2022 Volume 62 Issue 5 Pages 970-976
A series of tensile tests of polycrystalline high purity iron were carried out in order to trace microscopic orientations in different grains during plastic deformation. Crystal rotations were classified into two stages: one was the initial stage to the maximum strength or onset of necking, and the other was the subsequent stage from necking to fracture. Before the necking, two types of grain were observed: one rotated toward the [011] direction and the other did not rotate. During necking or plastic instability, the grains near the necking rotated toward the [111] direction. Activation of only a single slip system at the early stage did not follow the Taylor model which assumes multiple slip systems were active during deformation. In addition, it was observed that one grain was divided into two grains because a part of the grain rotated and the rest of the grain hardly rotated. Precise prediction of deformation of bcc metals requires improvement of the Taylor model by considering the transition of a single slip system to a multiple slip system, and a constraint on crystal rotation caused by adjacent grains. Necking due to tensile deformation was observed in grains oriented toward the [011] direction and local areas close to the necking or plastic instability finally rotated toward the [111] direction when the specimen fractured. Such rotation was also observed in a single crystal tensile test, because the lattice was released from various constraints on rotation.
Understanding the mechanical properties of materials is essential when the materials are machined and shaped into products. Applying stress to metallic materials causes plastic deformation, in which dislocation slips primarily occur on lattice planes in crystals and accumulation of the slips results in macroscopic deformation.
Slip systems are dependent on the crystal structures, the composition of materials, and so on.1) The slips in fcc metals generally occur in the ⟨110⟩{111} slip system, and it is confirmed that only a single slip system is active at the early stage of fcc metal deformation.2,3) On the other hand, the slip system in bcc metals is complex. It has been established that the slip direction in bcc metals is the ⟨111⟩ direction and the deformation of bcc metals is usually considered as starting with multiple slips but not with only a single slip system.4,5,6,7,8,9) Referring to the previous research of slip systems in bcc metals,4,5,6,7,8,9) the slip plane has not been firmly determined: possible slip planes in bcc metals could be every plane along the ⟨111⟩ direction, or only the {110}, {112}, and {123} planes. Recently, it has been reported that the primary slip plane in bcc metals is the {110} plane at low temperatures and the {112} plane is replaced with the {110} plane at high temperatures.10,11) In the case of iron, the {112} plane is considered to be the primary slip plane at room temperature. Kumagai et al.12,13) suggested that only a single slip system is active at the early stage of deformation in bcc metals, although the primary slip plane alters depending on the initial orientation, temperature, and other conditions.
These findings have been investigated using mainly single crystal specimens in the bcc structures.14) In practice, most products are made from polycrystalline materials. Thus, understanding the deformation behaviour of polycrystalline materials is more important than understanding this behaviour in single crystals.
The deformation behaviour of polycrystalline specimens is more complex because it is affected by constraints on grain rotation due to adjacent grains in addition to the activity of slip systems. According to the literature,15,16,17) grains rotate to a certain orientation along the tensile or the compression axes. The rotation results in the formation of texture. The texture is, however, non-uniform because the rotation behaviours of each grain depend upon the initial orientation, and this is restricted by the adjacent grains.
There are two approaches to describing deformation behaviours. The Taylor model predicts a formation of texture using a statistical technique. According to the Taylor model, bcc metals form the ⟨011⟩ and the mixture of ~25% ⟨001⟩ and ~75% ⟨111⟩ texture during tensile and compression deformation, respectively.16,18) Kumagai et al.12,13) reported the relationships between the initial orientation of a grain and its mechanical property. Using the relationships, the work hardening rate and the strain at which multiple slip systems are activated are estimated. The Taylor model describes macroscopic structures, and the results obtained by Kumagai et al. describe the rotation behaviour of each grain. In the present study, deformation behaviours were analysed using these theories.
Textures have strong effects on the quality of products because they generally involve anisotropic mechanical properties. Therefore, it is desired to predict and to control deformation behaviours at a deep level. A theory must be established, which describes the relationship between grain rotation and micro textures in the range of work hardening. Hence, it is necessary to clarify grain rotation characteristics by tracing the orientations in local areas during deformation.
In the present study, high purity polycrystalline iron19,20,21,22,23) was prepared for a tensile specimen of coarse grains. The advantages of high purity iron are as follows: i) elimination of the effect of impurities. The intrinsic properties can be investigated, if the level of impurities is as small as possible. ii) a large grain size: this makes it easy to trace points in grains and to observe differences in the orientation of each grain and local area. High purity iron was indispensable for carrying out the present study.
Thus, analysis of the orientation of the grains in the high purity iron polycrystalline specimen and of their traces during the tensile deformation was carried out. The obtained rotation behaviours were compared with the reported theories, the Taylor model and the results obtained by Kumagai et al.12,13,16,18) The purpose of this study is to propose a strategy to improve prediction of the deformation behaviour of polycrystalline bcc metals.
The whole flowchart of the experimental procedure is shown in Fig. 1. The details of each step are described below.
The flowchart of the experimental procedure consisting of preparation of one tensile test specimen and repeated tensile test.
High purity iron was prepared using valence-controlled anion-exchange separation followed by plasma arc melting in oxidising and reducing atmospheres.19,20,21,22,23) The purity of the high purity iron was 99.998 mass% analysed by glow discharge mass spectrometry24) as shown in Table 1. The solidified high purity iron in a button shape was cold rolled into a sheet, and then the specimen was cut into the shape shown in Fig. 2 using wire-cut electrical discharge machining, followed by annealing at 800°C in a hydrogen atmosphere for three hours for recrystallisation. It was deduced that the impurities did not affect recrystallisation during annealing, because the specimen had coarse grains. Therefore, the effect of impurities on deformation behaviour was supposed to be reduced as much as possible. The specimen was mechanically and electrochemically polished in order to remove a strain layer.
| / mass ppm | |||
|---|---|---|---|
| Ele. | Conc. | Ele. | Conc. |
| Al | 0.11 | Pd | 0.15 |
| Si | 0.11 | Cd | 0.15 |
| P | 0.15 | ||
| Co | 1.7 | C | 5.1 |
| Ni | 0.13 | N | 8.1 |
| Cu | 12 | O | 6.0 |
| Sr | 0.18 | ||
| Purity | 99.998 mass% | ||
The concentrations of the other elements were less than 0.01 mass ppm.
The specimen size and the appearance of the tensile specimen made from high purity iron. (Online version in color.)
A tensile test was performed at room temperature and the crosshead speed was 0.05 mm·min−1, which was approximately 1.5×10−4 s−1. In order to trace the deformation behaviour, the same specimen was repeatedly subjected to a certain strain and the orientations in every crystal were determined before and after each tensile test. The AutoGraph AG-IS 10 kN made by SHIMADZU CORPORATION was used for the tensile test. The SU-6600, a Field Emission Scanning Electron Microscope (FE-SEM) made by Hitachi High-Tech Corporation equipped with Nordlys II, a detector of Electron Backscatter Diffraction (EBSD) made by Oxford Instruments plc was used for observation of the microstructure and determination of crystal orientation. The observations were made at 20 kV acceleration voltage and a working distance of 15 mm. The step size of EBSD analysis was 3.0 μm.
Figure 3 shows the stress-strain curve of the high purity iron specimen. Yielding in the polycrystalline high purity iron specimen was not clearly observed during deformation. Yielding was not observed in single crystal high purity iron, either.12) Necking was observed over the nominal strain of around 22% and the specimen fractured at the strain of 38%. The grain rotation will be discussed in two stages. The first stage was the initial state until reaching the nominal strain at which the necking began, and the second stage was from the necking to the fracture.
The stress-strain curve of the high purity iron specimen obtained by repeated tensile tests. The values are nominal strains after each tensile test. (Online version in color.)
Polycrystalline bcc metals have ⟨011⟩ texture during tensile deformation as a result of grain rotation, as predicted using the Taylor model.16,18) Figure 4 shows the inverse pole figure (IPF) maps of the high purity iron specimen in the tensile direction (RD) obtained from the normal direction (ND). It was supposed that all grains spread from the surface to the back, because the grains were coarse enough. As shown in the figure, grains III and V did not rotate, whereas ⟨011⟩ texture was formed in grains II and IV. In addition, the necking propagated across grains II and IV over the nominal strain of ~22%. Grain I was also aligned in the ⟨011⟩ direction after fracture. This implies that the rotation behaviours of each grain were different, and it was assumed that the rotation behaviour depended on the initial grain orientation. The rotation behaviours of each grain will be discussed in order to interpret the mechanisms of grain rotation in the polycrystalline bcc high purity iron specimen in detail.
The IPF maps of the high purity iron specimen in the tensile direction (RD) obtained from the normal direction (ND). The observed area is depicted as the hatched area in the specimen, and the IPF maps of the cross-hatched areas are displayed. The colour scale denoting grain orientation is shown above the IPF maps. The red circles with letters and the blue diamonds with numbers indicate the points at which the grain orientations were analysed after each deformation. The Roman numbers indicate the grains to be investigated. The necking was observed across grains II and IV, in which ⟨011⟩ oriented texture was formed during deformation. (Online version in color.)
Figure 5 shows the changes in intensity of the grain orientations in the high purity iron specimen during tensile deformation. Whole observed area formed ⟨011⟩ texture over ~22% nominal strain. However, there were grains which were not aligned in the ⟨011⟩ direction.
The intensity of the grain orientation in the high purity iron specimen during the tensile deformation. The changes in the whole observed area are demonstrated at the top (a) and those in the individual grain rotated (b) and not rotated (c) are shown at the bottom. The Roman numbers correspond to the grains displayed in Fig. 4. The grains were classified into two groups: one group consisted of the rotated grains I, II, and IV, and the other group consisted of the non-rotated grains III and V. (Online version in color.)
Grains III and V were initially aligned in the [111] and [001] directions, respectively, as shown in Fig. 4. Grains III and V were more strongly aligned in the [111] and [001] directions as the tensile deformation proceeded. The behaviours of grains III and V were against the Taylor model, which posits that all grains in bcc metals tend to align in the ⟨011⟩ direction during tensile deformation.16,18)
Grains II and IV among the rotated crystals were aligned in the [011] direction during the tensile deformation. The intensities of the orientation of grains II and IV were unchanged compared with grains III and V, as mentioned above. This implied that grains II and IV rotated constantly; on the other hand, grains III and V hardly rotated. Grain I was aligned to around the [012] direction at 21.6% nominal strain and then the intensities of the grain orientation were extended toward the [111] direction just before the fracture.
It should be noted that the rotation toward different orientation even in one grain was observed in grains I and II as shown in Fig. 4.
As mentioned above, the high purity iron tensile specimen was aligned in the ⟨011⟩ direction from the macroscopic perspective in accordance with the Taylor model.16,18) However, there were grains whose rotation behaviours were different from those from the macroscopic perspective. The difference in the rotation behaviours should be interpreted in order to obtain basic knowledge to understand and to predict the plastic deformation of bcc polycrystalline materials.
The grain rotations before and after the necking occurred should be separately discussed. The Taylor model assumes that an equivalent plastic strain is spread over all grains in polycrystalline specimens,16,18) therefore the strains of each grain are the same as the macroscopic plastic strain. However, the stress was concentrated around the necking after it was formed. The stress was not consistent anywhere in the specimen after the necking.
3.1. Crystal Rotations from Initial State to NeckingIn discussion of the grain rotation in polycrystalline materials, work hardening must be considered. The initial orientation of the grains was used for estimation of the extent of work hardening during tensile deformation using the results derived by Kumagai et al.12,13)
Kumagai et al.12,13) reported the significant relationship between the initial orientation and the grain rotation in a single crystal specimen. Two parameters were defined: χ is the angle between the maximum resolved shear stress plane and the (101) plane, and θ is the angle between the tensile axis of the specimen and the [001]–[011] symmetry line. Kumagai et al. revealed that the larger the χ is, the greater the work hardening rate is, and the larger the θ is, the greater the strain at which the double or multiple slip system is activated is. Only a single slip system operated before a double or multiple slip systems were activated. An active double or multiple slip system induced work hardening in crystals. Thus, the θ is also related to a strain at which work hardening was activated.
Figure 6 depicts the initial orientations of the grains in Fig. 4 and the angles of |χ| and θ. The order of the work hardening rates, (dσ/dε), and the strains at which the work hardening was activated, εWH, are estimated as follows using |χ| and θ displayed in Fig. 6 and the results derived by Kumagai et al.12,13)
| (1) |
| (2) |
The initial orientations of the grains displayed in Fig. 4 and their | χ | and θ. (Online version in color.)
The grain orientations in the local areas denoted by the numbers from 1 to 10 represented in Fig. 4 were traced during the tensile deformation in order to understand the rotation mechanisms of grains I, II, and IV, which were the grains that rotated during deformation. The traces of the grain orientations are shown in Fig. 7. The traces of the orientations in the local areas in grain I exhibited their rotations toward the [111] direction and the local areas in grains II and IV rotated toward the [111] direction.
The traces of the grain orientations in the local areas in grains I, II, and IV shown in Fig. 4. The outlined lines indicate the traces strained up to 21.6%, and the solid lines indicate the traces strained over 21.6%. The rotation angles from 0% to 21.6% strain, ϕ0–22, from 21.6% to 35.0% strain, ϕ22–35, and from 35.0% strain to the fracture, ϕ35–Fr., along the ⟨111⟩ direction lines, of the traced points are also displayed. The uncertainties of the angles are estimated ±1° because the angles were manually read using Wulff net. (Online version in color.)
The rotation angles in the local areas in the three stages, ϕ0–22 from 0% to 21.6% strain, ϕ22–35 from 21.6% to 35.0%, and ϕ35–Fr. from 35.0% to the fracture were read using Wulff net and are displayed in Fig. 7. ϕ0–22 reflects the rotation until necking occurred, and it could be assumed that each local area was equally stressed. In contrast, plastic instability occurred after the necking, with the result that the stress was concentrated in grains II and IV whereas the other grains were less affected by the stress.
The rotations of grains II and IV near the [001]–[011] symmetry line were less obvious compared with the rotations before the necking. The work hardening caused the decrease in the crystal rotation and double or multiple slip systems were active simultaneously, with the result that they rotated toward the [011] direction in accordance with the Taylor model.16,18) It is deduced that the rotation of the examined crystals was caused by a single slip system at the early stage. Afterwards, a double or multiple slip system was active. This conflicts with the general conception that a multiple slip system is active from the beginning of plastic deformation in polycrystalline bcc metals.
The local areas in grains II and IV, namely No. 5 to 10, rotated about 20° before the necking. The magnitudes of the rotation angle after the necking depend on the distances to the necking or the unrotated adjacent grains. ϕ22–35 of No. 6 was 8°, because No. 6 was the nearest point to the necking and the constraint on the rotation seemed to be the least among the examined points. The other points hardly rotated due to the constraint on the rotation caused by the adjacent grains and work hardening.
The traces in grain I corresponded to the distribution of the intensity of the crystal orientation demonstrated at the bottom of Fig. 5. The local areas in grain I, namely No. 1 to 4, rotated more than the local areas in grains II and IV. The work hardening in grain I occurred as soon as the specimen deformed whereas the work hardening in grains II and IV occurred later, referring to Eq. (2). The χ of grain I indicates the work hardening rate is the lowest level in the examined grains and comparable to grain II. Thus, grain I rotated more than the others due to the lower work hardening rate even though the work hardening was induced at the earliest point.
The orientations of grains III and V were consistent through the tensile test; however, the mechanisms causing non-rotation were different, as discussed below.
The work hardening of grain V was activated as soon as the specimen was deformed by the tensile test referring to Eq. (1), like grain I. However, (dσ/dε) of grain V was supposed to be greater than that of grain I, therefore grain V hardly rotated compared with grain I.
Grain III was initially aligned in the [111] direction. The bottom of Fig. 5 shows that the intensity around the [111] direction increased as the tensile deformation proceeded. This means that grain III slightly rotated toward the [111] direction and Eq. (2) suggests that only a single slip system was active at the early stage. This rotation behaviour goes against the Taylor model, which is based on the multiple slip system being active during deformation and describes every grain as rotating toward the ⟨011⟩ direction.
It is difficult to discuss the rotation behaviours of the grains oriented toward the [011] and [111] directions in the polycrystalline specimen because the rotation behaviours of such single crystals have not been investigated in detail as far as the authors know. Further investigation is warranted of why the grains oriented toward the [011] and [111] directions hardly rotate.
As discussed above, the rotation behaviours in the polycrystalline high purity iron specimen were elucidated using not only the Taylor model but also through estimation using the χ and the θ. The Taylor model16,18) assumes that multiple slip systems operate simultaneously. However, the estimation using the χ and the θ12,13) assumes that a single slip system worked in the initial stage of tensile deformation. Hence, there are two cases of rotation behaviours: one is interpreted assuming a single slip system and the other is interpreted assuming a double or multiple slip system. Both theories are necessary to illustrate the plastic deformation of bcc metals, although it is not clear in the present study which theory is more significant for which case.
In addition, a constraint on the crystal rotation caused by the adjacent grains must be considered in polycrystalline specimens. In grains I and II, different rotation behaviours were observed in one crystal, as shown in Fig. 4. Each part of grains rotating toward different orientations has a grain boundary with grains in different orientations. It was found that a part bordering on non-rotated grains hardly rotated; the concerned parts in grains I and II were adjacent to grains V and III, respectively.
Consequently, the Taylor model,16,18) the estimation of the rotation behaviours of each crystal using the χ and the θ,12,13) and consideration of the constraint on rotation caused by the adjacent grains are important in order to understand the rotation behaviour of polycrystalline bcc metals. The details of the constraint mechanism must be revealed by another investigation in order to describe precisely the plastic deformation of polycrystalline bcc metals.
3.2. Crystal Rotations from Necking to FractureThe plastic instability was induced, and the stress was concentrated on grains II and IV after the necking occurred. The area around the necking exhibited a rotation behaviour different from the rest of the specimen. The traces of the orientation at the local areas of a, b, and c denoted in Fig. 4 are shown in Fig. 8.
The traces of the grain orientations at the local areas of a, b, and c denoted in Fig. 4. The outlined lines indicate the traces strained up to 21.6%, and the solid lines indicate the traces strained over 21.6%. The rotation angles are also shown following the manner of Fig. 7. (Online version in color.)
The outlined lines, which are the traces before the necking, indicate that the crystal rotated toward the [111] direction and the rotation angles were 22±1°. After the necking, the local areas rotated to different angles even though every local area rotated toward the [111] direction. The rotation angles of ϕ22–35 deviated 5° and the average was 11°, thus, the deviation was too large, half of the average. The difference in the rotation angles before and after the necking implies a transition from uniform to non-uniform deformation.
The rotation behaviours at the local areas of a, b, and c until the necking occurred were equivalent to those at the local areas of No. 5 to 10. After the necking, the local areas of a, b, and c rotated toward the [111] direction, unlike No. 5 to 10. The reason was that the local areas of a, b, and c were far away from the grain boundaries and the effect of constraint on the rotation caused by the adjacent grains was small. Furthermore, the section area was reduced because of the necking and thus the lattice could rotate as freely as a single crystal, which generally rotates toward ⟨111⟩.12,13) This rotation behaviour around the necking was deemed a characteristic rotation in polycrystalline bcc metal specimens.
The grain rotations or orientation changes of grains in polycrystalline 99.998 mass% high purity iron specimen of coarse grains caused by tensile deformation were characterised.
The coarse grains in polycrystalline specimens exhibited the characteristic different rotation behaviours depending on their initial orientation, although it is confirmed that the structure from the macroscopic perspective oriented toward the ⟨011⟩ direction, in accordance with the Taylor model. The results obtained in the present study offer significant fundamental knowledge to predict the precise deformation of polycrystalline bcc metals with fine grains.
We acknowledge Professor M. Fujinami for supporting our research activity on high purity metals and encouraging us to submit this paper for publication in the special issue on “Frontier in characterisation of materials and processes for steel manufacturing”.
