be located between Æ0 0 1æ and Æ1 1 1æ except for the specimen with the 001 initial orientation. In contrast, the grain orientation in the 001 specimen is distributed near the center of the stereographic unit triangle. The difference in the grain orientations in the deformed state may cause a difference in the grain orientations in recrystallized specimens. The crystal orientations of deformed 101, 111 and 213 singlecrystal specimens were found to be sharply concentrated near Æ1 0 1æ because of crystal rotation associated with slip deformation by compression, whereas the crystal orientation of deformed 001 single crystal was spread between Æ0 0 1æ and Æ1 1 3æ, which are both consistent with the result predicted by Calnan [42] for the crystal rotation in copper under compression. The recrystallized grains in a singlecrystal specimen were sometimes related to the deformed matrix by a 40 Æ1 1 1æ rotation [43]. However, we could
3620
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
Fig. 1. Inverse pole figures for SUS304L polycrystals recrystallized at different temperatures from single crystals with different orientations. These inverse pole figures were obtained from the cross-sections perpendicular to the compression axis. These specimens were uniaxially compressed to 40% strain before annealing.
not find such a relation between the recrystallized grains and deformed matrix. This is probably because of the introduction of extensive twin-variants in the microstructure due to a low stacking fault energy in SUS304L stainless steel. Furthermore, one can see that the grain orientation in the 101, 111 and 213 specimens annealed at 1200 K is likely to be localized near 101 orientation in contrast to those in other samples annealed at higher temperatures. This is because they predominantly arise from unrecrystallized areas, namely from deformed grains. Accordingly, we excluded the data associated with the unrecrystallized specimens from any analyses discussed in the following section.
tend to be less localized for low stacking fault energy face-centered cubic materials, with decreasing effective grain size. It is evident that the increase of twin (R3) boundaries is predominantly responsible for the increase in the number of CSL boundaries, as in other materials with a lower stacking fault energy [45]. Furthermore, the interaction of twin boundaries with random boundaries often causes segments of random boundaries to change into CSL boundaries, resulting in the random boundary network being broken up [24,40]. These findings show that the grain growth, that is, the grain boundary migration, will be accompanied by the formation of R3 twin boundaries as suggested by Gleiter [46].
3.2. Relation between GBCD and grain size The GBCD is closely related to the grain size. The frequency of CSL boundaries has been found to decrease with increasing grain size for polycrystalline materials with body-centered cubic and face-centered cubic structures having a high stacking fault energy produced by thermomechanical processing [44]. However, in the case of recrystallized SUS304L austenitic stainless steel having a low stacking fault energy, the frequency of CSL boundaries increases with increasing grain size as shown in Fig. 2 because of multiple twinning during grain growth. As the result of multiple twinning, grain orientation distributions
Fig. 2. Changes in the frequencies of low-angle, R3 and CSL boundaries as a function of grain size in SUS304L stainless steel.
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
3.3. Resistant triple junction distribution Following Kumar et al. [40], the frequency of triple junctions resistant to percolation of intergranular degradation, f2CSL/(1 f3CSL), was measured using OIM data for recrystallized SUS304L and will be discussed in connection with both the grain size and the GBCD. Fig. 3(a) shows the frequency of resistant triple junctions as a function of the grain size. The resistant triple junction fraction f2CSL/(1 f3CSL) appears to depend on the grain size in a parabolic manner. As mentioned above, the interaction of twin boundaries with random boundaries often results in the formation of segments of CSL boundaries according to the R-product rule, which causes an increase of the resistant triple junction fraction. The finding in Fig. 3(a) suggests that a larger extent of grain boundary migration is necessary to produce more twin boundaries. Fig. 3(b) presents the relationship between the frequency of resistant triple junctions and the frequency of CSL boundaries. For comparison, data for Inconel 600 [40] and Cu [40] are included in Fig. 3(b). It is evident that the frequency of resistant triple junctions increases with increasing CSL boundary fraction. Kumar et al. suggested that percolative paths in the microstructure will be broken if the resistant triple junction fraction is more than 35% according to the random percolation model [40]. In other words, the percolation threshold based on the triple junction distribution is a frequency of resistant triple junctions of 35%. An extrapolation of the data plotted in Fig. 3(b) gives the frequency of CSL boundaries as approximately
Fig. 3. Changes in the frequency of resistant triple junction as functions of (a) the grain size and (b) the frequency of CSL boundaries.
3621
70% at the resistant triple junction fraction of 35%. Interestingly, the estimated value of CSL boundary fraction is well consistent with the CSL fraction corresponding to the percolation threshold experimentally determined according to the maximum random boundary clusters as mentioned in the following section. 3.4. Random boundary cluster length and percolation threshold Since the character of single triple junctions is a measure for the evaluation of grain boundary connectivity, we need to know how long or how many random boundaries are interconnected in the grain boundary network. Accordingly, we measured the length of each random boundary cluster, i.e., the total length of all interconnected random boundaries in each cluster. Fig. 4 shows an example of a random boundary cluster identification: all grain boundaries (Fig. 4(a)) and only random boundaries (Fig. 4(b)). An interconnection of random boundaries highlighted by a bold black line in Fig. 4(b) is an example of a single random boundary cluster. We especially pay attention to the
Fig. 4. Example of the random boundary cluster identification: (a) showing full networks of grain boundaries and (b) only the random boundaries. The R3 and random boundaries are shown by bold black and thin black lines, respectively, in (a). The interconnected random boundaries highlighted by bold black line in (b) is an example of a single random boundary cluster.
3622
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
maximum cluster of random boundaries because it would essentially relate to percolation length of intergranular phenomena. Fig. 5 shows the maximum (Fig. 5(a)) and the average (Fig. 5(b)) random boundary cluster lengths in SUS304L stainless steel as a function of the grain size. The maximum random boundary cluster length, Smax, is likely to decrease with increasing grain size, although the data scatter is large. In contrast to this experimental observation, according to the percolation theory, the maximum cluster mass (length) of bonds susceptible to percolation depends only on the frequency of susceptible bonds and does not depend on the size of the lattice. As shown in Fig. 2, the frequency of CSL boundaries increases with increasing grain size in SUS304L. In addition, an increase of CSL boundary fraction yields a decrease in the maximum random boundary cluster length as shown in the following section. Thus, the observed grain size dependence of Smax may have resulted from the grain size dependence of the CSL boundary fraction. The average random boundary cluster mass, Save, seems to be less dependent on grain size. Fig. 6(a) and (b) shows Smax and Save, respectively, as a function of the frequency of CSL boundaries. It is found that the maximum random boundary cluster length Smax depends significantly on the CSL boundary fraction. An important finding is that Smax in terms of the random boundary connectivity drastically decreases with increasing CSL boundary fraction in the range of CSL boundary fraction 60–80%. In contrast, Save is less dependent on the CSL boundary fraction as shown in Fig. 6(b).
Fig. 5. Lengths of (a) the maximum and (b) the average random boundary clusters as a function of the grain size.
Fig. 6. Lengths of (a) the maximum and (b) the average random boundary clusters as a function of the frequency of CSL boundaries.
In previous work on grain boundary engineering, the experimental results have been discussed in connection with a percolation threshold (35% resistant (65% susceptible) boundaries) from a randomly assembled network. As mentioned in Section 1, Schuh et al. [32] pointed out that the percolation threshold would shift toward a resistant boundary fraction of 50–75% when the crystallographic constraint is enforced. Thus, the application of the percolation theory based on a randomly assembled network to
Fig. 7. Percolation probability along random boundaries as a function of the frequency of CSL boundaries, which leads to the percolation threshold occurring at approximately 70% of CSL boundaries. The percolation thresholds based on random percolation and on constrained percolation by Schuh et al. are shown for comparison.
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
understand bulk properties related to percolation phenomena can be misleading. However, to our knowledge, the percolation threshold for a random boundary network
Fig. 8. Relationship between the maximum random boundary cluster length and the frequency of resistant triple junctions. Table 2 The frequencies of CSL boundaries and resistant triple junctions, and the maximum length of random boundary clusters in the specimens for corrosion tests Specimen
GBCD, FR
Max. cluster length (lm)
f2CSL/(1
A B C D
0.68 0.80 0.55 0.55
7600 2300 10500 16800
0.11 0.28 0.10 0.19
f3CSL)
3623
has not been experimentally determined on the basis of microstructural observation. It is useful to give the percolation threshold as a critical value for the design and control of the GBCD in grain boundary engineering. According to the percolation theory, the percolation probability along susceptible boundaries can be expressed by the ratio of the maximum cluster length (mass) to the size of the system. The inflection point on a percolation probability curve as a function of the resistant boundary fraction gives a percolation threshold. Fig. 7 shows the percolation probability of SUS304L polycrystals as a function of the frequency of CSL boundaries, where the percolation probability is given by the maximum random cluster length normalized by the total length of full grain boundaries in the area analyzed. The observed percolation probability curve, which was obtained by the least squares fitting procedure using a power law function, gives the percolation threshold occurring at 70 ± 5% CSL boundaries (30 ± 5% random boundaries). The obtained value of percolation threshold is much higher than the theoretical value from the random percolation theory, approximately 35% resistant boundaries (65% susceptible boundaries), but agrees well with the value estimated from the constrained percolation model [34] within experimental error. The present results based on OIM data are limited to 2D microstructure topology. In the light of percolation models [1,33,34,47], the percolation threshold for 3D topology will be further increased to more than 70% CSL boundaries.
Fig. 9. SEM micrographs for specimen A and specimen B with frequencies of CSL boundaries of 68 and 80%, respectively, after the ferric sulfate–sulfuric acid test for 24 h: (a) · 200; (b) · 500.
3624
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
3.5. Relation between random boundary cluster length and resistant triple junction fraction The relation between the maximum random boundary cluster length Smax and the resistant triple junction fraction f2CSL/(1 f3CSL) is shown in Fig. 8. It is found that Smax is a function of f2CSL/(1 f3CSL) though data scatter is relatively large. The maximum random boundary cluster length Smax is likely to decrease with increasing f2CSL/ (1 f3CSL). 3.6. Influence of grain boundary connectivity on intergranular phenomena In previous sections, grain boundary connectivity was qualitatively evaluated on the basis of the percolation analyzed by both the triple junction distribution and the random boundary cluster length, and then examined in terms of the GBCD. In this section, we correlate experimentally measured f2CSL/(1 f3CSL) and Smax with corrosion property of SUS304 polycrystals. For this purpose,
four types of SUS304 specimens with different grain boundary microstructures were subjected to ferric sulfate–sulfuric acid tests. The annealing conditions and the evaluated microstructural parameters for each SUS304 specimen are shown in Tables 1 and 2, respectively. In particular, the comparison of corrosion properties between specimens C and D is particularly interesting because these specimens have the same CSL boundary fraction but different random boundary connectivities. Fig. 9 shows SEM micrographs for specimen A and specimen B after the ferric sulfate–sulfuric acid test for 24 h. As seen in Table 2, the frequencies of CSL boundaries are 68% (below the percolation threshold) and 80% (above the percolation threshold) in specimens A and B, respectively. The SEM micrographs reveal that grain boundaries were heavily corroded in specimen A, while there is no significant sign of heavy intergranular corrosion in specimen B. These observations show that a high frequency of CSL boundaries (more than the percolation threshold) gives rise to a pronounced resistance to intergranular corrosion.
Fig. 10. SEM micrographs of the surfaces and the cross-sections in specimens C and D after the ferric sulfate–sulfuric acid test for 48 h, showing the influence of grain boundary connectivity on corrosion percolation. The frequency of resistant triple junctions is higher in sample D (19%) than in sample C (10%) but both samples have the same frequency of CSL boundaries (55%).
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
Furthermore, it is worth examining how the connectivity of susceptible (random) boundaries can affect intergranular corrosion. It would be expected that intergranular corrosion depends on the connectivity of susceptible boundaries. In the light of this prediction, a question arises: what would be an appropriate ranking parameter to best reflect percolative properties? For this purpose, two specimens (specimens C and D), which had the same CSL boundary fraction (55%) but different random boundary connectivities, were subjected to ferric sulfate– sulfuric acid tests, and the results were compared to the experimentally obtained parameters given in Table 2. Although the grain boundary microstructures were characterized by OIM analyses on the specimen surface, similar microstructure can be expected on the specimen surface and the cross-section parallel to corrosion percolation, because twin-dominated microstructures have essentially a random texture. Fig. 10 shows SEM micrographs of the surfaces and the cross-sections of specimens C and D after the ferric sulfate–sulfuric acid test for 48 h. Of particular importance is the observation that the corrosion in the two samples is quite different because of different random boundary connectivities even though the grain boundary character distribution is the same. Sample C displays extensive intergranular corrosion percolation. In contrast, specimen D is immune from corrosion percolation, although slight intergranular corrosion is observed on the specimen surface. The resistant triple junction fraction is approximately twice as high in specimen D than in specimen C. Conversely, the maximum random boundary cluster length is lower in specimen C than in specimen D. Although there is a tendency for the length of the maximum random boundary cluster to decrease with increasing resistant triple junction fraction, as shown in Fig. 8, we selected these samples (C and D) for corrosion tests from all the SUS304 specimens in order to assess what is the more useful ranking parameter associated with the grain boundary connectivity to reflect percolative phenomena. Judging from the results mentioned above, the resistant triple junction fraction was more reflective of percolative intergranular corrosion than the maximum random boundary cluster length. 4. Conclusions Connectivity and percolation in random grain boundary networks in austenitic stainless steel were studied in connection with the GBCD. The connectivity of random grain boundaries was quantitatively evaluated using both the triple junction distribution and the random boundary cluster length, and then these measured parameters were correlated with intergranular corrosion of SUS304 stainless steel. The main results obtained were as follows. 1. The frequency of percolation-resistant triple junctions, f2CSL/(1 f3CSL), increases with increasing frequency of CSL boundaries.
3625
2. The maximum length of random boundary clusters (the maximum length of interconnected random boundary networks) drastically decreases with increasing frequency of CSL boundaries probably near the percolation threshold, leading to a percolation threshold occurring at approximately 70 ± 5% CSL boundaries (30 ± 5% random boundaries) and at approximately 35% resistant triple junctions. 3. The connectivity of random boundaries, which are susceptible to intergranular degradation, has a strong influence on intergranular corrosion in SUS304 stainless steel polycrystals. The resistant triple junction distribution is a more important ranking parameter than the maximum of random boundary cluster length for susceptibility to percolative intergranular corrosion. The higher the resistant triple junction fraction, the more the SUS304 polycrystals are immune from intergranular corrosion. Acknowledgements The authors would like to express their thanks to Prof. H. Kokawa (Tohoku University) for his arranging the corrosion tests and useful discussions, Profs. T. Soji (Tohoku University) and P. Lejcek (Institute of Physics, Academy of Sciences of the Czech Republic), Drs. R. Ishibashi, T. Horiuchi, J. Kuniya and M. Yamamoto (Hitachi Ltd) for their useful discussions, Mr. T. Matsuzaki (Tohoku University) for his help with experimental works, Mr. M. Michiuchi for his help with corrosion tests and Dr. V. Yardley (Tohoku University) who kindly read and corrected the manuscript. A SUS304L stainless steel single crystal was supplied by Hitach Ltd. This work was partially supported by a Grant-in-Aid for the innovative and viable nuclear energy technology development program from the Institute of Applied Energy (IAE), and a Grant-in-Aid for Basic Research (A) (15201015) from Japan Society for the Promotion of Science (JSPS). These supports are greatly appreciated. References [1] Wells DB, Stewart J, Herbert AW, Scott PM, Williams DE. Corrosion 1989;45:649. [2] Gaudett MA, Scully JR. Metall Mater Trans 1994;25A:775. [3] Procter RPM. Mater Sci Eng 1994;A184:135. [4] Brumm MW, Grabke HJ, Wagemann B. Corros Sci 1994;36:37. [5] Sklenicka V. Mater Sci Eng 1997;A234–236:30. [6] Lehockey EM, Palumbo G, Lin P, Brennenstuhl AM. Scripta Mater 1997;36:1211. [7] Tsurekawa S, Watanabe T. Mater Res Soc Symp Proc 2000;586: 237. [8] Yamaura S, Tsurekawa S, Watanabe T. Mater Trans 2003;44:1494. [9] Gleiter H, Chalmers B. Prog Mater Sci 1972;16:1. [10] Chadwick GA, Smith DA, editors. Grain boundary structure and properties. Academic Press; 1976. [11] Ishida Y, editor. Trans JIM 1986; suppl 27. [12] Sutton AP, Balluffi RW. Interfaces in crystalline materials. Oxford Science Publishers; 1995. [13] Watanabe T. Res Mech 1984;11:47. [14] Watanabe T, Fujii H, Oikawa H, Arai KI. Acta Metall 1989;37:941. [15] Hirano T. Acta Metall Mater 1990;38:2667.
3626
S. Tsurekawa et al. / Acta Materialia 54 (2006) 3617–3626
[16] Crawford DC, Was GS. Metall Trans 1992;23A:1195. [17] Watanabe T, Hirano T, Ochiai T, Oikawa H. Mater Sci Forum 1994;157–162:1103. [18] Lin P, Palumbo G, Erb U, Aust KT. Scripta Metall Mater 1995;33:1387. [19] Palumbo G, Lehockey EM, Lin P, Erb U, Aust KT. Mater Res Soc Symp Proc 1997;458:273. [20] Lehockey EM, Palumbo G. Mater Sci Eng 1997;A237:168. [21] Thaveeprungsriporn V, Was GS. Metall Mater Trans 1997;28A:2101. [22] Lehockey EM, Palumbo G, Lin P, Brennenstuhl A. Metall Mater Trans 1998;29A:387. [23] Lehockey EM, Limoges D, Palumbo G, Sklarchuk J, Tomantschger K, Vincze A. J Power Sources 1999;78:79. [24] Shimada M, Kokawa H, Wang ZJ, Sato YS, Karibe I. Acta Mater 2002;50:2331. [25] Kobayashi S, Yoshimura T, Tsurekawa S, Watanabe T. Mater Trans 2003;44:1469. [26] Ishibashi R, Horiuchi T, Kuniya J, Yamamoto M, Tsurekawa S, Kokawa H, et al. Mater Sci Forum 2005;475–479:3863. [27] Furuya Y, Hagood NW, Kimura H, Watanabe T. Mater Trans JIM 1998;39:1248. [28] Watanabe T. Mater Sci Eng 1994;A176:39. [29] Palumbo G, King PJ, Aust KT, Erb U, Lichtenberger PC. Scripta Metall Mater 1991;25:1775.
[30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41]
[42] [43] [44] [45] [46] [47]
Wang G, Zuo L, Esling C. Philos Mag A 2002;82:2499. Nichols CS, Clarke DR. Acta Metall Mater 1991;39:995. Schuh CA, Minich RW, Kumar M. Philos Mag 2003;83:711. Frary M, Schuh CA. Philos Mag 2005;85:1123. Stauffer D, Aharony A. Introduction to percolation theory. London: Taylor and Francis; 1992. Schuh CA, Kumar M, King WE. Acta Mater 2003;51:687. Watanabe T. J Phys 1985;46:C4–C555. Brandon DG. Acta Metall 1966;14:1479. Fortier P, Aust KT, Miller WA. Acta Metall Mater 1995;43:339. Fortier P, Miller WA, Aust KT. Acta Mater 1997;45:3459. Kumar M, King WE, Schwartz AJ. Acta Mater 2000;48:2081. Kobayashi S, Kobylansky A, Nagano T, Tsurekawa S, Watanabe T. In: Sakai T, Suzuki HG, editors. Proc. 4th Int. Conf. on Recrystallization and Related Phenomena. Japan Institute of Metals; 1999. p. 167. Calnan EA. Acta Metall 1954;2:865. Humphreys FJ, Hatherly M. Recrystallization and related annealing phenomena. Pergamon; 1995. Watanabe T. Textures Microstruct 1993;20:195. Lin P, Palumbo G, Aust KT. Scripta Mater 1997;36:1145. Gleiter H. Acta Metall 1969;17:1421. McGarrity ES, Duxbury PM, Holm EA. Phys Rev E 2005; 71:026102.
