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Strengthening mechanisms in nanostructured Al/SiCp composite
manufactured by accumulative press bonding
Sajjad Amirkhanlou a,b,c,*, Mehdi Rahimian c,d, Mostafa Ketabchi a, Nader Parvin a, Parisa Yaghinali
a, Fernando Carreño b
a Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran
b Department of Physical Metallurgy, CENIM-CSIC, Av. Gregorio del Amo 8, 28040 Madrid, Spain
c Institute of Materials and Manufacturing, Brunel University London, London UB8 3PH, United Kingdom
d IMDEA Materials Institute, C/Eric Kandel 2, 28906, Getafe, Madrid, Spain
* Corresponding author: Email: [email protected];
Abstract
The strengthening mechanisms in nanostructured Al/SiCp composite deformed to high
strain by a novel severe plastic deformation process, accumulative press bonding (APB),
was investigated. The composite exhibited yield strength of 148 MPa which was 5 and 1.5
times higher than that of raw aluminum (29 MPa) and aluminum-APB (95 MPa) alloys,
respectively. A remarkable increase was also observed in the ultimate tensile strength of
Al/SiCp-APB composite, 222 MPa, which was 2.5 and 1.2 times greater than the obtained
values for raw aluminum (88 MPa) and aluminum-APB (180 MPa) alloys, respectively.
Analytical models well described the contribution of various strengthening mechanisms.
The contribution of grain boundary, strain hardening, thermal mismatch, Orowan, elastic
mismatch and load-bearing strengthening mechanisms to the overall strength of the
Al/SiCp micro-composite were 64.9, 49, 6.8, 2.4, 5.4 and 1.5 MPa, respectively. Whereas
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Orowan strengthening mechanism was considered as the most dominating strengthening
mechanism in Al/SiCp nanocomposites, it was negligible for strengthening of the micro-
composite. Al/SiCp nanocomposite showed good agreement with quadratic summation
model; however, experimental results exhibited a good accordance with arithmetic and
compounding summation models in the micro-composite. While average grain size of the
composite reached 380 nm, it was less than 100 nm in the vicinity of SiC particles as a
result of particle stimulated nucleation mechanism.
Keywords: Accumulative press bonding (APB); Severe plastic deformation (SPD);
Strengthening mechanisms; Analytical models; Metal matrix composites; Nanostructured
materials
1- Introduction
Aluminum matrix composites (AMCs), reinforced with particulate reinforcement, have
attracted considerable attention in automotive and aerospace industries, due to their low
weight and high mechanical properties [1, 2]. Silicon carbide (SiCp) is considered as a
typical cost effective particulate reinforcement used widely in AMCs because of its high
strength and modulus [3, 4]. Traditional processing routes for fabrication of Al/SiCp
composite, including casting, powder metallurgy and spray forming encounter various
shortcomings. The main drawbacks of those liquid state techniques [5, 6] can be referred as
SiCp agglomeration, weak adhesion and undesirable chemical reaction occurred between
Al and SiCp [7, 8]. However, manufacturing techniques in solid state can overcome the
above problems [9-11]. Microstructure and mechanical properties of Al/SiCp composite,
manufactured by accumulative roll bonding (ARB) as a solid-state process, was evaluated
by Jamaati et al. [12-14]. Accumulative press bonding (APB), introduced for the first time
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in our previous works, is another severe plastic deformation process [15, 16] enabling us to
fabricate particle reinforced AMCs. Uniform distribution of reinforcement, nano/ultra-fine
structure and high mechanical properties are obtained using APB process [17-20]. Many
researches were focused on the fabrication and characterization Al/SiCp composites
prepared by metal forming processes [21, 22]. However, individual contributions of
various micromechanics strengthening factors in AMCs deformed to high strain were not
investigated in previous studies. In this study the novel APB process was utilized for
fabrication of Al/SiCp composite and the effect and proportion of various strengthening
mechanisms on the final yield strength was assessed. Moreover, advanced microstructural
characterization techniques were employed to verify each strengthening mechanism.
2- Experimental procedure
As-received AA1050 aluminum sheets, chemical composition is given in Table 1, and SiC
particles with an average size of 10 m were used as raw materials. Aluminum sheets with
the dimensions of 100 mm 50 mm 1.5 mm were annealed at 623 K (350 ºC) for 1 h.
The accumulative press bonding (APB) process for manufacturing of the Al/10 vol.% SiCp
composite was schematically reported in ref. [23, 24]. The aluminum sheets were
degreased in acetone bath followed by scratch brushing with 0.4 mm wire diameter and
peripheral speed of 2800 rpm. The reinforcement particles were uniformly spread between
surfaces by a hand sprayer. A hydraulic press machine was utilized to form a mechanical
bond between two stacked sheets, in a channel die, where the thickness of sheets reduced
by 50%. The APB process was performed at ambient temperature. The fabricated sheet
was cut in two pieces and the whole mentioned process was repeated 5 times in order to
increase SiC particles to 10 vol.%. Thereafter, the above process was repeated 7 times but
without any reinforcement addition. The same process was employed for the production of
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the monolithic aluminum in which the aluminum sheets were processed by APB without
adding any SiCp powder through the process.
Tensile tests were performed according to ASTM E8 standard at a rate of 1.610−1 s−1 by
a Houndsfield H50KS machine. The gauge width, thickness and length of specimens were
6, 1.5 and 25 mm, respectively. Various microstructural aspects of specimens were
investigated by transmission electron microscopy (TEM, JEOL JEM 2000 FX II, JEOL
Ltd. Tokyo, Japan) operating at 200 kV and field-emission scanning transmission electron
microscopy (FE-STEM, HITACHI S-4800, Hitachi Ltd., Tokyo, Japan) operating at 10 kV
complemented by energy-dispersive spectroscopy (EDS, 10mm2 SDD Detector X-ACT,
Oxford instrument, Oxford, England). Also the grain boundary characterization was
performed by electron backscattered diffraction (EBSD, JEOL JSM 6500 F) adjusted at 20
kV with a working distance of 15 mm, step size of 80 nm and tilt angle of 70º. Thin foils
required for EBSD, TEM and STEM investigations were mechanically ground and
punched into 3 mm discs with an average thickness of less than 100 μm. The discs were
subsequently thinned to perforation using a twin-jet electropolishing facility (TenuPol-5,
Struers) with a solution of 30% nitric acid and 70% methanol at 11 V and 245 K (−28 ºC).
The X-ray pattern of the manufactured Al/SiCp composite was recorded with an X-ray
diffractometer (XRD). The XRD experiment was conducted by a Philips X’PERT MPD X-
ray diffractometer with CuKα radiation in the range of 2θ=25 °−95 ° using a step size of
0.05 ° and a counting time of 1 s per step. Consequently, XRD patterns were analyzed via
X’Pert HighScore software.
3- Results and discussion
The stress-strain curves of annealed aluminum (Al), monolithic aluminum (Al-APB) and
Al/SiCp-APB composite are shown in Figure 1. According to the Figure 1, the yield
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strength of the aluminum, which is 29 MPa, was improved by 5 times, as it increases to
148 MPa. A remarkable increase was also observed in the ultimate tensile strength of
Al/SiCp-APB composite, 222 MPa, which was 2.5 and 1.2 times greater than the obtained
values for raw aluminum (88 MPa) and aluminum-APB (180 MPa) alloys, respectively.
Although this study has not been done previously, relevant composites fabricated via other
production processes are summarized in Table 2. The superior strength of the produced
composite through APB process is obtained mainly due to the uniform distribution of
particles, formation of ultra-fine structure and low level of porosity. The enhancement of
composite’s strength can be described by different mechanisms. In following sections,
microstructural evidences and theoretical models are employed to explain each
strengthening mechanism.
3-1- Grain boundary
Figure 2 shows STEM micrographs of Al/SiCp composite after various cycles of APB
process. It is observed that gradual grain refining occurred during process and grains are
slightly elongated in the longitudinal direction. Average grain size reduced to 380 nm after
14 cycles of APB, Figure 2e. Grain refining is the most desirable strengthening mechanism
because it is only mechanism which leads to simultaneous increment of strength and
toughness [25, 26]. The formation mechanism of nano grains by the APB process is
considered as continuous dynamic recovery (CDR). In CDR the size of small (sub) grains
remains constant, whereas grains misorientation increases. In fact, there isn’t any
nucleation and growth of deformed nuclei in CDR, because the dislocations glide directly
from one side of grain to the other side resulting in the increment of grains misorientation.
This is the most equilibrated way of obtaining the finest and sharpest histogram of grain
sizes, which leads to the highest misorientation for the given processing conditions. The
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grain refinement mechanisms of pure aluminum under APB process were discussed in our
previous studies [19, 20]. However, two other factors encourage CDR of Al/SiCp
composite including severe shear deformation and micro-size particles. In fact, finer grain
size can be obtained in APB process on account of the present of non-deformable
reinforcements. Figure 3 displays the interface of the SiC particle and aluminum matrix.
The finer grain sizes are recognized in the vicinity of SiC particles where the average grain
size measured less than 100 nm. When the composite is exposed by deformation during the
process, the existence of non-deformable particles induces strain to their vicinity. As a
result, the vicinity of particles is fertilized to form new boundaries due to the introduction
of a high dislocation density, referred as particle stimulated nucleation (PSN) [27, 28]. The
accumulation of dislocations in the vicinity of particles facilitated the formation of fine
grains by continuous dynamic recovery mechanism. Consequently, the average grain size
of the composite, 380 nm, is finer than that of monolithic aluminum which is 450 nm [19].
Other factor, considered for grain refinement of pure aluminum and the composite, is
severe shear deformation. TEM micrographs of surface and center of the monolithic
aluminum after one APB cycle are shown in Figure 4. Comparison of Figure 4a and b
demonstrates the higher density of dislocation tangle zones on the surface. This
observation is attributed to the severe shear strain exists between the sample and press
anvil. In each APB cycle, the surface containing higher dislocation density is moved
toward the center resulting in homogeneous distribution of dislocation through the bulk
material. Therefore, dislocations formed because of severe shear contribute to the final
grain refinement. Grain boundary strengthening (∆ σGB) can be explained by well-known
Hall-Petch equation (Eq. 1) [29]. Higher fractions of grain boundaries existing in finer
grain structures increase the number of obstacles against dislocation movement.
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∆ σGB=k y (DG)−12 (1)
where DGis average grain size, k y is constant and typically equal to 40 MPa √ μm for
aluminum alloys [19, 30]. While the grain boundary strengthening was calculated 5.2 MPa
for Al [20], it increased to 59.6 MPa and 64.9 , for Al-APB and Al/SiCp composite,
respectively.
3-2- Thermal mismatch (TM)
Discrepancy of thermal expansion coefficient (CTE) between matrix and reinforcement
acts as a dislocation generation source [31, 32]. Since, thermal expansion coefficient of the
matrix, 23×10−6K−1, differs from the SiCp reinforcement, 4×10−6 K−1, strain is induced to
the matrix around the particles resulting in dislocation formation, as shown in Figure 5a.
Multi-directional thermal stresses at the particle/matrix interface, which are induced by the
difference of thermal expansion between aluminum and SiC particles, result in mismatch
strain around the particles. The system makes an attempt to reduce internal energy,
mismatch strain, via introducing new dislocations [33, 34]. High dislocation density in the
vicinity of particles, observed in Figure 5a, can arrange and form new grain boundaries via
continuous dynamic recovery during APB process, as shown in Figure 5b. Strengthening
effect of thermal mismatch (∆ σTM) can be expressed by the following equations [35, 36]:
∆ σTM=αGb√ ρTM (2)
where G is shear modulus (~25.4 GPa for aluminum) and α is the average value of
dislocation strengthening efficiency (∼1 for pure metals [37]) and b is the Burgers vector
(=0.286 nm [38]). Dislocation density, resulted from CTE mismatch, is governed by
particles volume fraction, V p, difference between processing and ambient temperature,
∆T=100K (100℃) [39], and variation between CTE of particles and matrix,
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∆C=CTE Al−CTESiC=19×10−6K−1. Dislocation density induced by thermal mismatch can
be calculated by [40]:
❑TM=12V p∆T ∆Cb (1−V p )d p
(3)
The amount of ∆ σCTE is calculated around 6.8 MPa for Al/SiCp composite, while this
mechanism is not taken into account for Al and Al-APB alloys.
3-3- Elastic mismatch (EM)
The difference of elastic modulus between matrix and reinforcement introduce an
additional dislocation into the composite in order to reduce induced plastic strain. The
density of generated dislocation due to elastic modulus mismatch can be estimated by Eq.
(4). These dislocations induce additional strength to the composite which is expressed by
Eq. (5) [41]:
ρEM=8V p
bd pε (4)
∆ σEM=αGb√ ρEM (5)
where is yield strain (0.2%) and ❑EM is density of dislocations caused by elastic
mismatch [42]. Whereas, due to absence of reinforcement in Al and Al-APB, there is no
elastic mismatch strengthening effect, it is calculated around 5.4 for Al/SiCp composite.
3-4- Strain hardening
Figure 6 displays EBSD/orientation imaging microscopy (OIM) and grain boundary maps
of Al/SiCp composite. The red/gray lines correspond to the low angle grain boundaries
(LAGBs) having misorientations 2-15º, and the high angle grain boundaries (HAGBs) are
shown as black lines which have misorientations above 15º. The fraction of high angle
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grain boundaries (f HAGB) and the mean misorientation angle of the boundaries (θ) for the
Al/SiCp composite were 73% and 35º, respectively. According to EBSD results, it is
obvious that APB process had a significant effect on the development of an ultra-fine grain
structure surrounded mainly by high-angle boundaries. Formation of the well-developed
high angle boundary during APB process is attributed to the rearrangement of the
dislocations via short-range diffusion [43-46]. As a result of mechanical deformation,
dislocations will be generated resulting in the increment of strength. It is well known that
dislocations tend to array and form low angle grain boundaries during severe plastic
deformation process. Therefore, low angle grain boundaries can be considered as a
dislocation resource. In other word, HAGBs contribute to the grain boundary strengthening
mechanism which is determined by Hall-Petch relation, whereas dislocation strengthening
mechanism is related to LAGBs, as explained by Hansen et al. [47]. The strength imposed
by LAGBs to the system is expressed by:
∆ σDis=αMGb√ ρDis (6)
where is the dislocation strengthening efficiency (the average value = 0.24) and M is the
Taylor factor (for aluminum is 3.06). Following equation shows the density of dislocations
introduced by LAGBs to the system [48, 49]:
ρDis=3 (1−f HAGB )θLAGB
bdr(7)
whereθLAGB ,f HAGB and drare the mean misorientation of LAGBs, volume fraction of
HAGBs and average LAGBs spacing that is measured from EBSD results. ∆ σDis is 8, 47
and 49 MPa for initial aluminum, Al-APB and Al/SiCp composite processed by APB,
respectively.
3-5- Orowan strengthening
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Orowan mechanism corresponds to the interaction of the particles and dislocations in
which nano particles pin dislocations resulting in bowing dislocation around particles and
create Orowan rings. Increment of yield strength, in polycrystalline materials, induced by
Orowan mechanisms can be calculated by [41, 50]:
∆ σorowan=0.4MGb ln(√2/3d
b )π √2/3d (√π /4 v p−1)√1−ϑ
(8)
where ϑ is the Poisson’s ratio (0.33). A small contribution of Orowan strengthening
mechanism, ∆ σorowan=2.4 MPa, in Al/SiCp micro-composite can be interpreted by large
distance of micro-size particles.
3-6- Load-bearing
FE-SEM micrographs of Al/SiCp composite after several APB cycles are shown in then
Figure 7. With increasing number of cycles, the laminar structure is converted into the
homogeneous structure. The formation mechanism of this structure is explained
comprehensively in our previous study [17, 18]. It should be briefly pointed out that
aluminum plastic flow, because of applied stress during APB, led to refinement and
dispersion of SiCp clusters. The high pressures associated with APB resulted in the
squeezing of the Al-matrices within the SiCp clusters producing homogenous structure.
Formation of strong bond between the particles and matrix due to extensive pressure can
be another advantage of current process. Since, in the tensile test a fraction of stress is
transferred to particles, having higher modulus and strength compared with matrix,
composite can withstand higher load than monolithic aluminum. In order to achieve
maximum potential of load-bearing effect, homogeneous distributed particles having
strong bond with matrix are required. Figure 8 displays SEM micrographs of Al/SiCp
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composite produced by APB together with its EDS and X-ray maps. Al4C3 phase, observed
usually in the cast Al/SiCp composites, exhibits detrimental effect on interfacial bonding
and mechanical properties on account of its brittle nature [51]. The X-ray maps (Figure 8b-
f) and X-ray diffraction pattern (Figure 9) show that there is no evidence of undesired
phase such as Al4C3 in the microstructure considered as the advantage of solid state
fabrication of Al/SiCp composite by the current process.
Well distributed particles endure a proportion of applied force imposed directly by tensile
test. The contribution of load-bearing mechanism in increasing of yield strength is
expressed by Eq. 9, which is the modification of shear-lag model:
∆ σLoad=0.5 vpσ m (9)
where vp and σ m are referred to volume fraction of particles and matrix yield strength,
respectively. ∆ σLoad is 1.5 MPa for Al/SiCp composite.
The total yield strength is calculated by three well-known models referred as arithmetic
summation (Eq. 10), quadratic summation (Eq. 11) and compounding methods (Eq. 12)
[41, 52, 53]:
σ Arith.=σ m+∆σ TM+∆σ EM+∆σ Load+∆σ Dis+∆σGB+∆σOrowan (10)
σ Quad.=σ m+√(∆σTM)2+(∆σEM )2+(∆σ Load)2+(∆σ Dis)
2+(∆σGB)2+(∆σOrowan)
2 (11)
σ Comp.=σm+∆ σGB+√(∆σTM )2+(∆σ EM)2+(∆σ Load)2+(∆σ Dis)
2+(∆σOrowan)2 (12)
Contribution of the various strengthening mechanisms as well as yield strength, obtained
by various models and tensile tests, are displayed in Table 3. The influence of each factor
on yield strength of micro-composite is evaluated against that of nanocomposite, which
was investigated in our previous study [20].
Matrix flow through micro-particles is easier than nanoparticles so nanocomposite is
associated with smaller grain (280 nm) compare with composites reinforced with micro-
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particles (380 nm). Therefore, improvement of yield strength due to grain boundary
mechanism is 75.6 MPa for nanocomposite, while this value is 64.9 for Al/SiCp micro-
composite. Although grain boundaries strengthening mechanism has conquered the second
place enhancing mechanical properties in the nanocomposite, it is promoted to first place
in the micro-size composite. By decreasing volume fraction of reinforcement/matrix
interfaces in the macro-composite compare with the nanocomposite, dislocation density
formed in the matrix of micro-composite due to thermal and elastic mismatch is
significantly decreased. Whereas Orowan strengthening mechanism was considered as the
most important strengthening mechanism in nanocomposites, it is negligible for
strengthening of the micro-size composites. As a result of large size and distance of
reinforcement, grains and subgrains interact with dislocations instead of interacting with
SiC particles. Strain hardening and grain boundary strengthening mechanisms are
considered as the two most effective strengthening mechanisms in Al/SiCp micro-
composite. The load transfer effect in both composites is negligible because of particulate
shape and low volume fraction of reinforcement. Since the number of active strengthening
mechanisms in Al/SiCp nanocomposite is considerably higher than the micro-composite,
the final experimental yield strength of the nanocomposite increased up to 210 MPa. Based
on the result of calculations performed by each model, it is understood that experimental
result exhibits a good accordance with arithmetic summation and compounding models in
micro-composite. However, nanocomposite shows good agreement with quadratic
summation model, as demonstrated in previous study [20]. Short dislocation gliding
distance in the nanocomposites imposed by well distributed nanoparticles and concomitant
very fine grains results in the overestimating of calculated results compared with
experimental one. In other words, the first obstacle on the way of dislocation movement,
which can be LAGBs, HAGBs or nanoparticles, leads to the strengthening of
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nanocomposite. Therefore, it is expected that considering the contribution of strain
hardening (LAGBs), grain boundaries (HAGBs) and Orowan (nanoparticles) mechanisms
together in strengthening of nanocomposite, exhibiting an overestimation of the resistance
of the alloy.
4- Conclusions
In the present investigation, the micromechanics strengthening in nanostructured Al/SiCp
composite deformed to high strain by a novel severe plastic deformation process,
accumulative press bonding (ARB), was investigated. The improvement in yield strength
of Al/SiCp composite was described by various strengthening mechanisms. Advanced
microstructural techniques were employed to present evidences of each strengthening
mechanism. The conclusions drawn from the results can be summarized as follows:
1) Homogeneous distribution of SiC particles (with average particle size of 10 µm) was
successfully achieved after 14 cycles of APB process.
2) The EDS maps and X-ray diffraction pattern showed that there was no evidence of
detrimental phases in the microstructure of Al/SiCp composite considered as the
advantage of solid state fabrication process.
3) Nanostructured Al/SiCp composite with the average grain size of 380 nm and well-
developed high-angle grain boundaries (73% high angle boundaries and 35° average
misorientation angle) was obtained by performing 14 cycles of APB process.
4) As a result of particle stimulated nucleation mechanism, grain size of the composite
was less than 100 nm in the vicinity of SiC particles.
5) The yield strength of the aluminum, being 29 MPa, was improved by 5 times, as it
increased to 148 MPa.
6) The contribution of grain boundary, strain hardening, thermal mismatch, Orowan,
elastic mismatch and load-bearing strengthening mechanisms were 64.9, 49, 6.8, 2.4,
5.4 and 1.5 MPa, respectively. Clearly, strain hardening and grain boundary
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mechanisms demonstrate higher contribution to the overall strength of the Al/SiCp
composite.
7) Al/SiCp nanocomposite showed good agreement with quadratic summation model,
however, based on the result of calculations performed by each model, it is understood
that experimental result exhibits a good accordance with arithmetic and compounding
summation models in micro-composite.
Acknowledgment
The authors acknowledge financial support from CICYT (Spain) under program
MAT2012-38962-C03-01, and the Ministry of Science, Research and Technology of Iran.
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Table captions:
Table 1. Chemical composition of AA1050 sheets.
Table 2. Summary of AMCs strength from literatures.
Table 3. Contribution of strengthening mechanisms and yield strength obtained by
theoretical models and experiment in Al/SiCp composites.
Figure captions:
Figure 1. Engineering stress-strain curves of annealed aluminum (Al), monolithic
aluminum (Al-APB) and Al/10 vol.% SiCp composite produced by APB process.
Figure 2. STEM micrographs of Al/SiCp composite after different APB cycles; (a) 2, (b) 5,
(c) 7 and (d) 10 and (e) 14 cycles.
Figure 3. STEM micrograph of aluminum/SiCp interface.
Figure 4. TEM micrographs of aluminum after one cycle of APB process; (a) surface (b)
center of specimen.
Figure 5. TEM micrographs of Al/SiCp interface after 14 cycle of APB process.
Figure 6. Al/SiCp composite after 14 APB cycle: (a) EBSD/OIM and (b) grain boundary
maps.
Figure 7. FE-SEM micrographs of Al/SiCp composite after (a) 1, (b) 3, (c) 5 and (d) 10 and
(e) 14 APB cycles.
Figure 8. (a) SEM micrograph of Al/SiCp composite along with its (b) aluminum, (c)
silicon and (d) carbon X-ray maps. EDS analysis of points (e) 1 and (f) 2.
Figure 9. X-ray diffraction (XRD) pattern of Al/SiCp composite.
434
435
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439
440
441
442
443
444
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447
448
449
450
451
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453
454
455
456
20
Tables:
Table 1. Chemical composition of AA1050 sheets.
Element Al Si Fe Mn Cu Mg Zn Ti
wt.% Bal. 0.2 0.22 0.02 0.01 0.01 0.01 0.01
457
458
459
460
461
21
Table 2. Summary of AMCs strength from literatures.
AMCs Methods Reinforcement
particle size
YS (MPa) UTS (MPa) Reference
Al/5 wt.% Al2O3 Casting 20 µm ~112 ~157 [54]
Al/5 vol.% SiCp Casting 8 µm ~80 ~115 [55]
Al/3 wt.% Al2O3 Casting 50 nm ~107 ~162 [54]
Al/20 vol.% Al2O3 Casting+extrusion 12 µm ~175 ~220 [56]
Al/2 vol.% SiCp Friction stir welding 15 nm ~130 ~108 [57]
Al/20 vol.% SiCp Powder metallurgy 17 µm ~87 ~107 [58]
Al-5Cu/13vol.% SiCp Powder metallurgy 10 µm ~134 ~175 [59]
Al/10vol.% SiCp Accumulative press bonding 10 µm 180 222 Present work
462
463
464
465
22
Table 3. Contribution of strengthening mechanisms and yield strength obtained by
theoretical models and experiment in Al/SiCp composites.
Strengthening mechanisms and yield strength Al/SiCp micro-composite Al/SiCp nano-composite
Grain boundary (∆ σGB) 64.9 75.6
Thermal mismatch (∆ σTM) 6.8 39.6
Elastic mismatch (∆ σTM) 5.4 34.4
Strain hardening (∆ σDis) 49 42
Orowan looping (∆ σOrowan) 2.4 172
Load-bearing (∆ σLoad) 1.5 0.3
Experimental yield strength (σ Ex .) 148 210
Calculated arithmetic yield strength (σ Arith.) 159 393
Calculated quadratic yield strength (σ Quad.) 111 228
Calculated compounding yield strength (σ Comp .)144
289
466
467
468
469
