Microstructure Dependent Dislocation Density Evolution in Micro-macro Rolled CNT/Al Composite

Flake powder metallurgy combined with micro/macro rolling was employed to produce CNT/Al composites. The effect of deformation mode on the lamellar ultrafine grain structure and on the dislocation density was analyzed. Additionally, a model based on microstructure and processing parameters is proposed to analyze the effect of size, aspect ratio and crystallography texture of the matrix grains on dislocation density. It was shown that the dislocation density depends on CNTs dispersion degree and CNT-aluminum interfacial bonding level as a consequence of micro rolling process, as well as on the grain refinement, crystallography texture, and high aspect ratio resulted from macro-rolling process. It was demonstrated that the micro/macro rolling process provides the lamellar ultrafine grains with higher dislocation storage capability with respect to equiaxed grains. The described process indicated that it could provide good combination between the CNTs dispersion, CNT-aluminum interfacial bonding as well as crystallography texture, size and shape of the matrix grains.

subgrain size (low angle boundary spacing [27]) with increasing strain, misorientation some of them gradually increase and which may become HAGBs. Additionally, other types of HAGBs such as new HAGBs and pre-existing HAGBs can form. Former is due to different orientation paths during subsequent deformation and latter attributes to increase the grain boundaries with increasing strain.
Since elongation of the original grains increase the HAGBs in the microstructure, therefore it is worth emphasizing that the imposed strain during MMR process is effectively affected by grain boundary density which in turn affects the dislocation density. By considering the strain limitations during secondary plastic deformation processes, it is necessary to understand how way and how much can be applied a huge plastic strain ( > 4) to a material (herein CNT/Al composite) to obtain a good coordination of CNT dispersion, reaction CNT-Al, and microstructure properties of the matrix grains such as size, geometry and crystallography texture.
Here, it will be proposed a microstructural property-based model which is containing the lamellar ultrafine-grains to calculate the dislocation density with relation to grain size, shape and crystallography texture. To this end, the required strain for achieving to a lamellar UFG architecture during preparing process is calculated. The nanoscale architecture is produced by means of a novel and smart SPD technique derived from flake PM technique that so-called micro-macro rolling (MMR) process. Actually, a strategy of task allocation two-stage rolling, one in micro-scale and the other in macro-scale is used to tailor lamellar UFGed architecture of CNT/Al composite. The effect of different reductions of macro-rolling process on the CNT dispersion, the reaction extent of CNT with aluminum as well as the size, shape, and crystallography of the matrix grains are studied.

Experimental procedure
Spherical aluminium powders with mead diameter of 40 µm and CNTs were selected as the raw materials. 1.0 and 1.5 wt.% of CNTs is chosen as appropriate content for reinforcing. Flake PM technique via solution approach and following conventional rolling process was employed to fabricate UFGed CNTs/Al composite. Firstly, to ensure the breaking of CNTs clusters, they were dispersed in ethanol, assisted by an ultrasonic shaker for 1 h to get a gel-like dispersion. After that, the raw Al powders are added in the gel-like CNTs-ethanol solution, stirred and then dried in vacuum at 70℃ for 2 h to obtain CNTs/Al spherical powders. To make the composite, flake PM via a dualspeed BM route [18,45] conducted using a planetary ball mill at low-speed BM(LSBM) at 160rpm for 8h, hereafter denoted as 160/8, followed by high-speed BM (HSBM) at 270rpm for 1h, hereafter denoted as 270/1, in an argon atmosphere at 1 atm. Preliminary experiences demonstrated that the combination of LSBM and HSBM lads to uniform CNT dispersion in Al flakes thanks to LSBM, and good bonding of CNT/Al flakes thanks to HSBM. Vacuum hot pressing (VHP) was employed for the consolidation of the composite powders. Powders were firstly cold pressed before sintering at 550°C for 2 hours in a graphite die. The processing of the studied composites is shown in Figure 1. The rolling processing conditions sequence is shown in table 1. where the TKD and TEM specimens were prepared by the lift-out method using focused ion beam system (FIB, FEI Scios).
Tensile and hardness tests were performed to measure the materials mechanical properties. Tensile

Deformation model
Concerning the overall strain of MMR process, it is approximately consistent with the sum of the overall reduction of bulk materials during both micro-rolling ( ) and macro-rolling process ( ). Therefore, the total strain imposed can be decomposed into its micro rolling induced strain and macro rolling induced strain parts as given in Eq.1.
During milling the powder evolution follows five different stages [1]. Among all stages, the particle flattening (the first stage) results from plastic deformation, leading to change the spherical aspect to plate (flake)-shape appearance. The typical HSBM method caused severe damage and excessive interfacial reaction of CNTs, while LSBM enhances the dispersion of CNTs and minimizes the damage. The amount of strain that a metallic particle experienced by one collision can be expressed as in Eq. 2 [2,3]: Where h = 2 [48] where is the mean diameter of the as-received powder, is the balls speed (m/s), is the ball radius, is the balls density, and is the vital Vickers hardness.
The number of collisions experienced by each particle during ball milling process can be calculated through Eq. 3.
Where is a constant related to the milling instrument, is defined as the charge ratio (mass of balls/mass of powder), is the frequency of milling, is the powder density and is the time of the milling.
The frequency of collisions in a planetary ball milling can be expressed as in Eq. 4: Where si the number of balls and K is a constant and was evaluated to be approximately 1.5 [49]. and are the rotational speed of disk of the mill and of the vial, respectively. And ~ -2 for 500ml planetary ball milling system in our lab.
The time required to flatten the spherical aluminium powder particles is proportional to the time interval between different ball collisions, (in minutes), that can be expressed by Eq. 5 [50]: Where and are the volume of powder associated with each ball and the powder volume affected by a collision, respectively. can be calculated by Eq. 6: Where ℎ = 2 .
The volume fraction of aluminium particles can be defined by Eq. 7 [51] : Where , , and is the volume fraction of aluminium powders, CNTs, PCA and balls in LSBM process.
The variation of the powder hardness during milling is a fundamental parameter affecting the imposed strain to powder. Maurice et al. [52] showed that the variation of hardness of milled powder by increasing imposed strain during milling can be calculated by eq. 8.
The strain is determined from Eq. 9.
And is the deformation of the powder trapped between two balls and is calculated by Eq. 10.
Where 0 is the initial powder hardness, is the strength coefficient , is the work-hardening exponent of powder and is the distance from the center of two powders in contact.
As a first assumption, the variation of the hardness onto the powder surface will be only considered.
In such condition, = .
Therefore, the strain imposed to the overall aluminium powder particles during LSBM as a microrolling model can be expressed as Eq. 11: Therefore, by using Eq. 1-5, can be re-written as in Eq. 12: Where A is a constant related to the milling instrument.
The reduction ratio for normal rolling can be obtained as described in Eq. 13: Where ℎ 0 and ℎ are the original thickness and final thickness of the specimens, respectively.
By considering each of the matrix powders experiences the same deformation, Tan et al. [53] showed that ratio of the original transverse length, 0 , and the final short transverse length, , should be given by Eq. 14.
After applying the macro-rolling, short-transverse length of matrix powder, , and the original matrix powder size, should have an approximately same ratio with that of the change in thickness (Eq. 15), Therefore, it can be expected that the imposed strain during macro-rolling process to the materials can be expressed as Eq. 16.
Therefore, it can be concluded that overall strain imposed after MMR process is given by Eq. 17.
In the proposed model, the focus will be on the strengthening resulted from the evolution of dislocation during plastic deformation strain ( ). Therefore, since then, it will be paid to the impacts of the plastic strain imposed during MMR process on the shape, size and crystallography texture parameters of the matrix. Therefore, the contribution of MMR process on the generation of dislocations should be considered separately, namely as in Eq. 18.
The formation of several domains which in turn reflects the different orientations inside grains, are directly affected by the micro-strain imposed during micro-rolling process. Actually, the misorientation between the domains inside the CNTs/Al composite particle ranges between that of low angle grain boundaries (LAGBs) to high angle grain boundaries (HAGBs). In early stages of milling, the LAGBs first increases due to the produced dislocation walls and subgrains, and then decreases due to the rearrangement of LAGBs through dynamic recovery.
However, it is found that the LAGB extent in aluminium alloys remains approximately constant at strains larger than 1-2 [27]. Many HAGBs formed, but they did not evolve into new grains banding the grain interiors in order to create just regions of different orientation. Hence, by progressing the milling, the increase not only in the density of LAGBs but also in the density of HAGBs occurred.
The former is arisen from the large changes in orientation inside the lamellar grains and latter is originated from the gradual increasing of the misorientation in subgrain boundaries as a consequence of the increased dislocations density.
To calculate the dislocation density caused by − , the dislocation density evolution in grain boundaries and grain interior should be considered. Hence, it should be first calculated the number of dislocations arriving at grain boundaries ( 0 ) during imposed plastic strain ( − ). Besides, the effect of deformation geometry on the density of HAGBs should also be considered in the micro-rolling process. To this end, the situation is summarized in Eq. 19 [54][55][56].
Where λ is the average distance between slip bands which is equal to the width of lamellar grain. 0 * is the maximum number of dislocations or screening at a GB and λ is the average length of dislocation loops. are Taylor factor and Bergers' vector for aluminum.
Recently, Razavi-Tousi et al. [57] proposed an interesting technique to calculate the grain boundary density according to processing the misorientation data for EBSD patterns. The method is summarized in Eq. (20).
Where is the boundaries density with misorientation per area, the frequency of counted pixels with misorientation , the step size of EBSD image, the total pattern pixels number and is the indexed pixels to the total number of pixels ratio.
Where and are the average aspect ratio of the subgrains and grains with LAGBs and HAGBs, respectively. Therefore, the contribution of grain boundaries in increasing the dislocation density during MMR process, can be expressed from Eq. 24: In ultrafine-grain CNTs/Al composites, the evolution of dislocation inside grain interior ( ) during the deformation process is governed by the following dynamic process, due to dislocation-dislocation pinning, annihilation of dislocations as a consequence of dynamic recovery and an additional term (-) which reflect dynamic recovery of additional dislocation at GBs due to decrease grain size [5,58]. During the process of deformation, the evolution of dislocations density for a given strain  Owing to the presence of CNTs, the strain incompatibility between different grains should be considered, therefore = 1.25, otherwise = 1 if only the grain boundaries dislocations are considered [59].
The dislocation annihilation in FCC metals can be described by Eq. 27.
Where g = ( ) and is the volume of the oblate sphere that is calculated by Eq. 30.
Where and are half of the length and width of the micro-rolled grain.
Since the majority of the lamellar grains sectioned by transverse LAGBs as well as HAGBs throughout the grains during ball milling process, thus the average area sweap by dislocation, , can be expressed by Eq. 31.
Therefore, basing on these considerations, Eq. (28) can be re-written through Eq. 32 Where − is aspect ratio for the lamellar aluminium grain after micro-rolling process.
Micro-rolling process originally resulted in the flattening of powder particles as a consequence of plastic deformation imposed during transferring the kinetic energy of balls to powder particles; no overall texture is developed by imposing deformation due to continuously change of stress direction and deformation mode for each particle. However, secondary plastic deformation process, as is here macro-rolling process, is responsible to form the crystallography texture. Furthermore, in many FCC materials, dislocation density and distribution depend on crystallography texture of the grains with respect to the stress axis [62].
Therefore, it should be also considered the contribution of crystallography texture parameter on the dislocation density related to the macro-rolling process. To this end, the percentage of (ℎ ) oriented grains along rolling direction, ℎ , can be calculated by Eq. 33.
Where M is the Taylor factor and is the average glide distance of the dislocations. Since, the distance between the center and edge of the lamellar UFGs is the minimum distance for gliding the dislocations, it is hence logical to assume that the short transverse length of matrix grain is equal to the average glide distance of the dislocations. Hence, it can be expressed by Eq. 35.
= cos (35) Therefore, the density of the dislocations is given by Eq. 36.
By and large, the overall density of dislocation resulted from plastic deformation imposed during MMR process can be calculated through Eq. 37.

Microstructural evolution
The microstructure of the CNTs/Al composite with 1.0 % of carbon nanotubes as a function of the thickness reduction during hot rolling is shown in Figure 3. From the first glance, it can be found that the grains are mostly consisted of UFG grains (>100nm) while some rod-like Al4C3 (<10 nm in diameter) are also visible. Plus, the average of grain size of Al is decreased as the thickness reduction increases. However, formation of rod-like Al4C3 is inevitable as a consequence of compressing force and collision frequency which were directly proportional to the milling speed [18,63] as well as pressure caused by conventional rolling process [33]. Blocked dislocations Blocked dislocations that was consistent with previous studies [63,64]. The addition of CNTs leads to the significant increase of UFG grains, and with the CNT content increasing, the proportion of UFG grains increases in CNT/Al composites as the thickness reduction increases. From the perspective of the overall grain size distribution, as the CNT content increases, the grain size becomes smaller which attributed to the strong pinning effect of CNTs. Especially when the CNT content is 1.5 wt.%, all the grain sizes are smaller than 300nm and showed an acceptable homogeneity in the UFG range.
Developing the thickness reduction from 10%, 30%, and 50% causing a large number of CNTs are singly dispersed on the grain boundaries, as shown by the white arrow, while a small amount of Al4C3 nanorods, as shown by the red arrow, are distributed in the grain interiors at all thickness reductions.
A close inspection of the figures 3 and 4, can be depicted that the CNT-enriched zones are formed near the grain boundaries due to thermodynamically equilibrium. Accordingly, the probability of dislocation annihilation is decreased, and dislocation generation and accumulation gradually overtook its annihilation as the governing mechanism of deformation [15] as the imposed strain caused by conventional rolling process increases.
The mean grain size measurements for all the studied conditions are listed in Figure 5. the main results are that the grain size decreases as the thickness reduction increases for both the reinforcement percentages; in addition, the composite with 1.5% of carbon nanotubes reveals finer grain sizes with respect to the material with 1.0% of CNTs, evolving towards an equiaxed structure. The uniform distribution of CNTs is confirmed through the observation of EBSD maps shown in Figure 6 on the normal direction (ND) of CNT/Al rolled composites. There was an obvious equiaxed structure to some extent elongated grains along with RD in both 1 and 1.5 wt.% of CNTs/ Al. It can be seen that CNTs were found to be aligned unidirectionally to some extent, which should be the RD due to the shear stress during rolling process [65]. Both maps belong to the material deformed with 50% of thickness reduction.
The grain size in equiaxed structure was determined primarily by the amount of the shear deformation the Al powders experienced during milling especially LSBM and then followed by thickness reduction of the conventional rolling. With increasing thickness reduction, the UFG grains structure was gradually pronounced. The UFG Al grain in the 1 wt. % and 1.5 wt.% CNT/Al composite were found to have relative shear textures with the dominant (001)<110> of rotated cube texture, consistent with the results observed in CNT/Al composites produced by SPS and hot rolling process [63,65].

Mechanical properties
The tensile properties of the studied materials are shown in Figure 7. It is obvious that the flow stress is increased with increasing the thickness reduction of 10, 30 and 50% for both 1 wt.% and 1.5 wt.% CNT-Al composite, indicating that the flow stress has a dependency of both strain and consistent. In fact, as 1 wt.% of CNT content increased to 1.5 wt.%, the flow stress increase for all the thickness reductions, indicating strength depends on the CNT content. Plus, the observed variations of total elongation are basically retributed to the strain hardening capacity especially at higher strain where the accumulated dislocation density is significant. Considering the concept of tensile ductility, it can be fairly pointed out that tensile ductility depends on the uniform accumulation of dislocations in the UFG grains. In fact, the strain hardening capability can be manifested by the ability of the accumulation of dislocation in grains which conversely related to grain size. So, it expected that by increasing the dislocation density, this criterion is improved as seen in Figure 7. The average dislocation velocity for a given strain rate and strain can be connected to strain rate by: Where A is an experimentally constant, equal to 10 9 , and is the plastic strain, • strain rate.
In fact, under higher strain, dislocation velocity decrease which resulted in enhancing dislocation number and more interactions between dislocations, leading to increase dislocation density.
Therefore, it can be concluded that the internal stresses are increase, affecting the dislocation behavior especially in their generation, annihilation, and accumulation under different strains. It expected that by developing the accumulation of dislocation in CNT-enriched regions, the strain hardening capability increase, leading to enhance the tensile ductility of the CNT/Al composites.
The hardness behaviour is shown in Figure 8. The fracture surfaces of the tensile tested materials are shown in Figure 9. nanotubes. Both maps belong to the material deformed with 50% of thickness reduction.
The fracture surfaces aspect reveals a uniform distribution of very fine dimples replying the materials grain size. The main difference is represented by the more pronounced voids coalescence with formation of larger craters in the 1.5% CNTs reinforced material with respect to the 1.0 % CNTs one.
It is believed that a larger concentration of carbon nanotubes leads to stress concentration in certain locations leading to intergranular fracture more pronounced as the nanotubes concentration increases.

Conclusions
The microstructural and mechanical evolution of carbon nanotubes reinforcing aluminium composites produced via flake metallurgy and rolling are described in the present paper. All the produced composites do not show carbon nanotubes agglomeration for all the selected reinforcing percentages. As the CNTs percentage increases, pronounced grain refinement is obtained. All the studied materials showed ultrafine grained structures. Grain refinement is more efficient as the rolling thickness reduction increases. The increase in deformation is accompanied with more pronounced textures and mechanical strength increase. The fracture surfaces observations revealed a very ductile behaviour of the tensile deformed materials.

Declarations:
The manuscript was not submitted to other journals for simultaneous consideration.
The submitted work is original and was not published elsewhere in any form or language.
Results were presented clearly, honestly, and without fabrication, falsification or inappropriate data manipulation.
No data, text, or theories by others are presented.