Effect of Spatial Distribution of SiC Particles on the Tensile Deformation
Behavior of Al-10 vol%SiC Composites
Di Zhang
*, Kenjiro Sugio, Kazuyuki Sakai
*, Hiroshi Fukushima and Osamu Yanagisawa
Mechanical System Engineering, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan
The effect of particle clustering distribution on the damage accumulation and the deformation behavior is investigated in the particle reinforced metal-matrix composites. The clustering tendency of the Al-10 vol%SiC composite is evaluated by the normalized 2-dimensional local number density (LND2D) of the particle. It is found that the uniform material having a spatial distribution close to the random distribution has higher flow stress and larger elongation. The particle/matrix delamination is easy to occur preferentially at the particles of larger size in the more clustered regions in tensile deformation. Composites with lower clustering tendency have larger strain hardening capacity than those with more clustering one. [doi:10.2320/matertrans.48.171]
(Received September 15, 2006; Accepted November 20, 2006; Published January 25, 2007)
Keywords: Al-10 vol%SiC composite, particle clustering, tensile properties, particle/matrix delamination
1. Introduction
Particle reinforced metal matrix composites (PMMCs) are now emerging as an important class of engineering materials. The aluminum and silicon carbide (Al-SiC) system, which is the most commonly studied composite, is particularly used in automotive, aerospace and other engineering systems during the last few decades due to their potentially superior mechanical properties, such as high specific modulus, strength and thermal stability. However the advantages of these kinds of materials often diminish by the particle fracture and interfacial delamination leading to void forma-tion in the matrix. Most of the experimental and numerical studies1–7)have been carried out to understand the effect of
the morphological variables, such as the particle volume fraction, particle size, shape and orientation on the deforma-tion and damage behavior of the alloy. Experimental evidence and numerical results8–15) also demonstrated that
the spatial distribution of the second phase particles played an important role on the mechanical properties and the damage mechanism of the composites.
The spatial distribution of the second phase particles in composites is much more clustered when there is an obvious difference between the matrix particle sizes and the rein-forcement particle sizes. The ‘‘relative particle size (RPS) ratio’’,16)which is defined as the ratio of the average powder
particles sizes between the matrix and the reinforcement, is a beneficial method to control the clustering tendency. The optimization of this RPS ratio results in a homogeneous microstructure and better mechanical properties. Stone et al.16) studied the effect of RPS ratio on the mechanical
properties of the PMMCs, but they did not establish any quantitative relation between the RPS ratio and the mechan-ical properties. Prasad et al.17,18) carried out a systematic
study. They found that the decrease in the RPS ratio resulted in the increase in strength and elongation, as a result of homogeneous distribution of SiC particles. However this kind of research did not provide any systematic correlation
with the mechanism of the particle damage.
In this paper, we introduce ‘‘normalized 2-dimensional local number density’’ ([LND2D]) from measurement as the clustering parameter instead of the RPS ratio and investigate the relation between LND2D and the mechanical properties for Al-10 vol%SiC composite. We discuss how the clustering parameter LND2D exerts an influence on the deformation properties and its relation with the damage behavior of the particles.
2. Experimental Procedure
2.1 Material preparation
The matrix material used in the present study was the pure Al powder having the composition of Cu, Fe, Si with different average particle sizes of about 1mm, 3mm, 20mm
and 30mm, respectively. The reinforced material was the SiC powder with particle size of 2–3mm. The chemical compo-sition of these powders is shown in Table 1. Five samples (Sample 1–Sample 5) were prepared. For the Sample 1, Al powders (90 vol%) and SiC powders (10 vol%) were mixed in ethyl alcohol for 60 minutes applying ultrasonic vibration and then blended for 24 hours using a blending machine. For the other four samples, the Al powders (90 vol%) and SiC powders (10 vol%) were blended in dry condition for 24 hours. The detail of the five samples is summarized in Table 2.
[image:1.595.306.550.690.786.2]The mixed powders were consolidated up to 99–99.2% of the theoretical density using a spark sintering technique
Table 1 Chemical composition of Al and SiC powders (mass%).
Particle size Al Cu Fe Si
1mm 99.9 — 0.09 0.03
3mm 99.9 0.005 0.04 0.01
20mm 99.9 0.001 0.08 0.06
30mm 99.9 — 0.07 0.04
Particle size SiC Fe Al Ca Cr Na Mn Ni
2–3mm 99.7 0.2 0.06 0.01 0.007 0.008 0.02 0.006 *Graduate Student, Hiroshima University
described elsewhere.19)The sintering process was carried out
in a vacuum with an atmosphere less than1:33103Pa to limit the oxidation of the sample. The sintering condition is given in Table 3.
The uniaxial tensile tests were carried out at room temperature using tensile testing machine to obtain the basic mechanical properties such as flow stress, ultimate tensile strength and elongation. The cylindrical samples with a 20 mm gauge length and 8 mm diameter were loaded at a constant crosshead speed of2:0103s1.
The samples after failure were cut in the longitudinal direction and metallographic samples near fracture surface were prepared. A scanning electron microscopy (SEM) was used to observe the microstructure, such as the particle spatial distribution, particle damage and the interfacial delamination between the matrix and the reinforcement.
2.2 Definition of LND2D (2-dimensional Local Number Density)
At first, particles are arranged in 2-dimensionally closest, hexagonal ordering as Fig. 1(a), keeping a given 2-dimen-sional particle number density, (particle number in unit area). Let us define a measuring circle with a gravity center (GC) of noticed particle and radius, R, so that the number density in the circle is equal to the given value, including the GCs of the noticed and nearest neighbor particles. Then¼ 7=ðR2Þ and R is represented as eq. (1). In this case of ‘‘ordering’’, local number (LN) of all GC is equal to 7, and probability (P) and cumulative probability (CP) of LN is shown in Fig. 1(a0).
R¼ 7
1
2
¼1:49312 ð1Þ
In Poisson field20)where points are randomly distributed in
2-dimensional space (schematically shown in Figure 1(b)), probability ofk, point number included in areaA, at arbitrary position is represented by eq. (2).
PðkÞ ¼ðAÞ
k
k! expðAÞ k¼0;1;2 ð2Þ
Fig. 1(b0).
PðkÞ ¼ 7
ðk1Þ
ðk1Þ!expð7Þ k¼1;2;3 ð3Þ
When particles are arranged in clustering state (schemati-cally shown in Fig. 1(c)), probability histogram of LN must extend to right, larger LN (schematically shown in Fig. 1(c0)). Then we consider that the LN of GC in the measurement circle is a proper parameter to evaluate spatial arrangement of particulate second phase.
In this paper, normalizing measured LN divided by 7 of the ordering arrangement (eq. (4)),
½LND2D ¼LN
7 ð4Þ
clustering tendency is evaluated by the relative frequency of [LND2D]. Hereafter, the normalized LND2D ([LND2D]) is referred to ‘‘2-dimensional local number density’’.
2.3 Quantitative characterization of microstructure
In this study, image analysis was carried out using computer software developed by us to evaluate the spatial distribution of particles. After the images had been captured from a SEM, thresholding was carried out to identify SiC particles and the information of each SiC particle was recorded. [LND2D] was calculated from the GC of each particle using the computer software. It has been made clear that measurement for more than 2000 particles is needed to obtain reliable values of [LND2D].21)
3. Results and Discussion
3.1 Undefomed microstructures
The typical microstructure of the five samples, consists of reinforcement particles surrounded by Al matrix, is shown in Figures 2(a) to (e). As shown in the pictures, all sintered material exhibits very small voids at the particle/matrix inteface, mostly in the clustering parts. It is shown in Sample 4 and Sample 5 that SiC particles agglomerate in the interstices of Al matrix particles and this lead to a hetero-geneous distribution of the reinforcement.
Figure 3 presents the cumulative relative frequency (CRF) of [LND2D] for the five samples, along with a random distribution that is calculated by Poisson field theory. The average of [LND2D] ([LND2D]av) and the standard
devia-tion of [LND2D] ([LND2D]stdev) are shown in Table 4. The
CRF curves of [LND2D] shift to right from Sample 1 to 5. The difference of curves is significant especially at largest [LND2D]. The cumulative distribution of Sample 1 and Sample 2 is narrower than the other three samples. The clustering tendency of Sample 1 is smaller than Sample 2 though the RPS ratio of these samples is same. It means that wet blending with ultrasonic vibration is more effective than dry blending to prepare homogeneous samples. It is thought
2 0.2 0.7 0.1 1.11 99.0
3 0.9 0.1 1.30 99.2
4 0.2 0.7 0.1 7.05 99.2
5 0.1 0.1 0.7 0.1 10.33 99.0
[image:2.595.46.291.95.197.2]RPS ratio = Al (average particle size)/SiC(average particle size)
Table 3 The sintering conditions.
Pulse discharge time (minute)
Holding time (minute)
Holding
temperature (K) Max. load(MPa)
[image:2.595.46.292.247.285.2]that [LND2D] is an appropriate parameter for quantitative analysis of the clustering tendency.
3.2 Tensile properties
Figures 4(a) and (b) show flow stress ("¼0:06), ultimate tensile strength and elongation of the five samples having different [LND2D]avrespectively. The uniaxial tensile tests
were repeated for each [LND2D]avwith at least two samples,
which gives an indication of scatter in values. An obvious tendency of decreasing flow stress, ultimate tensile strength and ductility with the increasing [LND2D]avis observed from
the figure. While the sample with [LND2D]avlower than 1.15
[image:3.595.72.525.70.582.2]has a higher flow stress, ultimate tensile strength and elongation than the other three samples, those with [LND2D]av higher than 1.15 does not show an obvious
variation of these values. This result seems to indicate that small variations in the degree of clustering, below the values of 1.15 for [LND2D]av, lead to a substantial improvement of
the tensile properties. The corresponding effects on the associated fracture process will be discussed in the next section. Thus the clustering parameter of [LND2D] gives a good indication of the tendency of flow stress, tensile strength and elongation. This experimental results is in agreement with the results of Prasadet al.16)and Murphyet
20
40
60
80
100
0
5
10
15
20
25
0
20
40
60
80
100
CP, P (%)
LN
0
0
20
40
60
80
100
CP, P (%)
P
CP
P
CP
(a')
(b')
(c')
(a)
(b)
CP, P (%)
(c)
al.,22)who reported almost the same tendency of decreased
tensile strength and the elongation with the increasing clustering parameter.
The tensile instability can be described by the Considere criterion, in which the stress is related to the strain-hardening rated=d"as Ref. 6),
d
d"¼ ð5Þ
The flow stress and the strain-hardening rate are plotted against plastic strain in Fig. 5(b) in order to describe the onset of instability in these materials. In Figure 5(a), the flow curves are truncated at the necking beginning strain. After the start of plastic deformation (0.2% offset), the flow stress of
both composites can be divided into two regions. First the work hardening rate decreases sharply with the increasing strain at a medium strain. It is important to notice that strain hardening rate of the more clustered composites decreases faster with strain than it does in more homogeneous material. Then, after a large strain, the work-hardening rate is almost constant with increasing strain. It is seen that the instability strain coincides closely with the intersection point of these curves, in accord with Considere criterion.
3.3 Particle damage and accumulation
We now turn our attention to the development of the particle damage and accumulation during tensile deforma-tion. Figure 6 shows that many particles fail by delamination
(c)
(d)
(e)
4
µ
m
[image:4.595.70.525.71.571.2]of a particle/matrix interface, while the particle crack does not play an important role on the particle failure. The small voids may grow along the particle/matrix interface between the particles very close to each other.
Figures 7(a) to (d) show the CRF of [LND2D] and size of delaminated particles near the fractured surface after tensile test for sample 2 and sample 5. Figures 7(a) and (c) show that the [LND2D]avfor delaminated particles is larger than whole
particles. Figures 7(b) and (d) also show that the particle/ matrix interface delaminates mostly at larger particles.
All sintered material exhibits very small voids at the
0.0 0.5 1.0 1.5 2.0 2.5
0 20 40 60 80 100
CRF(%)
[LND2D]
Random (theory) Sample1 Sample2 Sample3 Sample4 Sample5
[image:5.595.59.284.73.252.2]Fig. 3 Cumulative relative frequency (CRF) of 2-dimensional local number density ([LND2D]) for the prepared samples.
Table 4 Average of [LND2D] ([LND2D]av) and standard deviation of [LND2D] ([LND2D]stdev) for the five samples.
Sample 1 2 3 4 5
[LND2D]av 1.09 1.13 1.19 1.28 1.32
[LND2D]stdev 0.352 0.367 0.459 0.480 0.454
(a)
(b)
Sample 1
Sample 2
Sample 3
Sample 4 Sample 5
170
175
180
185
190
195
200
205
210
215
Stress,
σ/
MPa
Flow stress(ε=0.06) Ultimate tensile strength
1.10
1.15
1.20
1.25
1.30
11
12
13
14
15
Elongation (%)
[LND2D]
avFig. 4 Relation between average [LND2D] ([LND2D]av) and the tensile properties, (a) tensile flow stress, tensile strength, and (b) elongation.
(a)
(b)
0
20
40
60
80
100
120
140
160
180
200
[LND2D] av 1.13 1.32
Stress,
σ/
MPa
0.00 0.02 0.04 0.06 0.08 0.10
64
128
256
512
1024
2048
4096
Stress,
σ/
MPa
Strain,
ε
stress [LND2D]av=1.13 tangent modulus [LND2D]av=1.13 stress [LND2D]av=1.32 tangent modulus [LND2D]av=1.32
Fig. 5 (a) tensile flow curves (b) tangent modulus for the samples with different average [LND2D] ([LND2D]av).
Tensile direction
1
µ
m
Delamination
[image:5.595.314.541.75.384.2] [image:5.595.46.290.341.382.2] [image:5.595.60.286.431.755.2] [image:5.595.313.540.440.598.2]particle/matrix inteface, mostly in the clustering parts. On the other hand, probability of exsiting small voids at the interface may increase with the increasing particle size. Then, in conclusion, the SiC particles of larger particle size in more clustered regions are easy to be delaminated. Previous work4)
on the Al-SiC composites indicated that the particle fracture increases with increasing particle size. This is due to the consideration that the probability of defects in reinforce-ments increases with increasing particle size. This is coincidence with our reults, though there is a difference in damage mode.
Figure 8(a) shows the relationship between the number fraction (NF) of delaminated particles and [LND2D]av of
initial undeformed samples, while Figure 8(b) illustrates the relationship between [LND2D]avof the delaminated particles
after tensile test and [LND2D]av of initial undeformed
samples. The NF and [LND2D]av of delaminated particles
increase with increasing initial [LND2D]av up to 1.15 and
then they are almost same when [LND2D]av is higher than
1.15. The experimental results show that the presence of a critical clustering degree, which provides a minimum strengthening corresponding to a maximum number fraction of delaminated particles.
Figure 9 shows that the NF of delaminated particles is strain dependent. The NF of delaminated particles in the sample increases more dramatically in the sample with
[LND2D]avof 1.32 than that with [LND2D]avof 1.13 at any
given value of the strain, both of which increase with the increasing strain. The delamination is more frequent during tensile deformation for particles of the more inhomogeneous microstructures, because they have more regions of larger local number density of the particles.
Stress in tensile deformation can be decided by balancing its increase by strain hardening of Al matrix and its decrease by the damage of reinforcement particle. The composite with more heterogeneous spatial distribution of particles has a substantial levels of delamination produced at small strain. This leads to a sharp reduction of the strain-hardening rate of the composite, and as a result, the composite fractures at lower plastic strains compared with more homogeneous samples. Previous studies9)demonstrated that largest strain
and stress concentrations occur in the matrix region between the closely packed particles. The nucleation of void by the interface delamination is more frequent and may grow more rapidly at the clustered regions due to the stress concen-trations induced in the elastic particles and the plastic matrix. As a result, composites with stronger clustering tendency present lower strain hardening capacity than those of the homogeneous ones as shown in Figure 5 and the noticeable reduction in the tensile properties as shown in Figure 4.
(c)
(d)
0
20
40
CRF (%)
random (theory) all particles[LND2D]av=1.13 delaminated particles [LND2D]av=1.57
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0
20
40
60
80
100
CRF (%)
[LND2D]
random (theory) all particles [LND2D]av=1.32
delaminated particles [LND2D]av=1.67
0
1
2
3
4
5
Particle size, D/
µ
m
all particles delaminated particles all particles delaminated particles [image:6.595.75.526.71.425.2]4. Conclusion
In this investigation, the effect of reinforcement spatial distribution on the damage accumulation and the tensile behavior was studied in an Al matrix composite reinforced with 10 vol% SiC particles. From the experimental results, the following conclusions can be made:
(1) The determination of the normalized 2-dimensional local number density [LND2D] is simpler and appears to be benefit for quantifying the clustering tendency of the composites.
(2) In tensile deformation, SiC particles of larger particle size in more clustered regions are easy to be delami-nated from matrix in the composites with reinforcement size range of 2–3mm.
(3) Composites with stronger clustering present lower strain hardening capacity than those of the homoge-neous ones due to their stronger tendency of particle/ matrix delamination.
(4) The more homogeneous spatial distribution of rein-forcement particles brings improved tensile properties, higher flow stress, tensile strength and larger elonga-tion.
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(a)
(b)
0
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NF of delaminated particles (%)
1.10
1.15
1.20
1.25
1.30
1.45
1.50
1.55
1.60
1.65
[LND2D]
av, del.
[LND2D]
avFig. 8 Relation between average [LND2D] ([LND2D]av) of each sample and (a) the number fraction (NF) of delaminated particles and (b) the average [LND2D] of the delaminated particles ([LND2D]av,del.).
0.00
0
0.04
0.08
0.12
0.16
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NF of delaminated particles (%)
Strain,
ε
[LND2D]av 1.13 1.32
[image:7.595.58.286.72.401.2] [image:7.595.310.542.77.261.2]