2017 Volume 58 Issue 2 Pages 218-224
The influence of texture on the shear bands and workability in bending was examined by using an age-hardened polycrystalline high concentration of Ni-Si copper alloys with various recrystallization textures. Samples with dominant the Cube orientation of {001}<100>, the RD-rotated Cube orientation of {012}<100>, the BR orientation of {362}<853>, and the R orientation of {231}<346> were employed. The formation of shear bands and the bending workability depended on the texture in the W-shape bending test, in which the bending direction was RD. The sample with a strongly developed Cube orientation showed the best bending workability. In comparison, the samples with the developed BR orientation and random orientation showed poor bending workability. The shape of the cracks generated by bending was linear, and these cracks developed in the shear bands, which were inclined at 35–40° from the surface. To elucidate the mechanism behind shear band formation, inhomogeneous deformations were investigated using the FE-SEM/EBSD method. The dependence on the crystallographic orientations was discussed using the full constraint Taylor model premising both the plane strain compression and the shear strain modes.
Shear bands are an area where the shear strain is concentrated through several crystal grains. In the area, the grains deform cooperatively despite the different geometric arrangements of the slip system in each grain. The majority of the macroscopic strain is borne by the shear bands. To the mechanisms of such shear bands, much interest has been submitted. Many researchers have used various approaches to study this mechanism, including microstructural analyses1–5), crystallographic geometric softening6–8), continuum mechanics9,10), and the crystal plasticity finite element method (CPFEM)11–13). Many of these studies have done by employing heavily rolled materials. The formation process of the shear bands depends on material properties such as the ease of occurrence of twinning deformation or the rolling texture4).
Shear bands are observed not only during cold-rolling but also during bending. Since the surface is free during bending, shear plastic flow is more likely to occur. During the plastic bending process, cracks are often initiated in the shear bands. It has been reported that bending workability is notably influenced by a recrystallization texture14–16). There is a need for further investigation to elucidate the mechanism behind the dependence of shear bands on crystallographic orientation. A crystallographic orientation markedly influences several fundamental deformation behavior, including (i) the interaction of dislocations and the manner of dislocation accumulation17,18), (ii) the easiness of cross slip19), and (iii) the sum of crystal shear due to slip deformation, i.e., the Taylor factor20–22). Usually, these effects are interlaced.
In this study, to focus on the (iii), we employed polycrystalline samples of high-concentration Cu–Ni–Si alloys with various recrystallization textures. The Cu–Ni–Si system is an alloy with high hardness due to δ-Ni2Si precipitation23–26). To observe in detail the inhomogeneous deformation associated with the change of surface shape, the FE-SEM/EBSD method was used. By these methods, the formation mechanism and the texture dependence of the shear bands during bending were examined.
After melting and homogenizing the Cu-Ni-Si system alloys, the alloys were hot rolled and milled to remove surface scale. The chemical compositions are shown in Table 1. Then, the 0.2-mm-thick strips were obtained by cold rolling and annealing. Test samples were then prepared by solution treatment and aging. Four kinds of samples with different textures in a 3.8%Ni alloy were prepared by the arrangement of conditions in the above process. Based on the {111}, {100}, and {110} pole figures measured on the sample surface16) by the Schulz reflection method using the CuKα radiation, we analyzed the orientation distribution function (ODF) at the 22nd rank.
| Ni | Si | Zn | Sn | Cr | Mg | Cu | |
|---|---|---|---|---|---|---|---|
| 2.3Ni alloy [UNS 64775] |
2.30 | 0.65 | 0.50 | 0.15 | 0.15 | 0.10 | Bal. |
| 3.8Ni alloy No. 1–4 [UNS 64790] |
3.76 | 0.89 | 0.51 | 0.15 | 0.20 | 0.09 | Bal. |
Because of recrystallization during the solution treatment, the influence of dislocations prior to bending was able to be ignored. The mean grain size measured with the intercept method including twin boundaries were 3.7 μm, 4.0 μm, 3.8 μm, 3.5 μm, and 4.6 μm for Nos. 1–4 and the 2.3% Ni alloy, respectively. These values were similar to one another, and thus, their influence could be ignored27). Because the solution treatment and aging conditions were identical for Nos. 1–4, the precipitation states were also identical. In this way, these Nos. 1–4 allowed for evaluation of only the influence of the recrystallization texture.
The tensile test was performed at room temperature using the specimen of JIS-13B, in which the rolling direction was parallel to the tensile direction and the strain rate was 3.3 × 10−3 s−1.
Bending test, in which the sample was bent into a W-shape, was performed using a press metal die as shown in Fig. 1(a). To change the surface strain due to bending, the bending radius R was changed from 0 mm to 0.4 mm. (These bending conditions are indicated as 0R and 0.4R, respectively, in this paper.) The smaller the bending radius, the larger the strain induced on the surface. The sample coordinate systems are shown in Fig. 1(b): 1 is the longitudinal direction (LD) of bending, 2 is the transversal direction (TD) of bending, and 3 is the normal direction (ND) of the sample surface. The rolling direction in the sample preparation corresponds to the LD. The width and the thickness of the sample were 10 mm and 0.2 mm, respectively. Because the sample width is sufficiently greater than the thickness, contraction in the TD was negligible near the center along the width28).
(a) Press metal die used in the 90° W-type bending test and (b) sample coordinate system in the bending sample.
The deformation microstructures and crystallographic orientations in the bent samples were observed using the field emission scanning electron microscopy/electron back-scattering diffraction (FE-SEM/EBSD) method. This observation was performed on the TD cross section at the apex of bending. The cross section was obtained by argon ion irradiation to minimize the influence of the affected layer. The scan step was set to 0.1 μm, and the measurement points with confidential index (CI) values of less than 0.05 were not reliable and were excluded29). These points were shown in black on the crystal direction and image quality (IQ) maps. Using the crystal grain boundaries as a marker in the EBSD map, we examined the localized shear deformation. Specifically, we used the grain boundaries that were perpendicular to the shear direction. In addition, based on the distribution of the IQ, we qualitatively identified the strain distribution. The IQ is a measure of the clarity of the Kikuchi pattern, and the more the lattice becomes strained, the more it decreases. However, because the IQ depends on the crystallographic orientation and minor unevenness of the surface, we used this parameter along with the crystal direction map.
The plane strain compression and the two types of shear strains were defined as shown in Fig. 2, where positive and negative shear were defined based on the method used by Dillamore, et al.6). The angle between the LD and the shear direction was defined as β.
Definition of strain mode in the schematic viewed from the TD: (a) plane strain compression, (b) positive shear strain, and (c) negative shear strain.
Figure 3 shows the ODF analysis. The Euler angles of typical texture components are displayed at the bottom right of the figures. Figure 3(a) shows the strong development of the Cube orientation {001}<100> and the R orientation {231}<346> in No. 1. Figure 3(c) shows the development of the BR orientation {362}<853> and the RDW (RD-rotated Cube) orientation {012}<100> in No. 3. Figure 3(b) shows that No. 2 has the same texture component as those in No. 1 and No. 3. Figures 3(d) and (e) show that the maximum orientation density was 4, indicating a random texture in No. 4 and the 2.3% Ni alloy. These four kinds of texture components are commonly observed in copper alloys30–32).
Orientation distribution function (ODF) analysis: (a) No. 1, (b) No. 2, (c) No. 3, (d) No. 4, and (e) the 2.3% Ni-alloy. Euler angles of the typical texture component are displayed at the bottom right of the figures.
Figure 4 shows stress–strain curves. In this figure, a result from ordinary tough pitch copper (TPC) is also displayed for comparison. Although the slope of the elastic region was different33), the plastic flow stresses for Nos. 1–4 with different textures were nearly the same. Compared to that of the 2.3% Ni alloy, the yield strength of Nos. 1–4 was 100 MPa higher, and the hardening rates of these samples were also higher. Compared to TPC, the yield stress and work hardening rate of the Cu-Ni-Si alloys were very high by the effect of the fine precipitates. The breaking strains were from 0.14–0.15 for all five samples. These were mostly uniform elongation.
Stress-strain curves from the uniaxial tensile test. Tough-pitch copper (TPC) is shown for comparison.
Table 2 shows the results of observing the bent surface from the ND with the optical microscope. Under 0R and 0.1R conditions, large cracks formed in No. 3 and No. 4, whereas small cracks formed in No. 2 and no crack formed in No. 1. Specifically, No. 1 was found to have better bending workability than the 2.3% Ni alloy with low flow stress. A comprehensive determination based on the scale of the cracks indicated that the order of bending workability was as follows: No. 1 > the 2.3% Ni alloy > No. 2 > No. 4 > No. 3. Specifically, a correlation was observed between the volume of the BR orientation and decreasing bending workability. In this way, the bending workability was notably different depending on the texture and had no correlation with the breaking strain in the tensile test. Figures 5(a)–(e) show the optical micrographs obtained from the TD section after the 0R bend test of Nos. 1–4 and the 2.3% Ni alloy, respectively. A low magnification micrograph is also displayed at the bottom right of the figures, in which the observed region corresponds to the apex of bending. No. 1 showed a particularly favorable bent outer surface that was slightly wrinkled. In contrast, a large crack was observed in No. 3 and No. 4. In No. 2 and the 2.3% Ni alloy, a small crack was observed. The shapes of the cracks from the surface were linear as indicated by the white arrows in Figs. 5(b)–(e). The cracks from the surface were not generated along the grain boundaries. They developed in a direction inclined at 35–40° to the upper surface.
| 0R | 0.1R | 0.2R | 0.3R | 0.4R | |
|---|---|---|---|---|---|
| No. 1 | good | good | good →EBSD |
good | good →EBSD |
| No. 2 | crack | crack | good | good | good |
| No. 3 | large crack | large crack | large crack | crack | good |
| No. 4 | large crack | crack | crack →EBSD |
crack | good →EBSD |
| 2.3Ni alloy | crack | good | good | good | good |
Forms after the 0R bending test on the TD cross section at the central part of the sample's width: (a) No. 1, (b) No. 2, (c) No. 3, (d) No. 4, and (e) the 2.3% Ni alloy. White arrows indicate the cracks.
The results from No. 4, which had a random texture show how multiple crystal grains deform cooperatively. Figures 6(a)–(c) show the crystal direction map in the LD and TD and an IQ map obtained from No. 4 after the 0.4R bending test, respectively. The sets of arrows and numbers underlined in Fig. 6(b) indicate the shear direction and the shear displacement in micrometers estimated by steps of the grain boundaries, respectively. These steps were confirmed at 16 locations and were 0.3–0.9 μm in length. Among them, a row of the shear displacements was observed from the upper center (indicated by grain A in Fig. 6(b)) to the bottom right (indicated by grain B). Also, due to the local orientation change around the TD, we were able to see the shear strain. In the shear deformation areas in grains A and B, the crystal direction along the LD changed substantially compared to the surroundings: from purple to watery in grain A and form damask to faint yellow in grain B (Fig. 6(a)). Whereas, the crystal directions along the TD were nearly unchanged (Fig. 6(b)). In this way, the shear bands through several grains were confirmed even under the small strain. In addition, the yellow arrows in Fig. 6(c) indicate the surface steps formed by the shear bands, which were demonstrated by a relatively dark band-like contrast in the IQ map. The shear bands were in a direction inclined at 36° to the LD.
FE-SEM/EBSD image of sample No. 4 after the 0.4R bending test: (a) crystal direction map in the LD, (b) crystal direction map in the TD, and (c) image quality map. The ‘x’ in (a) indicates grains A and B. The set of arrows and the underlined numbers in (b) indicate the shear direction and the shear displacement, respectively. The yellow arrows in (c) indicate the surface steps formed by the shear bands.
Figures 7(a)–(c) show the crystal direction map in the LD, an IQ map, and an optical micrograph of the same region after the 0.2R bending test, respectively. We were able to see the negative shear band from the curvature of the parallel twin boundary in the n-region and the positive shear band from the steps of the grain boundary in the p-region as shown in Fig. 7(a). The width of these shear bands was approximately 5 μm. In the n-region, there were sets of grains with the same orientations on both sides of the crack. This indicated that the mode-2 crack developed inside the shear band in the n-region. Figure 8 shows an enlarged image near the crack in Fig. 7, demonstrating the state of the sample before the displacement due to shear banding generated the crack. We cropped the image in the upper left of the crack that is surrounded by a dotted yellow line and physically moved it along the crack (along the yellow arrow) so that the grains of the same orientation would meet. Figure 8 shows the formation of an angular groove with a depth of approximately 4 μm just before shear banding generated the crack. This depression was formed by both the negative and positive shear bands and then, acted as a stress concentration point. Thus, this groove triggered concentration of the shear and generation of the crack.
FE-SEM/EBSD images of sample No. 4 after the 0.2R bending test: (a) crystal direction map in the LD, (b) image quality map, and (c) optical microscope image. White triangles indicate the end point of the crack. The ‘n’ and ‘p’ in (a) indicate the negative and positive shear bands, respectively.
Enlarged image near the crack in Fig. 7 demonstrating the state before the displacement due to shear banding with generation of the crack. The yellow arrow indicates the vector of parallel moving of the cropped area surrounded by yellow dashed line. The ‘x’ indicates grains C, D, and E.
In this way, the localized shear deformation and resulting surface shape changes occurred in conjunction. At the locations where cracks were observed, the positive and negative shear bands developed in two directions, which is a typical configuration11,15). The formation process of such shear bands and the crack are schematically illustrated in Fig. 9. First, localized shear deformation occurred [i], which induced the steps on the sample surface. The steps caused a stress concentration [ii] and the initiation of new shear deformation [iii]. With the formation of the new shear band, the stress concentration encouraged at the groove on the surface [vi], and then, the generation of a mode II crack was induced in the shear band with a large amount of shear displacement [v]. Thus, the shear bands and the surface shape change formed a vicious circle towards the generation of a crack.
Schematic diagram of the plastic flow and the surface shape change during bending. [i]–[v] present the progress of bending.
Figures 10(a) and (b) show the crystal direction map in the LD and the IQ map of No. 1 after the 0.4R bending test, respectively. The sets of arrows and the numbers underlined in Fig. 10(a) are labeled in the same way as in Fig. 6(b). There were very few shears in this case compared to No. 4. Figures 11(a)–(c) show the crystal direction map in the LD and TD and the IQ map after the 0.2R bending test, respectively. The shear bands and surface unevenness were quite minor compared with No. 4. Specifically, in the Cube grains, local shearing was not confirmed. In addition, the shading in the IQ map was dense, indicating uniform deformation. Even if the bending deformation progressed, the crystallographic orientation close to the Cube orientation was maintained, although there was dispersion around the TD.
FE-SEM/EBSD images of sample No. 1 after the 0.4R bending test: (a) crystal direction map in LD and (b) image quality map. The set of arrows and the underlined numbers in (a) indicate the shear direction and shear displacement, respectively.
FE-SEM/EBSD observation of sample No. 1 after the 0.2R bending test: (a) crystal direction map in the LD, (b) crystal direction map in the TD, and (c) image quality map.
It was experimentally revealed in this study that bending workability was related to inhomogeneous microstructures such as shear bands, which were significantly influenced by the sample's preferred crystallographic orientation distribution. To examine the formation conditions of the shear bands, we will discuss the Taylor factor M as a criterion of the change in deformation modes. The velocity gradient tensor L is as follows:
| \[\boldsymbol{L}^{\mathit{pla}} = d\dot{\varepsilon} \begin{pmatrix} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & -1 \end{pmatrix}\ \mathit{for}\ \mathit{plane},\] | (1) |
| \[\boldsymbol{L}^{\mathit{shear}\text{-}\mathit{posi}} = d\dot{\varepsilon} \begin{pmatrix} 1 & 0 & -\tan \beta \\ 0 & 0 & 0 \\ \cot \beta & 0 & -1 \end{pmatrix}\ \mathit{for}\ \mathit{positive}\ \mathit{shear},\] | (2) |
| \[\boldsymbol{L}^{\mathit{shear}\text{-}\mathit{nega}} = d\dot{\varepsilon} \begin{pmatrix} 1 & 0 & \tan \beta \\ 0 & 0 & 0 \\ -\cot \beta & 0 & -1 \end{pmatrix}\ \mathit{for}\ \mathit{negative}\ \mathit{shear},\] | (3) |
| \[\boldsymbol{D} = \sum\nolimits_i \dot{\gamma}^{(i)} \left[ \frac{1}{2} \left( \boldsymbol{s}^{(i)} \otimes \boldsymbol{m}^{(i)} + \boldsymbol{m}^{(i)} \otimes \boldsymbol{s}^{(i)} \right) \right],\] | (4) |
| \[M = \mathit{min} \left( \sum\nolimits_i \left| d\dot{\gamma}^{(i)} \right| \right)/d\dot{\varepsilon}.\] | (5) |
| \[\sigma = M \cdot \tau.\] | (6) |
First, we derived $M^{\mathit{pla}}$ from $\boldsymbol{L}^{\mathit{pla}}$ and $M^{\mathit{shear}}$ from $\boldsymbol{L}^{\mathit{shear}}$ for some grains in the randomly oriented sample (No. 4). Figure 12 shows the $M^{\mathit{pla}}$ and $M^{\mathit{shear}}$ of grains A and B shown in Fig. 6 and grains C, D, and E shown in Fig. 8 as a function of the shear angle β. The values of $M^{\mathit{pla}}$ are indicated by dashed lines in the figures. We substituted the crystallographic orientations at the point near the shear bands indicated with an ‘x’ in Figs. 6(a) and 8 for the crystallographic orientations at the time that the shear deformation had started. As shown in Fig. 12(a), grains A and B had a very different $M^{\mathit{pla}}$ and $M^{\mathit{shear}}$ depending on the different crystallographic orientation. On the other hand, both grains had a common range of β where $M^{\mathit{shear}}$ was lower than $M^{\mathit{pla}}$ for β = 30–40°. This indicated that the shear deformation along 30–40° was relatively likely to occur. $M^{\mathit{shear}}$ for β = 32–36° was particularly low. The result of this calculation corresponded well with the observation that the shear band penetrated both grains with β = 36° (Fig. 6). A similar tendency was shown in Fig. 12(b), in which the shear deformation was relatively likely to occur with a range of β = 31–44° in grain C and β = 33–44° in grain D and E. A particularly low common angle was 36°, which corresponded well with a shear band and crack penetrating these grains at 37° (Fig. 7). Even if the texture was random, there was a commonly advantageous deformation mode in neighboring grains, which induced the generation of a shear band penetrating these grains.
Relationship between the FC (full constraint) Taylor factor and strain mode: (a) grains A and B and (b) grain C, D, and E. Dashed lines indicate the values of Mpla.
Second, assuming that the orientation distribution did not change significantly as the bending progressed, $M^{\mathit{plane}}$ and $M^{\mathit{shear}}$ were calculated regarding typical recrystallization orientations. With regard to the orientation near the Cube and the RDW orientations, $M^{\mathit{pla}} \fallingdotseq M_{\mathit{min}}^{\mathit{shear}} \fallingdotseq 2.5$. This indicated that a shear was not favorable, which was the reason that No. 1 did not form shear bands easily and the reason for the good bending workability of No. 1 and No. 2. On the other hand, for the BR orientation, where a correlation with lowering bending workability was observed, $M^{\mathit{pla}} = 3.8$ and $M_{\mathit{min}}^{\mathit{shear}} = 3.3$. This indicated that the shear mode was advantageous in this case. This was likely the reason for the largest cracks in No. 3. For the R orientation, $M^{\mathit{pla}} = 3.5$ and $M_{\mathit{min}}^{\mathit{shear}} = 3.4$. These results were intermediate when selecting a deformation mode.
Last, we calculated the average Taylor factor $\overline{M^{\mathit{pla}}}$ using the ODF analysis coefficients16), which were 3.08, 3.22, 3.33, and 3.29 for Nos. 1–4, respectively. A small $\overline{M^{\mathit{pla}}}$ correlated with a good bending workability. Since $M^{\mathit{pla}}$ was relatively low for the $M^{\mathit{shear}}$, the shear band was further prevented. In this way, we were able to interpret the series of experimental results with the FC Taylor theory assuming $\boldsymbol{L}^{\mathit{pla}}$ and $\boldsymbol{L}^{\mathit{shear}}$.
In the above discussion, we assumed that the strain velocity tensor D was only composed of the crystal slip deformation. On the other hand, orientation gradients were clearly observed in the deformed grains with EBSD analysis. This suggested that a part of D was compensated for by the geometrically necessary dislocations (GNDs). The GNDs should increase the flow stress through curvature and twisting of the lattice34) while also corresponding to a decrease in the sum of the slip shear strains than that of full constraint condition35). At present, however, the clear dependence of crystallographic orientation on the density of the GNDs has not been confirmed. More strictly, examination of this influence is necessary. In addition, in the shear band, it is possible to change $\tau$ in eq. (6) if a dynamic recovery or morphological change of precipitate were to occur. The influences of the deformation microstructure on slip resistance should be included in any future macroscopic deformation analyses.
Inhomogeneous deformation in the bending for the high-concentration Cu–Ni–Si alloys with various recrystallization textures was examined.
(1) In the sample with a random texture, shear banding was observed even under a small strain. The shear bands caused a change in the surface shape, at which point, a crack was initiated. The crack propagated in the shear bands.
(2) In the sample with a strongly developed Cube orientation, the shear bands and the accompanying surface roughness were notably suppressed. Compared to the 2.3% Ni alloy with a random orientation, the bending workability was better and the strength was ≥20% higher. As such, texture control was shown to be a useful technique that could achieve both a high strength and excellent bending workability.
(3) The dependence of crystallographic orientation on the formation of the shear band was discussed using the full constraint Taylor model based on the premise of both the plane strain compression and shear strain modes. Even if the texture was random, there was a common favorable shear mode in neighboring grains, which induced a shear band. The Cube and the RDW orientations were advantageous for suppression of the shear, whereas the BR orientation was not.
