Determination of grain boundary mobility during recrystallization by statistical evaluation of electron backscatter diffraction measurements

Materials Characterization 117 (2016) 99–112

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Determination of grain boundary mobility during recrystallization by statistical evaluation of electron backscatter diffraction measurements I. Basu ⁎, M. Chen, M. Loeck, T. Al-Samman, D.A. Molodov Institute of Physical Metallurgy and Metal Physics, RWTH Aachen University, 52056 Aachen, Germany

a r t i c l e

i n f o

Article history: Received 13 January 2016 Received in revised form 19 April 2016 Accepted 30 April 2016 Available online 3 May 2016 Keywords: Grain boundary mobility Recrystallization Aluminium Electron back scattered diffraction (EBSD) Growth anisotropy

a b s t r a c t One of the key aspects influencing microstructural design pathways in metallic systems is grain boundary motion. The present work introduces a method by means of which direct measurement of grain boundary mobility vs. misorientation dependence is made possible. The technique utilizes datasets acquired by means of serial electron backscatter diffraction (EBSD) measurements. The experimental EBSD measurements are collectively analyzed, whereby datasets were used to obtain grain boundary mobility and grain aspect ratio with respect to grain boundary misorientation. The proposed method is further validated using cellular automata (CA) simulations. Single crystal aluminium was cold rolled and scratched in order to nucleate random orientations. Subsequent annealing at 300 °C resulted in grains growing, in the direction normal to the scratch, into a single deformed orientation. Growth selection was observed, wherein the boundaries with misorientations close to Σ7 CSL orientation relationship (38° 〈111〉) migrated considerably faster. The obtained boundary mobility distribution exhibited a non-monotonic behavior with a maximum corresponding to misorientation of 38° ± 2° about 〈111〉 axes ± 4°, which was 10–100 times higher than the mobility values of random high angle boundaries. Correlation with the grain aspect ratio values indicated a strong growth anisotropy displayed by the fast growing grains. The observations have been discussed in terms of the influence of grain boundary character on grain boundary motion during recrystallization. © 2016 Elsevier Inc. All rights reserved.

1. Introduction The exclusive property of grain boundaries, i.e. interfaces between crystallites of the same phase with different crystallographic orientations, is their ability to move in response to applied forces. Grain boundary motion, by which the crystalline solid is rearranged atom by atom, is the fundamental process of grain microstructure evolution in the course of recrystallization and grain growth during annealing subsequent to plastic deformation. The motion of grain boundaries is controlled by their mobility m and the applied driving force p. As was predicted theoretically [1,2] and corroborated by many experiments with different driving forces [3–9], the boundary migration rate v is proportional to the acting driving force, given as, v ¼ mp

ð1Þ

Grain boundary motion is a thermally activated process and the boundary mobility thus shows an Arrhenius temperature dependence, i.e.   H m ¼ m0 exp − ð2Þ kT where H is the activation enthalpy of grain boundary migration. ⁎ Corresponding author. E-mail address: [email protected] (I. Basu).

http://dx.doi.org/10.1016/j.matchar.2016.04.024 1044-5803/© 2016 Elsevier Inc. All rights reserved.

It is well-established that grain boundary mobility is to a great extent determined by the grain boundary character, which is commonly reduced to the orientation relationship between adjacent grains and the orientation of the grain boundary plane. The orientation dependence of grain boundary mobility was first evidenced by developing distinctive crystallographic textures during annealing of deformed polycrystals. The classical growth selection experiments in deformed Al single crystal by Lücke with co-workers [10–14] revealed that the grains with the fastest growth rate were found to be misoriented relative to the deformed matrix by a rotation angle of slightly N40° around an axis close to ⟨111⟩. The well pronounced non-monotonic dependences of the grain boundary migration rate and the migration activation energy on the misorientation angle were also observed in experiments on bicrystals of various metals [9,15–26]. The higher velocity values and the lower activation energies were associated with the boundaries corresponding to the low Σ Coincidence Site Lattice (CSL) orientation relationships. Measurements of grain boundary motion in Al bicrystals [19,25] have shown that tilt grain boundaries with ⟨111⟩ rotation axis and rotation angle of about 40° have the highest mobility. According to the understanding that grain boundaries with highly periodic coincidence structure (low Σ CSL or special boundaries) move faster than off-coincidence (random) boundaries and due to the close vicinity of 40° ⟨111⟩ misorientation to the Σ7 CSL (Coincidence Site Lattice) orientation relationship, the Σ7

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Fig. 1. Schematic illustration of the experimental procedure used for the recrystallization study.

(38.2° ⟨111⟩) tilt boundary was identified as the most mobile boundary in Al [27,28]. However, as was pointed by Lücke [14], the overwhelming statistics of growth selection experiments substantiated that the rotation angles for the fastest moving ⟨111⟩ boundaries were even larger than 40°: “The orientation for the maximum growth rate is definitely not the 38°b111N rotation”, “… the angle of rotation lies between 41° and 42°, where practically no coincidences exist” [14]. Later investigations on the dependence of the mobility of ⟨111⟩ tilt boundaries in Al bicrystals upon angular misorientation values confined between 37° and 43° [29–31], revealed that the temperature dependence of boundary mobility is different for the boundaries with different misorientation angles, and there is a temperature, referred to as the compensation temperature Tc, where the mobility values of different boundaries were similar. Both the activation energy and the preexponential factor were obtained to be maximum for a misorientation angle of 40.5° and minimum for the exact Σ7 orientation (38.2°). Correspondingly, at temperatures lower than Tc, which is about 450 °C in high purity Al [29–31], the mobility was higher for grain boundaries with lower activation energy, in particular it was at maximum for the exact Σ7 boundary, whereas in the high temperature range the maximum misorientation shifted to 40.5° [29–31]. These results directly explained why growth selection experiments [10–13], which were performed at temperatures above 600 °C, distinctly identified a 40° ⟨111⟩ boundary as having the highest mobility. For modeling the microstructure and texture evolution during recrystallization, it is indispensable to determine the migration rate of the moving boundaries of the new recrystallized grains/nuclei, by using Eq. (1) for example. Therefore, knowledge of boundary mobility and estimating its orientation dependence are decisive in accurately modeling recrystallization. It can also be important to extract boundary mobility data from recrystallization experiments because the mobility of stored-energy-driven boundaries can be expected to differ from that of curvature-driven boundaries [7]. For the measurements of grain boundary mobility during recrystallization, an experimental procedure was utilized, wherein grains are allowed to grow from a scratch into a single deformed orientation. The scratch enables nucleation of random orientations thus negating oriented nucleation effects. Huang and Humphreys [7,32,33] utilized this approach combined with in situ annealing in a scanning electron microscope [34] to measure grain boundary mobility during recrystallization of a single-phase Al-0.05 wt.% Si alloy. The obtained maximum mobility values corresponded to boundaries with misorientation angles in the range between 35° and 45° about axes within ±10° of ⟨111⟩. The difference between this broad peak and the sharp peaks found in experiments with curvature-driven boundaries was attributed to local porosity or excess volume associated with interaction of migrating grain boundaries with point defects and dislocations [7]. A similar

investigation on single crystal Al-Zr alloy, conducted by Taheri et al. [35] confirmed that ⟨111⟩ high angle boundaries in Al are the most mobile in general. In good agreement with the measurements of boundary mobility, where curvature was utilized as a driving force [29–31], a minimum in migration activation energy and maximum mobility at low temperatures were observed for the 38° ⟨111⟩ boundary. Also, as it was found in experiments on bicrystals, at high temperatures the mobility of this boundary becomes a local minimum [35]. In previous investigations [7,32,33,35] grain boundary mobility measurements during recrystallization have primarily employed insitu annealing procedure. Even though in-situ measurements provide the necessary spatial and temporal evolution of the microstructure, the obtained datasets lack statistical sufficiency due to the associated experimental difficulties. However, considering that both nucleation and growth of new grains are essentially stochastic processes on a large scale, i.e. depend more upon the local environment than the global, statistical corroboration of such measurements becomes imperative. The present study hence proposes a new approach, whereby the spatial and temporal effects on determining the boundary mobility are compensated by measuring substantially larger data sets, which allow obtaining statistically more reliable mobility values. In order to test the validity and efficiency of the aforementioned method under practical considerations, aluminium, as a model material, was employed in the current study due to sufficiently available literature data on grain boundary mobility and its misorientation dependence in face-centered-cubic (fcc) metals. Future investigations would aim at application of this method upon materials with low symmetry crystal structures, such as hexagonal-close-packed (hcp) metals, whereby statistically more accurate and reliable grain boundary mobility data can be generated. Such information is essential in order to design optimized processing techniques resulting in desirable textures and microstructures. 2. Material and experiments Conically shaped high purity aluminium (99.999%) single crystals with two different orientations were fabricated using vertical Bridgman technique. Orientation determination by means of standard Laue technique revealed respective initial orientations given by, (i) [311] direction deviating by ~5° from sheet normal (ND) and [152] aligned with rolling direction (RD) denoted as ‘Type-I’; and (ii) [111] direction deviating from the ND by about 7°, with [110] along RD labeled as ‘Type-II’. Monocrystalline specimens of 65 mm length, 25 mm width and 3 mm thickness were machined from the grown single crystals by electrodischarge machining. These specimens were then subjected to multipass cold rolling treatment at different strain values, such that the specimens conforming to ‘Type-I’ orientation were rolled to a final thickness

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Fig. 2. (a) Simplified representation of recrystallization nuclei with different orientation gx growing into a deformed monocrystalline matrix with orientation gd upon annealing; (b) impingement events between recrystallized grains growing from a heterogeneous scratch (top view) during annealing; and (c) surface and bulk nucleation events at the scratch (side view). The yellow points indicate the location of nuclei.

reduction of 67% and the ‘Type-II’ ones to about 20%. The rolled specimens maintained their single orientation characteristic. In order to stimulate artificial nucleation by surface defects, samples of dimensions 12 mm × 10 mm × 1 mm fabricated from the rolled specimens were rubbed with a grinding emery paper as randomly as possible and then scratched along the RD by means of a sharp tool. The scratched samples with attached thermocouples were subjected to annealing trials at 300 °C in sand bath furnace with a heating rate of ~170 °C/s for durations ranging from ~ 2 s to 20 s, subsequently followed by water quenching. Fig. 1 gives a reference schematic illustrating the processing of the investigated material. For determining the driving force for recrystallization (cf. Section 3.4) multiple microhardness measurements were conducted on the rolled material using a load of 1 N. An average of 8 to 12 measurements per sample was taken. In order to quantify the impact of simultaneous recovery in the deformed matrix during annealing treatment, hardness measurements on still deformed matrix in the annealed specimens were performed. The scratched and annealed specimens were prepared by mechanical grinding to a depth of about 150 μm followed by 1 μm diamond polishing. Specimens for EBSD analysis were additionally electropolished at 25 V for duration of 25 s using A2 reagent without water. Optical microstructures were obtained after anodizing the samples with Barker's reagent. Automated EBSD measurements were conducted using a LEO-1530 scanning electron microscope equipped with a field emission gun, operating at 20 kV and an HKL-Nordlys II EBSD detector. Analysis on the obtained raw data was performed using commercial EBSD software and the MTEX toolbox [36]. The acquired EBSD orientation data was translated into model input using the algorithm described in Section 3.5. In order to achieve statistically

relevant grain orientation data, 33 low magnification EBSD mappings on several specimens in deformed and partially recrystallized conditions were acquired. An average step size between 0.3 μm and 0.4 μm was used for all EBSD measurements. The average indexing rate of Kikuchi patterns was ~ 70–90%, which were further noise reduced using a minimum of 5 indexed neighbors. The remaining zero solutions were shown in black. 3. Method formulation 3.1. Mobility equation Fig. 2a shows a highly simplistic schematic, wherein nuclei of different orientations grx grow into a deformed single crystal matrix with orientation gd. Nucleation is assumed to be site-saturated and begins at time t = 0. The nucleus/grain growth is assumed to be 2-dimensional, i.e. thickness of nucleation layer can be neglected. In the proposed method to estimate the grain boundary mobility and determine its dependence on grain misorientation, the experimentally measured high angle (N15°) grain misorientation values gd − grx were grouped into discrete classes Δg with equal class width of 4°, i.e. 16°–20°, 20°–24°, etc. Assuming all nuclei experience free growth in a deformed single crystal matrix, the mean boundary migration rate vΔg for a recrystallizing nucleus of a given misorientation class Δ g having radius rΔg after period of time t can be expressed as:

KvΔg ¼

rΔg t

ð3Þ

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Fig. 3. Equivalent grain radius (req Δg) calculation for an anisotropically growing recrystallized grain with Δ g° misorientation relative to a deformed matrix with orientation gd using a) grain boundary length conversion approach and b) free growth distance parameter.

where K is a proportionality constant accounting for the growth anisotropy and assumes unity for perfectly isotropic growth (spherical grains). According to Eq. (1), the average mobility of boundaries of a given misorientation class Δg moving under the recrystallization driving force prx can then be written as: mΔg ¼

rΔg t∙prx

ð4Þ

3.2. Equivalent radius for non-spherical nucleus In reality, nuclei growth would be essentially anisotropic yielding in most cases non-spherical shapes. In such scenario rΔg would ideally correspond to the mean radius of curvature or equivalent grain size. The method proposes two approaches by means of which, an equivalent grain size is determined. 3.2.1. Boundary length conversion Fig. 3a provides a schematic illustration of the equivalent grain radius calculation via. grain boundary length conversion approach. For a non-circular grain the equivalent grain size req Δg can be expressed as [37] ∑1Δg LΔg LΔg rx;d total ¼ πnΔg πnΔg n

r eq Δg ¼

ð5Þ

where LΔg rx, d is the measured grain boundary length for a recrystallized grain with orientation grx and misorientation Δg with respect to the deformed matrix; LΔg total is the total boundary length of all grains belonging to misorientation class Δg, and nΔg is the number of instances where the Table 1 Micro-hardness and approximated deformation stored energy upon rolling. Thickness reduction (%)

Logarithmic true strain (ln(h1/h0))

Vickers hardness (kg/mm2)

Averaged driving force (MPa)

67

1.1

35.1 ± 1.7

1.13

Fig. 4. (a) Example of topological transformation of an EBSD-IPF map into the grain domains used as input in the calculations; (b) basic algorithm behind the implemented recursive ‘divide and conquer’ technique for the topological transformation shown in (a).

misorientation between a recrystallized grain and deformed matrix equals Δg. 3.2.2. Free growth distance Alternatively, especially for recrystallized grains with a higher degree of impingement with neighboring grains (see Section 3.5), the mobility of boundaries can be determined by utilizing the distance migrated by their unimpinged sections (free growth distance), as shown in Fig. 3b, for rΔg in Eq. (4). All grains/nuclei grow from the scratch into the deformed single crystal matrix. The corresponding free growth distance for a grain is, therefore, defined as the farthest distance traversed by its boundary in the direction normal to the scratch. 3.3. Driving pressure for growth of recrystallized nuclei The dislocation density ρ in the deformed matrix gives rise to stored deformation energy. The difference in the stored energy density across the boundary of the recrystallized nucleus acts as the driving pressure for recrystallization prx and is given approximately as [28] 2

prx ¼ ρEdis ¼ αρGb

ð6Þ

where Edis = αGb2 is the dislocation energy per unit length of dislocation line with G being the shear modulus and b as the Burgers vector, α is a constant of the order of 0.5. The available driving pressure can be estimated utilizing a set of experimental data obtained by means of hardness measurements in the deformed matrix. Cahoon et al. [38]

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Fig. 5. (a) Microstructure generated by CA simulations, CA volume of 800 cells × 152 cells × 82 cells; (b) artificial orientation image map extracted from the mid-plane, highlighted in (a); (c) predefined mobility function in red along with mobility values evaluated from simulated microstructures using boundary length conversion (in green columns) and free growth distance (in blue columns) approach, both approaches show good qualitative and quantitative agreement; (d) experimental microstructure illustrating an instance (see grain enclosed in red box) of growth anisotropy effects on the grain shape.

proposed the following relation for deriving yield stress τy from Vickers hardness Hv values, τy ¼

Hv ∙0:1m−2 3

ð7Þ

where, m = n + 2, with m being the Meyers hardness coefficient and n the strain hardening exponent. If strain hardening is neglected (n ≈0), Eq. (7) reduces to τy ≈0:34∙H v

ð8Þ

Moreover, τy of a material is directly dependent on the dislocation density ρ that can be expressed as: τy ¼ cGb√ ρ

ð9Þ

where c is a constant of ≈0.5 for metals undergoing moderate to high deformation. By combining Eq. (6), (8) and (9) the driving pressure for recrystallization can be hence expressed in terms of Vickers hardness as: prx ≈

ð0:34 Hv Þ2 0:5G

ð10Þ

Table 1 provides the measured average hardness value and the calculated dislocation stored energy, i.e. driving pressure for recrystallization, for the specimen after 67% rolling reduction. It is, however, worthwhile to indicate that the aforementioned approach was adopted in the current work primarily owing to its overall

simplicity in determining the driving forces due to stored dislocation densities. From a more fundamental perspective, microhardness measurements though providing qualitatively reasonable information often lack the ability to exactly quantify the dislocation density for the accurate estimation of driving pressures. In this respect, for more correct estimation of driving pressures the techniques such as detailed X-ray analysis [39,40], electron channeling contrast imaging [41] and high resolution EBSD analyses [42] must be employed. 3.4. Orientation averaging and topological transformation of experimental data The indexed points acquired from a 2D-EBSD measurement are topologically transformed into the grain domains using a recursive “divide and conquer”-algorithm (Fig. 4). This is achieved in primarily two steps as described in Sections 3.4.1 and 3.4.2. 3.4.1. Translation of measurement points to grains The spatial coordinates of the orientations from the EBSD data are sequentially organized in a matrix, such that they mimic the topology of the experimentally observed microstructure (Fig. 4a). From the orientation value of each indexed point, the corresponding misorientation between neighboring points can be calculated. Those neighboring misorientation values that lie within the critical high angle boundary criterion, defined by 15°, are classified as belonging to a single grain. For each point to point misorientation corresponding to a value exceeding 15°, a vertex of a polygonal grain is created. In case of accurate experimental indexing, the individual vertices enclose to spatially recreate one

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Fig. 6. Optical micrographs of the rolled monocrystalline samples with the applied scratch for the recrystallization experiments, (a) prior to and (b) upon annealing at 300 °C for a few seconds; The {111} EBSD pole figure depicts the orientation of the deformed matrix.

grain. Then for each of the recreated grains the grain area, grain centroid and grain circumference are calculated. From all measurement points corresponding to a respective grain, the average orientation of the grain is calculated using the algorithm suggested in [43]. The mean intra-grain misorientation or the grain orientation spread is then determined by calculating the average of all misorientation values corresponding to each indexed point in a particular grain with respect to the mean grain orientation. Only in cases when the mean intra-grain misorientation is within 1°, the grain is designated as recrystallized. 3.4.2. Identification of neighboring grains and spatial rearrangement In order to spatially reconstruct the microstructure, the neighborhood of each grain needs to be determined. In this case, it is assumed that the grain neighborhood is a transitive property of the point neighborhood. For instance, if p0 and p1 are neighboring points such that point p0 belongs to grain g0 and p1 belongs to grain g1, then it can be

further implied that grains g0 and g1 are neighboring grains. For each grain a list of all neighbors and the attributes of shared grain boundary segments are hence obtained. The different grains identified in this way are spatially arranged to imitate the experimentally obtained results from EBSD measurements (Fig. 4b). 3.5. Data analysis by means of statistical filtering One of the unavoidable features of recrystallization is the impingement of recrystallized grains after certain duration of annealing (Fig. 2b). This would invoke a “compromise type” of growth, wherein the nuclei come in contact with multiple orientations so that both grain boundary misorientation and corresponding boundary mobility are changing. To overcome this problem, the model applies a ‘primary’ filter called the Grain Impingement Ratio (GIR) that measures the fraction of grain boundary length impinged. This filter is set such that those nuclei with high impingement fractions are filtered out. The

Fig. 7. (a) EBSD image quality (IQ) map, (b) inverse pole figure and (c) grain orientation spread maps taken in the vicinity of the scratch; (d) comparison between the correlated experimental misorientation distribution and a random Mackenzie distribution; (e) {111} pole figures of the region in (a) reproduced in terms of single orientation scatter and contour data.

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Table 2 Statistical compilation of relevant microstructure parameters along with EBSD maps for different misorientation classes utilizing a GIR filter value of 0.6. Max_mob (mmaxΔg) (m4 J− 1 s−1)

GIR (%)

63.00

9.52 × 10–10

0.472

22.45

530.00

8.00 × 10–9

0.598

12

23.82

317.20

4.79 × 10–9

0.232

28–32

16

25.74

512.00

7.74 × 10–9

0.389

34

32–36

29

16.04

1096.80

1.66 × 10–8

0.546

38

36–40

54

4.08

3077.20

4.65 × 10–8

0.529

42

40–44

28

9.52

972.40

1.47 × 10–8

0.499

46

44–48

23

10.48

616.00

9.30 × 10–9

0.000

50

48–52

19

14.48

380.00

5.76 × 10–9

0.440

54

52–56

16

9.54

340.80

5.14 × 10–9

0.472

58

56–60

23

6.66

264.00

3.99 × 10–9

0.588

62

60–64

4

214.40

3.24 × 10–9

0.524

Dev from ⟨111⟩ (°)

Class ID (Δgclass°)

Class width (Δgwidth°)

18

16–20

2

27.20

22

20–24

9

26

24–28

30

Grain_num (nΔg)

12.0

GB_len (μm)

Microstrucrure maps

Class ID: Mean grain boundary misorientation value between recrystallized and deformed grain. Class width: Range of grain boundary misorientation values corresponding to misorientation class ‘Agclass’. Grain_num: Number of grains remaining in misorientation class ‘Agclass’ after applied GIR filter of 0.6. Dev from ⟨111⟩: Mean deviation of the grain boundary misorientation axis from ⟨111⟩. GB_len: Maximum grain boundary perimeter corresponding to misorientation class ‘Agclass’. GIR: Fraction of grain boundary length shared between recrystallized grains for the largest grain corresponding to misorientation class ‘Agclass’. Max_mob: Maximum mobility value corresponding to misorientation class ‘Agclass’. Microstructure maps: EBSD maps highlighting the largest grain in each class in red, corresponding to misorientation class ‘Agclass’ (Deformed subset in green and recrystallized grains in white).

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value of GIR ranges from 0 (accounting for no impingement) to 1, which indicates a fully impinged grain. This leads to the fact that lower GIR values would apply more stringent data filtering conditions. Besides impingement, the problem of nucleation being a 3dimensional process also needs to be considered. This means that not all grains examined on the specimen surface have nucleated at the surface but could have rather originated from the bulk (Fig. 2c). In such cases, the measured grain-size parameter will not always correspond to the actual grain radius, since the measured cross-section of a grain growing from the bulk will always be smaller than that of its midplane. Thus, in simple terms, the largest grains would be the ones expected to show greater conformity to the 2D-nucleation assumption. Therefore, the data set obtained after primary filtering was sorted on the basis of size with respect to each misorientation class Δg. This ‘secondary’ filter is denoted as the Boundary Length Filter (BLF). The BLF is defined such that only those grains corresponding to highest grain boundary length values are chosen, since the mobility values corresponding to largest ones will be the closest to reality. The BLF is thus always assigned a value of 1, which considers only the maximum grain boundary length corresponding to each misorientation class. 3.6. Method validation using cellular automata (CA) simulations Preliminary method validation by means of CA based simulations, wherein synthetic microstructures describing growth of randomly oriented nuclei in a deformed monocrystal were utilized. The CA approach was modified in order to adapt to local and temporal constraints by introduction on demand of a scalable subgrid which can subdivide a cell into subcells, if necessary. This facilitates enhanced resolution of the microstructure that is then described as a collection of deformed, partially

and fully recrystallized cells. For more details regarding this approach, the reader is referred to [44]. The CA comprised of ~ 10 million cells, enclosed by a cuboidal volume of dimensions – 800 cells × 82 cells × 152 cells as depicted in Fig. 5a. A homogeneous dislocation density and single orientation was assigned to deformed matrix. Nucleation was site saturated and 1660 nuclei of diverse orientations were randomly placed in the nucleation layer designated by the transverse plane (c.f. Fig. 5a). The recrystallized nuclei were arbitrarily assigned predefined mobilities on the basis of their degree of angular misorientation with respect to the matrix. Nuclei were allowed to grow isotropically into the deformed matrix, at a rate determined by Eq. (1). The model tacitly assumes that the grain boundary segments of the recrystallized grains cease to move upon impingement with one another. The simulation was run over 8 internal time steps and the grains extracted from the mid plane, as shown in Fig. 5a and b, were analyzed using the method proposed in the current work. Fig. 5c represents the calculated mobility values (shown in blue and green columns), corresponding to a GIR = 0.6 and BLF = 1, upon analysis of artificial orientation maps derived from the simulated microstructures. When juxtaposed with the predefined mobility function (shown in red in Fig. 5c), the calculated mobility values show reasonable agreement. Fig. 5b evinces multiple grains (colored in red) belonging to the 38° misorientation class but possessing different sizes. This observation strongly corroborates the previously described bulk nucleation behavior (c.f. Section 3.5) where in the cross-section area of the grain can vary depending on its nucleation depth from the investigated surface. Fig. 5b and d also distinguish between the influence of lateral impingement and growth anisotropy on the evolution of grain shape. On comparing the CA microstructures (with isotropic growth) in Fig. 5b with the

Fig. 8. Grain number fraction and grain area fraction distribution as a function of misorientation class for different imposed GIR filter values of (a) 0.3, (b) 0.5, (c) 0.7 and (d) 1.

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experimental ones (c.f. Fig. 5d), it is quite obvious that the latter displays elongated shapes as a result of anisotropy in grain boundary motion. 4. Microstructural characterization Fig. 6 shows optical micrographs of the scratched specimen after 67% total thickness reduction (Fig. 6a) and after annealing (Fig. 6b), where the scratch vicinity has undergone complete recrystallization. The initial orientation in this case was of ‘Type-I’. The orientation of the deformed matrix (112) ⟨111⟩ (with a spread of ~±5°) measured by means of EBSD is displayed in terms of (111) pole figure in Fig. 6a. Annealing treatments of the scratched rolling specimens resulted in extremely rapid recrystallization kinetics. Significant growth was achieved within few seconds of annealing time, and the recrystallized grains seemed to consume the deformed matrix readily after annealing of ~10 s. Recrystallized grains grew outwards into the deformed matrix, perpendicular to the scratch length, i.e. towards the transverse direction (TD). The larger grains demonstrated either a conical or elliptical morphology, whereas the smaller grains seemed to have impinged at a much earlier stage. No new recrystallized grains were observed away from the scratch. Fig. 7a presents a representative image quality (IQ) map of the optical microstructure shown in Fig. 6b. The sampled area corresponds to a region adjacent to the scratch, with the latter positioned at the bottom edge of the mapping. The inverse pole figure (IPF) coloring in Fig. 7b indicates grains with diverse orientations growing into a purple colored deformed matrix with (112) crystallographic planes oriented parallel to the sheet plane. Certain orientations, characterized by their significantly larger grain sizes in comparison to others, showed enhanced growth rates. The corresponding grain orientation spread (GOS) map shown in Fig. 7c reveals that the internal misorientation spread within the recrystallized grains remained within 1°. Fig. 7d shows the corresponding grain boundary fraction as a function of misorientation angle distribution (red plot) vs. the misorientation angles distribution for a randomly textured polycrystal after Mackenzie (blue plot). The plot shows a distinct peak corresponding to misorientation angle of ~ 38°, being most likely associated with grain boundaries shared between recrystallized and deformed grains. Grain boundaries with misorientation angles b 15° may correspond to the deformed structure, as well as the low angle grain boundaries that form between impinged recrystallized grains of neighboring misorientation classes. The corresponding EBSD texture reproduced in terms of {111} scatter and recalculated pole figures indicated a large spread of recrystallized grain orientations (Fig. 7e).

107

for GIR values b1, i.e. when considering only those grains with lower degrees of impingement (c.f. Fig. 8a–c). For the unfiltered data set (GIR = 1), the grain number fraction distribution tends to be leveled out (c.f. Fig. 8d) in the high angle boundary regime. On the other hand the grain area fraction distribution reveals a distinct peak between 36° and 40°, with its percentage contribution varying inversely with increasing GIR value (c.f. Figs. 8a–d). Interestingly, unlike the number fraction, the qualitative characteristic of the area fraction distribution is virtually independent of the level of grain impingement filter. 5.2. Grain boundary mobility Fig. 9a presents the calculated maximum boundary mobility mmax Δg corresponding to each misorientation class. The data set considered was obtained after implementing a GIR filter of 0.6 and a second BLF filter of 1, i.e. considering only the largest grains from each misorientation class (cf. Section 3.5). The calculated mobilities indicate a maximum –8 value of mmax m4/J ⋅ s for the angular interval of 36°–40°. 38° ≅ 4.7 × 10 For other high angle boundaries the mmax Δg values were found to be in the range of 10–10 to 10–9 m4/J⋅s. Fig. 9a also gives the average deviation of the measured misorientation axes from the ⟨111⟩ axis, calculated for misorientation classes between 28° and 52°. A minimum deviation of ~±4° was found for the misorientation angle interval between 36° and 40°. On both lower and higher sides from the 38° class mark, the deviation of the rotation axes from ⟨111⟩ increases. Fig. 9b shows the

5. Statistical analyses of experimental data The experimentally obtained EBSD maps were superimposed to obtain a repository of a total of 839 recrystallized grains, described in terms of their spatial orientation, grain boundary length, grain area, grain centroid and grain diameter. The resultant data set was then analyzed to reproduce the dependencies of various parameters relevant to nucleus growth/grain boundary migration on the misorientation angle between recrystallized grains and deformed matrix. The forthcoming sections present the results and trends. Table 2 illustrates a statistical compilation of the various relevant grain parameters along with related EBSD microstructures obtained after an analysis run for an imposed GIR = 0.6. 5.1. Grain area and grain number fraction Fig. 8 shows histograms describing the variation of grain number fraction and grain area fraction with respect to misorientation angle. The distributions shown correspond to different levels of the GIR filter, ranging from 0.3 to 1, applied to the initial data set. With respect to grain number fraction, the maximum peak at 38° ± 2° is discernable

Fig. 9. (a) Calculated maximum boundary mobility mmax Δg and the average deviation of misorientation axis from 〈111〉 with respect to different misorientation classes; (b) variation of maximum boundary mobility in 38° misorientation class and analyzed sample size of recrystallized grains with respect to different GIR filter values ranging from 0.1 to 1.

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variation of mobility values corresponding to 38° misorientation class mmax 38° with respect to different levels of imposed GIR filter values. As shown, the plot can be divided into two regimes, separated by an impingement criterion of 0.6. When only the grains with low impingement fraction (GIR b 0.6) are analyzed, the resultant maximum mobility for 38° misorientation also decreases. For GIR values above 0.6, mmax 38° becomes independent of the GIR filter assuming a constant value of ~4.7× 10−8 m4/J⋅s. It is noted here that the size of the filtered data set corresponding to each GIR value is significantly reduced with decreasing filter values affecting the statistics.

Physically, this means that the grains with highly mobile 38° ± 2° boundaries show maximum growth anisotropy relative to the grains of other misorientation classes. Fig. 10c plots the mean aspect ratio of grains as a function of deviation of their misorientation axes from the ⟨111⟩ axis, calculated for misorientation classes between 28° and 52°. The progression reveals that misorientation axes closer to ⟨111⟩ show a larger aspect ratio, in other words, higher growth anisotropy.

5.3. Grain shape characteristics

The current work proposes an experimental method to measure grain boundary motion during recrystallization. The method utilizes a statistically viable technique to predict grain boundary mobility during recrystallization regardless of the type of material or crystal structure. Using CA simulations it is shown that the proposed technique ensures good data reproducibility. The validity of the technique is further demonstrated by measuring the grain boundary mobility in pure Al. The forthcoming section will hence discuss the obtained results in terms of its physical interpretation of grain boundary motion during recrystallization of pure Al. Furthermore the overall qualitative and quantitative nature of the suggested methodology will be assessed.

In the course of the performed analysis, the grain aspect ratio dependence on the misorientation angle was also considered. For a particular grain, the aspect ratio is defined as the length to width ratio (Fig. 10a). Hence, an aspect ratio of 1 corresponds to a perfectly spherical grain. Deviation from this ideal value is an indication of grains with elongated morphologies (cf. Figs. 5d and 6b). The variation of mean aspect ratio with respect to different misorientation classes is represented as a histogram plot in Fig. 10b. Following the mobility trends (cf. Fig. 9a), the aspect ratio shows a distinct maximum in the class interval of 36°–40°.

6. Discussion

Fig. 10. (a) Schematic showing grain aspect ratio calculation given as length upon width; (b) variation of mean aspect ratio with degree of misorientation for an applied GIR value of 0.6; (c) mean aspect ratio as a function of deviation of the misorientation axis from ⟨111⟩ calculated for misorientation classes lying between 28° and 52°.

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Fig. 11. (a) EBSD image quality (IQ), (b) GOS, (c) IPF and (e) unit cell mappings on the as-deformed state after 20% rolling reduction, showing site-saturated nucleation with diverse orientations at the bottom of the scratch; (d) experimentally measured MODF in red and random Mackenzie misorientation distribution in black dashed lines.

6.1. Nucleation and growth characteristics The approach for determining the grain boundary mobility suggested in the current work is based on a critical assumption of a site saturated random nucleation behavior, emerging from the scratch. In the present case, significant nucleus growth was observed at very short annealing times, possibly indicating an absence of a well-defined incubation process. For this reason, additional rolling specimens with lower deformation strains were investigated. Fig. 11 presents an EBSD analysis of a monocrystalline specimen with a ‘Type-II’ starting orientation that was cold rolled to ~ 20% thickness reduction and subsequently scratched. Fig. 11a presents an image quality (IQ) map of the scratched region, in which fine equiaxed grains can be observed at the scratch pit. From the GOS map, it can be seen that these fine grains exhibit GOS values b1°, which indicates that they were readily recrystallized in the deformed state without annealing (Fig. 11b). This behavior is quite likely attributed to the imparted additional deformation during scratching and the concomitant frictional heat released during the process, which can stimulate dynamic nucleation of new, strain-free grains. Fig. 11c is an IPF map indicating that post rolling the deformed matrix assumed a [111] || ND orientation, whereas the recrystallized nuclei/grains displayed relatively random orientations. The grain boundary misorientation angle distribution of the recrystallized fraction of the microstructure (solid line in Fig. 11d), agrees almost perfectly with the Mackenzie plot for a random distribution (dashed line). Fig. 11e displays a

magnified unit cell representation of a recrystallized area, indicating further evidence of random orientation behavior. The presence of a well-defined nucleation regime in the deformed state also explains the rapid recrystallization kinetics observed during static annealing treatments. This fits reasonably well with the assumption made earlier about a site saturated nucleation since the recrystallization nuclei are already present at the beginning of annealing. The rapid recrystallization/growth kinetics in turn minimizes additional effects of recovery on the stored energy, which is essentially a time dependent process. Mean hardness values in specimens annealed for ~ 6 s, corresponding to the matrix that is not yet consumed by the recrystallized grains was 34.08 ± 1.13 HV, indicating negligible deviation from the ones reported in the cold deformed condition (35.11 HV, c.f. Table 1). It must be noted here that since recovery in the deformed single crystal matrix occurs concomitantly with growth of recrystallized grains in the scratch region, accurate quantitative prediction of local driving pressures becomes difficult to realize. In this respect, the experimental characterization employed in the current study only provides a qualitative estimate of the driving force from stored dislocation density. Future studies will focus upon incorporating appropriate methodologies to quantify temporal effects on stored dislocation densities. In contrast to a relatively homogeneous nucleation behavior, microstructures after annealing indicated heterogeneous growth characteristics, with nuclei/grains of certain orientations growing at the expense of others (cf. Figs. 6b and 7). Such oriented growth behavior is a characteristic

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Fig. 12. EBSD IPF mappings near the scratch after recrystallization annealing acquired (a) on the sheet plane and (b) the lateral face for 20% as-deformed specimen (specimen schematic indicating the planes of observation); (c) average misorientation profile across Σ7 ⟨111⟩ boundary between A and B points labeled in (b); (d) schematic illustration of the spatial orientation of the misorientation axis and grain boundary plane for pure ⟨111⟩ twist and tilt boundaries.

feature of fcc metals and is primarily attributed to the strong dependence of the ease of boundary migration on the grain boundary energy and the characteristic boundary mobility. The sudden increase in the grain boundary fraction (Fig. 7d) and grain area fraction (Fig. 8) of the 36°–40° misorientation class is a clear indication of such oriented growth behavior. 6.2. Dependence of boundary mobility on misorientation and orientation of the boundary plane The boundary mobility values obtained in the current work from recrystallization experiments utilizing the proposed microstructural approach were compared with the results of previous investigations. As mentioned in the introduction, early studies on growth selection during recrystallization performed at temperatures above 600 °C reported ⟨111⟩ boundaries with misorientation angles slightly larger than 40° to be the most mobile grain boundaries in Al [10–14]. This important finding was further corroborated by measurements on Al bicrystals [29–31], which additionally reported that for lower temperatures (b 450 °C) the maximum mobility shifts to the exact Σ7-38.2° ⟨111⟩ misorientation. The results from the present study revealed a distinct maximum mobility peak corresponding to misorientation angles of 38° ± 2° around ⟨111⟩ (±4°), indicating excellent quantitative agreement with previous literature data. The misorientation dependence of grain boundary mobility in Al obtained in recrystallization experiments [7,10,12–14,32,33] can typically be approximated as a non-monotonic Gaussian scatter with a maximum

peak at about 40° ⟨111⟩. The peak value is usually one to two orders of magnitude larger than the mobility of random high angle boundaries. This trend is also observed in the current work. The calculated ratio between maximum mobility for the 38° class mark and other high angle boundary mobility values was in some cases 10 and higher (cf. Fig. 9a). Considering earlier studies on grain boundary migration in Al bicrystals [19,25,29–31], the maximum mobility for the Σ7 boundary at 300 °C, derived from the reduced mobility; A = m ∙ γ (γ is the grain boundary surface tension) are in the range of ~10–10–10-11 m4/J⋅s (assuming γ ≅ 0.5 J/m2). This is about two to three orders of magnitude –8 lower than the highest mobility mmax m4/J ⋅ s, obtained in 38° ≅ 4.7 × 10 the current study. This difference can be considered as an indication that the mobility of boundaries driven by the deformation stored energy may differ from the mobility of curvature-driven, yet geometrically similar, boundaries [7]. Interestingly, mobility measurements performed by Huang and Humphreys on 5N-Al during recrystallization yielded maximum mobility values in the range of ~10–8–10-9 m4/J⋅ s at 300 °C. The quantitative agreement between the mobility values in the current investigation with those observed in the reference [33] reiterates the aforementioned conjecture that the grain boundary migration driven by stored energy difference is distinctive from curvature driven boundary motion. However, the reported mobility peak in [7,33] was observed for boundaries with a misorientation of 40° ⟨111⟩ allowing an angular deviation of ~10°. On the other hand, results reported from recrystallization experiments performed by Taheri et.al [35] indicated a sharp mobility maximum corresponding to the 38° ⟨111⟩ misorientation at 300 °C, thereby corroborating the observations in the present study. It

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is worth noting that even though grain boundary migration during recrystallization displays significantly higher mobility values, its characteristic dependence upon the grain boundary misorientation conforms to that observed for curvature driven boundary motion [29–31]. Grain shape aspect ratio measurements in the current work revealed a maximum corresponding to the high mobility boundaries with misorientation angles in the range of 36°–40° (cf. Fig. 10b), which point to an anisotropic growth behavior. Such growth anisotropy can be attributed to the dependence of boundary mobility on the orientation of the boundary plane. It has been established that ⟨111⟩ tilt boundaries can move orders of magnitude faster than pure twist boundaries [45]. It can therefore be expected that grain boundary segments with a larger ⟨111⟩ tilt component will move faster than those with a prevailing twist component. Fig. 12 shows the results of EBSD measurements corresponding to an annealed state after 20% rolling reduction, displayed in IPF coloring with respect to ND, depicting complete recrystallization in the vicinity of the scratch. In order to approximately estimate the orientation of grain boundary planes, the measurements were acquired on the RD-TD sheet plane (Fig. 12a) and the ND-TD transverse plane of the rolled specimen (Fig. 12b). The ⟨111⟩ direction, depicted by the arrow in the deformed matrix was oriented parallel to the sheet normal ND. As evident, the microstructures revealed strong growth anisotropy, displayed particularly by those grains with higher growth rates. Fig. 12b depicts a Σ7 ⟨111⟩ boundary (identified by measuring the average misorientation profile across the grain boundary, as shown in Fig. 12c), outlined by dashed and solid lines. The dashed red lines indicate the grain boundary plane trace corresponding to those boundary segments, which are close to a twist configuration (grain boundary normal parallel to ⟨111⟩ direction). By contrast, the grain boundary traces shown in solid black lines possess a higher fraction of the tilt character (grain boundary normal perpendicular to ⟨111⟩ direction). The arrows indicate the approximate orientation of the grain boundary normal. Fig. 12d shows a schematic illustration of twist and tilt grain boundary geometry with the grain boundary normal being parallel to the rotation axis in the former and perpendicular in the latter case. Such partition of the grain boundary into tilt and twist components can explain the observed anisotropic shape of recrystallized grains, arising from a growth direction (along TD) that is essentially normal to the tilt region of the grain boundary plane (cf. Fig. 12a and b). The high aspect ratio corresponding to grains with misorientation axes close to ⟨111⟩ direction (cf. Fig. 10c) further corroborates the aforementioned migration behavior. 7. Summary and conclusions The present study proposes a statistical microstructural method to determine grain boundary mobility as a function of grain misorientation angle in metals during recrystallization. The technique utilizes sequential filters categorized as a primary impingement filter and a secondary grain size filter to account for recrystallization impingement effects and the nucleation taking part in the bulk. The recrystallization experiments performed, demonstrated pronounced growth selection in the recrystallizing nuclei, whereby the grain boundaries with misorientations close to the Σ7 CSL orientation relationship migrated significantly faster than the others. The obtained grain boundary mobility values varied non-monotonically with the misorientation angle, producing a distinct peak at misorientations of 38° ± 2° about the ⟨111⟩ ± 4° axes. The corresponding maximum mobility was estimated to be 4.7 × 10–8 m4/J⋅s. The boundary mobility values during recrystallization were observed to be almost two to three orders of magnitude larger than those measured during curvature-driven grain boundary motion in a pure Al material of the same purity. This pointed to the difference of the migration mechanisms of boundaries moving under the influence of deformation stored energy difference and curvature driving force, respectively. The fast growing grains displayed strong growth anisotropy, such that the tilt component of the boundary segments migrated significantly faster than the twist components, giving rise to non-spherical,

111

elongated grain morphology. The observed growth anisotropy is attributed to the dependence of boundary mobility on the orientation of the boundary plane. Future work will examine the applicability of this method for determining the grain boundary mobility in hexagonal close-packed (hcp) metals.

Acknowledgements The financial support of the Deutsche Forschungsgemeinschaft (DFG), Grant no. AL 1343/1-2 is gratefully acknowledged. The authors also thank Jann-Erik Brandenburg and Konstantin Molodov for their valuable assistance during fabrication of single crystals and EBSD analysis.

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