aluminum composites

aluminum composites

Accepted Manuscript Interface-induced strain hardening of graphene nanosheet/aluminum composites Yuanyuan Jiang, Run Xu, Zhanqiu Tan, Gang Ji, Genlian...

NAN Sizes 0 Downloads 10 Views

Accepted Manuscript Interface-induced strain hardening of graphene nanosheet/aluminum composites Yuanyuan Jiang, Run Xu, Zhanqiu Tan, Gang Ji, Genlian Fan, Zan Li, Ding-Bang Xiong, Qiang Guo, Zhiqiang Li, Di Zhang PII:

S0008-6223(19)30097-1

DOI:

https://doi.org/10.1016/j.carbon.2019.01.094

Reference:

CARBON 13898

To appear in:

Carbon

Received Date: 11 December 2018 Revised Date:

18 January 2019

Accepted Date: 27 January 2019

Please cite this article as: Y. Jiang, R. Xu, Z. Tan, G. Ji, G. Fan, Z. Li, D.-B. Xiong, Q. Guo, Z. Li, D. Zhang, Interface-induced strain hardening of graphene nanosheet/aluminum composites, Carbon (2019), doi: https://doi.org/10.1016/j.carbon.2019.01.094. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

Graphical Abstract

ACCEPTED MANUSCRIPT Interface-induced strain hardening of graphene nanosheet/aluminum composites Yuanyuan Jianga, Run Xua, Zhanqiu Tana*, Gang Jib, Genlian Fana, Zan Lia, Ding-Bang Xionga, Qiang Guoa, Zhiqiang Lia*and Di Zhanga a

State Key Laboratory of Metal Matrix Composites, School of Materials Science and

b

RI PT

Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

Unité Matériaux et Transformations (UMET) CNRS UMR 8207, Université de Lille, 59655, Villeneuve d'Ascq, France

SC

Abstract

Interface effect was a key mechanism for the deformation of metal matrix composites, which has not been well understood yet in those reinforced with

M AN U

nanoreinforcements. In this study, we prepared graphene nanosheet reinforced aluminum (GNS/Al) composites exhibiting improved tensile strength from 233 to 287 MPa while retaining good uniform elongation from 5.5 to 5.8% compared with the unreinforced Al, thanks to the interface-induced strain hardening capability. The strain hardening behaviors of the GNS/Al composites were discussed in terms of forest

TE D

hardening and back stress hardening by using the tensile loading-unloading tests and further quantitatively analyzed through a modified strain hardening model based on the dislocation behaviors, where the contributions of grain boundaries and interfaces were

EP

distinguished. It turns out that the interface-induced forest hardening was the main reason for improving the strain hardening capability and uniform elongation of the

AC C

GNS/Al composites. Microstructural characterization revealed that, the additional strain hardening capability of the composites should be from the higher dislocation storage capability of the GNS-Al interfaces than Al grain boundaries and the accommodation of geometrically necessary dislocations near the GNS-Al interfaces. The present work provides a new insight to the design of both strong and ductile metal matrix

*

Corresponding author. Tel : +86-(0)21-54745834

Tan), [email protected] (Zhiqiang Li)

E-mail address: [email protected] (Zhanqiu

ACCEPTED MANUSCRIPT nanocomposites. 1. Introduction Aluminum matrix composites with high strength and good ductility (uniform elongation) are attractive for structural applications, especially considering the urgent

RI PT

call for the light-weighting. The higher strength can help by making transportation vehicles lighter to improve their energy efficiency while good ductility is also required to prevent catastrophic failure during service [1, 2]. Uniform elongation is the strain

SC

before localized deformation (necking) occurring under tensile stress, thus it should be paid more attention to evaluate the ductility of materials, considering that necking is very dangerous in structural applications [3, 4].

M AN U

Graphene reinforced aluminum (Graphene/Al) composites exhibited greatly enhanced strength and stiffness after achieving uniform dispersion of graphene, which have emerged as a potential and favorable candidate for the next generation of lightweight structural material [5, 6]. Unfortunately, the accompanying loss of ductility would hinder the application of graphene/Al composites [7, 8]. For example, the 1.50

TE D

vol.% graphene/Al composites reported by Li et al. [9] exhibited a Young’s modulus up to 87.1 GPa and a tensile strength up to 302 MPa, while the uniform elongation of the composites was as low as 3.18%. Tensile strength is composed of yield strength and

EP

strain hardening during tension. Correspondingly, various strengthening mechanisms have been well proposed to understand the yield strength enhancement of the

AC C

graphene/Al composites, e.g. grain refinement strengthening (Hall-Petch effect) [7, 10], thermal mismatch strengthening [11], Orowan strengthening [12], load transfer behavior [13, 14], etc. Nevertheless, the plastic deformation mechanisms of graphene/Al composites, which are crucial for their strain hardening and uniform elongation, haven’t been fully understood yet. It is well known that the plastic deformation of metals is governed by the accumulation, movement and annihilation of mobile dislocations. The dislocation storage processes give rise to both forest hardening and back stress hardening [15, 16].

ACCEPTED MANUSCRIPT Forest hardening is the non-directional short-range interactions between mobile dislocations and forest dislocations, which act as obstacles to hinder the movement of additional mobile dislocations on active slip planes [1, 17]. Back stress hardening is the directional long-range interactions between mobile dislocations and forest dislocations,

RI PT

which would stop the dislocation source from emitting more dislocations since they are from the same dislocation source and have the same Burgers vector [3, 18, 19]. According to Brown and Stobbs [20], when the local internal stress exceeds a threshold,

SC

it would cause plastic relaxation, which may lead to the partial release of the internal stress as well as the global back stress [21]. Fundamentally, the interactions of dislocations with each other and with the various constituents of the microstructure, e.g.

M AN U

grain boundary, twin boundary, interface, and precipitate, determined the strain hardening and plastic deformation of the material [22-25]. For example, Sinclair et al. [26] reported that the work hardening of polycrystal copper was strongly grain size dependent (arising due to the storage of dislocations at grain boundaries), and proposed a physical model to describe the grain size effect. The corresponding storage of

TE D

additional forest dislocations and development of long-range internal stress contributed to both forest hardening and back stress hardening. This influence would then be affected by dislocation screening and dynamic recovery effects at grain boundaries.

EP

Additionally, Xu et al. [27] investigated the strain hardening behavior of the carbon nanotube reinforced aluminum (CNT/Al) composites through the loading-unloading

AC C

tests as well as the modelling of both grain size effect and composite effect. It was concluded that the deformation incompatibility between CNTs and Al matrices could result in the accumulation of strain gradient geometrically necessary dislocations (GNDs) [28]. The accompanying interfacial back stress strengthening was crucial for the improved strain hardening capability and uniform elongation of the CNT/Al composites. In the early work of graphene/Al composites, a few theoretical and experimental studies have shown that the interactions between dislocations and graphene-Al

ACCEPTED MANUSCRIPT interfaces could have a huge impact on the strain hardening behavior as well as the strength and ductility of the composites [9, 29-31]. For instance, Kim et al. [29] first discovered the build-up of dislocations at the graphene interface of the metal-graphene nanolayered composites by molecular dynamics (MD) simulations. Li et al. [9] and

RI PT

Zhao et al. [32] discussed that the strain hardening behavior of the graphene/Al composites was governed by the competition between dislocation multiplication and annihilation via the interface. However, these literatures were limited to either MD or

simply

qualitative

description,

the

relationships

between

SC

simulations

interface-dislocation interactions and the plastic deformation of the composites have not been thoroughly analyzed, and the corresponding mechanical model for quantitatively

M AN U

describing the structure-property correlations have not been explored yet. In addition, similar to the deformation incompatibility in CNT/Al composites [27, 33], strain gradient GNDs should also accommodate at the graphene-Al interface, but their influence on the strain hardening and plastic deformation of the graphene/Al composites has not been discussed yet.

TE D

In present study, the tensile strain hardening behaviors of the graphene nanosheet reinforced aluminum (GNS/Al) composites are focused on in terms of forest hardening and back stress hardening. The contribution of forest hardening and back stress

EP

hardening to the flow stress is estimated with the tensile loading-unloading tests. The interface-induced hardening is modeled and quantitatively analyzed to understand the

AC C

plastic deformation of the GNS/Al composites. Besides, the origins of interface-induced hardening mechanism are also characterized and discussed. 2. Experimental procedures 2.1 Composite fabrication The fabrication procedure of the GNS/Al composites was based on our previous reports [6]. Atomized spherical Al powders (Diameter: ~14 µm; Purity: ~99.8%) and graphene nanosheets (GNSs, Thickness: 3~10 nm) , were used as the raw materials. In previous literature [32, 34-36], the volume fraction of graphene in composites varies

ACCEPTED MANUSCRIPT greatly from 0.07 to 12 vol.%, with 0.50 vol.% mostly used. Meanwhile, considering that more GNSs may cause problems such as stacking, the volume fractions of GNSs were selected to be 0.25 and 0.50 vol.%. Al powders, 0.25 vol.% or 0.50 vol.% GNSs (converted by mass fraction) were firstly ball-milled at 200 rpm for 6 h with 0.5 wt.%

RI PT

stearic acid (used as processing control agent) and then cold-welded at 450 rpm for 0.5 h. The ball milling processes were conducted using a 0.6 dm3 stainless steel jar filled with Ar atmosphere at 1 atm and a ball-to-powder weight ratio of 20:1. The cold-welded

SC

GNS/Al particles were then pressed into Ø40 mm columns at 500 MPa, sintered in vacuum at 540 °C for 2 h, and hot extruded into Ø8 mm rods at 400 °C with an extrusion ratio of 25:1. For comparison, the unreinforced Al samples were also

M AN U

fabricated following the same processing. 2.2 Microstructure characterization

The microstructures of the unreinforced Al and GNS/Al composites were characterized by scanning electron microscopy (SEM, MIRA3) and transmission electron microscopy (TEM, JEOL 2100F & FEI Tecnai G2 20 twin microscope).

TE D

Specimens parallel to ED-TD planes were cut from center section of the as-extruded rods separately, where ED is the extrusion direction and TD is the transverse direction. For SEM/EBSD characterization, specimens were prepared by mechanical polishing

EP

and followed by ion polishing in order to obtain strain-free surface. MIRA3 SEM equipped with an OXFORD INSTRUMENTS NordlysMax3 electron backscatter

AC C

diffraction (EBSD) detector was used to collect results with acceleration voltage of 20 kV. The EBSD maps were recorded with step size of 100 nm in a view to detect ultrafine grains. The HKL Channel 5 software (HKL Technology A/S) was used for data acquisition and treatment. Equivalent average grain size was estimated by averaging the length and width of at least 350 grains in SEM/EBSD results. The Taylor factor, M, is related to the crystallographic structure and the texture of the material, which could be calculated from SEM/EBSD data sets with the Taylor factor tool in the HKL CHANNEL 5 software using the simplified Bishop & Hill method [37]. High-resolution

ACCEPTED MANUSCRIPT TEM (HR-TEM) and scanning TEM (STEM) was used to characterize the microstructure and dislocation configurations of the GNS/Al samples before and after deformation. The diffraction condition of the STEM images is multi-beam condition (Bragg’s condition) since it allows us to clearly identify the entire grain and determine

RI PT

the positions of GNS, which is conducive to investigate the relationship between dislocations and interface/grain boundary. An FEI Tecnai G2 20 twin microscope equipped with a Nanomega Astar unit was used to perform automated crystal

SC

orientation mapping (TEM ACOM). A precession nano-beam diffraction mode with the spot size of a few nanometers was performed for data acquisition. Precession angle and step size were set to 1° and 10 nm, respectively. GND maps are estimated from the

M AN U

TEM ACOM data using the Nye tensor [38]. The GND analysis tools in ATEX software developed by B. Beausir and J.-J. Fundenberger [39] were used to estimate GND maps. All TEM ACOM maps were treated by spike correction with 5 loops for spike and the spike minimum number of 6 neighbors, Kuwahara filters with 2 interactions and GND calculation within the disorientation angle from 0 ° to 5°. Any disorientation greater

accumulation. 2.3 Mechanical tests

TE D

than 5o was excluded since it is caused by a grain boundary, but not by GND

EP

The uniaxial tensile tests and loading-unloading tests along the extrusion direction were performed on the rod samples of 4 mm in diameters and 20 mm in gauge lengths

AC C

with a Zwick Z100 testing machine at a constant strain rate of 5·10-4 s-1 at room temperature. Young’s modulus of each sample was measured using resonance test at room temperature on a Nihon-tech ET-RT instrument. At least three specimens of each condition were tested to verify reproducibility. 3. Results 3.1 Microstructures of the GNS/Al composites Fig. 1a-c are the TEM images of the unreinforced Al, 0.25 and 0.50 vol.% GNS/Al composites. GNSs were homogeneously dispersed at Al grain boundaries and aligned

ACCEPTED MANUSCRIPT along the extrusion direction, as indicated by the red arrows in Fig. 1b and c. As the GNS/Al composites experienced plastic deformation during hot extrusion, the presence of GNSs would restrict the growth of the Al grains, resulting in the smaller grain size in the composites, compared to the unreinforced Al. Fig. 1d shows the HR-TEM image of

RI PT

the tightly-bonded GNS-Al interface in the GNS/Al composites. The lattice fringes of an individual GNS in the GNS/Al composites had a spacing of ~0.34 nm, which is in accordance with the interplanar spacing of (0002) of graphite [40]. In addition, the

SC

interfacial reaction products, Al4C3, were not found under TEM observations, thus the interfacial bonding should not be chemical bonding. According to our previous study [6], the GNS pull-out phenomenon was rarely observed on the fractography, indicating that

M AN U

a strong interfacial bonding instead of weak mechanical bonding was formed at the

AC C

EP

TE D

GNS-Al interface [41], probably physical bonding or diffusion bonding.

Fig. 1 TEM images of (a) the unreinforced Al, (b) 0.25 vol.% and (c) 0.50 vol. % GNS/Al composites; (d) HRTEM image of a GNS embedded in Al matrix.

ACCEPTED MANUSCRIPT The SEM/EBSD inversed pole figures of the unreinforced Al, 0.25 and 0.50 vol.% GNS/Al composites along the extrusion direction are shown in Fig. 2a-c, respectively. Majority of grains in all the samples are observed to be elongated grains with <111> fibrous texture along the extrusion direction. The Taylor factors of the samples was

RI PT

estimated from the SEM/EBSD results, which were estimated to be ~3.05, ~3.22 and ~3.25 for the unreinforced Al, 0.25 and 0.50 vol.% GNS/Al composites, respectively. Fig. 2d-f show the statistical grain size distributions of the as-fabricated samples. As

SC

shown, the average equivalent grain sizes (equivalent circle diameters) of the unreinforced Al, 0.25 and 0.50 vol.% GNS/Al composites are ~885 nm, ~840 nm and

EP

TE D

M AN U

~770 nm, respectively.

Fig. 2 SEM/EBSD inversed pole figure maps of the ED-TD cross-section of (a) the

AC C

unreinforced Al, (b) 0.25 and (c) 0.50 vol. % GNS/Al composites. The inserted ED and TD represent the extrusion direction and transverse direction, respectively. (d-f) The corresponding grain size distributions of the unreinforced Al, 0.25 and 0.50 vol. % GNS/Al composites.

3.2 Tensile behaviors of the GNS/Al composites The typical engineering stress-strain curves and true stress-strain curves of the unreinforced Al and GNS/Al composites are shown in Fig. 3a and b, and the mechanical properties were listed in Table 1. As shown, the GNS/Al composites exhibited a good balance between strength and elongation compared to previous reports [8, 14, 42],

ACCEPTED MANUSCRIPT where the introduction of graphene resulted in the decrease of elongation, attributing to various problems such as poor graphene dispersion, excessive grain refinement of Al matrix, and severe interfacial reaction. According to our previous study [6], under proper ball milling conditions, a proper combination of ultrafine-grained Al matrix with

RI PT

well-preserved, uniformly-dispersed graphene could be achieved, which helped to maintain good elongation while improving tensile strength. Since the total elongation of the GNS/Al composites is good, they are good candidates to study the plastic

SC

mechanism of mechanical behavior. The tensile strengths of the unreinforced Al, 0.25 and 0.50 vol.% GNS/Al composites are 233 MPa, 257 MPa and 287MPa, with the corresponding uniform elongations of 5.5%, 5.7% and 5.8%, respectively. As shown,

M AN U

the GNS strengthened Al matrices without sacrificing their uniform elongation. According to the Considère criterion [43], the GNS/Al composites derive their good ductility from their higher strain hardening rates (Θ = ∂σ⁄∂ε) than the unreinforced Al for the entire plastic deformation, as shown in Fig. 3c and d. As the volume fraction of GNSs increased, the strain hardening rates of the samples increased gradually, resulting

TE D

in the highest tensile strength and uniform elongation of the 0.50 vol.% GNS/Al composites. Thus, it is interesting to explore the origins of the higher strain hardening in

AC C

EP

the composites than the unreinforced Al.

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

Fig.3 (a) The typical engineering stress-strain curves, (b) true stress-strain curves, (c) curves of strain hardening rate as a function of stress, and (d) curves of stress and strain

TE D

hardening rate as a function of strain for the unreinforced Al and GNS/Al composites. Table 1 Mechanical Properties of the unreinforced Al and GNS/Al composites

Material

Modulus

AC C

(GPa)

Al

0.2%

offset

offset

EP

Young’s

0.02%

yield

strength

Ultimate Uniform

Total

elongation

elongation

(%)

(%)

tensile

yield strength strength (MPa)

(MPa)

(MPa)

71.0±1.2

115±6

193±3

233±1

5.5±0.5

17.4±1.3

72.5±0.8

126±5

207±7

257±3

5.7±0.6

17.6±1.8

74.9±0.7

134±6

215±5

287±3

5.8±0.4

17.3±1.6

0.25 vol.% GNS/Al 0.50 vol.% GNS/Al

To probe the origins of the higher strain hardening rates and flow stress of the

ACCEPTED MANUSCRIPT GNS/Al composites, the tensile loading-unloading tests [43, 44] at intervals of 0.5% nominal strain were performed to investigate the Bauschinger effect, from which the contribution of forest hardening and back stress hardening to the flow stress could be estimated according to the increasing rates of effective stress and back stress with

RI PT

plastic strains, respectively. This methodology has been widely applied in many previous literatures [3, 25, 45]. As shown in Fig. 4, during unloading, the reverse plastic flow starts even when the applied stress is still in tension, which means that the GNS/Al

SC

composites exhibit strong Bauschinger effect [46]. Generally, a larger hysteresis loop during the loading-unloading tests represents a stronger Bauschinger effect [47]. As shown in Fig. 4a, the hysteresis loop becomes larger with increasing tensile strain and

M AN U

the hysteresis loops of the GNS/Al composites are larger than those of the unreinforced Al during the whole loading-unloading tests. The effective stress (σ (σ ) can be calculated as σ

=

(

)

+



and σ = σ

) and back stress

− σ , where σ

denotes the flow stress, σ is the unloading yield stress and σ∗ is the thermal part of

TE D

the flow stress [15, 27]. Here, an offset of 0.02% was chosen to determine the yield strength of the composites, which was less influenced by tensile strain hardening than

AC C

EP

an offset of 0.2% [48].

ACCEPTED MANUSCRIPT Fig. 4 (a) Loading-unloading curves of the unreinforced Al and GNS/Al composites; (b-d) flow stress, effective stress, and back stress at different plastic strains in the unreinforced Al, 0.25 and 0.50 vol.% GNS/Al composites, respectively. As shown in Fig. 4b-d, compared with the unreinforced Al, the GNS/Al composites

RI PT

exhibited higher effective stress (during the whole plastic strain) and back stress (at low plastic strain), resulting in higher flow stress than the unreinforced Al. In the GNS/Al composites, the effective stress increased obviously throughout the plastic deformation,

SC

which was the main contribution of the higher strain hardening in the GNS/Al composites. It can also be observed that the increasing rate of effective stress in the GNS/Al composites was higher than that of the unreinforced Al, resulting in the higher

M AN U

strain hardening rates in the GNS/Al composites. In addition, the increase of back stress in the GNS/Al composites before the plastic strain of 1% could also contribute to the strain hardening at the initial stage of plastic deformation. 3.3 Dislocation evolution at the GNS-Al interface

It has been widely accepted that strain hardening results from the dynamic

TE D

interactions of dislocations with each other and with various constituents of the microstructure, e.g. forest dislocation, grain boundary and interface [22, 25, 26]. Thus, it is necessary to characterize different dislocation configurations in the GNS/Al

EP

composites before and after plastic deformation in order to better understand and

AC C

analyze the strain hardening and plastic deformation of the composites.

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

Fig. 5 Characterization of interface-affected stored dislocations in 0.50 vol.% GNS/Al composites at (a, b) zero strain, (c, d) 2% strain and (e, f) 5.8% strain, respectively. The white frame in (d) marked the area where some dislocations were observed at the grain

TE D

boundary with GNSs; the yellow frame in (d) marked the area where almost no dislocation was observed at the pure grain boundary without GNSs. Fig. 5 provides the existence of dislocation pinning and storage at the GNS-Al interface during plastic deformation. Fig. 5a, c and e are the TEM images of the 0.50

EP

vol.% GNS/Al composites with 0 strain, 2% strain and 5.8% strain (the uniform elongation) respectively, and the corresponding bright-field STEM images were shown

AC C

in Fig. 5b, d and f. The red arrows in Fig. 5a, c and e, and the red dotted lines in Fig. 5b, d and f represent the positions of GNS, which could be determined in the TEM images through underfocused lens described in Supplement S1. As shown in Fig. 5b, d and f, the number of the stored dislocations in the GNS/Al composites increased significantly with the plastic strain. In Fig. 5d, some dislocations were observed at the grain boundaries where GNSs were present, as indicated by the white frame, while almost no dislocations were observed at the pure grain boundaries without GNSs, as indicated by the yellow frame. When comparing the white and yellow frames in Fig. 5d, more

ACCEPTED MANUSCRIPT dislocation lines terminate at the GNS-Al interface rather than the pure grain boundary, which means that the GNS-Al interface can store more dislocations than the pure grain boundary. It indicates that the dislocation annihilation rates at the GNS-Al interface might be lower than pure grain boundary. The additional interface-stored dislocations

M AN U

SC

d), which is consistent with the previous study [49].

RI PT

would contribute to the higher strain hardening in the GNS/Al composites (Fig. 3c and

TE D

Fig. 6 TEM and ACOM characterization of the 0.50 vol.% GNS/Al composites at zero and 2% strains: (a, e) TEM images; (b, f) enlarged TEM images of the red frame in (a, e), and the corresponding (c, g) inverse pole figure maps of the Z axis and (d, h) GND

EP

maps. The white frames in (d) and (h) marked the area where the distribution of GNDs is denser when the GNS-Al interface spacing is smaller.

AC C

The accommodation of GNDs near the GNS-Al interfaces during plastic deformation was characterized in Fig. 6. The TEM images of 0.50 vol.% GNS/Al composites at zero and 2% strains are shown in Fig. 6a and e, and the enlarged TEM images, inverse pole figures and GND maps of the red frames in Fig. 6a and e are shown in Fig. 6b-d and f-h, respectively. The white dotted arrows in Fig. 6a and e and the white dotted lines in Fig. 6b, d, f, and h represented the positions of GNS. The GND maps were estimated with TEM ACOM and the Nye tensor. As indicated by the white and red solid arrows in Fig. 6d and h, more GNDs accommodated near the GNS-Al interfaces rather than the pure grain boundary after the plastic strain of 2%. Besides,

ACCEPTED MANUSCRIPT compared with the GND maps of the unreinforced Al under zero and 2% strains in Supplement S2, more strain gradient GNDs would accommodate in the GNS/Al composites rather than the unreinforced Al after plastic deformation. It indicated that the accommodation of strain gradient GNDs near the GNS-Al interfaces would also

RI PT

contribute to the higher strain hardening of the GNS/Al composites. Especially in the area with smaller GNS-Al interface spacing, the distribution of GNDs is denser, as shown by the white frames in Fig. 6d and h. It indicated that the contribution of strain

SC

gradient GNDs would be greater when reducing the GNS-Al interface spacing. 4. Discussion

4.1 Effects of interface-dislocation interactions on the strain hardening

M AN U

The tensile and Bauschinger experiments reported in Section 3.2 illustrate that both forest hardening (reflected as effective stress) and back stress hardening contribute to the macroscopic flow stress of the GNS/Al composites. The physical picture emerging from the TEM observations in Section 3.3 suggests that during plastic deformation, more dislocations will be stored at the GNS-Al interface and more strain gradient GNDs

TE D

will be accommodated there, contributing to the higher strain hardening rates of the GNS/Al composites than those of the unreinforced Al. On the one hand, the intrinsic characteristics of GNSs, e.g. planar geometry, high

EP

mechanical strength and flexibility, render the two-dimensional GNSs as not only efficient obstacles to dislocation motion and propagation across in the GNS-Al interface

AC C

but also the dislocation absorber for preventing dislocation pile-up [31]. Thus, the competition of dislocation multiplication and dislocation annihilation at the interface determined the storage of dislocations at the GNS-Al interface and the overall deformation of the GNS/Al composites, which is consistent with previous studies [9, 32]. On the other hand, during the deformation of the GNS/Al composites, the Al matrices would deform earlier than GNSs due to the huge stiffness difference between graphene (~1 TPa) and Al (~70 GPa) [50]. The incompatible mechanical deformation between GNSs and Al matrices would generate non-uniform strain gradients at the

ACCEPTED MANUSCRIPT GNS-Al interface, leading to the bending of lattice and the accommodation of GNDs. As illustrated in Fig. 7, the additional interface-stored dislocations and strain gradient GNDs accommodation could affect the deformation behavior of the GNS/Al composites in the following two ways. Firstly, the total number of forest dislocations will increase,

RI PT

which could produce the non-directional short-range local stress for a dislocation to move. Secondly, they will also provide long-range interactions with mobile dislocations, exerting a directional long-range back stress opposed to the applied stress in the case of

SC

forward loading. At the macroscopic level, the first effect will contribute to forest hardening while the second one will contribute to back stress hardening. When the local stress at the GNS-Al interface exceeds a threshold, plastic relaxation would occur, with

M AN U

the activation of the secondary slip and the build-up of forest dislocation. Meanwhile, plastic relaxation may cause the release of long-range internal stress and global back

EP

TE D

stress [51, 52].

AC C

Fig. 7 Illustration of the origin of forest hardening and back stress hardening induced by GNS-Al interface in GNS/Al composites. The σb-GBDs refers to the back stress induced by the grain boundary dislocations and σb-IDs refers to the back stress induced by the interface dislocations.

Besides, the addition of GNSs would also lead to the refinement of Al grains. The dislocations stored at the vicinity of grain boundary will also contribute to both forest hardening and back stress hardening (considering screening effects) [26]. Similarly, the strain hardening behavior of the unreinforced Al was determined by the interactions

ACCEPTED MANUSCRIPT between dislocation and grain boundary. A modified strain hardening model was developed to quantitatively estimate the tensile stress-strain curves of the unreinforced Al and GNS/Al composites, considering both forest hardening and back stress hardening. The contributions of GNS-Al interface and grain refinement on the strain

RI PT

hardening and ductility of the GNS/Al composites were also discussed based on the simulated results.

4.2 Interface-induced forest hardening and back stress hardening mechanisms

SC

4.2.1 Role of the GNS-Al interface in dislocation density evolution

The evolution of dislocation density with strain was first proposed by Kocks and Mecking [53, 54], involving a storage contribution due to dislocation-dislocation

M AN U

pinning and an annihilation term owing to dynamic recovery which is temperature- and strain rate-dependent. Bréchet and Delincé et al. [22, 26] introduced the effects of grain boundary dislocations

to

model

the

evolution

of

dislocation

densities

in

polycrystalline/ultrafine-grained metals. On the basis of their works, considering the additional interface-stored dislocations, the evolution of total stored dislocation density,

!"

TE D

ρ , with plastic strain (ε ) in the GNS/Al composites can be written as = M $k &ρ − k ρ +

'(

)

(1 − V, ) -1 −

./ .∗/

0+

'1

V -1 ) ,

.

− .∗ 02

(1)

EP

where M is the Taylor factor, k is the storage constant, equals to 0.235 nm-1 [52]. k is the dynamic recovery constant, k 3 and k 5 are related to additional sources of forest

AC C

storage due to the grain boundary and interface respectively. b is the Burger vector of Al, which is 0.286 nm [33]. d is the average grain diameter of Al, and V, is the GNS-Al interface as a percentage of total grain boundary. Since the loading is tension along the extrusion direction, and considering the {111} texture, the values of M were estimated to be ~3.05, ~3.22, ~3.25 for the unreinforced Al, 0.25 and 0.50 vol.% GNS/Al composites from the SEM/EBSD results, respectively. The values of VI were estimated to be 10.3% and 18.8% for the 0.25 and 0.50 vol.% GNS/Al composites respectively, according to the TEM images as well as the size of grains and GNSs and the volume fraction of GNSs. Considering the errors of measurement and calculation,

ACCEPTED MANUSCRIPT here we use the VI values of ~10% and ~20% for the model calculations. The number of dislocations stopped at a grain boundary (n9) and a GNS-Al interface (n ) can be calculated as [16], =>!"

02

n = n∗ $1 − exp -−

=>!"

02

.∗/ .∗

(2)

RI PT

n9 = n∗9 $1 − exp -−

(3)

where λ is the mean spacing between slip lines, n∗9 and n∗ are the maximum number

in the model are listed in Table 2.

SC

of dislocations at a grain boundary and a GNS-Al interface, respectively. All parameters

Table 2 Physical meaning and values of symbols in relations Meaning

Value

Reference

Friction stress of Al

1.6 MPa

[55]

Hall–Petch coefficient of Al

0.04 MPa/√m

[56]

Taylor constant

0.2

[52]

μ

Shear modulus of Al

25.4 GPa

[33]

μ∗

Shear modulus of GNS

53 GPa

[57]

b

Burgers vector of Al

0.286 nm

[33]

γ

Accommodation factor

0.75

[58]

D

Modulus correction factor

2.09

[58]

k

Storage constant

0.235 nm-1

[52]

M AN U

Symbol Physical constants d

Average grain diameter of Al

f

Volume fraction of GNSs

GNS-Al interface as a percentage of

V,

TE D

total grain boundary

Initial dislocation density

ε

Plastic strain

σ99 kA

AC C

α

B

EP

ρ9

Estimated parameters (according to characterization results)

ACCEPTED MANUSCRIPT M

Taylor factor

β

Average aspect ratio of GNSs

~40

dJ

Average diameter of GNSs

~200nm

The dihedral angle between the crystal plane where GNSs located and the {111} slip plane of Al

λ

Mean spacing between slip lines

72nm

Maximum number of dislocations at

SC

Adjustable parameters (fitted to experimental data)

n∗9

k

grain boundary

4.8

M AN U

n∗

~0.9

RI PT

θ

Maximum number of dislocations at

16

GNS-Al interface

Dynamic recovery constant

5.9

k3

TE D

Efficiency of dislocations at the

grain boundary with respect to forest

10.9

hardening

Efficiency of dislocations at the interface with respect to forest

EP

k5

0.1

hardening

Screening parameter

305 nm

SSD density due to grain boundary

Calculated with

and GNS-Al interface of GNS/Al

eq. 1

GND density due to GNS-Al

Calculated with

interface of GNS/Al

eq. 4

SSD density due to grain boundary

Calculated with

of Al

eq. 5

AC C

w

Calculated parameters ρ

ρ ρM

ACCEPTED MANUSCRIPT

ε∗

Calculated with Unrelaxed plastic strain eq. 8

Additionally, the mechanism-based strain gradient plasticity approaches have been widely employed to predict the role of GNDs in MMCs. The GND density, ρ , with

ρ =

RI PT

plastic strain can be calculated with [27, 59], 5 !" N)O

(4)

where f, β, and dJ are the volume fraction, aspect ratio, and average in-plane

SC

diameter of GNSs in composites, respectively. The average values of β and dJ were estimated to be ~40 and ~200 nm from the TEM images.

M AN U

Similarly, when V, =0, the total dislocation density, ρM , of the unreinforced Al should be written as eq. (5) without considering ρ , which is P

!"

= M $k &ρM − k ρM +

'(

.

-1 − ./∗ 02 ) /

(5)

4.2.2 Interface-induced forest hardening and back stress hardening mechanism The forest hardening is due to the storage of interface dislocations and the

TE D

associated contribution to the flow stress of the GNS/Al composites is assumed to follow a Taylor evolution law [22, 52]:

∆σS,R = Mαμb&ρ + ρ

(6)

GPa) [33].

EP

where α is the Taylor constant, which is 0.2 [52]. μ is the shear modulus of Al (25.4

AC C

The back stress hardening is a complex aspect of the problem since both interface

dislocations and grain boundary dislocations contribute to the back stress, as discussed in Section 4.1. The grain boundary back stress hardening was calculated analytically by the developed Kocks-Mecking approach considering the efficiency of screening [22]. The interface-induced back stress hardening could be calculated analytically by Brown and Clarke using Eshelby’s theory of elastic inclusions taking plastic relaxation into account [58]. Thus, the back stress hardening of the GNS/Al composites could be written as

ACCEPTED MANUSCRIPT ∆σSTU. = M

V

)

( /))

n9 -1 − [1 − (

.

] / 0 + 4γDμfε∗

(7)

( /))Y .∗/

where w is the screening parameter, γ is the accommodation factor [58], D is the modulus correction factor, and ε∗ is the unrelaxed plastic strain. D can be written as V

[58], where μ∗ is the shear modulus of GNS (53GPa) [57]. The unrelaxed plastic

RI PT

V∗

strain, ε∗ , can be calculated using the approach of Brown and Stobbs [20] modified for the case of plate-shaped reinforcements [52]: .

ε∗ = =)

(8)

SC

O RU.\

where dJ is the average planar diameter of GNSs in composites, θ is the dihedral

M AN U

angle between the crystal plane where GNSs located and the {111} slip plane of Al. Here, we assume that GNSs were aligned along the extrusion direction, namely the direction of the tensile axis. Therefore, sinθ can be estimated to be ~0.9 by Eular angles from the SEM/EBSD results.

Therefore, the flow stress of the GNS/Al composites, σS_ σS_

kA

B

√d

+ ∆σa`

b

+ Mαμb&ρ + ρ +

TE D

= σ99 + M

V

)

n9 c1 − [1 − (

, can be expressed as

( /)) (

/))Y

.

] ./∗ d + 4γDμfε∗

(9)

/

where the first term σ99 is the lattice friction stress of Al (1.6 MPa) [55]; the second

EP

term is the Hall-Petch relationship describing grain boundary strengthening and k A b

is the

AC C

is the Hall–Petch coefficient of Al (0.04 MPa/√m) [56]; the third term ∆σa`

B

strengthening effect of GNSs on yield strength of the composites through load transfer; the fourth term is the Taylor relationship describing forest dislocation strengthening; the fifth and sixth terms are the back stresses induced by grain boundary and interface dislocations, considering the screening effect and plastic relaxation, respectively. Among them, ∆σa`

b

is usually calculated by several micromechanical models such as

Eshelby model, shear-lag model, etc. [60]. However, none of those models are proven to be universal in the graphene/Al composites. Here we assume that

f e P e

g

= g f and P

ACCEPTED MANUSCRIPT ∆σa`

b

S = σS` − σM ` [27], where σ` is the tensile yield strength of the GNS/Al

composites, σM ` is the yield strength of the unreinforced Al calculated with eq. (10) (when ε = 0), and ES and EM are the young’s modulus of GNS/Al and Al in Table 1.

RI PT

The calculation results of the yield strength of the 0.25 and 0.50 vol.% GNS/Al composites are respectively 93 MPa and 101 MPa, which are less than the experimental yield strength in Table 1. This is because the experimentally measured yield strength is

SC

the strength after partial strain hardening while the calculated result is the strength at which the dislocations begins to multiply. Since the volume fraction of GNS was small, the contribution of load transfer to the strength improvement was small at the yield

M AN U

point of the composites, which is consistent with the results calculated by Shear-lag model (4.2 and 8.5 MPa for the 0.25 and 0.50 vol.% GNS/Al composites, respectively) [13, 61]. It is somewhat different from CNT/Al composites where the load transfer strengthening effect was more significant, mainly originating from the much higher volume fraction of CNTs [60, 62].

TE D

Similarly, the flow stress of the unreinforced Al, σM _ σM _

= σ99 + M

V

)

kA

B

√d

, can be expressed as:

+ Mαμb&ρM +

n9 c1 − [1 − (

( /))

.

] /d

( /))Y .∗/

(10)

EP

When λ=75 nm, w=305 nm, k =0.235 nm-1, k =5.9, k 3 =10.9, k 5 =0.1, n∗9 =4.8,

AC C

n∗ =16, and the initial dislocation density, ρ9 , equals to 6·1013 m-2, 8.5·1013 m-2, and 1·1014 m-2 for the unreinforced Al, 0.25 vol.% and 0.50 vol.% GNS/Al composites successively, the calculated true stress-strain curves fits well with the three experimental tensile curves, as shown in Fig. 8a-c. In order to clarify the contributions of different mechanisms, the calculated results of each term in Eq. 9 to the flow stress of the 0.50 vol.% GNS/Al composites at typical strains were shown in Fig. 8d. It can be seen that forest dislocation strengthening contributes more to the flow stress than the others and its value increases with the strains, contributing to the strain hardening and uniform elongation of the composites, which is consistent with the experimental results.

ACCEPTED MANUSCRIPT Meanwhile, the predicted true stress-strain curves of 840nm Al and 770nm Al (equivalent to the grain size of the 0.25 and 0.50 vol.% GNS/Al composites, respectively) were shown in Fig. 8e, together with the three fitted curves in Fig. 8a-c. Compared to Al with the same grain size, the GNS/Al composites exhibited higher

RI PT

strain hardening rates, resulting in higher strength and ductility. This indicated that grain refinement could improve the strength of the material while its ductility would be greatly sacrificed due to the decline in dislocation storage capacity and then the decline

SC

in strain hardening capability. The GNS-Al interface dislocations, including both additional interface-stored dislocations and strain gradient GNDs, played a significant role in improving the strain hardening rates of the GNS/Al composites, promoting the

AC C

EP

TE D

M AN U

strength-ductility balance of the composites.

Fig. 8 (a-c) The experimental and calculated true stress-strain curves of the unreinforced Al, 0.25 and 0.50 vol.% GNS/Al composites, respectively; (d) Separate contribution of different mechanisms to the flow stress of the 0.50 vol.% GNS/Al composites at typical strains; (e) Separate contribution of grain refinement and GNS-Al interface to the flow stress of the 0.25 and 0.50 vol.% GNS/Al composites. In summary, the special two-dimensional structure of GNSs has a significant effect on the plastic deformation of the GNS/Al composites, and there are some similarities

ACCEPTED MANUSCRIPT and differences compared with one-dimensional CNTs. As demonstrated by Xu et al. [27], CNT-induced interfacial back stress contributed primarily to the extra strain hardening in CNT/Al composites, which also resulted from the elastic loading of CNTs. However, for the two dimensional GNS, the GNS-induced interfacial back stress

RI PT

contributed a small part to the strain hardening of the composites. Moreover, the GNS-Al interfaces are effective barriers to the movement of mobile dislocations, resulting from the two-dimensional planar structure of GNS and its large specific

SC

surface area. Thus, the GNS-Al interfaces are significant to the strain hardening and plastic deformation behavior of the GNS/Al composites. The contribution of the GNS-Al interface to the flow stress of the composites could be well explained by the

M AN U

forest hardening and back stress hardening mechanisms. It should be noted that further increasing the number of GNS-Al interface will probably give rise to the strength and ductility of the GNS/Al composites. However, the influence of further grain refinement caused by increasing the number of interfaces cannot be ignored. Considering this, it is potential to improve the strain hardening capability and uniform elongation of the

TE D

GNS/Al composites through well-designed architectures. For example, the gradient architecture [44, 63, 64] would probably coordinate the contradiction between the increased number of interface and further grain refinement, and improve the strength

EP

and ductility of the GNS/Al composites simultaneously. Thus, the correlation between the architecture and interface-induced hardening is expected to provide routes towards

AC C

superior strength and ductility in the GNS/Al composites, which needs to be further studied.

5. Conclusions

We have studied the effects of the interface on the strain hardening behavior and

mechanical properties of the GNS/Al composites. The evolution of effective stress and back stress was investigated with the loading-unloading test, and a modified strain hardening model was developed to quantitatively estimate the strain hardening and mechanical properties of the GNS/Al composites. Besides, the origins of the

ACCEPTED MANUSCRIPT interface-induced hardening mechanisms are also characterized and discussed. The main conclusions are: (1) The GNS/Al composites exhibit an improved tensile strength (from 233 MPa to 287 MPa) and good ductility (uniform elongation from 5.5% to 5.8%) simultaneously,

RI PT

which can be primarily attributed to the higher strain hardening rates than the unreinforced Al in uniaxial tension.

(2) The loading-unloading tests reveal that, the increase of back stress only contributes

SC

to the higher strain hardening in the early stage of deformation. It is the increase of effective stress that is responsible for the higher strain hardening rates throughout the plastic deformation of the GNS/Al composites.

M AN U

(3) The interface-dislocation interactions during plastic deformation of the GNS/Al composites are experimentally observed. More dislocation stored at the interface, which indicates that the dislocation annihilation rates at the GNS-Al interface might be lower than pure grain boundary. Extra strain gradient GNDs accommodated in

the interface.

TE D

the vicinity of the interface, which is due to the mechanical incompatibility across

(4) A modified strain hardening model is developed to considering the contribution of grain refinement and GNS-Al interface. It is found that the higher strain hardening

EP

rate of the GNS/Al composites should be determined by the interface, which mainly promotes forest hardening by producing additional

interface-stored dislocations

AC C

and strain gradient GNDs. It can be proposed that proper architecture design could

provide routes towards superior strength and ductility in the GNS/Al composites through the interface-induced hardening mechanisms.

Acknowledgements

This work was supported by the Natural Science Foundation of China (Nos. 51671130, 51771110, 51771111, 51871149), the Ministry of Science & Technology of China (Nos. 2016YFB1200506, 2016YFE0130200, 2017YFB1201105), the Ministry of Education of China (Nos. 62501036031, B16032), Aeronautical Science Foundation of

ACCEPTED MANUSCRIPT China (2016ZF57011), and Shanghai Science & Technology Committee (Nos. 15JC1402100, 17ZR1441500, 14DZ2261200, 14520710100). References [1] Shao CW, Zhang P, Zhu YK, Zhang ZJ, Tian YZ, Zhang ZF. Simultaneous

RI PT

improvement of strength and plasticity: Additional work-hardening from gradient microstructure. Acta Materialia 2018;145:413-28.

[2] Zhou W, Yamamoto G, Fan Y, Kwon H, Hashida T, Kawasaki A. In-situ

SC

characterization of interfacial shear strength in multi-walled carbon nanotube reinforced aluminum matrix composites. Carbon 2016;106:37-47.

[3] Wu X, Yang M, Yuan F, Wu G, Wei Y, Huang X, et al. Heterogeneous lamella

M AN U

structure unites ultrafine-grain strength with coarse-grain ductility. Proceedings of the National Academy of Sciences of the United States of America 2015;112:14501-5. [4] Zhao YH, Liao XZ, Cheng S, Ma E, Zhu YT. Simultaneously Increasing the Ductility and Strength of Nanostructured Alloys. Advanced Materials 2006;18:2280-3. [5] Li Z, Fan G, Tan Z, Guo Q, Xiong D, Su Y, et al. Uniform dispersion of graphene

TE D

oxide in aluminum powder by direct electrostatic adsorption for fabrication of graphene/aluminum composites. Nanotechnology 2014;25:325601. [6] Jiang Y, Tan Z, Xu R, Fan G, Xiong D-B, Guo Q, et al. Tailoring the structure and

EP

mechanical properties of graphene nanosheet/aluminum composites by flake powder metallurgy via shift-speed ball milling. Composites Part A: Applied Science and

AC C

Manufacturing 2018;111:73-82.

[7] Zhang H, Xu C, Xiao W, Ameyama K, Ma C. Enhanced mechanical properties of Al5083 alloy with graphene nanoplates prepared by ball milling and hot extrusion. Materials Science and Engineering: A 2016;658:8-15. [8] Zhang Y, Li X. Bioinspired, Graphene/Al2O3 Doubly Reinforced Aluminum Composites with High Strength and Toughness. Nano letters 2017;17:6907-15. [9] Li Z, Guo Q, Li Z, Fan G, Xiong DB, Su Y, et al. Enhanced Mechanical Properties of Graphene (Reduced Graphene Oxide)/Aluminum Composites with a Bioinspired

ACCEPTED MANUSCRIPT Nanolaminated Structure. Nano letters 2015;15:8077-83. [10] Li Z, Zhao L, Guo Q, Li Z, Fan G, Guo C, et al. Enhanced dislocation obstruction in nanolaminated graphene/Cu composite as revealed by stress relaxation experiments. Scripta Materialia 2017;131:67-71.

RI PT

[11] Bhadauria A, Singh LK, Laha T. Effect of physio-chemically functionalized graphene nanoplatelet reinforcement on tensile properties of aluminum nanocomposite synthesized via spark plasma sintering. Journal of Alloys and Compounds

SC

2018;748:783-93.

[12] Fadavi Boostani A, Yazdani S, Taherzadeh Mousavian R, Tahamtan S, Azari Khosroshahi R, Wei D, et al. Strengthening mechanisms of graphene sheets in

M AN U

aluminium matrix nanocomposites. Materials & Design 2015;88:983-9. [13] Shin SE, Choi HJ, Shin JH, Bae DH. Strengthening behavior of few-layered graphene/aluminum composites. Carbon 2015;82:143-51.

[14] Zhao M, Xiong D-B, Tan Z, Fan G, Guo Q, Guo C, et al. Lateral size effect of graphene on mechanical properties of aluminum matrix nanolaminated composites.

TE D

Scripta Materialia 2017;139:44-8.

[15] Feaugas X. On the origin of the tensile flow stress in the stainless steel AISI 316L at 300 K: back stress and effective stress. Acta Materialia 1999;47:3617-32.

EP

[16] Fribourg G, Bréchet Y, Deschamps A, Simar A. Microstructure-based modelling of isotropic and kinematic strain hardening in a precipitation-hardened aluminium alloy.

AC C

Acta Materialia 2011;59:3621-35. [17] Jiang J, Britton TB, Wilkinson AJ. Evolution of dislocation density distributions in copper during tensile deformation. Acta Materialia 2013;61:7227-39. [18] Withers PJ, Stobbs WM, Pedersen OB. The application of the eshelby method of internal stress determination to short fibre metal matrix composites. Acta Metallurgica 1989;37:3061-84. [19] Feaugas X, Haddou H. Effects of grain size on dislocation organization and internal stresses developed under tensile loading in fcc metals. Philosophical Magazine

ACCEPTED MANUSCRIPT 2007;87:989-1018. [20] Brown LM, Stobbs WM. The work-hardening of copper-silica. Philosophical Magazine 1971;23:1201-33. [21] Proudhon H, Poole WJ, Wang X, Bréchet Y. The role of internal stresses on the

RI PT

plastic deformation of the Al–Mg–Si–Cu alloy AA6111. Philosophical Magazine 2008;88:621-40.

[22] Delincé M, Bréchet Y, Embury JD, Geers MGD, Jacques PJ, Pardoen T. Structure– optimization

of

ultrafine-grained

dual-phase

steels

using

a

SC

property

microstructure-based strain hardening model. Acta Materialia 2007;55:2337-50.

Materialia 2012;66:982-5.

M AN U

[23] Bouaziz O. Strain-hardening of twinning-induced plasticity steels. Scripta

[24] Bardel D, Perez M, Nelias D, Dancette S, Chaudet P, Massardier V. Cyclic behaviour of a 6061 aluminium alloy: Coupling precipitation and elastoplastic modelling. Acta Materialia 2015;83:256-68.

[25] Ma X, Huang C, Moering J, Ruppert M, Höppel HW, Göken M, et al. Mechanical

2016;116:43-52.

TE D

properties of copper/bronze laminates: Role of interfaces. Acta Materialia

[26] Sinclair CW, Poole WJ, Bréchet Y. A model for the grain size dependent work

EP

hardening of copper. Scripta Materialia 2006;55:739-42. [27] Xu R, Fan G, Tan Z, Ji G, Chen C, Beausir B, et al. Back stress in strain hardening

AC C

of carbon nanotube/aluminum composites. Materials Research Letters 2017;6:113-20. [28] Ashby MF. The deformation of plastically non-homogeneous materials. Philosophical Magazine 1970;21:399-424. [29] Kim Y, Lee J, Yeom MS, Shin JW, Kim H, Cui Y, et al. Strengthening effect of single-atomic-layer graphene in metal-graphene nanolayered composites. Nature communications 2013;4:2114. [30] Ovid’ko IA, Sheinerman AG. Competition between plastic deformation and fracture processes in metal–graphene layered composites. Journal of Physics D: Applied

ACCEPTED MANUSCRIPT Physics 2014;47:495302. [31] Yang M, Weng L, Zhu H, Fan T, Zhang D. Simultaneously enhancing the strength, ductility and conductivity of copper matrix composites with graphene nanoribbons. Carbon 2017;118:250-60.

RI PT

[32] Zhao L, Guo Q, Li Z, Li Z, Fan G, Xiong D-B, et al. Strain-rate dependent deformation mechanism of graphene-Al nanolaminated composites studied using micro-pillar compression. International Journal of Plasticity 2018;105:128-40.

SC

[33] Dong S, Zhou J, Hui D. A quantitative understanding on the mechanical behaviors of carbon nanotube reinforced nano/ultrafine-grained composites. International Journal of Mechanical Sciences 2015;101-102:29-37.

M AN U

[34] Yu Z, Yang W, Zhou C, Zhang N, Chao Z, liu H, et al. Effect of ball milling time on graphene nanosheets reinforced Al6063 composite fabricated by pressure infiltration method. Carbon 2019;141:25-39.

[35] Yuan Q-h, Zhou G-h, Liao L, Liu Y, Luo L. Interfacial structure in AZ91 alloy composites reinforced by graphene nanosheets. Carbon 2018;127:177-86.

TE D

[36] Nieto A, Bisht A, Lahiri D, Zhang C, Agarwal A. Graphene reinforced metal and ceramic matrix composites: a review. International Materials Reviews 2016;62:241-302. [37] Bishop JFW, Hill R. CXXVIII. A theoretical derivation of the plastic properties of a

EP

polycrystalline face-centred metal. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 2012;42:1298-307.

AC C

[38] Pantleon W. Resolving the geometrically necessary dislocation content by conventional electron backscattering diffraction. Scripta Materialia 2008;58:994-7. [39] Beausir B, Fundenberger J-J. Analysis Tools for Electron and X-ray diffraction. ATEX - software, wwwatex-softwareeu, Université de Lorraine - Metz 2017. [40] Jiang N, Wang CL, Won JH, Joen MH, Mori Y, Hatta A, et al. Interface characterization of chemical-vapour-deposited diamond on Cu and Pt substrates studied by transmission electron microscopy. Applied Surface Science 1997;117:587-91. [41] Chen B, Li S, Imai H, Jia L, Umeda J, Takahashi M, et al. Load transfer

ACCEPTED MANUSCRIPT strengthening in carbon nanotubes reinforced metal matrix composites via in-situ tensile tests. Composites Science and Technology 2015;113:1-8. [42] Wang J, Li Z, Fan G, Pan H, Chen Z, Zhang D. Reinforcement with graphene nanosheets in aluminum matrix composites. Scripta Materialia 2012;66:594-7.

RI PT

[43] Kiser MT, Zok FW, Wilkinson DS. Plastic flow and fracture of a particulate metal matrix composite. Acta Materialia 1996;44:3465-76.

[44] Yang M, Pan Y, Yuan F, Zhu Y, Wu X. Back stress strengthening and strain

SC

hardening in gradient structure. Materials Research Letters 2016;4:145-51.

[45] Hu X, Jin S, Zhou H, Yin Z, Yang J, Gong Y, et al. Bauschinger Effect and Back Stress in Gradient Cu-Ge Alloy. Metallurgical and Materials Transactions A

M AN U

2017;48:3943-50.

[46] Xiang Y, Vlassak JJ. Bauschinger effect in thin metal films. Scripta Materialia 2005;53:177-82.

[47] Xiang Y, Vlassak JJ. Bauschinger and size effects in thin-film plasticity. Acta Materialia 2006;54:5449-60.

TE D

[48] Kouzeli M, Mortensen A. Size dependent strengthening in particle reinforced aluminium. Acta Materialia 2002;50:39-51.

[49] Li Z, Wang H, Guo Q, Li Z, Xiong DB, Su Y, et al. Regain Strain-Hardening in

EP

High-Strength Metals by Nanofiller Incorporation at Grain Boundaries. Nano letters 2018;18:6255-64.

AC C

[50] Zhou W, Fan Y, Feng X, Kikuchi K, Nomura N, Kawasaki A. Creation of individual few-layer graphene incorporated in an aluminum matrix. Composites Part A: Applied Science and Manufacturing 2018;112:168-77. [51] Atkinson JD, Brown LM, Stobbs WM. The work-hardening of copper-silica: IV. The

Bauschinger

effect

and

plastic

relaxation.

Philosophical

Magazine

1974;30:1247-80. [52] da Costa Teixeira J, Bourgeois L, Sinclair CW, Hutchinson CR. The effect of shear-resistant, plate-shaped precipitates on the work hardening of Al alloys: Towards a

ACCEPTED MANUSCRIPT prediction of the strength–elongation correlation. Acta Materialia 2009;57:6075-89. [53] Mecking H, Kocks UF. Kinetics of flow and strain-hardening. Acta Metallurgica 1981;29:1865-75. [54] Kocks UF, Mecking H. Physics and phenomenology of strain hardening: the FCC

RI PT

case. Progress in Materials Science 2003;48:171-273.

[55] Maung K, Earthman JC, Mohamed FA. Inverse Hall–Petch behavior in diamantane stabilized bulk nanocrystalline aluminum. Acta Materialia 2012;60:5850-7.

SC

[56] Chen B, Shen J, Ye X, Jia L, Li S, Umeda J, et al. Length effect of carbon nanotubes on the strengthening mechanisms in metal matrix composites. Acta Materialia 2017;140:317-25.

monolayer

graphene

prepared

2012;12:1013-7.

M AN U

[57] Liu X, Metcalf TH, Robinson JT, Houston BH, Scarpa F. Shear modulus of by chemical

vapor

deposition.

Nano

letters

[58] Brown LM, Clarke DR. Work hardening due to internal stresses in composite materials. Acta Metallurgica 1975;23:821-30.

TE D

[59] Dong S, Zhou J, Hui D, Wang Y, Zhang S. Size dependent strengthening mechanisms in carbon nanotube reinforced metal matrix composites. Composites Part A: Applied Science and Manufacturing 2015;68:356-64.

EP

[60] Tjong SC. Recent progress in the development and properties of novel metal matrix nanocomposites reinforced with carbon nanotubes and graphene nanosheets. Materials

AC C

Science and Engineering: R: Reports 2013;74:281-350. [61] Shin SE, Bae DH. Deformation behavior of aluminum alloy matrix composites reinforced with few-layer graphene. Composites Part A: Applied Science and Manufacturing 2015;78:42-7. [62] Nam DH, Cha SI, Lim BK, Park HM, Han DS, Hong SH. Synergistic strengthening by load transfer mechanism and grain refinement of CNT/Al–Cu composites. Carbon 2012;50:2417-23. [63] Wu X, Jiang P, Chen L, Yuan F, Zhu YT. Extraordinary strain hardening by gradient

ACCEPTED MANUSCRIPT structure. Proceedings of the National Academy of Sciences of the United States of America 2014;111:7197-201. [64] Xu P, Luo H, Li S, Lv Y, Tang J, Ma Y. Enhancing the ductility in the age-hardened aluminum alloy using a gradient nanostructured structure. Materials Science and

AC C

EP

TE D

M AN U

SC

RI PT

Engineering: A 2017;682:704-13.