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Geometrically necessary dislocations distribution in face-centred cubic alloy with varied grain size
Materials Characterization 162 (2020) 110205
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Geometrically necessary dislocations distribution in face-centred cubic alloy with varied grain size ⁎
Jiayi Zhanga,b, Bin Wanga, , Hao Wangb, a b
T
⁎
Department of Materials Science and Engineering, Central South University, Changsha 410083, PR China Department of Mechanical Engineering, Faculty of Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117575, Singapore
A R T I C LE I N FO
A B S T R A C T
Keywords: Geometrically necessary dislocation Grain size Ductility Deformed Annealing
The evolution of geometrically necessary dislocation (GND) distribution in the deformed 6061 alloy is studied with electron back scatter diffraction (EBSD) and transmission electron microscope (TEM). In dynamic recrystallized state, the average GND density is 8.70 × 1014 m−2 with grain size ~30 μm. In annealed state, the average GND density decreases by an order of magnitude, from 6.81 × 1015 to 7.32 × 1013 m−2 (annealing temperature from 200 to 500 °C) accompanied by increasing grain size. Moreover, the sample has greatest ductility with lowest GND density. According to the tendency of dislocations in TEM, GND gradually migrate from near (200) plane to near (220) plane with increasing annealing temperature. Additionally, GND mainly concentrate on the grain boundaries in the deformed state, and the GND distribution is more homogenous after annealing. It is shown that the GND density is related to the grain boundary type and misorientation angle between adjacent grains. The relationship between average GND density and grain size is approximately parabolic.
1. Introduction Face-centred cubic alloys (FCC) have high stacking fault energy, such as Al, Cu and Ni. When FCC alloys are subjected to plastic deformation, subgrains are separated by dislocation planar arrangement [1]. Dislocations in crystals could be divided into two different categories: geometrically necessary dislocation (GND) and statistically stored dislocation (SSD) [2,3]. SSD evolve from random trapping processes and do not produce significant misorientation. GND are linked to strain gradient field due to geometrical constraints of the crystal lattice, and play a considerably important role in microstructural length-scale effects on strength of alloys. When alloys are subjected to non-homogeneous severe deformation, the corresponding strain gradient gives rise to GND so as to keep continuity in the crystal [4]. In order to achieve ideal ductility of alloys, the annealing process is generally used after deformation, and accompanied by recovery and recrystallization of grains, resulting in variations of the strain gradient. Humphreys [5] studied several types of grain microstructure with different sizes, like deformed, fibrous, kink, shear bands and equiaxed grains, after plastic deformation and annealing process. The formation of deformed and recrystallized grains is influenced by grain orientation and size. Moreover, the low-angle grain boundaries (LAGBs) will transfer to the high-angle grain boundaries (HAGBs) ⁎
during annealing process. Zhang et al. [6] found that the microstructures evolved from banded microstructures to fine and equiaxed grains after annealing, grain size decreased from 70 to 19.3 μm. Najafi et al. [7] demonstrated that the fraction of HABs increased with the increasing passes of equal channel angular pressing, and the dislocation density increased through 4 passes and reduced with 6 passes of equal channel angular pressing (ECAP). Merriman et al. [8] elaborated a wellorganized dislocation structure forming in many polycrystalline metals during plastic deformation, and investigated that the formation of cell structure obviously depends on the external deformation gradient, with the largest excess dislocation density occurring in grains of {0 1 1}[1 2 2] orientation for plane strain deformation. Despite many research works concerning the grain and dislocation variations during thermomechanical process, little references of grain information (size, orientations, grain boundary types, etc.) is in regard to studying how GND form, distribute, evolve, and affect the strength of materials. Large numbers of dislocations emerge in the deformation process, and the density of total dislocations can be measured using many techniques, such as counting the individual dislocations in transmission electron microscopy (TEM) and obtaining diffraction peaks by X-ray [9]. However, the measurement of GND density is more complicated and only became feasible thanks to the developed standard of orientated mapping technique by electron back scatter diffraction (EBSD)
Corresponding authors. E-mail addresses: [email protected] (B. Wang), [email protected] (H. Wang).
https://doi.org/10.1016/j.matchar.2020.110205 Received 7 January 2020; Received in revised form 15 February 2020; Accepted 15 February 2020 Available online 18 February 2020 1044-5803/ © 2020 Elsevier Inc. All rights reserved.
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t tensor δij and a position vector → x . The dislocation density tensor (α) described by Nye [15]:
with Kikuchi Diffraction [10,11]. The lattice curvature can be calculated by measuring the orientations within a small adjacent grain volume, from which the GND density can be derived through dislocation density tensor [12]. Based on this method, Marion et al. [13] calculated that the average GND density of the steel with 24 vol% martensite is 1.9 × 1014 m−2, and that of the steel containing 38 vol% martensite is 2.4 × 1014 m−2. Eralp et al. [14] calculated the first-order strain gradients and the GND densities of Cu single crystal from the data of EBSD tomography, and found the connection between hardness and GND density. In view of the above, few studies are concentrated on the grain information which are affected by GND formation and evolution, resulting in the ultimate performance differences of FCC metals. The main aim of this study is contacting the grain information with GND density and observation and calculation of the GND within deformed Al alloy at different annealing temperatures.
αij =
∑t
t bit l tj δ (→ x −→ x )
(1)
The lattice curvature tensor (κ) can be introduced by lattice rotation vector θ [16]:
κij =
∂θi ≕θij ∂x j
(2)
Dislocations are related heterogeneous elastic strain fields and curvatures, for the absence of elastic strains (εij), the simplified equation to Nye's relations [17]: (3)
αik = κki − δki κ
κki = αik −
1 δki αmm 2
(4)
The orientation of a crystalline lattice is described by the rotation required to achieve the particular orientation from a chosen reference orientation. The difference of orientation between two orientations is similarly defined by the rotation required to obtain one orientation from the other and introduced by a disorientation angle Δθ and rotation → axis r . The disorientation vector can be derived from the two adjacent orientations in several ways, like from the disorientation matrix Δg = (gA)−1 gB as:
2. Materials and methods 2.1. Experiments A deformed Al-0.8Mg-0.6Si wire alloy was used in this study, the specific preparation process could be referred to the previous study [6]. The nominal compositions of the alloys are shown in Table 1. The alloy was hot extruded into a rod with ϕ9.5 mm at 480 °C. Subsequently, the extruded rod was cold drawn to wires with a diameter of 3.1 mm. The deformation strain of the alloy was 2.24, and the alloy was further subjected to the annealing treatment at 200, 300 and 500 °C for 3.5 h. Tensile tests of rod and wire samples (with a length of 100 mm) were conducted on an MTS Landmark testing machine at room temperature, and five tensile tests were carried out on each sample. Microstructure characterizations were carried out using EBSD and transmission electron microscopy (TEM). TEM observations were carried out with an FEI Tecnai F20 system operated at 200 kV. EBSD measurements were performed on an FEI Helios Nanolab 600i focused ion beam/scanning electron microscopy (FIB/SEM) system with an accelerating voltage of 20 kV. For choosing step size, it can affect the distinction between SSD and GND, because this parameter defines the implicit Burgers vector. This size dependence can be investigated if the measurement is performed with a suitable step size. To this purpose, step size of 100, 200, 300, 500, 1000 and 1500 nm are chosen for experimental measurement, the EBSD maps with an initial step size of 100 nm were processed, until the microstructural features completely disappeared at a step size of 1500 nm. Among the all the chosen step sizes, the 300 nm is the finest step size for microstructural features, so as to calculate the EBSD data. All the samples were carried out in the same step size. The HKL Channel 5 and ATEX analysis software were used to process the EBSD data.
Δθk = −εkij Δgij
Δθ 2 sin Δθ
(5)
As for the disorientation between two adjacent points separated spatially by Δ→ x , the lattice curvatures can be expressed as:
κkl =
Δθk ∂θk ≈ Δxl ∂xl
(6)
Since local lattice orientations are resolved only in the plane of investigation (along x1 and x2) while not perpendicular to it (along x3), only the six components κi1 and κi2 (i = 1, 2, 3) of the curvature tensors are obtained, but not the components κi3 as differentiation along the third direction is impossible. From the calculation of lattice curvature, five GND components of the dislocation density Nye tensor can be acquired from 2D EBSD mapping, i.e. α12, α13, α21, α23, and α33 [18]. From the six available curvature components, five components of the dislocation density tensors can be derived:
α12 = κ21, α13 = κ31
(7)
α21 = κ12, α23 = κ32
(8)
α33 = −κ11 − κ22, α11 − α22 = κ11 − κ22
(9)
The GND density, namely ρGND , which can be defined as the entrywise norm of Nye tensor divided by Burgers vector (b) length in Eq. (5): 2D
1 2 2 2 2 2 α12 + α13 + α 21 + α 23 + α33 b
2.2. GND density analysis
2D ρGND =
Combined with the continuous dislocation theory, the GND density distribution near the surface of material can be obtained by EBSD. EBSD measurement also helps identify the crystallographic orientation within a pixel, and the lattice curvature can be calculated using adjacent orientated pixel. Dislocations are line defects resulting in relative dis→t placements of the crystalline lattice. A line vector l indicates the →t dislocation direction, a Burgers vector b is the displacement, unit
In FCC crystal structure, FCC crystals have 18 unique dislocation systems, GNDs are either pure screw dislocations with line and Burgers vectors along 〈110〉 (6 types) or pure edge with 〈110〉 Burgers vectors and 〈112〉 line directions (12 types). Dislocations of mixed character are considered as linear combinations of pure edge and screw systems. It is noted that the densities of the all dislocation must be positive.
(10)
3. Results
Table 1 The chemical composition of Al-Mg-Si alloy cable (wt%).
3.1. GND distribution maps of dynamic recrystallization
Elements
Mg
Si
Zn
Cu
Al
Mass
0.80
0.60
0.20
0.15
Balance
EBSD maps of the hot-extruded sample are presented in Fig. 1. The microstructure of as-extruded sample consists of different sized equiaxed grains. The average of the grain size is 30 μm with 2
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Fig. 1. EBSD maps of (a) IPF (RD: radial direction, ED: extrusion direction) and (b) HAGBs (red line) and LAGBs (blue line) distribution in hot-extruded sample. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
can be deduced that α12(κ21) has largest lattice curvature among the five curvature components, what's more, indicating larger disorientation angle between two adjacent points. Combined with Fig. 1, LAGBs with smaller grain areas on the two-dimensional plane have higher GND density, corresponding to a grain size of ~12 μm. Dynamic recrystallization can occur immediately after deformation with residual temperature, which begins with migration of existing HAGBs as well as migration and coalescence of subgrains [19]. These processes are initiated where energy is greatest, such as grain boundary edges or intersections. In order to keep continuity by GND, they mainly concentrate on the LAGBs, which leads to the phenomenon seen on the GND density map (Fig. 2).
approximately 92% dynamic recrystallization based on analysis with the Channel 5 software. The grains exhibit anisotropy after dynamic recrystallization, as shown in the inserted inverse pole figure (IPF) of Fig. 1(a), comprising (001), (110) and (111) directions. Fig. 1(b) displays the HAGBs (2°–15°) and LAGBs (> 15°) distribution after hot extrusion, and the volume fractions of the HAGBs and LAGBs are 90.8% and 9.2%, respectively. According to Eq. (5), Fig. 2 shows the calculated GND components and entry-wise norm of dislocation density Nye tensor of hot-extruded sample. The noise level with GND density distribution in Fig.2 is 0.067°. The entry-wise norm GND density map seems to demonstrate higher densities near grain boundaries. In addition, there is an obvious order to the averaged magnitudes over the GND components, α12 > α33 > α21 > α22 > α13. Linking up with Eqs. (6) to (10), it
Fig. 2. EBSD maps showing five GND components and entry-wise norm of dislocation density Nye tensor. 3
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Fig. 3. Evolution of (a, c and e) GND density distribution (colour scale implies log GND density, in line per m2) and (b, d and f) grain boundary types after different annealing temperature (red line: HAGBs, blue line: LAGBs). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
shows the tensile strength and elongation of the samples. As it can be seen, the sample has the highest tensile strength (301 MPa) and lowest elongation (6.4%) after annealing at 200 °C. On the contrary, the lowest tensile strength (165 MPa) and highest elongation (13.5%) belong to the sample after annealing at 500 °C. It should be noted that the GND density measurements here present beginning of the tensile tests and the work-hardening rate of tensile tests may depend on the grain size or texture. According to the analysis of previous study [6], the main strengthening mechanism relies on two factors: grain size and dislocation. Combing these aspects to determine the strength, it should be noted that the effect of grain boundary strengthening is obviously much weaker than that of recrystallization softening. Thus, the main strengthening mechanism is dislocation strengthening, and the variation of mechanical property is related to the revolution of GND density. According to the GND density data from EBSD analysis software, the statistics of GND density for hot-extruded and annealed samples are shown in Fig. 4. From this histogram, GND density decreases on both sides of the maximum frequency. Obviously, increasing annealing temperature results in a decrease in the average of GND density from ~1 × 1015 to 1 × 1013 m−2. In hot-extruded sample, the average of GND density is 8.70 × 1014 m−2, and the average of GND density is 6.81 × 1015, 1.24 × 1014 and 7.32 × 1013 m−2 for the samples annealed at 200, 300 and 500 °C, respectively. As the annealing temperature increases, the average of GND density decreases by an order of magnitude. Combined with the mechanical properties of samples at different status, it can be found that the tensile strength decreases and the ductility increase due to the decreased GND density. Linking up with Figs. 3 and 4, it can be inferred that the GND density is closely related to the grain size. Thus, it may be deemed that the sample has greatest ductility with lowest GND density in this experiment.
3.2. GND distribution with regard to grain size and grain boundary types Fig. 3 demonstrates a clear evolution of the GND distribution with variation of grain sizes and grain boundary types. After cold deformation, equiaxed grains appear around the parent-grains at a certain temperature, where these recrystallized grains nucleate on the grain boundaries, and then the grains merge and grow with the increased temperature. From this figure, it can be roughly seen that the GND density decreases (Fig. 3(a), (c) and (e)), and the volume fraction of HAGBs increases (Fig. 3(b), (d) and (f)) with increasing annealing temperature. With different intensities of GND density distribution at different states, the estimated noise levels with GND density distribution are 0.52°, 0.095° and 0.056° for Fig. 3(a), (c) and (e), respectively. Furthermore, with the increasing temperature, there are fewer GND concentrated on the grain boundaries, and the GND distribution is homogenous. Actually, a relative decline of GND density is indicative of the decrease of homogenous local strain due to annealing process [20]. It is also worth noting that the decreasing GND density accompanies the increasing grain size. Jiang et al. [21] also manifested that the high GND density near grain boundary would result in small grains tending to have a higher average GND density. Since different annealing temperatures result in different grain microstructure, the mechanical properties are also different. Table 2
Table 2 The tensile strength and elongation of the samples at different status. Sample
Tensile strength (MPa)
Elongation (%)
Hot-extruded Annealing 200 °C Annealing 300 °C Annealing 500 °C
268 301 167 165
8.6 ± 0.1 6.4 ± 0.1 13.4 ± 0.1 13.5 ± 0.1
± ± ± ±
5 4 4 2
4
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3.3. TEM observations of dislocations To further characterize the orientation and evolution of GND at different states, Fig. 5 shows the view of dislocations from the grains. The TEM micrographs were recorded along the [001] direction, and the corresponding selected area diffraction patterns were taken in the [001]Al direction. From the dislocations shown in Fig. 5(a), there are two main orientated dislocations—one kind of dislocation is orientated along the (220) plane, and the other is orientated within 10° of the (200) plane, as indicated by the red and blue dot lines, respectively. Additionally, the dislocations almost concentrate on the subgrain boundaries, which is consistent with the EBSD results (Fig. 2) of the hotextruded sample. For annealing at 200 °C, the dislocations are mainly along the (200) plane, and the grains are subdivided into fine subgrains (~500 nm) by dislocation boundaries. For annealing at 300 °C, the subgrains grow after migration of dislocation, and the dislocations are mainly orientated 30° of the (220) plane. By contrast, for annealing at 500 °C, the completely recrystallized subgrains grow up in enormous grains appeared with triangular grain boundary. Moreover, few dislocations concentrate on the grain boundaries, and the dislocation density significantly decreases with increasing annealing temperature. Combined with the EBSD results of Fig. 3, the decreased GND density in the annealed samples (at 300 and 500 °C) may be attributed to dynamic
Fig. 4. The statistics of GND density for hot-extruded sample and the samples annealed at different temperatures.
Fig. 5. View of dislocations in the grains by TEM: (a) hot-extruded state, (b) sample annealed at 200 °C, (c) sample annealed at 300 °C, and (d) sample annealed at 500 °C. 5
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homogeneous, reducing the misorientation between adjacent grains (as shown in Fig. 3(b), (d) and (f)). Some Refs [23–25] have reported that the grains will be ultrafine during recovery and recrystallization process, and the polycrystalline behaviour of FCC metal tends to be more uniform. Additionally, the low GND density does not mean that there is no need for GND at high annealing temperature stage. As shown in Fig. 3(f), the grains present the equiaxed instead of elongated shape, and the volume fraction of HAGBs increases to 92.8%. In static recrystallization process, grain boundaries gradually move in the steady state (triangular boundary), as shown in Fig. 5(d). This may give rise to a partial increase of grain size. When grains grow to a certain extent, a process starts by emerging GND walls in grain interiors and ends by removing some GND at grain boundaries, which results in decreasing GND density. Thus, the grains with higher GND densities (mainly concentrated around the LAGBs) will be eliminated by the movement of grain boundaries in static recrystallization. 4.2. The relationship between GND and misorientation distribution
Fig. 6. The relationship between average GND density and grain size of samples at different states.
When a material is deformed, strain heterogeneities appear in the grains and differ from neighbour grains. In order to accommodate the deformation between adjacent grains, strain heterogeneities display itself by lattice curvatures, which result in large orientation differences in the same parent grains. In annealing process, the misorientation between grains will change due to the evolution of the crystallographic texture, which is also related to the variations of grain size. At a given deformed/annealed state of FCC metals, the correlated misorientation distribution (CMD) can be acquired from experimental data and random pair misorientation distribution (RPMD) can be acquired from function calculation of misorientation distribution. GND density is related to the difference between the CMD and RPMD [26]. At a given deformed state of the polycrystalline, one can obtain the experimental CMD. The CMD can be called a “correlated” misorientation distribution due to construction from first adjacent misorientation. One can also calculate misorientation distribution between grains which are not neighbours. It can be calculated by computing the misorientation of a given grain with other grains that are chosen randomly [19]. Fig. 7 presents the CMD and RPMD for hot-extruded and annealed samples. For low annealing temperature at 200 °C, the CMD is similar to the RPMD; nevertheless, for the hot-extruded higher annealing temperature (300 and 500 °C) the CMD curves fluctuate obviously. The CMDs are more dispersed with large grain size (Fig. 7(a), (c) and (d)) than that with small grain size (Fig. 7(b)). Additionally, the difference between CMD and RPMD is more significant with largest grain size (annealed at 500 °C). This is attributed to the texture of the material, and main ideal orientation between adjacent grains is 60° [27]. The quantitative relationship between CMD and RPMD can be expressed by Eq. (6) [19]:
recovery of dislocation structures. From TEM observations, it can be deduced that GND may gradually migrate from near (200) plane to near (220) plane, and then submerge at grain boundaries with increasing annealing temperature. Different GND distribution and density will create different sizes of subgrains. As a result, the evolution of GND could induce the variation of grain size. 4. Discussion 4.1. Grain size and its relation to GND As known, GND density distributes heterogeneously in deformed FCC metals. In this study, the GND density is much lower in the grain interiors compared with GND near grain boundary in the deformed sample, and GND density is higher for the smaller grains on average. According to Ashby's theory [22], dislocations gliding at grain boundaries can lead to the accumulation of high GND density, as dislocations are required to keep continuity and prevent formation of grain overlap. The experimental results presented in Fig. 5 are in good agreement with Ashby's theory. Fig. 6 reveals the relationship between average GND density and grain size, showing the approximately parabolic relation. The sample annealed at 200 °C has the smallest average grain size with highest GND density. The sample annealed at 500 °C has the largest average grain size with lowest GND density. For the deformed and noncompletely recrystallized sample, the high GND density near the grain boundaries is a result of dislocation glide, pile-up, and accumulation across the grain interiors, as shown in Fig. 5. Additionally, with the increasing annealing temperature, fewer GND concentrate on the grain boundaries, and the GND distribution is more homogenous. The variation in GND density can be attributed to two reasons—grain fragmentation at large strains and heterogenetic degrees of GND walls [18]. In hot-extruded state, the grains are deformed and fragmented due to a large strain, resulting in GND density increasing and distributing on the grain boundaries. The fragmented grains group the GND into walls in the process of continuous deformation, resulting in the increase of GND density. Meanwhile, the fragmented grains recover and recrystallize under the high temperature in the hot extrusion process. Dynamic recrystallization leads to the decreasing of GND density. Thus, the GND density should depend on the temperature and strain of hot extrusion, which also determine the grain size. For low annealing temperatures, most fragmented grains are in recovery state. There is still considerable residual stress remaining in the metals, and the recovery process can gradually lead to the elimination of the deformation heterogeneities existing between adjacent grains, i.e. changing the deformation mode from heterogeneous to more
= R
∫ [C (g ) − R (g )]2 dg
(6)
is a function of where C(g) is defined as CMD, R(g) is RPMD, and R equivalent average strain of the given material. It shows an effect of CMD and RPMD on the GND density. As a result, Fig. 8 plots the re . An obvious trend can be oblationship between GND density and R . At served, there is a linear relationship between GND density and R has low value which indicates little difference high GND density, the R for the sample annealed 200 °C is between CMD and RPMD, e.g. the R (0.06) 0.03. The sample annealed at 500 °C has the largest value of R due to the significant difference between CMD and RPMD. Combined with the relationship of grain size and GND density (Fig.7), it is shown . that the grain size is proportional to the value of R In dynamic recrystallization, the new grain boundaries are divided by GND. The grain boundary movement is preferentially along the adjacent grains where higher dislocation density can be observed. As seen from the EBSD map of the hot-extruded sample (Fig. 1(a)), the 6
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Fig. 7. Based on EBSD analysis of correlated misorientation distribution (CMD) and random pair misorientation distribution (RPMD) between grains of different samples: (a) hot-extruded state, (b) sample annealed at 200 °C, (c) sample annealed at 300 °C, and (d) sample annealed at 500 °C.
better compatibility between adjacent grains, due to the low GND concentration on the grain boundaries. Therefore, it is inferred that static recrystallization is taking place in a specified way, which may lead to the decrease of GND density and homogeneous GND distribution in FCC materials. 5. Conclusions The evolution of geometrically necessary dislocation (GND) distribution in the deformed 6061 alloy is studied with EBSD and TEM in this paper. The conclusions are summarized as follows: (1) After hot extrusion, the average GND density of the sample is 8.70 × 1014 m−2 with average grain size ~30 μm, and the GND mainly concentrate on the grain boundaries. (2) After annealing at different temperatures, the average GND density decreases from 6.81 × 1015 to 7.32 × 1013 m−2, corresponding to annealing temperature from 200 to 500 °C and accompanied by the increasing grain size. The sample (after annealing at 500 °C) has greatest ductility with lowest GND density. (3) The relationship between average GND density and average grain size shows an approximately parabolic relation. In addition, the difference between correlated misorientation distribution and random pair misorientation distribution is more significant with largest grain size.
of samples at different Fig. 8. The relationship between GND density and R states.
adjacent grains show distinct orientations and anisotropy. The difference in orientations requires activated slip systems and hence high dislocation density. Another reason for the large misorientation angle may be that the adjacent grains are not completely compatible, resulting in a large GND density. For static recrystallization, e.g. annealing at 200 °C, the misorientation angle mainly scatters from 32.5°–55.5°. As for annealing at 500 °C, the misorientation angle scatters at 5°–20° and 37.5°–55.5°. The small misorientation angle means
Declaration of competing interest The authors declare that they have no known competing financial 7
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interests or personal relationships that could have appeared to influence the work reported in this paper.
[10] J.A. Venables, C.J. Harland, Electron back-scattering patterns e a new technique for obtaining crystallographic information in the scanning electron microscope, Philos. Mag. 27 (1973) 1193–1200. [11] F.J. Humphreys, Review e grain and subgrain characterisation by electron backscatter diffraction, J. Mater. Sci. 36 (2001) 3833–3854. [12] C.F. Gu, L.S. Toth, B. Beausir, Modeling of large strain hardening during grain refinement, Scr. Mater. 66 (2012) 250–253. [13] M. Calcagnotto, D. Ponge, E. Demir, et al., Orientation gradients and geometrically necessary dislocations in ultrafine grained dual-phase steels studied by 2D and 3D EBSD, Mater. Sci. Eng. A 527 (2010) 2738–2746. [14] E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer, Investigation of the indentation size effect through the measurement of the geometrically necessary dislocations beneath small indents of different depths using EBSD tomography, Acta Mater. 57 (2009) 559–569. [15] J.F. Nye, Some geometrical relations in dislocated crystals, Acta Metall. 1 (1953) 153–162. [16] E. Kröner, R. Balian, et al. (Eds.), Physics of Defects, North-Holland, Amsterdam, 1981, pp. 219–315. [17] W. Pantleon, Resolving the geometrically necessary dislocation content by conventional electron backscattering diffraction, Scr. Mater. (11) (2008) 994–997. [18] W. Pantleon, Stage IV work-hardening related to misorientations in dislocation structures, Mater. Sci. Eng. A 387-389 (2004) 257–261. [19] L.S. Toth, C.F. Gu, B. Beausir, J.J. Fundenberger, M. Hoffman, Geometrically necessary dislocations favor the Taylor uniform deformation mode in ultra-finegrained polycrystals, Acta Mater. 117 (2016) 35–42. [20] B. Beausir, C. Fressengeas, N. Gurao, L.S. Toth, et al., Spatial correlation in grain misorientation distribution, Acta Mater. 57 (2009) 5382–5395. [21] J. Jiang, T.B. Britton, A.J. Wilkinson, Evolution of dislocation density distributions in copper during tensile deformation, Acta Mater. 61 (2013) 7227–7239. [22] M.F. Ashby, The deformation of plastically non-homogeneous material, Philos. Mag. 21 (1970) 399–424. [23] C.F. Gu, M. Hoffman, L.S. Toth, Y.D. Zhang, Grain size dependent texture evolution in severely rolled pure copper, Mater. Charact. 101 (2015) 180–188. [24] W. Skrotzi, A. Eschke, B. Joni, T. Ungar, L.S. Toth, et al., New experimental insight into the mechasims of nanoplasticity, Acta Mater. 61 (2013) 7271–7284. [25] X. Ren, Y. Huang, W. Zhou, L. Zhao, Q. Wang, et al., Influence of pre-recovery on recrystallization behavior, microstructure and mechanical properties of twin-roll cast AA6016 sheet, Mater. Sci. Eng. A 764 (2019) 138159. [26] C. Chen, Y. Beygelzimer, L.S. Toth, J.J. Fundenberger, Microstructure and strain in protrusions formed during severe plastic deformation of aluminum, Mater. Lett. 159 (2015) 253–256. [27] F. Montheillet, M. Cohen, J.J. Jonas, Axial stresses and texture development during the torsion testing of Al, Cu and Alpha-Fe, Acta Metall. 32 (1984) 2077–2089.
Acknowledgements The authors gratefully acknowledge the Jinbei Electric Cable Co. Ltd. for providing the necessary laboratory equipment, 2011 Program of the Ministry of Education of China, and Singapore Ministry of Education Academic Research Fund Tier 1 (Grant No.: R-265-000-593114) and Tier 2 (Project No: MOE2018-T2-1-140) for financial support. References [1] B. Bay, N. Hansen, D.A. Hughes, D. Kuhlmann-Wilsdorf, Evolution of fcc deformation structures in polyslip, Acta Metall. Mater. 40 (1992) 2503–2510. [2] S. Naghdy, P. Verleysen, R. Petrov, L. Kestens, Resolving the geometrically necessary dislocation content in severely deformed aluminum by transmission Kikuchi diffraction, Mater. Charact. 140 (2018) (225-22). [3] J. Jiang, T.B. Britton, A.J. Wilkinson, Measurement of geometrically necessary dislocation density with high resolution electron backscatter diffraction: effects of detector binning and step size, Ultramicroscopy 125 (2013) 1–9. [4] D. Liu, Y. He, X. Tang, H. Ding, P. Hu, et al., Size effects in the torsion of microscale copper wires: experiment and analysis, Scr. Mater. 66 (2012) 406–409. [5] F.J. Humphreys, M. Hatherly, Recrystallization and Related Annealing Phenomena, Pergamon Press, Oxford, UK, 1996. [6] J. Zhang, M. Ma, F. Shen, D. Yi, B. Wang, Influence of deformation and annealing on electrical conductivity, mechanical properties and texture of Al-Mg-Si alloy cables, Mater. Sci. Eng. A 710 (2018) 27–37. [7] S. Najafi, A.R. Eivani, M. Samaee, H.R. Jafarian, J. Zhou, A comprehensive investigation of the strengthening effects of dislocations, texture and low and high angle grain boundaries in ultrafine grained AA6063 aluminum alloy, Mater. Charact. 136 (2018) 60–68. [8] C.C. Merriman, D.P. Field, P. Trivedi, Orientation dependence of dislocation structure evolution during cold rolling of aluminium, Mater. Sci. Eng. A 194 (2008) 28–35. [9] T. Ungar, J. Gubicza, G. Ribarik, A. Borbely, Crystallite size distribution and dislocation structure determined by diffraction profile analysis: principles and practical application to cubic and hexagonal crystals, J. Appl. Crystallogr. 34 (2001) 298–310.
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Materials Characterization journal homepage: www.elsevier.com/locate/matchar
Geometrically necessary dislocations distribution in face-centred cubic alloy with varied grain size ⁎
Jiayi Zhanga,b, Bin Wanga, , Hao Wangb, a b
T
⁎
Department of Materials Science and Engineering, Central South University, Changsha 410083, PR China Department of Mechanical Engineering, Faculty of Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117575, Singapore
A R T I C LE I N FO
A B S T R A C T
Keywords: Geometrically necessary dislocation Grain size Ductility Deformed Annealing
The evolution of geometrically necessary dislocation (GND) distribution in the deformed 6061 alloy is studied with electron back scatter diffraction (EBSD) and transmission electron microscope (TEM). In dynamic recrystallized state, the average GND density is 8.70 × 1014 m−2 with grain size ~30 μm. In annealed state, the average GND density decreases by an order of magnitude, from 6.81 × 1015 to 7.32 × 1013 m−2 (annealing temperature from 200 to 500 °C) accompanied by increasing grain size. Moreover, the sample has greatest ductility with lowest GND density. According to the tendency of dislocations in TEM, GND gradually migrate from near (200) plane to near (220) plane with increasing annealing temperature. Additionally, GND mainly concentrate on the grain boundaries in the deformed state, and the GND distribution is more homogenous after annealing. It is shown that the GND density is related to the grain boundary type and misorientation angle between adjacent grains. The relationship between average GND density and grain size is approximately parabolic.
1. Introduction Face-centred cubic alloys (FCC) have high stacking fault energy, such as Al, Cu and Ni. When FCC alloys are subjected to plastic deformation, subgrains are separated by dislocation planar arrangement [1]. Dislocations in crystals could be divided into two different categories: geometrically necessary dislocation (GND) and statistically stored dislocation (SSD) [2,3]. SSD evolve from random trapping processes and do not produce significant misorientation. GND are linked to strain gradient field due to geometrical constraints of the crystal lattice, and play a considerably important role in microstructural length-scale effects on strength of alloys. When alloys are subjected to non-homogeneous severe deformation, the corresponding strain gradient gives rise to GND so as to keep continuity in the crystal [4]. In order to achieve ideal ductility of alloys, the annealing process is generally used after deformation, and accompanied by recovery and recrystallization of grains, resulting in variations of the strain gradient. Humphreys [5] studied several types of grain microstructure with different sizes, like deformed, fibrous, kink, shear bands and equiaxed grains, after plastic deformation and annealing process. The formation of deformed and recrystallized grains is influenced by grain orientation and size. Moreover, the low-angle grain boundaries (LAGBs) will transfer to the high-angle grain boundaries (HAGBs) ⁎
during annealing process. Zhang et al. [6] found that the microstructures evolved from banded microstructures to fine and equiaxed grains after annealing, grain size decreased from 70 to 19.3 μm. Najafi et al. [7] demonstrated that the fraction of HABs increased with the increasing passes of equal channel angular pressing, and the dislocation density increased through 4 passes and reduced with 6 passes of equal channel angular pressing (ECAP). Merriman et al. [8] elaborated a wellorganized dislocation structure forming in many polycrystalline metals during plastic deformation, and investigated that the formation of cell structure obviously depends on the external deformation gradient, with the largest excess dislocation density occurring in grains of {0 1 1}[1 2 2] orientation for plane strain deformation. Despite many research works concerning the grain and dislocation variations during thermomechanical process, little references of grain information (size, orientations, grain boundary types, etc.) is in regard to studying how GND form, distribute, evolve, and affect the strength of materials. Large numbers of dislocations emerge in the deformation process, and the density of total dislocations can be measured using many techniques, such as counting the individual dislocations in transmission electron microscopy (TEM) and obtaining diffraction peaks by X-ray [9]. However, the measurement of GND density is more complicated and only became feasible thanks to the developed standard of orientated mapping technique by electron back scatter diffraction (EBSD)
Corresponding authors. E-mail addresses: [email protected] (B. Wang), [email protected] (H. Wang).
https://doi.org/10.1016/j.matchar.2020.110205 Received 7 January 2020; Received in revised form 15 February 2020; Accepted 15 February 2020 Available online 18 February 2020 1044-5803/ © 2020 Elsevier Inc. All rights reserved.
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t tensor δij and a position vector → x . The dislocation density tensor (α) described by Nye [15]:
with Kikuchi Diffraction [10,11]. The lattice curvature can be calculated by measuring the orientations within a small adjacent grain volume, from which the GND density can be derived through dislocation density tensor [12]. Based on this method, Marion et al. [13] calculated that the average GND density of the steel with 24 vol% martensite is 1.9 × 1014 m−2, and that of the steel containing 38 vol% martensite is 2.4 × 1014 m−2. Eralp et al. [14] calculated the first-order strain gradients and the GND densities of Cu single crystal from the data of EBSD tomography, and found the connection between hardness and GND density. In view of the above, few studies are concentrated on the grain information which are affected by GND formation and evolution, resulting in the ultimate performance differences of FCC metals. The main aim of this study is contacting the grain information with GND density and observation and calculation of the GND within deformed Al alloy at different annealing temperatures.
αij =
∑t
t bit l tj δ (→ x −→ x )
(1)
The lattice curvature tensor (κ) can be introduced by lattice rotation vector θ [16]:
κij =
∂θi ≕θij ∂x j
(2)
Dislocations are related heterogeneous elastic strain fields and curvatures, for the absence of elastic strains (εij), the simplified equation to Nye's relations [17]: (3)
αik = κki − δki κ
κki = αik −
1 δki αmm 2
(4)
The orientation of a crystalline lattice is described by the rotation required to achieve the particular orientation from a chosen reference orientation. The difference of orientation between two orientations is similarly defined by the rotation required to obtain one orientation from the other and introduced by a disorientation angle Δθ and rotation → axis r . The disorientation vector can be derived from the two adjacent orientations in several ways, like from the disorientation matrix Δg = (gA)−1 gB as:
2. Materials and methods 2.1. Experiments A deformed Al-0.8Mg-0.6Si wire alloy was used in this study, the specific preparation process could be referred to the previous study [6]. The nominal compositions of the alloys are shown in Table 1. The alloy was hot extruded into a rod with ϕ9.5 mm at 480 °C. Subsequently, the extruded rod was cold drawn to wires with a diameter of 3.1 mm. The deformation strain of the alloy was 2.24, and the alloy was further subjected to the annealing treatment at 200, 300 and 500 °C for 3.5 h. Tensile tests of rod and wire samples (with a length of 100 mm) were conducted on an MTS Landmark testing machine at room temperature, and five tensile tests were carried out on each sample. Microstructure characterizations were carried out using EBSD and transmission electron microscopy (TEM). TEM observations were carried out with an FEI Tecnai F20 system operated at 200 kV. EBSD measurements were performed on an FEI Helios Nanolab 600i focused ion beam/scanning electron microscopy (FIB/SEM) system with an accelerating voltage of 20 kV. For choosing step size, it can affect the distinction between SSD and GND, because this parameter defines the implicit Burgers vector. This size dependence can be investigated if the measurement is performed with a suitable step size. To this purpose, step size of 100, 200, 300, 500, 1000 and 1500 nm are chosen for experimental measurement, the EBSD maps with an initial step size of 100 nm were processed, until the microstructural features completely disappeared at a step size of 1500 nm. Among the all the chosen step sizes, the 300 nm is the finest step size for microstructural features, so as to calculate the EBSD data. All the samples were carried out in the same step size. The HKL Channel 5 and ATEX analysis software were used to process the EBSD data.
Δθk = −εkij Δgij
Δθ 2 sin Δθ
(5)
As for the disorientation between two adjacent points separated spatially by Δ→ x , the lattice curvatures can be expressed as:
κkl =
Δθk ∂θk ≈ Δxl ∂xl
(6)
Since local lattice orientations are resolved only in the plane of investigation (along x1 and x2) while not perpendicular to it (along x3), only the six components κi1 and κi2 (i = 1, 2, 3) of the curvature tensors are obtained, but not the components κi3 as differentiation along the third direction is impossible. From the calculation of lattice curvature, five GND components of the dislocation density Nye tensor can be acquired from 2D EBSD mapping, i.e. α12, α13, α21, α23, and α33 [18]. From the six available curvature components, five components of the dislocation density tensors can be derived:
α12 = κ21, α13 = κ31
(7)
α21 = κ12, α23 = κ32
(8)
α33 = −κ11 − κ22, α11 − α22 = κ11 − κ22
(9)
The GND density, namely ρGND , which can be defined as the entrywise norm of Nye tensor divided by Burgers vector (b) length in Eq. (5): 2D
1 2 2 2 2 2 α12 + α13 + α 21 + α 23 + α33 b
2.2. GND density analysis
2D ρGND =
Combined with the continuous dislocation theory, the GND density distribution near the surface of material can be obtained by EBSD. EBSD measurement also helps identify the crystallographic orientation within a pixel, and the lattice curvature can be calculated using adjacent orientated pixel. Dislocations are line defects resulting in relative dis→t placements of the crystalline lattice. A line vector l indicates the →t dislocation direction, a Burgers vector b is the displacement, unit
In FCC crystal structure, FCC crystals have 18 unique dislocation systems, GNDs are either pure screw dislocations with line and Burgers vectors along 〈110〉 (6 types) or pure edge with 〈110〉 Burgers vectors and 〈112〉 line directions (12 types). Dislocations of mixed character are considered as linear combinations of pure edge and screw systems. It is noted that the densities of the all dislocation must be positive.
(10)
3. Results
Table 1 The chemical composition of Al-Mg-Si alloy cable (wt%).
3.1. GND distribution maps of dynamic recrystallization
Elements
Mg
Si
Zn
Cu
Al
Mass
0.80
0.60
0.20
0.15
Balance
EBSD maps of the hot-extruded sample are presented in Fig. 1. The microstructure of as-extruded sample consists of different sized equiaxed grains. The average of the grain size is 30 μm with 2
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Fig. 1. EBSD maps of (a) IPF (RD: radial direction, ED: extrusion direction) and (b) HAGBs (red line) and LAGBs (blue line) distribution in hot-extruded sample. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
can be deduced that α12(κ21) has largest lattice curvature among the five curvature components, what's more, indicating larger disorientation angle between two adjacent points. Combined with Fig. 1, LAGBs with smaller grain areas on the two-dimensional plane have higher GND density, corresponding to a grain size of ~12 μm. Dynamic recrystallization can occur immediately after deformation with residual temperature, which begins with migration of existing HAGBs as well as migration and coalescence of subgrains [19]. These processes are initiated where energy is greatest, such as grain boundary edges or intersections. In order to keep continuity by GND, they mainly concentrate on the LAGBs, which leads to the phenomenon seen on the GND density map (Fig. 2).
approximately 92% dynamic recrystallization based on analysis with the Channel 5 software. The grains exhibit anisotropy after dynamic recrystallization, as shown in the inserted inverse pole figure (IPF) of Fig. 1(a), comprising (001), (110) and (111) directions. Fig. 1(b) displays the HAGBs (2°–15°) and LAGBs (> 15°) distribution after hot extrusion, and the volume fractions of the HAGBs and LAGBs are 90.8% and 9.2%, respectively. According to Eq. (5), Fig. 2 shows the calculated GND components and entry-wise norm of dislocation density Nye tensor of hot-extruded sample. The noise level with GND density distribution in Fig.2 is 0.067°. The entry-wise norm GND density map seems to demonstrate higher densities near grain boundaries. In addition, there is an obvious order to the averaged magnitudes over the GND components, α12 > α33 > α21 > α22 > α13. Linking up with Eqs. (6) to (10), it
Fig. 2. EBSD maps showing five GND components and entry-wise norm of dislocation density Nye tensor. 3
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Fig. 3. Evolution of (a, c and e) GND density distribution (colour scale implies log GND density, in line per m2) and (b, d and f) grain boundary types after different annealing temperature (red line: HAGBs, blue line: LAGBs). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
shows the tensile strength and elongation of the samples. As it can be seen, the sample has the highest tensile strength (301 MPa) and lowest elongation (6.4%) after annealing at 200 °C. On the contrary, the lowest tensile strength (165 MPa) and highest elongation (13.5%) belong to the sample after annealing at 500 °C. It should be noted that the GND density measurements here present beginning of the tensile tests and the work-hardening rate of tensile tests may depend on the grain size or texture. According to the analysis of previous study [6], the main strengthening mechanism relies on two factors: grain size and dislocation. Combing these aspects to determine the strength, it should be noted that the effect of grain boundary strengthening is obviously much weaker than that of recrystallization softening. Thus, the main strengthening mechanism is dislocation strengthening, and the variation of mechanical property is related to the revolution of GND density. According to the GND density data from EBSD analysis software, the statistics of GND density for hot-extruded and annealed samples are shown in Fig. 4. From this histogram, GND density decreases on both sides of the maximum frequency. Obviously, increasing annealing temperature results in a decrease in the average of GND density from ~1 × 1015 to 1 × 1013 m−2. In hot-extruded sample, the average of GND density is 8.70 × 1014 m−2, and the average of GND density is 6.81 × 1015, 1.24 × 1014 and 7.32 × 1013 m−2 for the samples annealed at 200, 300 and 500 °C, respectively. As the annealing temperature increases, the average of GND density decreases by an order of magnitude. Combined with the mechanical properties of samples at different status, it can be found that the tensile strength decreases and the ductility increase due to the decreased GND density. Linking up with Figs. 3 and 4, it can be inferred that the GND density is closely related to the grain size. Thus, it may be deemed that the sample has greatest ductility with lowest GND density in this experiment.
3.2. GND distribution with regard to grain size and grain boundary types Fig. 3 demonstrates a clear evolution of the GND distribution with variation of grain sizes and grain boundary types. After cold deformation, equiaxed grains appear around the parent-grains at a certain temperature, where these recrystallized grains nucleate on the grain boundaries, and then the grains merge and grow with the increased temperature. From this figure, it can be roughly seen that the GND density decreases (Fig. 3(a), (c) and (e)), and the volume fraction of HAGBs increases (Fig. 3(b), (d) and (f)) with increasing annealing temperature. With different intensities of GND density distribution at different states, the estimated noise levels with GND density distribution are 0.52°, 0.095° and 0.056° for Fig. 3(a), (c) and (e), respectively. Furthermore, with the increasing temperature, there are fewer GND concentrated on the grain boundaries, and the GND distribution is homogenous. Actually, a relative decline of GND density is indicative of the decrease of homogenous local strain due to annealing process [20]. It is also worth noting that the decreasing GND density accompanies the increasing grain size. Jiang et al. [21] also manifested that the high GND density near grain boundary would result in small grains tending to have a higher average GND density. Since different annealing temperatures result in different grain microstructure, the mechanical properties are also different. Table 2
Table 2 The tensile strength and elongation of the samples at different status. Sample
Tensile strength (MPa)
Elongation (%)
Hot-extruded Annealing 200 °C Annealing 300 °C Annealing 500 °C
268 301 167 165
8.6 ± 0.1 6.4 ± 0.1 13.4 ± 0.1 13.5 ± 0.1
± ± ± ±
5 4 4 2
4
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3.3. TEM observations of dislocations To further characterize the orientation and evolution of GND at different states, Fig. 5 shows the view of dislocations from the grains. The TEM micrographs were recorded along the [001] direction, and the corresponding selected area diffraction patterns were taken in the [001]Al direction. From the dislocations shown in Fig. 5(a), there are two main orientated dislocations—one kind of dislocation is orientated along the (220) plane, and the other is orientated within 10° of the (200) plane, as indicated by the red and blue dot lines, respectively. Additionally, the dislocations almost concentrate on the subgrain boundaries, which is consistent with the EBSD results (Fig. 2) of the hotextruded sample. For annealing at 200 °C, the dislocations are mainly along the (200) plane, and the grains are subdivided into fine subgrains (~500 nm) by dislocation boundaries. For annealing at 300 °C, the subgrains grow after migration of dislocation, and the dislocations are mainly orientated 30° of the (220) plane. By contrast, for annealing at 500 °C, the completely recrystallized subgrains grow up in enormous grains appeared with triangular grain boundary. Moreover, few dislocations concentrate on the grain boundaries, and the dislocation density significantly decreases with increasing annealing temperature. Combined with the EBSD results of Fig. 3, the decreased GND density in the annealed samples (at 300 and 500 °C) may be attributed to dynamic
Fig. 4. The statistics of GND density for hot-extruded sample and the samples annealed at different temperatures.
Fig. 5. View of dislocations in the grains by TEM: (a) hot-extruded state, (b) sample annealed at 200 °C, (c) sample annealed at 300 °C, and (d) sample annealed at 500 °C. 5
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homogeneous, reducing the misorientation between adjacent grains (as shown in Fig. 3(b), (d) and (f)). Some Refs [23–25] have reported that the grains will be ultrafine during recovery and recrystallization process, and the polycrystalline behaviour of FCC metal tends to be more uniform. Additionally, the low GND density does not mean that there is no need for GND at high annealing temperature stage. As shown in Fig. 3(f), the grains present the equiaxed instead of elongated shape, and the volume fraction of HAGBs increases to 92.8%. In static recrystallization process, grain boundaries gradually move in the steady state (triangular boundary), as shown in Fig. 5(d). This may give rise to a partial increase of grain size. When grains grow to a certain extent, a process starts by emerging GND walls in grain interiors and ends by removing some GND at grain boundaries, which results in decreasing GND density. Thus, the grains with higher GND densities (mainly concentrated around the LAGBs) will be eliminated by the movement of grain boundaries in static recrystallization. 4.2. The relationship between GND and misorientation distribution
Fig. 6. The relationship between average GND density and grain size of samples at different states.
When a material is deformed, strain heterogeneities appear in the grains and differ from neighbour grains. In order to accommodate the deformation between adjacent grains, strain heterogeneities display itself by lattice curvatures, which result in large orientation differences in the same parent grains. In annealing process, the misorientation between grains will change due to the evolution of the crystallographic texture, which is also related to the variations of grain size. At a given deformed/annealed state of FCC metals, the correlated misorientation distribution (CMD) can be acquired from experimental data and random pair misorientation distribution (RPMD) can be acquired from function calculation of misorientation distribution. GND density is related to the difference between the CMD and RPMD [26]. At a given deformed state of the polycrystalline, one can obtain the experimental CMD. The CMD can be called a “correlated” misorientation distribution due to construction from first adjacent misorientation. One can also calculate misorientation distribution between grains which are not neighbours. It can be calculated by computing the misorientation of a given grain with other grains that are chosen randomly [19]. Fig. 7 presents the CMD and RPMD for hot-extruded and annealed samples. For low annealing temperature at 200 °C, the CMD is similar to the RPMD; nevertheless, for the hot-extruded higher annealing temperature (300 and 500 °C) the CMD curves fluctuate obviously. The CMDs are more dispersed with large grain size (Fig. 7(a), (c) and (d)) than that with small grain size (Fig. 7(b)). Additionally, the difference between CMD and RPMD is more significant with largest grain size (annealed at 500 °C). This is attributed to the texture of the material, and main ideal orientation between adjacent grains is 60° [27]. The quantitative relationship between CMD and RPMD can be expressed by Eq. (6) [19]:
recovery of dislocation structures. From TEM observations, it can be deduced that GND may gradually migrate from near (200) plane to near (220) plane, and then submerge at grain boundaries with increasing annealing temperature. Different GND distribution and density will create different sizes of subgrains. As a result, the evolution of GND could induce the variation of grain size. 4. Discussion 4.1. Grain size and its relation to GND As known, GND density distributes heterogeneously in deformed FCC metals. In this study, the GND density is much lower in the grain interiors compared with GND near grain boundary in the deformed sample, and GND density is higher for the smaller grains on average. According to Ashby's theory [22], dislocations gliding at grain boundaries can lead to the accumulation of high GND density, as dislocations are required to keep continuity and prevent formation of grain overlap. The experimental results presented in Fig. 5 are in good agreement with Ashby's theory. Fig. 6 reveals the relationship between average GND density and grain size, showing the approximately parabolic relation. The sample annealed at 200 °C has the smallest average grain size with highest GND density. The sample annealed at 500 °C has the largest average grain size with lowest GND density. For the deformed and noncompletely recrystallized sample, the high GND density near the grain boundaries is a result of dislocation glide, pile-up, and accumulation across the grain interiors, as shown in Fig. 5. Additionally, with the increasing annealing temperature, fewer GND concentrate on the grain boundaries, and the GND distribution is more homogenous. The variation in GND density can be attributed to two reasons—grain fragmentation at large strains and heterogenetic degrees of GND walls [18]. In hot-extruded state, the grains are deformed and fragmented due to a large strain, resulting in GND density increasing and distributing on the grain boundaries. The fragmented grains group the GND into walls in the process of continuous deformation, resulting in the increase of GND density. Meanwhile, the fragmented grains recover and recrystallize under the high temperature in the hot extrusion process. Dynamic recrystallization leads to the decreasing of GND density. Thus, the GND density should depend on the temperature and strain of hot extrusion, which also determine the grain size. For low annealing temperatures, most fragmented grains are in recovery state. There is still considerable residual stress remaining in the metals, and the recovery process can gradually lead to the elimination of the deformation heterogeneities existing between adjacent grains, i.e. changing the deformation mode from heterogeneous to more
= R
∫ [C (g ) − R (g )]2 dg
(6)
is a function of where C(g) is defined as CMD, R(g) is RPMD, and R equivalent average strain of the given material. It shows an effect of CMD and RPMD on the GND density. As a result, Fig. 8 plots the re . An obvious trend can be oblationship between GND density and R . At served, there is a linear relationship between GND density and R has low value which indicates little difference high GND density, the R for the sample annealed 200 °C is between CMD and RPMD, e.g. the R (0.06) 0.03. The sample annealed at 500 °C has the largest value of R due to the significant difference between CMD and RPMD. Combined with the relationship of grain size and GND density (Fig.7), it is shown . that the grain size is proportional to the value of R In dynamic recrystallization, the new grain boundaries are divided by GND. The grain boundary movement is preferentially along the adjacent grains where higher dislocation density can be observed. As seen from the EBSD map of the hot-extruded sample (Fig. 1(a)), the 6
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Fig. 7. Based on EBSD analysis of correlated misorientation distribution (CMD) and random pair misorientation distribution (RPMD) between grains of different samples: (a) hot-extruded state, (b) sample annealed at 200 °C, (c) sample annealed at 300 °C, and (d) sample annealed at 500 °C.
better compatibility between adjacent grains, due to the low GND concentration on the grain boundaries. Therefore, it is inferred that static recrystallization is taking place in a specified way, which may lead to the decrease of GND density and homogeneous GND distribution in FCC materials. 5. Conclusions The evolution of geometrically necessary dislocation (GND) distribution in the deformed 6061 alloy is studied with EBSD and TEM in this paper. The conclusions are summarized as follows: (1) After hot extrusion, the average GND density of the sample is 8.70 × 1014 m−2 with average grain size ~30 μm, and the GND mainly concentrate on the grain boundaries. (2) After annealing at different temperatures, the average GND density decreases from 6.81 × 1015 to 7.32 × 1013 m−2, corresponding to annealing temperature from 200 to 500 °C and accompanied by the increasing grain size. The sample (after annealing at 500 °C) has greatest ductility with lowest GND density. (3) The relationship between average GND density and average grain size shows an approximately parabolic relation. In addition, the difference between correlated misorientation distribution and random pair misorientation distribution is more significant with largest grain size.
of samples at different Fig. 8. The relationship between GND density and R states.
adjacent grains show distinct orientations and anisotropy. The difference in orientations requires activated slip systems and hence high dislocation density. Another reason for the large misorientation angle may be that the adjacent grains are not completely compatible, resulting in a large GND density. For static recrystallization, e.g. annealing at 200 °C, the misorientation angle mainly scatters from 32.5°–55.5°. As for annealing at 500 °C, the misorientation angle scatters at 5°–20° and 37.5°–55.5°. The small misorientation angle means
Declaration of competing interest The authors declare that they have no known competing financial 7
Materials Characterization 162 (2020) 110205
J. Zhang, et al.
interests or personal relationships that could have appeared to influence the work reported in this paper.
[10] J.A. Venables, C.J. Harland, Electron back-scattering patterns e a new technique for obtaining crystallographic information in the scanning electron microscope, Philos. Mag. 27 (1973) 1193–1200. [11] F.J. Humphreys, Review e grain and subgrain characterisation by electron backscatter diffraction, J. Mater. Sci. 36 (2001) 3833–3854. [12] C.F. Gu, L.S. Toth, B. Beausir, Modeling of large strain hardening during grain refinement, Scr. Mater. 66 (2012) 250–253. [13] M. Calcagnotto, D. Ponge, E. Demir, et al., Orientation gradients and geometrically necessary dislocations in ultrafine grained dual-phase steels studied by 2D and 3D EBSD, Mater. Sci. Eng. A 527 (2010) 2738–2746. [14] E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer, Investigation of the indentation size effect through the measurement of the geometrically necessary dislocations beneath small indents of different depths using EBSD tomography, Acta Mater. 57 (2009) 559–569. [15] J.F. Nye, Some geometrical relations in dislocated crystals, Acta Metall. 1 (1953) 153–162. [16] E. Kröner, R. Balian, et al. (Eds.), Physics of Defects, North-Holland, Amsterdam, 1981, pp. 219–315. [17] W. Pantleon, Resolving the geometrically necessary dislocation content by conventional electron backscattering diffraction, Scr. Mater. (11) (2008) 994–997. [18] W. Pantleon, Stage IV work-hardening related to misorientations in dislocation structures, Mater. Sci. Eng. A 387-389 (2004) 257–261. [19] L.S. Toth, C.F. Gu, B. Beausir, J.J. Fundenberger, M. Hoffman, Geometrically necessary dislocations favor the Taylor uniform deformation mode in ultra-finegrained polycrystals, Acta Mater. 117 (2016) 35–42. [20] B. Beausir, C. Fressengeas, N. Gurao, L.S. Toth, et al., Spatial correlation in grain misorientation distribution, Acta Mater. 57 (2009) 5382–5395. [21] J. Jiang, T.B. Britton, A.J. Wilkinson, Evolution of dislocation density distributions in copper during tensile deformation, Acta Mater. 61 (2013) 7227–7239. [22] M.F. Ashby, The deformation of plastically non-homogeneous material, Philos. Mag. 21 (1970) 399–424. [23] C.F. Gu, M. Hoffman, L.S. Toth, Y.D. Zhang, Grain size dependent texture evolution in severely rolled pure copper, Mater. Charact. 101 (2015) 180–188. [24] W. Skrotzi, A. Eschke, B. Joni, T. Ungar, L.S. Toth, et al., New experimental insight into the mechasims of nanoplasticity, Acta Mater. 61 (2013) 7271–7284. [25] X. Ren, Y. Huang, W. Zhou, L. Zhao, Q. Wang, et al., Influence of pre-recovery on recrystallization behavior, microstructure and mechanical properties of twin-roll cast AA6016 sheet, Mater. Sci. Eng. A 764 (2019) 138159. [26] C. Chen, Y. Beygelzimer, L.S. Toth, J.J. Fundenberger, Microstructure and strain in protrusions formed during severe plastic deformation of aluminum, Mater. Lett. 159 (2015) 253–256. [27] F. Montheillet, M. Cohen, J.J. Jonas, Axial stresses and texture development during the torsion testing of Al, Cu and Alpha-Fe, Acta Metall. 32 (1984) 2077–2089.
Acknowledgements The authors gratefully acknowledge the Jinbei Electric Cable Co. Ltd. for providing the necessary laboratory equipment, 2011 Program of the Ministry of Education of China, and Singapore Ministry of Education Academic Research Fund Tier 1 (Grant No.: R-265-000-593114) and Tier 2 (Project No: MOE2018-T2-1-140) for financial support. References [1] B. Bay, N. Hansen, D.A. Hughes, D. Kuhlmann-Wilsdorf, Evolution of fcc deformation structures in polyslip, Acta Metall. Mater. 40 (1992) 2503–2510. [2] S. Naghdy, P. Verleysen, R. Petrov, L. Kestens, Resolving the geometrically necessary dislocation content in severely deformed aluminum by transmission Kikuchi diffraction, Mater. Charact. 140 (2018) (225-22). [3] J. Jiang, T.B. Britton, A.J. Wilkinson, Measurement of geometrically necessary dislocation density with high resolution electron backscatter diffraction: effects of detector binning and step size, Ultramicroscopy 125 (2013) 1–9. [4] D. Liu, Y. He, X. Tang, H. Ding, P. Hu, et al., Size effects in the torsion of microscale copper wires: experiment and analysis, Scr. Mater. 66 (2012) 406–409. [5] F.J. Humphreys, M. Hatherly, Recrystallization and Related Annealing Phenomena, Pergamon Press, Oxford, UK, 1996. [6] J. Zhang, M. Ma, F. Shen, D. Yi, B. Wang, Influence of deformation and annealing on electrical conductivity, mechanical properties and texture of Al-Mg-Si alloy cables, Mater. Sci. Eng. A 710 (2018) 27–37. [7] S. Najafi, A.R. Eivani, M. Samaee, H.R. Jafarian, J. Zhou, A comprehensive investigation of the strengthening effects of dislocations, texture and low and high angle grain boundaries in ultrafine grained AA6063 aluminum alloy, Mater. Charact. 136 (2018) 60–68. [8] C.C. Merriman, D.P. Field, P. Trivedi, Orientation dependence of dislocation structure evolution during cold rolling of aluminium, Mater. Sci. Eng. A 194 (2008) 28–35. [9] T. Ungar, J. Gubicza, G. Ribarik, A. Borbely, Crystallite size distribution and dislocation structure determined by diffraction profile analysis: principles and practical application to cubic and hexagonal crystals, J. Appl. Crystallogr. 34 (2001) 298–310.
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