2021 Volume 62 Issue 2 Pages 239-245
The major objective of the present study was to investigate the effect of the constraint of grain-boundary sliding and its accommodation at triple junctions on the creep fracture of tricrystals. Tricrystals of pure aluminum and copper having ⟨110⟩-tilt Σ3, 3, 9 boundaries were grown by the Bridgman method. Creep tests were carried out for tensile specimens in which the Σ9 boundary made an angle of 45° with the tensile axis at temperatures above 0.80 TM, where TM stands for the melting temperature on the absolute temperature scale. In both aluminum and copper tricrystals, dominant grain-boundary sliding occurred along the Σ9 boundary. The aluminum tricrystal fractured along a plane across grains, far separated from the triple junction. In contrast, the copper tricrystal fractured via a complete separation along the Σ9 boundary followed by a tear-off of the remaining portion. This difference is accounted for by the different local deformation behaviors around the triple junctions to release the stress concentration induced by the constraint of Σ9 sliding, e.g., grain-boundary sliding along the Σ3 boundary in aluminum and crack formation along the Σ9 boundary in copper.
Grain-boundary sliding, i.e., the relative displacement of neighboring grains along a boundary, is known as a major deformation mode at temperatures above 0.5TM, where TM stands for the melting temperature on the absolute temperature scale. Grain-boundary sliding directly reflects the character of the boundary. The coincidence site lattice (CSL) theory1) is a simple method to geometrically characterize grain boundaries based on the orientation relationship between grains adjacent to the boundary. In the CSL theory, the lattices of neighboring grains are extended and overlapped. The fundamental number to describe the orientation relationship of the overlapped lattices is an odd-numbered Σ-value of 3 or larger. The Σ-value indicates that 1/Σ of the lattice sites is sheared by both lattices. To fully specify the geometrical character of the grain boundary, the crystallographic index of the boundary plane is necessary. For instance, a Σ3{111} boundary indicates that the grains adjacent to the boundary have a Σ3 relationship and the boundary plane is {111}. In face-centered-cubic (FCC) metals, e.g., aluminum (Al) and copper (Cu), the Σ3{111} boundary is a coherent twin boundary and is known to have the lowest energy among all CSL boundaries. Since the energy of the coherent twin boundary is proportional to the stacking fault energy (SFE) of the metal, the Σ3{111} boundaries in metals with low SFE are stable and do not slide easily at high temperatures.
The concept of grain-boundary engineering2) has long been studied on the basis of the idea that the performance of a polycrystalline material can be improved by increasing the ratio of low-energy boundaries, e.g., coherent twin boundaries (Σ3{111} boundaries in FCC metals), in the material. Studies showed that the ratio of low-energy boundaries was successfully increased through repeated deformation/recrystallization processes.3,4) If the ratio of Σ3 boundaries is increased, the possibility of encountering two Σ3 boundaries along a junction will increase. At the junction, a Σ9 boundary is formed following the branching rule of grain boundaries.5) It is known that the Σ9 boundary has much higher energy than the Σ3 boundary6,7) and slides much more easily at high temperatures. In the following, the junction at which two Σ3 boundaries and one Σ9 boundary meet is referred to as a Σ3, 3, 9 triple junction. High-temperature deformation around a Σ3, 3, 9 triple junction is of fundamental interest because a stress concentration is induced by the constraint of the Σ9 boundary sliding at the junction. It is expected that local deformation around the junction is activated to release the stress concentration, which affects the fracture of the material.
To study the deformation around a triple junction, it is preferable to use tricrystal specimens composed of three grains rather than to observe triple junctions in a polycrystalline material. However, far fewer experimental studies have employed tricrystal specimens than bicrystal specimens. This is probably due to the difficulty of growing orientation-controlled tricrystals. Hashimoto and co-workers8,9) carried out pioneering works on the initial stage of creep deformation of Al tricrystals having ⟨110⟩-tilt Σ3, 3, 9 boundaries. They showed that the suppression of grain-boundary sliding at the triple junction was accommodated by the formation of so-called folds, which were characterized as local slip bands activated on {111} or {100} planes. Recently, Okada et al.10) studied the creep deformation of Cu tricrystals of the same orientation. In the Cu tricrystals, due to the absence of slip on {100} planes, no fold formation was observed. Instead, short cracks formed along the grain boundaries. In the previous studies employing tricrystals with Σ3, 3, 9 boundaries,8–12) creep tests were carried out at relatively early stages of deformation. Deformation for longer testing times, especially fracture and its relationship with locally activated deformation around the triple junction, e.g., folds and cracks, is not clear at the present stage. In addition, experimental studies concerning high-temperature deformation of tricrystals were carried out mainly by the surface observation of deformed specimens.8–20) Observation of the interior of crept specimens is beneficial for investigating creep-induced damages in the interior of a specimen, which cannot be detected from the surface.
The major objective of the present study was to investigate the creep fracture of Al and Cu tricrystals having ⟨110⟩-tilt Σ3, 3, 9 boundaries. We also carried out cross-sectional observations of a Cu specimen crept for a relatively short time to detect the initial creep damage on the Σ9 grain boundary in the interior of the specimen.
Tricrystals having ⟨110⟩-tilt Σ3, 3, 9 boundaries are characterized by the misorientation angle, i.e., the tilt angle about a common axis between grains across each boundary, and by the dihedral angles, i.e., the angles between two boundaries.8) In an ideal Σ3, 3, 9 relationship, the tilt angles about a ⟨110⟩ axis are 70.5° and 39° for Σ3 and Σ9, respectively. Here, the 70.5° tilt about a ⟨110⟩ axis is equivalent to a 60° tilt about a ⟨111⟩ axis. When the boundaries are in the symmetrical positions, the boundary planes are {111} and {122} for Σ3 and Σ9 boundaries, respectively. The dihedral angles in the ideal tricrystal are 125° (between Σ3 and Σ9 boundaries) and 110° (between Σ3 boundaries). Figure 1 schematically shows the tilt angles θ1, θ2 and θ3 about the ⟨110⟩ axis perpendicular to the paper surface and the dihedral angles ϕ1, ϕ2 and ϕ3. In the figure, the two Σ3 boundaries are referred to as Σ3-1 and Σ3-2.
Grain orientation and boundary arrangement in a tricrystal having ⟨110⟩-tilt Σ3, 3, 9 boundaries. Tilt angles about the ⟨110⟩ axis are θ1, θ2 and θ3. Dihedral angles are ϕ1, ϕ2 and ϕ3. The Σ9 boundary makes an angle of 45° with the tensile axis (T.A.).
The purities of the starting materials used for the tricrystal growth were 99.999 mass% and 99.99 mass% for Al and Cu, respectively. The metal ingot and three single-crystalline seed crystals were placed at the upper and lower positions in a graphite mold, respectively. Crystal growth was carried out in a vacuum Bridgman furnace with a pressure below 4 × 10−3 Pa. After the ingot and the upper portion of the seed crystals were melted, the furnace was slowly moved upwards so that a tricrystalline ingot composed of three columnar grains having the same orientations as the seed crystals was obtained. Two Al tricrystals, A-1 and A-2, and one Cu tricrystal, C, were grown. Slices 3.5 mm thick were spark-cut from the grown tricrystal. The creep specimens with shoulders were spark-cut from the slices, in which the Σ9 boundary makes an angle of 45° with the tensile axis, as schematically shown in Fig. 1, so that the maximum shear stress acts on the Σ9 boundary. The middle portion of the specimen, i.e., the gauge portion, was 11 mm in length and 6 mm in width, and the triple junction was at the center of the gauge portion. After mechanical polishing, the surface of the specimen was finished by electrolytic polishing in 20 vol% perchloric acid in ethanol (cooled to −20°C prior to polishing) and in 35 vol% phosphoric acid in ethanol for Al and Cu, respectively. Coarse parallel lines having a spacing of 0.5 mm were scribed on the surface of the gauge portion using a diamond scriber to measure the amount of grain-boundary sliding. In some specimens, fine parallel lines having a spacing of 20 µm were scribed in an area of 1 mm × 1 mm square around the triple junction using femtosecond laser irradiation so that grain-boundary sliding close to the triple junction was detected. Two specimens each for Al and Cu were prepared, and they are referred to as specimens A-1, A-2 for Al and specimens C-1, C-2 for Cu. Specimens A-1 and A-2 were made from Al tricrystals A-1 and A-2, respectively. Specimens C-1 and C-2 were cut from the same Cu tricrystal C.
Creep tests were carried out in the Bridgman furnace using an apparatus to support and load the specimen. The atmospheres for the creep tests were air and argon (Ar) for Al and Cu, respectively. Creep tests were carried out until the fracture of specimens A-1 and C-1. The tests were terminated prior to the final fracture of specimens A-2 and C-2. Specimen C-2 was used to observe its cross sections in order to evaluate the creep-induced damages on the Σ9 boundary in the interior of the specimen. The conditions of the creep tests are summarized in Table 1. The temperature and stress of creep tests were the same as those in the previous study.10) They correspond to “transgranular creep fracture” (Al tricrystals) and “intergranular creep fracture” (Cu tricrystals) in the fracture mechanism maps.21) The procedures of cross-sectional observation are schematically shown in Fig. 2. First, a marker was drawn on the specimen surface using focused ion beam irradiation and the gauge portion was spark-cut in an appropriate size (Fig. 2(a)). Then one of the cross sections was mechanically polished to the marker (Fig. 2(b)). Finally, a part of the area under the marker was Ar-ion polished to obtain a smooth surface (Fig. 2(c)). A Hitachi ArBlade-5000 was used for ion polishing. Cross-sectional observation was carried out using a scanning electron microscope (SEM). Observation and orientation analysis were conducted by using an SEM, JEOL JSM-6400, combined with an electron backscatter diffraction analysis system, TSL OIM-5.
Preparation procedures for cross-sectional observation. (a) The gauge portion of a specimen is spark-cut. (b) One of the cross sections is mechanically polished to the marker. (c) A part of the area under the marker is Ar-ion polished to obtain a smooth surface for SEM observation.
The orientation relationships between grains across each grain boundary in the tricrystals are summarized in Table 2. A combination of rotation angle and axis was used to represent the orientation relationships. The deviations from the ideal relationships were small, and all tricrystals were confirmed to have Σ3, 3, 9 boundaries within Brandon’s criterion.22)
As shown in Table 1, specimen A-1 was deformed in tension under a tensile stress of 0.4 MPa at 0.86 TM. The creep test was interrupted at 600 s and 11.4 ks to observe the specimen surface. After the second observation (11.4 ks), the creep test was resumed until the final fracture at 616 ks.
At 600 s, small grain-boundary sliding was observed along the Σ9 boundary from the displacement of laser-scribed markers. The magnitude of sliding was zero at the triple junction and increased with the distance from the junction towards the maximum value of 3 µm. Fold formation was not observed at this stage.
At 11.4 ks, the Σ9 sliding increased to 30 µm at a point 700 µm from the triple junction. Grain-boundary sliding also occurred along the Σ3-2 boundary, as shown in Fig. 3. The magnitude of Σ3-2 sliding was 7.7 µm at a point 191 µm from the triple junction. This grain-boundary sliding is about one-fourth of that observed along the Σ9 boundary. Since the direction of Σ3-2 sliding was the opposite of that of the shear stress acting on the boundary, it is clear that the Σ3-2 sliding was transmitted by the Σ9 sliding via the triple junction. In other words, the Σ3-2 sliding was activated to accommodate the Σ9 sliding. Although a fold is recognized in grain A as indicated in the micrograph, the displacement of markers associated with the fold is much smaller than that along the Σ3-2 boundary.
SEM image taken around the triple junction (T.J.) of specimen A-1 after the 11.4 ks creep test. The displacement of laser-scribed markers clearly shows the grain-boundary sliding along the Σ3-2 boundary. A fold forms from the triple junction.
An SEM image after the final fracture is presented in Fig. 4. The fracture occurred across grains A and B along a plane about 6 mm from the triple junction, almost perpendicular to the tensile axis. It is apparent that the fracture occurred independently of the triple junction and grain boundaries. Large necking is recognized, i.e., the width of the fracture surface is about 30% of the initial value. The laser-irradiated square area of 1 mm × 1 mm around the triple junction was severely deformed. The area was extended to 1.95 mm in the tensile direction, i.e., the tensile strain reached 95% in the region. The magnitude of Σ3-2 boundary sliding was 68 µm, which is about one-fourth of that of the Σ9 boundary, 300 µm. Multiple folds parallel to the Σ9 boundary are also observed. The tops of the folds are on an extension of the Σ9 boundary, and the others are almost parallel to the Σ3-2 boundary. The displacements of markers associated with each fold were as small as those observed after the 11.4 ks creep. In a previous study,10) a sharp fold from the triple junction formed since the Σ9 boundary sliding was accommodated at the triple junction. Hence multiple folds formed in the present specimen due to the migration of the Σ9 boundary, which may have been induced by creep deformation.
SEM image of specimen A-1 taken after fracture at 616 ks. The fracture occurred across grains A and B, separated about 6 mm from the triple junction (T.J.). Multiple folds form from the migrating triple junction.
Specimen A-2 was deformed in tension under a tensile stress of 0.4 MPa at 0.86 TM. The creep test was interrupted five times to observe grain-boundary sliding, migration and fold formation. The rate of grain-boundary sliding was almost constant up to the creep time of 398 ks.
Grain-boundary sliding was considerably slower in specimen A-2 than in specimen A-1. For example, it took 38.4 ks for the Σ9 boundary to slide 30 µm, which was three times slower than the sliding for the Σ9 boundary in specimen A-1. This difference is not accounted for by the deviation from the ideal orientation relationship because, as shown in Table 2, the Σ9 boundary in specimen A-1 was closer to the ideal 39° ⟨110⟩ rotation but exhibited a threefold larger grain-boundary sliding rate than the Σ9 boundary in specimen A-2. Hence, the difference in grain-boundary sliding rates may be attributable to the morphological features of the boundary in the interior of the specimen, e.g., the flatness of the boundary plane and the inclination angle of the boundary with the specimen surface.
The sliding direction of the Σ3-2 boundary is reversed according to the position on the boundary, as clearly shown in the SEM image in Fig. 5, which was taken at 398 ks. This is because the Σ3-2 boundary slid in accordance with the Σ9 boundary close to the triple junction. On the other hand, in a region further distant from the triple junction, the Σ9 boundary slid in the same direction as the shear force acting on the boundary. Between the two regions, there is a region with no grain-boundary sliding. Similar to the case in specimen A-1, grain-boundary migration accompanying the triple junction occurred in specimen A-2, as shown in Fig. 5. Multiple fine folds with small displacements formed in Grain A.
SEM image of grain-boundary sliding along the Σ3-2 boundary in specimen A-2 after the 398 ks creep test. The sliding direction is reversed according to the position on the boundary. Grain-boundary migration accompanying the triple junction is recognized. Multiple folds form from the migrating triple junction.
Specimen C-1 was deformed in tension under a tensile stress of 4 MPa at 0.80 TM. The creep test was interrupted at 600 s and 260 ks to observe the specimen surface. After the second observation (260 ks), the creep test was resumed until the final fracture at 469 ks.
Grain-boundary sliding along the Σ9 boundary was zero at the triple junction and increased with distance from the junction. No fold formation was observed. These features are common to both specimens C-1 and C-2, irrespective of the testing time.
At 600 s, the magnitude of Σ9 boundary sliding was 18 µm at a position 500 µm from the triple junction. The formation of small voids about 1 to 2 µm in diameter was observed on the Σ9 boundary close to the triple junction.
An SEM image around the triple junction at 260 ks is presented in Fig. 6. We should note that the arrangement of grain boundaries is inverted from that in the Al specimens because the observation was made on the opposite surface. The magnitude of Σ9 sliding was 165 µm. A crack was formed from the triple junction along the Σ9 boundary.
SEM image taken around the triple junction (T.J.) of specimen C-1 after the 259 ks creep test. A crack forms from the triple junction along the Σ9 boundary.
An SEM image after the final fracture is presented in Fig. 7. From the morphology of the fracture surface, it is presumed that the fracture was initiated by a complete separation along the Σ9 boundary, followed by a tear-off of the remaining portion. The crack along the Σ9 boundary was induced by suppression of the Σ9 boundary sliding at the triple junction without accommodation, e.g., grain-boundary sliding on the Σ3 boundaries and fold formation from the triple junction. We can recognize cracks along the Σ3 boundaries. As described in the previous paper,10) short cracks were formed from the triple junction along the Σ3 boundaries. However, the cracks were shallow and did not penetrate through the specimen thickness and therefore had little effect on the final fracture of the specimen.
SEM image of specimen C-1 taken after fracture at 469 ks. The fracture initiated by separation along the Σ9 boundary, followed by a tear-off of the remaining portion.
The creep test was carried out at 0.80 TM under a tensile stress of 3.5 MPa for 600 s. The magnitude of sliding along the Σ9 boundary was 16 µm at a position 800 µm from the triple junction. The formation of small voids about 1 to 2 µm in diameter was observed on the Σ9 boundary close to the triple junction. Specimens C-1 and C-2 were prepared from the same tricrystal C. They exhibit similar grain-boundary sliding, i.e., 18 µm and 16 µm, under similar creep conditions. We assumed that C-2 was almost the same as C-1 and prepared for cross-sectional observation at the initial stage of creep deformation, i.e., 600 s. After the surface observation, the gauge portion was spark-cut, mechanically polished and Ar-ion milled to observe the cross section by SEM.
In order to evaluate creep-induced damage on the Σ9 boundary in the interior of the specimen, SEM observation was carried out at a cross section separated 3180 µm from the triple junction. An SEM image is presented in Fig. 8. As the arrows in the micrograph indicate, in the range from the surface to 300 µm depth, 11 voids were found on the Σ9 boundary. The linear density of voids, obtained simply by dividing 11 by 300 µm, is 0.037/µm. As shown in the enlarged micrograph, the voids were 2 to 4 µm in diameter. After the SEM observation, the cross section was mechanically polished and ion milled to observe the next cross section, separated by 1790 µm from the triple junction. Three voids, 1 to 3 µm in diameter, were observed in the range from the surface to 190 µm depth (0.016/µm). It is of interest that the distribution of voids on the Σ9 boundary is denser in the cross section further separated from the triple junction. This tendency shows that voids are more likely to form in a region where grain-boundary sliding is larger. It is presumed that for longer testing times, densely formed voids will coalesce and join with the mechanically formed crack from the triple junction, leading to the complete separation of the Σ9 boundary.
SEM image of void distribution along the Σ9 boundary in the interior of specimen C-2 after the 600 s creep test. The observed cross section was separated 3180 µm from the triple junction (T.J.).
In the Al tricrystal, intragranular deformation was dominant under the present experimental conditions, and the Σ3, 3, 9 boundaries had no effect on its fracture. In contrast, it is clear that the Σ3, 3, 9 boundaries caused embrittlement of the Cu tricrystal. The reason for no accommodation process in Cu is the lack of grain-boundary sliding along the Σ3 boundaries due to its lower stacking fault energy than Al. Another important factor is the lack of slip on {100} planes which most effectively accommodate the Σ9 grain-boundary sliding in the present Σ3, 3, 9 tricrystal.
Several internal voids were recognized on the Σ9 boundary far from the triple junction in a short creep, which were probably formed not by accommodation of the Σ9 boundary sliding at the triple junction, but by the Σ9 boundary sliding itself. The reason for the different void formation behaviors between Al and Cu tricrystals is not clear at the present stage. It might be related to the difference in grain-boundary diffusion to fill voids at the initial stage of their formation.
From the viewpoint of grain-boundary engineering, it might be suggested that the increase in Σ3 boundaries has an adverse effect on the prevention of Cu and other low-SFE materials from high-temperature brittleness.
Creep tests were carried out for Al and Cu tricrystals having ⟨110⟩-tilt Σ3, 3, 9 grain boundaries at temperatures of 0.86 TM (Al tricrystals) and 0.80 TM (Cu tricrystals). Dominant grain-boundary sliding occurred along the Σ9 boundary. The Al tricrystal fractured in the grains far separated from the triple junction at 616 ks. On the other hand, in the Cu tricrystal, fracture was initiated by separation along the Σ9 boundary, followed by a tear-off of the remaining portion at 469 ks. The different local deformations at the triple junction account for the large difference in the fracture behaviors between Al and Cu tricrystals. In the Al tricrystal, the Σ9 boundary sliding was accommodated mainly by grain-boundary sliding along one of the Σ3 boundaries. In the Cu tricrystal, neither Σ3 sliding nor fold formation occurred. The Σ9 sliding induced a crack along the boundary from the triple junction. From cross-sectional observation of the Cu tricrystal crept for a short time (600 s), voids formed along the Σ9 boundary in the interior of the specimen. It is presumed that for longer testing times, voids will coalesce and connect to the crack initiated from the triple junction, resulting in separation along the Σ9 boundary.
We are grateful to Mr. Atsunori Ohnishi for his technical assistance. This work was partly supported by The Amada Foundation.
