Effect of coarse precipitates on surface roughening of an FCC polycrystalline material using crystal plasticity

Computational Materials Science 126 (2017) 121–131

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Effect of coarse precipitates on surface roughening of an FCC polycrystalline material using crystal plasticity Jaimyun Jung a, Jae Ik Yoon a, Ji Hyun Moon a, Hyung Keun Park a, Hyoung Seop Kim a,b,⇑ a b

Department of Materials Science and Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Republic of Korea Center for High Entropy Alloy, Pohang University of Science and Technology (POSTECH), Pohang 37673, Republic of Korea

a r t i c l e

i n f o

Article history: Received 24 July 2016 Received in revised form 13 September 2016 Accepted 14 September 2016

Keywords: Crystal plasticity Polycrystalline materials Microstructure Finite element method

a b s t r a c t Effect of precipitates on surface roughening during stretching of a synthetic microstructure that is constructed with microstructural features equivalent to those of Al6061 alloy has been investigated under crystal plasticity framework. Single crystal plasticity simulations are first conducted to examine the interplay between precipitates and the matrix with typical rolling texture components. Afterwards, a banded structure with alternating Cube and Goss orientations is simulated to see the effect of precipitates and the spatial distribution of orientations on surface roughening. Lastly, the roughening behavior of a synthetic microstructure with morphological features identical to those of Al6061 alloy observed through electron back scattered diffraction and scanning electron microscopy images is investigated with crystal plasticity simulations. Results establish that precipitates act differently depending on the spatial distribution of kinematically weak and strong orientations. This study demonstrates how precipitates interact with different orientations and affect surface roughening of a precipitate hardened microstructure with and without texture bands. Ó 2016 Elsevier B.V. All rights reserved.

1. Introduction Aluminum alloys, due to their low density, high specific strength, and good formability, have become standard for hangon parts in many vehicle models. Sheets or profiles are usually formed into final parts by cold deformation. Thus, bendability becomes an important attribute of aluminum alloys in their applications. During bending deformation, the tensile region of aluminum alloys exhibits a notable surface roughening that leads to a considerable strain localization. A notable body of literature that models the deformation behavior of aluminum alloys has demonstrated that constituent precipitates, grain morphologies, and orientation distributions affect shear band formation or strain localization during bending deformation [1–5]. In particular, grain morphologies and texture bands are known to play a significant role in creating surface ridges [3–5]. Rossiter et al. [1], using single crystal plasticity simulations, revealed that surface roughness measured along a normal direction (ND) surface is most distinct with Brass, S, and Copper orientations while least with Cube and Goss orientations, meaning that rough⇑ Corresponding author at: Department of Materials Science and Engineering, Pohang University of Science and Technology (POSTECH), Pohang 37673, Republic of Korea. E-mail address: [email protected] (H.S. Kim). http://dx.doi.org/10.1016/j.commatsci.2016.09.017 0927-0256/Ó 2016 Elsevier B.V. All rights reserved.

ening is directly related to the relative ease of texture evolving during deformation. On the other hand, for polycrystalline materials, it was demonstrated that it is not the texture itself, but the difference in the strain accommodating capabilities of the adjacent orientations within a polycrystalline aggregate that affects the surface roughening behavior [1]. These findings are comparable to those by Romanova et al. [2], Shi et al. [3], and Lefebvre et al. [4] who discussed the importance of both spatial orientation distribution and mechanical properties on the onset of localized necking and surface roughening. Recently, Qin et al. [5] used a moving window method with simple roping model based on r-value predicted by the full constraints (FC) Taylor model to demonstrate that a heightened amplitude can be achieved by invoking a number of subsurface grain layers with an assumption of the homogeneous through-thickness texture. While surface roughening plays important roles in shear localization, which is often evaluated with spatially banded orientations, or a texture band, limited efforts on the effect of precipitates on surface roughening have been made. Precipitates are known to interact with their matrix at both microscopic and macroscopic levels that lead to macroscopic phenomena [6–11]. During deformation, at the microscopic scale, non-deformable precipitates cause strain incompatibility with respect to the deforming matrix, leading to changes in dislocation contents, cell and subgrain structures, misorientation, and deformation heterogene-

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ity [6]. The strain incompatibility at the precipitate-matrix interface is accommodated by dislocation generation, meaning that higher dislocation density can be expected from deformation of aluminum alloys with precipitates compared to a single phase aluminum. Moreover, cell size and cell misorientation are known to depend on the size of the inter-particle spacing. While, the increase in dislocation content due to precipitate-matrix strain incompatibility is reduced due to dynamic recovery at a high level of deformations, the matrix regions near the precipitates will exhibit heterogeneous deformation behavior with respect to the macroscopic deformation. Thus, the effect of precipitates on macroscopic phenomena, such as deformation characteristics [7–9], stress corrosion [10], and recrystallization [11], are evident and should not be overlooked in the case of surface roughening as well. Previous works using a digital image correlation (DIC) technique to observe the surface deformation behavior of polycrystalline materials proved that an effective quantitative assessment of the effect of microstructural features on deformation behavior can be made using crystal plasticity simulations with realistic microstructures [12–15]. Therefore, we will build a statistical dataset from experimental measurements made by EBSD and SEM to construct a synthetic microstructure via DREAM.3D [16], and use the microstructure for crystal plasticity simulations during a plane strain tension, which is the dominant deformation mode on the tensile region of a bending specimen. This type of numerical analyses using realistic microstructures has revealed valuable insights on micromechanics of polycrystalline materials [17–23]. In this work, the effect of precipitates on the surface roughening is investigated using the finite element method (FEM) simulations under the crystal plasticity framework. Initially, slip analyses and orientation changes are investigated to analyze the effect of precipitates on specific orientations under plane strain tension, which is the stretching region observed in the tensile region during bending. The single crystal plasticity simulations are carried out using common rolling texture components to exemplify how slip activities are affected by the presence of a single precipitate or a small cluster of precipitates. Afterwards, the effect of precipitates in banded structure with alternating Cube and Goss orientations is evaluated to illustrate the combined effect of precipitates and spatial distribution of orientations. Finally, the effect of precipitates on polycrystalline samples are analyzed with a synthetic microstructure. Local stress and strain states as well as orientation changes are examined with different orientation distributions. Experimental measurements are made and compared with initial microstructure used for simulations to ensure that the synthetic microstructures used for the simulations retain morphological features that are statistically equivalent to those obtained from EBSD and SEM images. Extensive numerical analyses indicated that precipitates do play a significant role in surface roughening of both single and polycrystalline materials, but the role the precipitates play rely heavily on whether or not a texture band, either microscopic or macroscopic, is present in the case of polycrystalline materials.

2. Experimental procedure As-received Al6061-T6 alloy sheet with a thickness of 2 mm was used for experiments to obtain microstructural and mechanical characteristics. The stress-strain curve of the Al6061-T6 specimen was obtained using a servo hydraulic universal testing machine (UTM, model 1361, Instron Co., USA) for tensile tests at room temperature. The tensile test in the rolling direction (RD) was made with dog bone-shaped plate specimens with a 5.0 mm, 2.5 mm, 1.0 mm in gauge length, width, and thickness, respectively, at a strain rate of 0.001 s
1. During all tensile tests, the

strains were measured using the DIC method in an optical strain gauge system (ARAMIS 5 M, GOM mbH, Germany) in order to measure highly accurate and precise strains [24]. Samples for EBSD were prepared using mechanical polishing up to 1200 grit in US mesh followed by electrolytic polishing with 80% ethanol mixed with 14% distilled water and 6% perchloric acid solution. Field emission gun XL30S scanning electron microscope (FESEM) at 25 keV was used for the EBSD measurements. Additionally, FESEM measurements were made to characterize volume fraction and morphology of precipitates. 3. Model set up 3.1. Crystal plasticity In this section, the modeling framework for describing both slip and twin induced deformation is summarized. The crystal plasticity framework follows the concept outlined by Kalidindi et al. [25]. In his work, slip is incorporated as additional kinematic degree of freedom for shear by prescribing the plastic velocity gradient in the following manner:

Lp ¼

Ns X

a

c_a Sasl

ð1Þ

S ¼ m  n;

ð2Þ

where c_a denotes plastic shearing rate at slip system a, Ns refers to the total number of slip, and Ss denotes slip systems. Also, slip-induced shear evolution is shown in Eq. (3) below in power law form [25]:

c_a ¼ c_0 jsa =sa j1=m signðsa =sa Þ;

ð3Þ

where, c_0 , sa , and sa refer to reference shear rate, resolved shear stress, and slip resistance on a slip system, respectively. The hardening law associated with slip systems is described as follows:

X s_a ¼ hs ð1
sa =ss0 Þ c_ k ;

ð4Þ

slip

where, s_a , ss0 , and hs refer to change in slip resistance rate, saturation value associated with slip system, and hardening rate of slip. Parameters for constitutive equations are fitted for precipitatecontaining matrix with weak cube texture, which is observed from EBSD measurements (Fig. 1a). The following parameters in Table 1 are fitted through repetitive simulations to match simulated and experimental engineering stress-strain curves (Fig. 1b). The precipitates are assumed to undergo linear elastic deformation throughout all the simulated works conducted in this study. The elastic constants for precipitates are obtained from existing literature [26]. 3.2. Construction of synthetic microstructure The reconstruction of 3D virtual microstructure starts with the acquisition of microstructural features from data acquired from the EBSD and SEM images. Because the Al6061 is a face centered cubic (fcc) material with precipitates, key features in microstructural reconstruction include grain size distribution, grain aspect ratio, orientation distribution, and precipitate size and spatial distributions. EBSD measurements are used to evaluate grain size distribution, grain aspect ratio, and orientation distribution. For precipitate features, SEM images are used to figure out the size and spatial distributions. Because the idea behind this work is to simulate the effect of precipitates within fcc polycrystalline materials with and without

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Fig. 1. Experimental results on (a) microtexture and (b) stress-strain curve of Al6061-T6 alloy.

Table 1 Fitted parameters for crystal plasticity simulation. C11 (MPa)

C12 (MPa)

C44 (MPa)

s0 (MPa)

hs (MPa)

ss0 (MPa)

c_ 0

m

108,000

61,000

29,000

105

500

180

0.001

0.01

a texture band, the orientation distribution obtained from EBSD image is of little concern because texture bands are typically in the range of mm in scale. Moreover, because synthetic microstructure built on such large dimension is inefficient due to the fact that manipulating the dimension of texture bands down to a microscopic level where only several grains are entailed within each band thickness is enough to simulate microscopic ridge patterns. Thus, the orientation distribution obtained from EBSD measurements is not taken into account in the synthetic microstructure. The main features taken into account by the synthetic microstructure are morphology and sizes of grains, and precipitates. 3.3. Simulation procedure The simulations are conducted with matrix sizes of 20  20  15 lm, 30  24  6 lm, and 200  200  20 lm for single crystals, the Takechi model, and the synthetic microstructure, respectively. Tension is applied up to 30% engineering strain for single crystal and Takechi model and 10% engineering strain for the synthetic microstructure. The simulations were carried out using ABAQUS 6.9 with user-material (UMAT) subroutines for crystal plasticity finite element simulations. In the case of synthetic microstructures, the microstructures that consist of microstructural features that are statistically equivalent to those observed in EBSD and SEM images are generated using the DREAM.3D software. Afterwards, constitutive parameters (Table 1) are prescribed under the crystal plasticity framework. Finally, the microstructure undergoes a plane strain tensile deformation along the RD with a strain rate of 0.001 s
1, which is identical to the experimental condition. 4. Results and discussions 4.1. Characterization of synthetic microstructure Fig. 2a shows the EBSD image obtained along the ND plane while Fig. 2b shows the SEM image of the Al6061-T6 alloy. The

Fig. 2. (a) EBSD images and (b) SEM image of microstructure of Al6061-T6 alloy taken along the ND plane.

grain size distribution, grain aspect ratio, and precipitate size distribution used as inputs are acquired from several EBSD and SEM image data such as those shown in Figs. 1 and 2. Because the orientation distribution for the simulations in this work is chosen to exhibit distinct roughening, the orientation distribution observed in the EBSD images is not reflected in the synthetic microstructure. Instead, spatially alternating bands of h1 0 0i//ND and h1 1 1i//ND fiber components are assigned to the synthetic microstructure (Fig. 3b). From the SEM observations, the morphology of the intermetallic precipitates is assumed to be spherical and the size to be 1 lm with a total surface fraction of roughly 1%. From Fig. 3, one can see that the grains are longer toward the RD, which is a characteristic of microstructure shown in Fig. 2. From Figs. 2 and 3 one can see that the virtual microstructure shares similar features as those observed in EBSD and SEM images. From the prior works on micromechanical simulations with reconstructed representative volume element [19,21–23,27–30],

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Fig. 3. (a) Synthetically generated virtual microstructure and (b) spatially banded microstructure with alternating h1 1 1i//ND (blue) and h1 0 0i//ND (red) components. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 4. Plastic deformation of single crystals with a single precipitate.

we believe that this representation is suitable for micromechanical studies conducted in this work. The full 3D microstructural reconstruction with microstructural features described above is accomplished with the DREAM.3D software. While the pixel-by-pixel representation will differ from those obtainable from the serial sectioning technique, the reconstructed microstructure would still be statistically equivalent in terms of grain size distribution, grain shape, and precipitate size and shape at the microscopic region of interest. 4.2. Effect of precipitates in single crystal Mechanically, a hard inclusion within a matrix causes the precipitate/matrix interface to undergo limited deformation and the

restraint is compensated by additional deformation, or localization, at matrix nearby. The same deformation behavior is observed from all rolling texture components when the precipitate is included in each single crystal during plane strain tension along RD. Lack of plastic deformation adjacent to precipitates is compensated by additional elongation as well as thinning near the periphery of each crystal (Fig. 4). Because polycrystalline materials with coarse precipitates may form precipitates that are clustered, it is worthwhile to investigate whether or not precipitate clustering manifests different mechanical behavior compared with that of the single precipitate. In general, clustering of smaller precipitates that add up to 1% in volume does not change how matrix and precipitates interact. On a more specific note, however, within the center of clustered precipitates,

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Fig. 5. Plastic deformation of single crystals four small precipitates.

Fig. 6. (a) Cube oriented single crystals with precipitates after 30% elongation and its slip activities in regions specified by (b) red cube and (c) red cross. The ideal slip activities when (d) no precipitate is present. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 7. Orientation of Cube crystals (a) with and (b) without precipitates after 30% engineering strain.

Fig. 8. Schematics of Takechi model (a) without precipitates, (b) with precipitates.

there exists a less deforming region that has to be compensated by deformation in the other regions (Fig. 5). While the plastic compensation is made near the periphery of each crystal, which is the same region for a single precipitate case, the shear localization is greater in the case of clustered precipitates than that of the single precipitate because not only the region surrounding the clustered precipitates, but also the region between the precipitates are less deformed. The resulting shape of the single crystal with a precipitate after the plane strain tension is different from that of the single crystal without a precipitate. The difference illustrated in Figs. 4 and 5 is due to a change in slip behavior. The addition of precipitates induces a strongly heterogeneous slip activity throughout the matrix. In Fig. 6a–c, one can see the Cube oriented matrix undergoes vastly different slip activities depending on whether or not

slips occur adjacent to the precipitates. The numbers one to twelve in each graph simply designate the twelve slip systems. The heterogeneity in slip activity induces scattering of orientations from the initial Cube orientation (Fig. 7). Fig. 6d shows how ideal slip activity and the resulting orientation change should look like when no precipitates are present. From Figs. 6 and 7 one can deduce that precipitates act as the obstacle that limits collective grain rotation by disrupting the ideal slip activity. In the case of surface roughening, however, precipitates may either enhance or reduce roughening behavior of single crystals. Without precipitates, surface roughening of a crystal is more intense when the orientation of crystal is strong. That is, the surface roughness is most distinct with Brass, S, and Copper orientations, which are texture components less prone to deformation induced rotation, while least distinct with Cube and Goss ori-

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Fig. 9. Effect of precipitates when loaded along TD in the Takechi model.

Fig. 10. Orientation change when loaded along TD in the Takechi model.

entations, which are texture components that easily evolve during deformations [1]. Nevertheless, when precipitates come into play, the behavior is entirely different. Surface roughness is distinct for all texture components (Figs. 4 and 5) due to the fact that even Cube and Goss texture components, with precipitates, undergo precipitate restraint induced reorientation. 4.3. Effect of precipitates in banded texture There has been a number of reports dealing with the cause of surface roughening of Al alloys. The general consensus on the cause is the texture bands that develop after processing Al alloys. One of

the first models presented to explain how texture bands result in ridging is the Takechi model (Fig. 8a). Within this model, the texture band is explicitly taken into account by subdividing a rectangle into several alternating crystals with different orientations along the transverse direction (TD). A similar approach has been used by Qin et al. [5] with Al6016 alloys and by Zhao et al. [31] with fcc materials. Simulated results on single crystals indicated that precipitates play an important role in both slip activity and the resulting texture evolution. Nevertheless, there is only a handful of works conducted on surface roughening that take into account the consequence of introducing hard precipitates within a matrix. Therefore, the simulated deformation behavior of the

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Fig. 11. Effect of precipitates on orientation change when loaded along TD up to 30% elongation in the Takechi model.

original Takechi model (Fig. 8a) with alternating Cube and Goss is compared with that of the Takechi model with precipitates (Fig. 8b) to observe the effect of precipitates when texture bands are present. In the case when precipitates are not present, tension along TD exhibits a difference in deformation behavior due to the difference in relative strain accommodating ability between Cube and Goss orientations (Fig. 9). In particular, a difference in grain rotation occurs in which the rotation is strongest near the surface (Fig. 10), and a slightly larger rotation occurs near the Cube/Goss interface compared to interior regions of each band (Fig. 10). The difference in grain rotation from the surface to interior regions of the specimen induces surface ridging that eventually leads to strong necking behavior after 30% elongation (Fig. 9). In the case when precipitates with the volume fraction of 0.01 are present, tension along TD still results in surface roughening behavior, but to a far lesser extent compared with that of the case when precipitates are not present. The limited roughening behavior is attributed to the limited grain rotation at the surface due to the fact that precipitates act as inhibitors for grain rotations. In fact, the precipitates act as a strong constraint that scatters the orientation crystals near the center and limits the rotation that occurs at the surface (Fig. 11). The difference in the slip between Cube and

Goss orientations eventually leads to the large ridging pattern, but once the precipitates are placed within each component, the slip difference is weakened due to the weakening of texture evolution of both orientation components. After 30% elongation, the specimen without precipitate exhibits very strong necking behavior while the specimen with the precipitate constrains the localization and limits the necking (Fig. 9). Tension along the RD, on the other hand, results in the limited surface roughness due to lack of difference in crystal rotation when precipitates are not present (Fig. 12). In fact, orientation changes do not seem to occur during the course of deformation (Fig. 13a). If precipitates are present, however, tension along the RD leads to a stronger roughening behavior compared with that of the case when precipitates are not present. This is due to the fact that precipitates act as localization sites for shear deformation. That is, while precipitates act as constraints for grain rotations, they also act as shear localization sites. When the RD is aligned with the tensile axis (TA), precipitates act as strong localization sites, leading to a deformation heterogeneity (Figs. 12 and 13b). This heterogeneity produces certain localization sites and eventually amplifies the roughening along the TD. On the other hand, with only texture banding, the ridging pattern along RD is hardly noticeable due to the relative similarity in both strength and overall slip activity. Distributing the precipitates at the boundaries marginally reduces the extent of necking when stretched along TD, while forming a rather heterogeneous ridging patterns when stretched along RD. The latter basically indicates that surface roughening occurs, but not in a patterned manner. The RD band structure is disturbed due to precipitate induced TD patterned roughening. This also mildly affects the necking behavior during TD stretching. 4.4. Effect of precipitates on micro-scale deformation For the Al6061 that is used as model microstructure in this study, texture bands are macroscopic and precipitates are much smaller than the grain size, meaning that macroscopic texture bands and precise morphological features of the microstructure cannot both be represented within the crystal plasticity framework. Thus, the synthetic microstructure is generated such that weak grain and strong grain clusters are alternating in a microscopic manner along TD. Under such cases, h1 0 0i//ND and h1 1 1i//ND fiber components are used to form a distinctive three layer banded structure (Fig. 3b). Crystal plasticity simulations are conducted to evaluate the effect of precipitates in a microscopically banded structure, which is similar to Al6061 specimen’s microstructure, and a non-banded structure. In the remaining context in this study, banded structure refers to microscopic bands, but the concept can be easily extended to macroscopic bands.

Fig. 12. Effect of precipitates when loaded along RD in the Takechi model.

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Fig. 13. Orientation change when loaded along RD in the Takechi model (a) without and (b) with precipitates.

Fig. 14. Effect of a synthetic microstructure with random orientation distribution on surface roughening during plane strain tension of 10% along TD: (a) without and (b) with precipitates.

Fig. 15. Effect of a synthetic microstructure with spatially banded orientations on surface roughening during plane strain tension of 10% along TD: (a) without and (b) with precipitates.

For both banded and non-banded structures, virtual microstructures are used with identical grain morphologies. In the case of banded structure, alternating layers of h1 1 1i//ND and h1 0 0i// ND fiber components were used for orientation distribution. On the other hand, in the case of non-banded structure, random orientation distribution was assigned. For non-banded structures, the variation in accumulated shear strain when plane strain tension was applied along RD or TD indicates the roughening behavior of the sample’s surface. Even though

the orientations are randomly assigned, the grains will undergo different deformation behaviors, and roughening behavior is expected. For polycrystalline materials, roughening depends largely on the difference in strain accommodating ability [1,2]. Thus, one can expect that microscale surface roughening will still occur even when texture bands are not present. Fig. 14 demonstrates this result by showing how grain rotation angle and shear strain that differ from grain to grain will lead to microscopic roughening behavior after plane strain tension of 10% along TD.

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Fig. 16. h1 0 0i//TA orientations (a) before deformation and after 10% elongation of microstructures (b) without and (c) with precipitates.

The effect of precipitates on the non-banded structure, unlike that of single crystals, is subtle and largely limited to strain localization. When tension is applied along the TD, which corresponds to the normal direction of elongated grains, the effect of precipitates is hardly noticeable. Strain localization is noticeable in the regions surrounded by the hard precipitates, highlighted by the red1 dotted box in Fig. 14b, but this is simply due to the fact that a hard inclusion within a matrix causes the precipitate/matrix interface to undergo limited deformation and the restraint is compensated by additional deformation, or localization, of matrix nearby. When tension is applied along TD for the banded structure without precipitates, surface ridging is very strong after 10% (Fig. 15a), which is comparable to the results based on Takechi model, but not as clear as that based on the Takechi model. This is because virtual microstructures introduce the grains with different orientations, and thereby different strain accommodating abilities even within each band. That is, within the weak h1 0 0i//ND fiber components and strong h1 1 1i//ND fiber components, there will be different thinning behaviors. The hard precipitates randomly placed throughout the matrix with a texture band play a different role compared to the hard precipitates in the matrix with a random orientation distribution. The precipitates act as rotation inhibition sites. Grain rotations at the surface, which are crucial in ridging in Al alloys with texture bands, are largely limited. Instead, like in the case of Takechi model, precipitates scatter grain orientations, leading to the reduced surface roughening due to the microscopic texture band (Fig. 15b). Fig. 15 also demonstrates that the grains that undergo rapid thinning when no precipitates are present are still thinning faster than the other grains when precipitates are present, but at a notably lower rate. In fact, the general strain rate is much more homogenized when precipitates are 1 For interpretation of color in Fig. 14, the reader is referred to the web version of this article.

present due to the fact that hard precipitates (i) minimize a difference in strain accommodating ability between different grains and (ii) inhibit surface grain rotation. Thus, the deforming behavior of each layer is more homogeneous for the precipitate containing specimen than the specimen without precipitates. The fact that synthetic microstructure with microscopic texture bands is schematically similar to the Takechi model suggests that the reduced roughening is attributed to the limitation in grain rotation at the surface due to precipitates. This is further supported by Fig. 16. One can see the orientation change of the specimen without precipitates differs from that of the specimen with precipitates after 10% tensile elongation. One can see that whether or not the specimen contains precipitates, a preferred h1 0 0i//TA and h1 1 1i//TA start to develop (Fig. 16). However, there is a difference in how fast grain rotates and the resulting textures are notably different. When precipitates are not present, weak h1 0 0i//TA orientations starts to resemble the Cube orientation while when precipitates are present the orientations are simply scattered with respect to the original orientations before deformation. Though the simulated results clearly indicate that precipitates affect surface roughening behavior, Jin and Lloyd [32] reported that increasing Fe content in 6111 Al alloys, while largely reduced the surface roughness of the alloys stretched in TD, showed little effect on roping. This partly conflicts with the results presented in this work. Most likely, the discrepancies are due to grain refinement and texture weakening from increasing Fe contents. The reduced grain size, in particular, can overshadow the effect of precipitates. We believe that because a number of microstructural changes such as grain refinement and texture weakening accompanies during precipitation, the effect of precipitates on surface roughening behavior is hard to distinguish and easily overlooked. The results presented in this work can be used in future works to isolate the effect of each microstructural feature on surface roughening behavior.

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5. Conclusions Only a handful of studies have taken into account the effect of precipitates when dealing with surface roughening as well as surface ridging of a realistic microstructure. The surface roughening of a virtual microstructure with morphological features equivalent to those of Al6061-T6 alloy was investigated under crystal plasticity framework to realize the effect of precipitates on surface roughening of fcc polycrystalline materials with a small volume fraction of coarse precipitates. This study demonstrated that one should not overlook the effect of precipitates when dealing with the surface behavior during deformation. The experimental data has been used to establish the constitutive parameters and microstructural characteristics for the simulations. The simulated results are then analyzed to come to the following conclusions: 1. Precipitates in a single crystal produces a non-deforming region near the vicinity of the precipitates, leading to the localized deformation away from the precipitates. In particular, when smaller precipitates are clustered within a single crystal, the less deforming region is enlarged, leading to further localization away from the precipitates. 2. Near the non-deforming region, grain rotations are disturbed such that the slip activity, and thereby the resulting morphology of the single crystals, differ significantly compared to the case when no precipitate is present. 3. Precipitates in banded structures induce a similar effect to those in single crystals. In this case, however, the localization is limited while the surface roughening is well reduced due to the limited grain rotation at the surface and near the interface where, without precipitates, strong grain rotations that lead to surface roughening occur. 4. When a microscopic texture band is not present, precipitates act mainly as strain localization sites and carry little effect on the roughening behavior of the microstructure. 5. Precipitates in the synthetic microstructure with microscopic texture bands essentially play the same role as those in the banded structure. Precipitates, by disturbing grain rotations of each grain, homogenized thinning behavior of the grains that would otherwise undergo a largely heterogeneous deformation behavior.

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