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Local Plastic Deformation of Kink Band Opposing External Stress in Mg–Zn–Y Alloy
2024 Volume 65 Issue 1 Pages 101-104
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2024 Volume 65 Issue 1 Pages 101-104
In order to determine a factor of kink strengthening, spatial distribution of crystal rotation, kink interface rotation and plastic strain in deformed kink bands was investigated. Fine mesh was drawn on kink microstructure using focused-ion beam to map the plastic strain caused by the further deformation. Results clearly showed the existence of local deformation in the opposite direction of the external stress. This opposing plastic deformation was explained well the observed crystal rotation and rotation of the kink interface, provided that the rank-1 connection was maintained during deformation. The constraint between connected kink bands was suggested to be the origin of this opposite deformation and one of the factors leading to kink strengthening.
The Mg–Zn–Y alloy developed by Kawamura et al.1) has a long-period stacking ordered (LPSO) phase. The LPSO phase has a periodic layered structure with the soft layer composed of α-Mg and the hard layer enriched with Zn and Y atoms.2–5) The easy-slip system in this layered structure is restricted to ⟨a⟩ basal plane due to the existence of the hard layer.6) Therefore, when the alloy is compressed from a direction parallel to the basal plane, the kink deformation becomes the dominant plastic deformation mode.7) Kink deformation is a plastic deformation in which shear deformation on a constrained slip plane and rigid body rotation occur simultaneously.8,9) The deformation products are kink band, ridge kink and ortho kink.9) The kink microstructure is defined as the structure in which these kinks are connected in this study. The kink/matrix interface and kink/kink interface are called the kink interface. The introduction of kink microstructure suppresses the basal slip and strengthen the alloy.10,11) This strengthening by the kink microstructure is called “kink strengthening”, but its mechanism has not been fully clarified.
Geometrical quantities of the kink such as the kink interface orientation and the crystallographic orientation between the matrix and kink affect the kink strengthening.12) However, there are few studies on the geometry of kink after the work of Hess and Barrett.13) Recently, Inamura14) systematically formulated the geometry of kink when only one slip system is active using the continuity of deformation (rank-1 connection). Inamura’s model not only describes the actual geometry of kink formed in LPSO-Mg alloy, but also reveals the formation of the disclination in the kink microstructure,14,15) suggesting that the disclination contributes to the strengthening. Furthermore, Inamura’s model shows that cooperative deformation is required for connecting kink bands to maintain the continuity of deformation under external load. Taylor model of plastic deformation of polycrystals takes such cooperative deformations into account.16) However, in case of that the number of slip system is very limited as in the material causes kink deformation, slip deformations with a negative Schmid factor, i.e. deformations against external forces, may also occur. The existence of such deformation is expected to contribute to the kink strengthening. In this study, we demonstrate the existence of such kink band in LPSO-Mg alloy by a quantitative analysis of plastic strain in kink bands.
Directionally solidified (DS) specimen with nominal composition Mg85Zn6Y9 (at%), consisting of the single phase of 18R LPSO phase, was used.17) Master ingot was prepared by induction melting and the DS specimens were prepared by Bridgman technique under Ar atmosphere. In the LPSO phase, (0001) is almost parallel to the growth direction.17)
Kink deformation occurs when a compressive load is applied in the direction parallel to the growth direction (0° compression).7,17) On the other hand, Schmid factor of basal slip is nearly 0.5 in some of the grains and basal slip occurs when the specimen is compressed from a direction inclined by 45° to the growth direction (45° compression).7,17) Basing on these plastic deformation behavior, a double compression test was carried out on the DS specimen to deform the kink microstructure.11) Figure 1 shows a schematic diagram of the double compression test. For the 0° compression, a rectangular specimen approximately 5 mm × 2.5 mm × 5 mm in size was made by an electrical discharge machine. The longitudinal direction of the specimen was parallel to the growth direction. The specimen surface was carefully finished by buffing to remove the damaged surface layer. Compression tests were carried out at a nominal strain rate of 1.67 × 10−4 s−1 at room temperature (RT) using Shimadzu AG-XPLUS. The load was stopped when the nominal plastic strain reached approximately 2%. In the 45° compression, a rectangular specimen of 2 mm × 2 mm × 4 mm in size was made from the specimen after 0° compression. The longitudinal direction of the specimen made an angle of 45° to the growth direction. The compression test was made under the same condition of 0° compression. The load was stopped when the nominal plastic strain reached approximately 4%.
Schematic diagram of a double compression test. The kink is formed by 0° compression and then deformed by 45° compression. The FIB-mesh was introduced before the 45° compression.
The specimen surface after 0° compression was buffed and finished by ion milling using ArBlade5000 (HITACHI). Field-emission gun-type scanning electron microscopy (FE-SEM, HITACHI SU5000) equipped with an EBSD detector (TSL OIM DVC5) was used for the observation of microstructure. The crystal orientation was analyzed using orientation imaging microscopy (OIM) software.
For simple and reliable analysis, a kink with crystal rotation axis of $\langle 1\bar{1}00\rangle $ which is perpendicular to the surface of observation is required. Such kink is formed by only one $\langle 11\bar{2}0\rangle $ basal slip out of 3,18,19) and then the plastic deformation by 45° compression becomes a plane-strain on the plane of the observation. Such kinks were selected and analyzed in this study. The change in crystal rotation angle of inside kink band (Δθ) and the rotation of the kink interface orientation (Δφ) were determined at the same location before and after the 45° compression. A rotation in which the right-handed screw advances in the direction of electron beam (e1 in Fig. 1) is defined as a positive rotation.
Mesh was introduced on the kink of interest by a focused ion beam machine (FIB, JIB-4500, JEOL) after 0° compression. The line width, grid spacing and depth of the mesh were 70 nm, 1 µm and 66 nm respectively. The horizontal direction of the mesh was set to be parallel along the basal plane. The shear strain (ε23) was determined from the lengths and relative angles of the edges of each mesh before and after the 45° compression using the infinitesimal deformation approximation. Spatial distribution of ε23 was mapped on the back scattered electron (BSE) image after 45° compression. After shear strain analysis, the mesh was removed by the ion milling for EBSD measurement.
The kink microstructure after the compression test is shown in Fig. 2(a)–(g). Figure 2(a) shows the Inverse Pole-Figure (IPF) map after 0° compression and the distribution of the crystal rotation axes at the positions indicated by the squares. The specimen surface normal orientation and crystal rotation axis are parallel to $\langle 1\bar{1}00\rangle $, indicating that this kink satisfies the conditions described in Section 2. Figures 2(b)–(d) show the Image Quality (IQ) map of the kink of interest, the spatial distribution of crystal rotation relative to the matrix and a schematic diagram of 2(c), respectively. The arrows in Fig. 2(c) indicate the position of kink interfaces. The kink interfaces are named K1, K2, the matrix is named M1, M2 and the kink band is named KB1, KB2 as shown in Fig. 2(d). The spatial distribution of the crystal rotation in KB1 depends on position and was +19°, +20° and +19° around $\langle 1\bar{1}00\rangle $ at the black points shown in Fig. 2(d). The distribution of crystal rotation in KB2 was +8° around $\langle 1\bar{1}00\rangle $ in the vicinity of K2 and decreased gradually from 8° to 0° away from K2. The kink interface between KB2 and M2 could not be determined from Fig. 2(b) and (c).
Kink microstructure after the compression tests. (a) IPF map of kink and the distribution of the crystal rotation axis, (b) IQ map of the kink, (c) map of crystal rotation relative to the matrix, (d) a schematic diagram of (c). (e)–(g) are IQ map of the kink deformed by 45° compression, the map of crystal rotation relative to the matrix and a schematic diagram of (f), respectively.
Figure 2(e)–(g) show the IQ map of KB1 and KB2 deformed by the 45° compression, the distribution of crystal rotation relative to matrix, and a schematic diagram of 2(f), respectively. The shear deformation of positive ε23 with Schmid factor of +0.5 is shown in the top right corner of Fig. 2(e) and (g). Kink interface K1 was curved and the kink interface was buckled into three parts. Δφ = −6°, −12° and −6° at the top, middle and bottom, respectively. Δφ = −4° for K2.
As shown in Fig. 2(d), the change in the crystal rotations, Δθ, was −12°, −13°, −12° at the top, middle and bottom part of KB1, respectively. Δθ was −4° in the vicinity of K2 in KB2.
Figure 3(a) and (b) show BSE images of the mesh before and after 45° compression, respectively. Figure 3(c) shows the distribution of ε23, with ε23 > 0.05 (red), 0 ≦ ε23 ≦ 0.05 (orange) and ε23 < 0 (blue). ε23 in M1, M2 and KB2 were larger than +0.05. The averaged values of ε23 in M1 and M2 were +0.149 and +0.110 respectively. The averaged value of ε23 in KB2 was +0.109. The shear acting at M1, M2 and KB2 coincided with the shear by the external load. On the other hand, the averaged value of ε23 in KB1 was 0. As shown in Fig. 3(c) shows, the deformation in KB1 was inhomogeneous and the shear with negative ε23, namely shear against the external load, partially occurred. The inset in Fig. 3(c) clearly shows this opposite shear.
BSE image of mesh (a) before 45° compression, (b) after 45° compression. Mapping of the shear strain is shown in (c) with red (ε23 > 0.05), orange (0 ≦ ε23 ≦ 0.05) and blue (ε23 < 0). The blue parts in (c) was sheard against the external load.
Experimental results clearly show the existence of kink band that deforms in the opposite direction to the external force. It is obvious that the existence of such regions contributes to the increase in the stress for plastic deformation. Notice that such “opposite deformation” does not contradict to the thermodynamics as long as the total strain of the specimen decreases the Gibbs energy. In the following, we semi-quantitatively discuss whether the observed deformation is consistent with the rank-1 connection of kinks. The rank-1 connection of kinks has been formulated in a previous report.14) We assume that the kinks were formed and deformed only by a single basal shear, and the rank-1 connection between KB1 and matrix is kept before and after 45° compression. Let θ be the crystal rotation of the kink band, $\hat{\mathbf{n}}$ the normal of the kink interface, s the magnitude of shear acting inside the kink band and sm the magnitude of shear in the matrix. We assume sm = 0 for 0° compression. We know that sm = 0.138 for 45° compression from the experiment. The relationship between θ, $\hat{\mathbf{n}}$ and s, sm by the rank-1 connection is given in previous studies.14,18) Using the experimental value of θ = 19°, the magnitude of shear s that occurred to form the kink band in the 0° compression is calculated to be 0.335. A schematic diagram of the kink band after 0° compression is shown in Fig. 4(a). We analyzed the geometry of the kink band in Fig. 4(a) deformed in the same direction to the external force (Fig. 4(b)) and in the opposite direction (Fig. 4(c)) so that the sign of the shear acting inside the kink band, which is consistent with the sign of the experimentally observed Δθ and Δφ, was determined.
(a) kink band (KB1) after 0° compression, (b) KB1 deformed in the same direction of external shear stress, (c) KB1 deformed in the opposite direction of external shear stress. Δθ and Δφ observed in the experiment are explained by the activation of shear which is opposite to the external stress as in (c).
Consider a situation where a basal slip with the magnitude of shear 0.138 acts on the matrix and the existing kink band by 45° compression. It is theoretically assumed that the shear acting inside the kink band is in the same direction to the external force in this situation. In this case, the magnitude of shear is sm = 0.138, s = 0.335 + 0.138 = 0.473. This situation is schematically shown in Fig. 4(b), where the dashed lines are the kink interfaces and the basal plane trace before 45° compression. The point is that the theoretically obtained Δθ and Δφ are positive in this case. This sense of rotation is opposite to those observed in the experiment.
Let us consider another case, using the experimentally observed Δφ and Δθ. The magnitude of shear occurred inside the kink band in the 45° compression was reproduced using the rank-1 connection. For Δφ ≦ −6° and Δθ ≦ −12° in K1, the magnitude of shear must be s ≦ −0.015. Figure 4(c) depicts this situation with sm = 0.138 and s = −0.015. Considering that the magnitude of shear to form the kink band in 0° compression is 0.335, a basal shear smaller than −0.35 must occur inside the kink band. In other words, according to the rank-1 connection, the observed Δφ and Δθ is consistent with the negative shear in the kink band. This is in good agreement with the directly observed negative shear in Fig. 3. Since Δθ and Δφ for KB1 were negative even outside of the meshed region, this kind of local deformation against the external load is expected to exist in some part of the specimen. The origin of the local deformation against the external force is considered to be the constraint between kinks as described in the rank-1 model by Inamura.14) It is suggested that such constraint between kink is also a possible origin of the kink strengthening.
In order to determine a factor of kink strengthening, spatial distribution of crystal rotation, kink interface rotation and plastic strain in deformed kink bands were investigated. Mapping of the plastic strain of deformed kink bands clearly showed the existence of local deformation in the opposite direction of the external loading. This opposite plastic deformation was explained well the observed crystal rotation and rotation of the kink interface, provided that the rank-1 connection was maintained during deformation. The constraint between connected kink bands was suggested to be the origin of this opposite deformation and one of the factors leading to kink strengthening.
This work was supported by JSPS KAKENHI for Scientific Research on Innovative Areas “MFS Materials Science” (Grant Number JP18H05481) and IIR Research Fellow Program.
