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Effects of random particle dispersion and size on the indentation behavior of SiC particle reinforced metal matrix composites
Materials and Design 31 (2010) 2818–2833
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Effects of random particle dispersion and size on the indentation behavior of SiC particle reinforced metal matrix composites Recep Ekici a, M. Kemal Apalak a,*, Mustafa Yıldırım b, Fehmi Nair a a b
Department of Mechanical Engineering, Erciyes University, Kayseri 38039, Turkey Graduate School of Natural and Applied Sciences, Erciyes University, Kayseri 38039, Turkey
a r t i c l e
i n f o
Article history: Received 24 November 2009 Accepted 2 January 2010 Available online 14 January 2010 Keywords: Metal matrix composites Non-linear behavior Finite element analysis Scanning electron microscopy Powder processing
a b s t r a c t This study investigates the effects of particle size, volume fraction, random dispersion and local concentration underneath a spherical indenter on the indentation response of particle reinforced metal matrix Al 1080/SiC composites. The ceramic particles in certain sizes and volume fractions were randomly distributed through the composite structure in order to achieve a similar structure to an actual microstructure as possible. The particle size and volume fraction affected considerably indentation depths and deformed indentation surface profiles. The indentation depth increases with increasing particle size, but decreases with increasing particle volume fraction. The experimental indentation depths were in agreement with numerical indentation depths in case the local particle concentration effect is considered. The local particle concentration plays an important role on the peak indentation depth. For small particle sizes and large volume fractions the random particle distribution affects the deformed surface profiles as well as the indentation depths. However, its effect is minor on residual stress and strain distributions rather than levels in the indentation region. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Particle reinforced metal matrix composites (PRMMCs) have become very promising materials due to their significant advantages over conventional materials such as high specific modulus, improved resistance to wear, improved resistance to high cycle fatigue and fatigue crack threshold, higher stiffness-to-weight ratio, low coefficient of thermal expansion and high thermal conductivity. They offer relatively isotropic properties compared to short fiber or whisker reinforced counterparts and ability to be formed using conventional metal manufacturing processes such as rolling, forging and extrusion to produce the finished product with low cost [1–5]. Their mechanical properties, i.e. tensile, wear and fatigue, depend on some micro-structural parameters such as reinforcement particle distribution, size, volume fraction and orientation. Consequently, the hardness as well as indentation behaviors of PRMMCs have attracted the researchers in recent years. The indentation test requires minimum specimen preparation and mounting in comparison with other traditional methods on the determination of the mechanical behaviors of PRMMCs, and can be easily performed several times on a single specimen of small volume materials and miniaturized structures using appro* Corresponding author. Tel.: +90 352 437 4901; fax: +90 352 437 5784. E-mail address: [email protected] (M. Kemal Apalak). 0261-3069/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2010.01.001
priate load level and indenter tip geometry [6–8]. Numerical modeling of the indentation process allows understanding the deformation mechanism, stress and strain fields through the metal matrix around the ceramic particles and particle–matrix interaction [6]. The present theoretical and experimental studies on the indentation behavior of the particle reinforced metal matrix composites concentrated on the deformation characteristics and a relation between overall strength and indentation hardness [9–14]. Shen et al. [15] investigated experimentally the correlation between hardness values and tensile properties, and showed that the composites including large reinforcement particles tended to fracture during their tensile tests whereas the local predominant compressive loads in the hardness test prevented the pre-existing fractures particles to weaken the composite material, and the hardness test overestimated the overall tensile strength. Shen and Chawla [16] presented a simple relationship between the macro-hardness and tensile strength of PRMMCs. They indicated an increase in the local particle concentration underneath the indenter which caused a significant overestimation of the tensile strength in case the matrix strength was relatively low. Shen et al. [17] also verified that enhanced matrix flow contributed to a localized increase in particle concentration underneath the indenter and resulted in a significant overestimation of the overall composite strength via the hardness test based on a numerical study considering the effects of particle size, particle volume fraction and matrix aging characteristics on
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MMCs with reasonable accuracy [26], but the microstructure of particulated MMCs having randomly distributed particulate reinforcements. A new random structure in a certain particle size and volume fraction yields to different stress and strain fields underneath the spherical indenter, therefore, the stress analyses were repeated for different particle arrangements until a stable respond is achieved from the indentation tests. The indentation tests were performed at different points at reasonable distances of the produced specimens in order to consider randomness of particle locations. In case any arbitrary set of composite structures with random particle arrangements is considered the hardness and indentation depths were predicted in some errors in comparison with the experimental ones. However, the predicted and experimental hardness and indentation depths are in good agreement for the composite structures with random distributions similar to those of the specimens produced in a certain of particle size and volume fraction. 2. Numerical modeling The indentation behavior of metal matrix composite structure under a spherical indenter was investigated using the non-linear finite element method (ABAQUS/Standard finite element software) [29]. The geometrical, material non-linearities and non-linearity arising due to the large deformations in the contact surface of the metal matrix region induced by a rigid indenter were taken into account. The composite structure was simplified to an axisymmetrical structure as a square region of 3 3 mm in size. The matrix and ceramic particles were modeled using 22,500 eight-noded biquadratic axisymmetric quadrilateral solid (CAX8R) finite elements with reduced integration of 20 20 lm in size. The element size was kept constant through all analyses. In an actual composite structure the reinforcement particles are distributed randomly in the metal matrix, and the particle geometry and size are not uniTable 1 Mechanical and physical properties of Al 1080 and SiC [27]. Property
Al 1080
SiC
Modulus of elasticity (E) (GPa) Poisson’s ratio ðmÞ Density ðqÞ
70 0.33 2700
420 0.17 3100
150 Al 1080 (99.8%) SiC
100 Stress (MPa)
the interrelationship between tensile strength and macro-indentation hardness. Kozola and Shen [18] showed that the indentation hardness can not scale with the overall strength of a discontinuously reinforced aluminum due to increasing particle concentration or particle crowding effect in the region underneath the indenter although the indenter size is much greater than the reinforcement particle size. Shen and Guo [19] determined the stress–strain behavior of a compact material system composed of a soft and elastic–plastic matrix and linearly elastic hard particles using the non-linear finite element method, and then used this stress–strain diagram in the indentation model behaving the metal matrix composite like a homogeneous material. The homogeneous material and two-phase composite models differed significantly due to the increased particle concentration underneath the indenter in the two-phase composite model. Pereyra and Shen [7] observed a particle concentration enhancement in post-indented metal–ceramic composite specimens using a large indenter size via quantitative metallography. They performed quantitative metallography on the post-indented metal matrix composite specimens and observed an evident increase in particle concentration due to the relatively large negative dilatational strain in metal matrix in comparison with ceramic particles [8]. Ege and Shen [20] pointed that a material containing internal pores exhibited an indentation behavior opposite to two-phase composites since local pore crushing occurred underneath the indenter, leading to the underestimated overall mechanical strength of composite material. Micro- or nano-scale indentation can be performed to investigate the local indentation behavior of heterogeneous particle reinforced metal matrix composites. Rosenberger et al [21] used the micro-indentation to understand the effect of the depth and diameter of the reinforcement in the hardness of MMC model with one particle at its centroid, and showed that the hardness measurements might be overestimated by 15–74% depending on the method employed and an ideal measurement might be achieved by an indenter diameter at least twice the reinforcement diameter. Pramanik et al. [22] investigated micro-indentation behavior of PRMMCs based on the stress–strain fields underneath a spherical indenter during the loading and unloading stages of the indenter. Durst et al. [23] presented the finite element simulations of the nano-scale indentation to determine the influence of the shape and aspect ratio of particles on the single-phase indentation behavior in particle-matrix systems. They observed a transitional indentation behavior from particle to matrix which is observed experimentally in precipitation-hardened nickel-based super-alloys. Olivas et al. [24] investigated the thermal residual stresses in SiC particle reinforced Al matrix composites via the nano-indentation. Their experimental results were in good agreement with the finite element analysis and proved the general credibility of applying spherical nano-indentation in characterizing the local surface residual stresses in the ductile matrix of MMCs. Mussert et al. [25] used the nano-indentation experimentally to measure the hardness and elastic modulus of aluminum alloy 6061 reinforced with Al2O3 in three different heat treatment conditions. However, the reinforcement particles have a random dispersion in the metal matrix. In general, this random distribution can affect the indentation response of particle reinforced metal matrix composites. The present study addresses the effects of reinforcement size and volume fraction in random geometric arrangements of reinforcements on the indentation behavior of Al 1080/SiC PRMMCs under a spherical indenter. Our methodology assumes a random particle arrangement in a certain size and volume fraction in the composite structure, which is analogous with real random particulate composite structure instead of a composite structure having arrayed particles in an order [7,8,15–22]. A model of periodic arrays may represent the microstructure of fiber-reinforced
50
0 0
0.05
0.1
0.15 Strain
0.2
0.25
Fig. 1. The true stress–strain diagram of Al 1080 (elastic–plastic) [28] and SiC (elastic) particles [19].
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RP
RP
2
3
2
1
3
1
RP
RP
2
2
3
3
1
1
Fig. 2. Sample FEM models showing the random distributions of SiC particles with different sizes: (a) 20, (b) 53, (c) 167 and (d) 478 lm in a volume fraction of 20%.
Table 2 SiC particle sizes and volume fractions of PRMMCs in FEM models. Particle size P s ðlmÞ in experiments Particle size P s ðlmÞ in FEM models
20
53
20
167
60
478
160
480
Aimed volume fraction V f (%)
Necessary element number
Vf (%)
Achieved element number
Vf (%)
Achieved element number
Vf (%)
Achieved element number
Vf (%)
Achieved element number
10 20 30
2250 4500 6750
10 20 30
2250 4500 6750
10 20 30
2250 4500 6750
9.99 19.91 29.87
2240 4480 6720
7.68 17.92 28.16
1728 4032 6336
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R. Ekici et al. / Materials and Design 31 (2010) 2818–2833 Table 3 The chemical composition (Wt. %) of the matrix material Al 1080 [27]. Material
% Al
% Cu
% Fe
% Mg
% Ga
% Si
% Mn
% Ti
% Zn
%V
Al 1080
Min 99.8
Max 0.03
Max 0.15
Max 0.02
Max 0.03
Max 0.15
Max 0.02
Max 0.03
Max 0.03
Max 0.05
Fig. 3. Sample SEM micrographs showing the random distributions of SiC particles with different sizes: (a) 20, (b) 53, (c) 167 and (d) 478 lm in a volume fraction of 20% before the indentation.
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cate particles in larger sizes (53, 167 and 478 lm) than 20 lm these particles are generated approximately using the base mesh element size ð20 lmÞ. Consequently, the actual particle sizes of 53, 167 and 478 lm are approximated to 60, 160 and 480 lm in the finite element models, respectively. Table 2 shows that the particle sizes as well as overall volume fractions in the finite element models are very close to those of the specimens used in the experiments. Since SiC particles are randomly distributed in each finite element model, ten random base models are considered for each of volume fractions 10%, 20% and 30% and each of particle sizes 53, 167 and 478 lm leading to 120 models. However, 30,000 random models for each particle size and each volume fraction are generated in order to determine the effect of increasing particle concentration underneath the indenter. A region of 1 1 mm2 in size in composite structure underneath the indenter is considered to evaluate the increase of particle concentration, and then the first ten models among ones with the densest concentration are chosen for the stress analyses for each particle size and volume fraction. All calculations were performed in an AMD Opteron Server with 4 CPUs in 2.4 GHz and 8 Gb Ram.
form. The three-dimensional model of this actual structure brings some computational difficulties. A region of 6 6 3 mm in size requires 13,500,000 three-dimensional solid finite elements with an edge length of 20 lm because the minimum particle size in the study is 20 lm. The total number of degrees of freedom in the model is extensive for a statistical study. Al 1080 (aluminum alloy in 99.8% purity) is an elastic-plastic matrix material whereas SiC (Silicon Carbide) particles are elastic. Mechanical and physical properties of Al 1080 and SiC particles are given in Table 1. Fig. 1 shows true stress–strain diagrams of Al 1080 and SiC. The yield stress of Al matrix was determined from its stress–strain curve based on the offset rule (0.2% offset). The aluminum has a yield stress of 24 MPa and a yield strain of 0.007. SiC particles were assumed to be perfectly bonded with the Al 1080 matrix and particle fracture was not considered. Quasi-static indentation was performed by pressing a rigid axisymmetric circular indenter onto the top surface of the composite structure. The right half of indenter and composite structure was considered. The symmetry conditions were applied to all nodes along the symmetry axis of the half-region whereas the bottom edge was fixed. The degrees of freedom of the indenter with a radius of 0.794 mm were represented with only a reference point whose horizontal displacement and rotation about the axis normal to the problem plane were fixed. The indenter was meshed using fifty rigid two-noded shell (RAX2) finite elements. The finite element models were considered for the volume fractions V f ¼ 10%; 20% and 30% for each of particle sizes Ps ¼ 20; 53; 167 and 478 lm (Fig. 2). The same particle sizes in the experiments were used for comparison. The simulations conform to the experimental requirements for the Rockwell T-scale hardness test. The direct indentation depth (in lm) instead of hardness number is considered since our objective is simply to define a reasonable numerical measurement of hardness indentation so as to facilitate a direct but qualitative comparison with the experimental results. A pressure load of 15 kg (150 N), that Rockwell T-scale hardness test requires is used in the finite element models. A flexible code was developed in Python language [30] in order to implement all variables representing the geometric and material properties of composite material to each of excessive number of finite element models, and the generated input file was evaluated by ABAQUS/Standard finite element software. The ceramic particles in a specific volume fraction are distributed randomly through the metal matrix the volume fraction of SiC particles is adjusted as a percentage of fixed finite element number (22,500), thus a volume fraction of 10% for SiC particles in the matrix corresponds to 2250 finite elements which were defined as SiC particles. SiC particles are selected randomly and saved in an element set. For each new analysis this element set was changed completely. In order to lo-
3. Experimental study Specimens were prepared using 99.8% pure aluminum (Al 1080) and 99.5% pure silicon carbide (SiC) powders. The chemical composition of the matrix material Al 1080 alloy is given in Table 3. The Al 1080-powder has a mean particle size of 44 lm whereas SiC powder has four different average sizes P s of 20, 53, 167 and 478 lm. All metal matrix composite specimens were produced using the powder metallurgy method in the reinforcement volume fractions V f of 10%, 20% and 30% for each reinforcement particle size. This method requires some processes, such as cold pressing and sintering, or hot pressing. Thus, the matrix (Al 1080) and the reinforcement (SiC) powders were blended by a motorized mixer to produce a homogeneous particle distribution, and were cold pressed. Finally, the compacted powder mixtures were hot pressed uniaxially in a single-end circular die made of hot-work tool steel under a pressure of 350 MPa inside a protective argon atmosphere at a temperature of 610–615 °C for a sintering time of 30 min. The cylindrical specimens are of 3 mm in height and 8 mm in radius. The standard Rockwell T-scale test was employed succesfully to the hardness indentation of unhardened materials, such as metals softer than hardened steel or hard alloys [31]. The hardness tests were performed by pressing a spherical steel indenter with a diameter of 1.588 mm into both the top or bottom at free surfaces and cross-sections perpendicular to hot pressing direction of the specimens at a minor and major load of 30 and 150 N, respectively. Six readings (at least) were taken from these sections of the specimens
Table 4 Experimental indentation results obtained from Rockwell T-scale hardness test. Indentation depth on the specimen cross-sections ðlmÞ
Indentation depth on the specimen surfaces ðlmÞ
1
2
3
4
5
6
1
2
3
4
5
6
10 20 30
66.08 48.96 39.68
67.44 49.52 40.56
67.60 49.28 37.92
67.20 49.36 40.24
67.76 47.08 38.48
66.76 50.61 42.68
66.76 50.88 39.48
66.64 51.92 39.60
65.08 49.12 43.32
66.64 47.04 41.04
64.84 50.12 42.52
64.44 48.44 42.74
66.44 49.37 40.69
53
10 20 30
68.96 53.24 44.16
66.64 49.16 46.32
70.32 54.84 45.44
67.52 52.64 45.24
69.56 53.16 45.80
68.40 52.86 46.16
68.92 50.48 50.40
69.16 51.96 51.80
67.12 52.04 48.76
67.96 51.04 51.46
67.44 53.48 51.04
68.64 52.24 50.56
68.39 52.26 48.09
167
10 20 30
70.60 60.00 47.76
69.40 57.76 51.28
67.12 59.12 52.40
68.08 58.80 51.80
70.50 59.58 51.20
70.22 60.08 52.00
70.64 59.68 48.08
70.96 59.72 50.84
70.40 61.20 50.00
72.24 62.00 50.24
69.56 60.14 51.42
69.84 59.82 50.38
69.97 59.83 50.62
478
10 20 30
72.52 59.20 49.40
73.60 62.56 53.64
69.44 59.52 49.92
70.20 63.36 49.76
70.06 62.28 52.08
72.44 59.86 53.72
73.84 63.44 52.18
76.45 63.52 51.88
72.24 66.44 54.72
71.00 64.52 48.56
70.68 62.32 48.92
72.50 61.12 52.56
72.09 62.35 51.45
Particle size P s ðlm
Volume fraction V f (%)
20
Mean indentation depth ðlmÞ
Table 5 Numerical indentation depths for low local particle volume fractions. Volume fraction Vf , %
20
10 20 30
10.08 20.13 29.49
62.42 33.74 17.55
10.04 18.57 29.81
64.06 37.42 22.42
10.00 20.00 30.25
60.53 34.89 22.90
9.96 20.97 30.17
65.78 34.17 15.90
10.28 19.57 30.37
51.26 36.33 12.90
9.20 19.37 29.93
60.90 36.49 20.62
8.60 21.41 28.77
61.39 32.32 19.53
10.04 19.93 29.45
58.71 30.81 16.78
10.12 21.25 30.41
54.78 34.43 23.00
9.80 20.37 29.53
59.94 33.18 21.90
59.98 34.38 19.35
53ð 60Þ
10 20 30
11.28 20.53 31.21
84.35 70.07 41.26
9.72 19.09 30.85
82.39 70.67 41.74
10.92 15.61 28.93
82.80 71.72 42.62
9.36 19.45 30.37
82.09 71.87 39.74
8.44 22.32 31.45
97.67 62.06 46.40
11.28 20.53 29.77
84.39 66.38 41.33
11.76 18.37 28.93
91.73 68.42 37.99
10.56 20.88 30.61
89.09 68.65 48.14
8.28 21.37 29.05
96.00 65.36 46.77
9.60 18.13 30.21
83.81 63.38 41.77
87.43 67.86 42.78
167ð 160Þ
9.99 19.91 29.87
6.00 17.61 28.49
134.39 106.28 74.68
12.48 24.25 31.37
134.09 104.70 63.42
11.64 14.73 23.37
132.43 103.72 73.92
7.68 13.69 24.00
134.34 104.28 72.42
10.24 17.29 21.77
135.81 107.12 74.51
14.57 21.77 26.25
117.80 100.39 68.99
10.80 29.77 21.45
136.64 92.13 68.30
2.56 20.97 35.53
141.43 101.52 76.74
10.24 11.85 32.97
134.43 96.61 79.84
13.29 25.61 35.21
137.66 108.30 74.64
133.90 102.51 72.75
478ð 480Þ
7:68 17.92 28.16
0.00 5.76 36.49
150.41 131.78 115.05
0.00 16.33 30.73
150.68 133.96 117.67
0.00 23.77 30.73
149.74 131.23 111.43
3.20 3.96 20.17
149.01 132.82 118.53
0.00 24.00 26.65
149.81 138.36 118.40
0.00 23.05 24.97
150.13 136.09 117.18
0.00 21.12 27.33
147.56 138.70 107.85
0.00 1.92 25.73
151.31 136.95 108.63
0.00 1.92 18.25
152.20 137.06 107.64
0.00 23.05 30.65
150.45 135.60 117.74
150.13 135.26 114.01
Numerical indentation depth, a
1
a
2
a
3
a
4
a
5
a
6
a
7
a
8
a
9
a
Mean indentation depth ðlmÞ
10
Local particle volume fraction in a region of 1 1 mm2 underneath the indenter.
Table 6 Numerical indentation depths for high local particle volume fractions.
a
Numerical indentation depth,
lm
Particle size P s ; lm
Volume fraction Vf , %
a
1
a
2
a
a
4
a
5
a
6
a
a
8
a
9
a
10
Mean indentation depth ðlmÞ
20
10 20 30
12.44 22.81 32.73
53.96 29.83 14.94
12.28 22.77 32.85
57.82 36.05 20.33
12.04 22.73 32.65
58.57 29.99 15.59
12.00 22.77 32.81
56.28 33.15 18.22
11.96 22.73 32.73
57.11 37.94 14.61
12.12 22.73 32.69
56.23 33.13 22.44
12.04 22.69 33.73
53.95 40.84 15.36
12.00 23.05 33.25
55.80 36.88 18.78
12.40 22.93 32.69
58.02 32.58 17.74
12.04 22.89 32.73
60.88 40.34 19.30
56.86 35.07 17.73
ð53ð 60Þ
10 20 30
16.57 27.01 36.61
56.91 58.76 46.42
15.25 26.49 36.49
70.29 55.29 47.52
15.37 26.29 37.33
70.40 58.20 24.44
15.29 26.41 36.37
62.19 68.07 28.67
15.21 27.13 36.33
72.52 50.20 40.73
15.09 26.77 37.58
95.02 52.29 25.31
15.85 26.17 36.45
71.90 46.71 48.10
15.37 27.01 36.45
73.27 48.17 33.15
15.73 26.65 36.45
80.02 55.64 20.74
15.37 26.21 36.33
68.92 52.77 50.12
72.14 54.61 36.52
167ð 160Þ
9.99 19.91 29.87
23.05 33.29 42.25
76.80 54.52 33.76
23.37 34.25 44.82
73.52 58.29 38.61
23.37 34.09 42.90
71.25 52.24 47.85
22.73 33.93 42.26
92.66 65.19 50.88
23.05 33.29 41.30
72.33 66.10 47.83
25.93 34.57 43.18
77.26 50.05 31.55
22.09 35.17 43.82
82.84 68.48 38.73
23.37 33.29 42.26
81.24 54.29 50.88
23.37 33.29 41.94
85.72 57.43 33.38
22.41 33.61 41.94
89.12 66.25 36.11
80.27 59.28 40.96
478ð 480Þ
17.68 17.92 28.16
45.13 53.78 62.42
84.86 64.05 73.33
45.13 57.62 65.31
76.72 65.95 66.89
45.13 55.70 63.39
105.63 81.75 76.35
45.13 58.58 58.58
73.04 47.60 75.19
44.18 67.23 77.19
76.67 50.47 66.46
49.74 57.62 58.58
92.76 59.30 50.90
43.22 56.90 63.71
100.94 73.00 44.94
46.10 53.78 64.35
79.55 45.45 66.95
45.13 53.74 66.75
79.10 69.00 40.14
44.18 66.59 59.54
69.90 82.52 48.60
83.92 63.91 60.98
3
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a
lm
Particle size P s ; lm
Local particle volume fraction in a region of 1 1mm2 underneath the indenter. 2823
R. Ekici et al. / Materials and Design 31 (2010) 2818–2833
to improve the reliability of the readings. In order to achieve a suitable positioning on the partitioned specimens during the hardness tests the specimens cut into two pieces were hot mounted into an acrylic hot mounting resin, and a free surface of 3 16 mm2 on the specimens was grinded, cleaned and polished before the hardness tests. The standard metallography was implemented on all samples [32]. The specimens were first hand-ground with SiC grinding papers through the sequence: 180, 240, 320, 400, 600, 1200 and 4000 grit and polished with a diamond paste to obtain a surface finish of 1 lm on an automatic polisher. Scanning electron microscopy (Leo Ò 440 SEM) and macroscopy (Nikon Stereozoom S-800) were used for photographic studies of indented and unindented sample surfaces. Fig. 3 shows SEM micrographs of the metal matrix composites with SiC particles of Ps ¼ 20; 53; 167 and 478 lm in size and a volume fraction of 20% in the Al matrix. These micrographs were taken at a magnification scale of 70 zoom (200 lm).
4. The effects of particle size and random particle dispersion
Indentation depth (µm)
In order to determine the effects of both particle size and volume fraction of the randomly dispersed reinforcement particles in the matrix on the indentation depth the non-linear stress analyses were carried out for PMMCs with 20, 53, 167 and 478 lm in particle size and 10%, 20% and 30% in volume fractions. Fig. 3
80 70 60 50 40 478
0.1
shows the SEM micrographs of the specimen sections with 20, 53, 167 and 478 lm in particle size and 20% in volume fraction. After the indenter was removed completely from the indentation region the six indentation depths taken from both cross-sections and free surfaces of specimens were compared in Table 4. The measurements of the indentation depth are very close on both free surfaces and sample cross-sections. As the particle size is increased the indentation depth is increased. This increase becomes evident as the volume fraction is increased. As the volume fraction is increased the region underneath the indenter behaves stiffer and the indentation depth decreases for all particle sizes. However, the elasto-plastic matrix deforms considerably in comparison with the elastic particles as the particle size is increased for a certain volume fraction, and the indentation depth increases relatively. Tables 5 and 6 show numerical indentation depths based on the non-linear finite element analyses for particle sizes ðP s Þ of 20, 53, 167 and 478 lm and volume fractions ðV f Þ of 10%, 20% and 30%. In order to show the change in the local volume fraction underneath the indenter the reinforcement particles were randomly distributed and the local volume fractions were calculated in a region of 1 1 mm2 for each of particle sizes and volume fractions. The ten numerical indentation depths and local volume fractions were tabulated in Tables 5 and 6, respectively, considering the local lower and higher particle volume fractions underneath the indenter than the overall volume fractions. Table 5 shows the indentations depths of the random particle dispersions in which the local vol-
Indentation depth (µm)
2824
150 100 50 478
0.1
0.2
0.2
167
167 53
Volume fraction (Vf)
20 0.3
Indentation depth (µm)
Particle size (Ps, µm)
53
Particle size (Ps, µm)
20 0.3
Volume fraction (Vf)
100 80 60 40 20 478
0.1
0.2 167 Particle size (P , µm) s
53 20 0.3
Volume fraction (Vf)
Fig. 4. Couple effect of both particle size (20, 53, 167 and 478 lm) and volume fraction (10%, 20% and 30%) on: (a) the experimental (Table 4), and numerical mean peak indentation depths (lm), (b) Table 5, and (c) Table 6.
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ume fractions are close to the overall volume fractions. The indentation depth increases with increasing particle size. However, the indentation depth decreases considerably with increasing volume. The numerical indentation depths exhibit similar trends to the experimental ones, but the numerical indentation depths deviate from the experimental indentation depths as the particle is increased. The random particle dispersion, especially underneath the indenter affects evidently the indentation depth. Table 6 also shows the numerical indentation depths in which the local volume fractions are considerably larger than the overall volume fractions. Similarly, the indentation depth increases with increasing particle size whereas increasing the volume fraction results in considerable decreases in the indentation depth. The numerical indentation depths exhibit a similar behavior to those of the experimental indentation depths. However, a considerable increase is observed in the local particle volume fraction underneath the indenter, which is causing evident decreases in the indentation depths in comparison with those in Table 5. Therefore, the numerical indentation depths approach to the experimental ones. The randomness of the ceramic particle distribution through the metal matrix af-
fects considerably the indentation depth; therefore, the numerical and experimental indentation depths can be expected to converge only if the random particle distribution and both particle geometry and size are similar in the sections of both the produced specimen and the numerical model. Fig. 4 shows the couple effect of both particle size and volume fraction on the mean peak indentation depth based on the hardness tests (Table 4) and numerical analyses (Tables 5 and 6). The experimental and numerical indentation depths show similar trends; thus, the indentation depth increases with increasing particle size but decreases with increasing volume fraction. Figs. 4b and c are plotted based on the random particle distributions with a close/larger local particle volume fraction to/than the overall particle volume fraction, respectively. Fig. 4c exhibits similar indentation depths to the experimental ones (Fig. 4a) on the contrary to Fig. 4b. It is evident that the local particle volume fraction, consequently, the random particle dispersion in the local region underneath the indenter as well as through the whole structure affects considerable the numerical and experimental indentation measurements.
200
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20 0.1
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Fig. 5. Individual effects of a) particle size and b) volume fraction on the mean peak indentation depths (lm) based on both the experiments and numerical analyses.
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Figs. 5a and b show individual effect of each particle size and volume fraction on the mean peak indentation depth based on the experimental and numerical analyses, respectively. As the particle volume fraction is increased from 10% to 30% for a particle size of 20 lm the mean indentation depth decreases by 39% and 68% based on the experimental and numerical results, respectively. This decrease appears as 69% in the numerical results for the high local particle volume fractions. As the particle size is increased from 20 to 478 lm for a volume fraction of 30% the mean indentation depth increases by 26% and 489% based on the experimental and numerical results, respectively and this corresponds to 244% in the numerical results for high local particle volume fractions. In case of the lower local particle concentrations (Tables 4 and 5, Fig. 5) the error levels between the experimental and numerical indentation depths are relatively less for small particle sizes (20– 53 lm), and the error levels increase with increasing particle size and volume fraction. The error level becomes minimal (9.7%) for a particle size of 20 lm and a volume fraction of 10% and maximal (122%) for a particle size of 478 lm and a volume fraction of 30%. In case of the higher local particle concentrations (Tables 4–6, and Fig. 5) the error level minimizes to 0.92% for the particle size of 167 lm and a volume fraction of 20% and maximizes to 56% for a particle size of 20 lm and a volume fraction of 30%. The local particle concentration underneath the indenter affects considerably the indentation depths. As the local particle concentration increases underneath the indenter this limited region behaves stiffer; therefore, and the indentation depth decreases. In practice, the composite has three-dimensional random particle size and dispersion on the contrary to the two-dimensional axisymmetric structure and constant square element geometry. In addition, the actual structure has particles having highly irregular shape and sharp corners and random local particle volume fractions depending on the overall particle volume concentration. The present theoretical model considers the elasto-plastic behavior of the matrix material and geometrical non-linearity occurring during the local
deformations of the indentation surface, and can predict accurately the general effect of both particle volume fraction and particle size. If the actual three-dimensional structure of the specimen can be transferred to the finite element model the error levels between the experimental and numerical indentation depths could be decreased evidently. However, this study shows that the random particle dispersion affects obviously the indentation behavior of the structure even for the same particle volume fraction and size. In addition, some cracks occurred around the indentation regions for the larger particle sizes whereas the elastic properties are assumed for SiC particles and the matrix damage is not considered in the theoretical models. Fig. 6 shows indentation regions of specimens having a volume fraction of 30% and particle sizes 20, 53, 167 and 478 lm. The particle cracks are observed especially for particle sizes of 167 and 478 lm. Therefore, the particle cracking contributes the permanent indentation depth to reduce; hence a lower indentation depth is measured than the predicted value. The particle cracking has an increasing effect of the estimation error. The experimental and numerical indentation depths decrease evidently as the particle size increases for a certain volume fraction. Thus, the inter-particle distance increases as the particle size increases for a certain volume fraction and the particle number decreases (Figs. 2 and 3). The small particles result in a higher stiffness. However, the large particles make the microstructure to be more ductile and to exhibit a lower resistance to the indentation deformation. Fig. 7 shows the effect of the particle size for a volume fraction of 20% on the equivalent residual stress reqv and plastic strain eeqv distributions in the matrix after the load is removed completely. The elastic ceramic particles are removed in the residual stress and strain distributions. The blank elements are ceramic particles. A transverse stress band is formed around the ceramic particles underneath the indenter, and enlarges laterally due to increasing indentation deformation in the aluminum matrix as the particle size is increased. As the volume fraction is kept con-
Fig. 6. Indentation surfaces of the PRMMC specimens with a volume fraction of 30% and particle size: (a) 20, (b) 53, (c) 167 and (d) 478 lm.
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Fig. 7. Effect of particle size on the residual von Mises stress and equivalent plastic strain distributions in the region underneath the indenter: (a) P s ¼ 20 lm ðV f ¼ 20%Þ, (b) P s ¼ 53 lm ðV f ¼ 20%Þ, (c) P s ¼ 167 lm ðV f ¼ 19:9%Þ and (d) P s ¼ 478 lm ðV f ¼ 17:9%Þ (see Table 5).
stant (20%) the mean residual stress level reduces with increasing particle size since most of the indentation load is transferred to the matrix and less number of ceramic particles. The residual stress levels decrease, the local stress concentration region enlarges and the indentation depth increases with increasing particle size. In addition, the residual stress and strain levels in the indentation region are dependent on the random particle distribution. The plastic
strains eeqv concentrate underneath the indenter and decay away from the indentation region. The particle size affects markedly the residual strain distributions through the aluminum matrix. A thin transverse strain band is formed for a microstructure with small particles in size (Fig. 7a) and the residual strains spread over a large region for larger particles in size (Fig. 7d). The random particle distribution also affects the residual strain distributions of the
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Fig. 8. Effect of particle volume fraction V f for a particle size of 167 lm on the residual von Mises stress and equivalent plastic strain distributions in the region underneath the indenter: (a) V f ¼ 0:0, (b) V f ¼ 10% (9.9%), (c) V f ¼ 20% (19.9%) and (d) V f ¼ 30% (29.9%) (see Table 5).
matrix surrounding these particles. Thus, the residual strain distribution is highly non-uniform for smaller particles ð20 lmÞ and becomes more uniform for larger particles ð478 lmÞ. The indentation depth decreases with increasing volume fraction of the particles. This becomes more evident for the large particle sizes. Fig. 8 shows the effect of the particle volume fraction for a certain particle size (167 lm) on the residual von Mises stress reqv and residual strain eeqv distributions in the limited region
underneath the indenter. The unreinforced Al 1080 (without particles) has continuous residual stress and strain distributions. However, the residual stress and strains concentrate in the metal matrix around the ceramic particles having a particle size of 167 lm for the particle volume fractions 10 (9.99 exactly), 20 (19.9 exactly) and 30 (29.9 exactly) per percent. The stress and strain distributions are uniform for the unreinforced Al 1080, but they become discontinuous as the particle volume fraction is in-
R. Ekici et al. / Materials and Design 31 (2010) 2818–2833
creased. In addition, the stress and strain distributions are dependent on the random particle dispersion; thus, they are formed around the elastic particles with respect to the random particle arrangement. A transverse stress band appears in the metal matrix around the ceramic particles underneath the indenter. The residual stresses spreads over a large region in the matrix for a lower particle volume fraction and concentrates in a narrow region underneath the indenter as the particle volume fraction is increased. The mean stress levels also reduce. The residual strain eeqv regions are localized underneath the indenter and the peak strain levels decay away from the indentation region. The random particle dispersion affects the residual strain levels and distributions around the ceramic particles in case the local particle volume fraction gets higher. Apalak et al. [33] showed that the local particle concentration increased in the limited region underneath the indenter. The hydrostatic pressure results in a volumetric compression in soft matrix than those in reinforced stiffer matrix and a small increase in the particle concentration is also observed. Figs. 7 and 8 show this volumetric change in the region under the indenter. This re-
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quires a larger indentation load to achieve a certain indentation depth. The enhancement of local particle concentration is observed in the SEM micrographs taken from the cross-sections of the indentation regions of the specimens having the particle volume fractions of 10%, 20% and 30% and a particle size of 167 lm (Fig. 9). The indentation depth is decreased and more ceramic particles concentrate around the free specimen surfaces as the volume fraction is increased. In addition, a limited matrix concentration results in the applied load to be carried by the ceramic particles rather than the metal matrix, consequently, the ceramic particles are observed to be cracked for the high particle volume fractions. Fig. 10 shows the effect of the particle size on the local particle concentration in the SEM micrographs taken from the cross-sections of the indentation regions of the specimens having particle sizes 20, 53, 167, 478 lm for a particle volume fraction of 20%. The enhancement in the local particle concentration is more evident for the small particle sizes (20 and 53 lm) than the large particle sizes (167 and 478 lm). The high particle volume fraction and the small particle sizes affect the local particle volume fraction during the indentation test. The randomness of the particle dispersion espe-
Fig. 9. SEM micrographs of the cross-sections of the indentation regions of PRMMC specimens having a particle size of 167 lm and particle volume fractions V f : (a) 10%, (b) 20% and (c) 30%.
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cially under the indenter affects both residual stress and strain distributions as well as the indentation depth. Figs. 11 and 12 show the effects of particle size, particle volume fraction and random particle dispersion on the deformed surface profiles and the indentation depths for each particle volume fraction V f ¼ 0:10; 0:20; 0:30 and for each the particle size P s ¼ 20;
53; 167; 478 lm based on ten random particle distributions for each case. The random ceramic particle distribution affects slightly the deformed surface profiles of indentation region for the large particle sizes (Ps ¼ 167 and 478 lm) and for the small volume fractions (V f ¼ 0:10 and 0.20). A random particle distribution affects evidently the deformed surface profiles for a small particle size
Fig. 10. SEM micrographs of cross-sections of the indentation regions of PRMMC specimens having a volume fraction of 20% and particle sizes P s : (a) 20, (b) 53, (c) 167 and (d) 478 lm.
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20 µm 53 µm 167 µm 478 µm
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40
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Fig. 11. The effects of random particle distributions on the surface profiles and the indentation depths of PRMMCs having particle sizes P s ¼ 20; 53; 167 and 478 lm and the particle volume fractions a) V f ¼ 10%, (b) 20% and (c) 30% (see Table 5).
ðPs ¼ 20 and 53 lmÞ and a large volume fraction ðV f ¼ 0:30Þ and results in small fluctuations in the deformed surface profiles corresponding to the ceramic particles. The smooth deformed indentation surface is degenerated with increasing particle volume fraction and decreasing particle size since more ceramic particles are located near the material free surface. Furthermore, the peak indentation depth is affected evidently by the random particle distribution especially in the small particle sizes and in the large volume fractions.
5. Conclusions This study investigates the effects of particle size, particle volume fraction, particle random dispersion and local particle concentration on both the indentation depth and the residual stress and strain distributions of an Al 1080/SiC particle reinforced metal matrix. The indentation depth decreased with increasing particle volume fraction but increased with increasing particle size. The experimental and numerical indentation depths were in good agreement if the changes in local particle concentration are considered. The random local particle concentration underneath the indenter appeared as an important parameter affecting the indentation depth. In case the random particle distribution is ignored the error levels between the experimental and numerical
indentation depths increase with increasing particle size rather than the particle volume fraction depending on the random particle distribution. The deformed surface profiles and the peak indentation depths are considerably affected by the random particle distribution, especially for small particle sizes and high volume fractions. The deformed surface profile is degenerated with increasing particle volume fraction and decreasing particle size since more ceramic particles are located around the free surface. The random particle dispersion also effects on the residual stress and strain distributions and levels. The residual stress concentrates underneath the indenter for small particle size and spreads over a large zone for large particle sizes. The residual strains only concentrate underneath the indenter and spreads over a slightly large region for large particle sizes. As the volume fraction is increased the residual strains and stresses concentrate in a limited region underneath the indenter by forming a stress band form. The random particle locations affect the formation of stress and strain distributions.
Acknowledgements Authors would like to thank for the financial support of the Sci_ entific and Technological Research Council of Turkey (TÜBITAK) under the contract: 106M020 and the Scientific Research Project Division of Erciyes University under the contract: FBT-06-30.
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Fig. 12. The effects of random particle distributions on the surface profiles and the indentation depths of PRMMCs having volume fractions V f ¼ 10%; 20% and 30% in the particle sizes a) P s ¼ 20, (b) 53, (c) 167 and (d) 478 lm (see Table 5).
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Contents lists available at ScienceDirect
Materials and Design journal homepage: www.elsevier.com/locate/matdes
Effects of random particle dispersion and size on the indentation behavior of SiC particle reinforced metal matrix composites Recep Ekici a, M. Kemal Apalak a,*, Mustafa Yıldırım b, Fehmi Nair a a b
Department of Mechanical Engineering, Erciyes University, Kayseri 38039, Turkey Graduate School of Natural and Applied Sciences, Erciyes University, Kayseri 38039, Turkey
a r t i c l e
i n f o
Article history: Received 24 November 2009 Accepted 2 January 2010 Available online 14 January 2010 Keywords: Metal matrix composites Non-linear behavior Finite element analysis Scanning electron microscopy Powder processing
a b s t r a c t This study investigates the effects of particle size, volume fraction, random dispersion and local concentration underneath a spherical indenter on the indentation response of particle reinforced metal matrix Al 1080/SiC composites. The ceramic particles in certain sizes and volume fractions were randomly distributed through the composite structure in order to achieve a similar structure to an actual microstructure as possible. The particle size and volume fraction affected considerably indentation depths and deformed indentation surface profiles. The indentation depth increases with increasing particle size, but decreases with increasing particle volume fraction. The experimental indentation depths were in agreement with numerical indentation depths in case the local particle concentration effect is considered. The local particle concentration plays an important role on the peak indentation depth. For small particle sizes and large volume fractions the random particle distribution affects the deformed surface profiles as well as the indentation depths. However, its effect is minor on residual stress and strain distributions rather than levels in the indentation region. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Particle reinforced metal matrix composites (PRMMCs) have become very promising materials due to their significant advantages over conventional materials such as high specific modulus, improved resistance to wear, improved resistance to high cycle fatigue and fatigue crack threshold, higher stiffness-to-weight ratio, low coefficient of thermal expansion and high thermal conductivity. They offer relatively isotropic properties compared to short fiber or whisker reinforced counterparts and ability to be formed using conventional metal manufacturing processes such as rolling, forging and extrusion to produce the finished product with low cost [1–5]. Their mechanical properties, i.e. tensile, wear and fatigue, depend on some micro-structural parameters such as reinforcement particle distribution, size, volume fraction and orientation. Consequently, the hardness as well as indentation behaviors of PRMMCs have attracted the researchers in recent years. The indentation test requires minimum specimen preparation and mounting in comparison with other traditional methods on the determination of the mechanical behaviors of PRMMCs, and can be easily performed several times on a single specimen of small volume materials and miniaturized structures using appro* Corresponding author. Tel.: +90 352 437 4901; fax: +90 352 437 5784. E-mail address: [email protected] (M. Kemal Apalak). 0261-3069/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2010.01.001
priate load level and indenter tip geometry [6–8]. Numerical modeling of the indentation process allows understanding the deformation mechanism, stress and strain fields through the metal matrix around the ceramic particles and particle–matrix interaction [6]. The present theoretical and experimental studies on the indentation behavior of the particle reinforced metal matrix composites concentrated on the deformation characteristics and a relation between overall strength and indentation hardness [9–14]. Shen et al. [15] investigated experimentally the correlation between hardness values and tensile properties, and showed that the composites including large reinforcement particles tended to fracture during their tensile tests whereas the local predominant compressive loads in the hardness test prevented the pre-existing fractures particles to weaken the composite material, and the hardness test overestimated the overall tensile strength. Shen and Chawla [16] presented a simple relationship between the macro-hardness and tensile strength of PRMMCs. They indicated an increase in the local particle concentration underneath the indenter which caused a significant overestimation of the tensile strength in case the matrix strength was relatively low. Shen et al. [17] also verified that enhanced matrix flow contributed to a localized increase in particle concentration underneath the indenter and resulted in a significant overestimation of the overall composite strength via the hardness test based on a numerical study considering the effects of particle size, particle volume fraction and matrix aging characteristics on
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MMCs with reasonable accuracy [26], but the microstructure of particulated MMCs having randomly distributed particulate reinforcements. A new random structure in a certain particle size and volume fraction yields to different stress and strain fields underneath the spherical indenter, therefore, the stress analyses were repeated for different particle arrangements until a stable respond is achieved from the indentation tests. The indentation tests were performed at different points at reasonable distances of the produced specimens in order to consider randomness of particle locations. In case any arbitrary set of composite structures with random particle arrangements is considered the hardness and indentation depths were predicted in some errors in comparison with the experimental ones. However, the predicted and experimental hardness and indentation depths are in good agreement for the composite structures with random distributions similar to those of the specimens produced in a certain of particle size and volume fraction. 2. Numerical modeling The indentation behavior of metal matrix composite structure under a spherical indenter was investigated using the non-linear finite element method (ABAQUS/Standard finite element software) [29]. The geometrical, material non-linearities and non-linearity arising due to the large deformations in the contact surface of the metal matrix region induced by a rigid indenter were taken into account. The composite structure was simplified to an axisymmetrical structure as a square region of 3 3 mm in size. The matrix and ceramic particles were modeled using 22,500 eight-noded biquadratic axisymmetric quadrilateral solid (CAX8R) finite elements with reduced integration of 20 20 lm in size. The element size was kept constant through all analyses. In an actual composite structure the reinforcement particles are distributed randomly in the metal matrix, and the particle geometry and size are not uniTable 1 Mechanical and physical properties of Al 1080 and SiC [27]. Property
Al 1080
SiC
Modulus of elasticity (E) (GPa) Poisson’s ratio ðmÞ Density ðqÞ
70 0.33 2700
420 0.17 3100
150 Al 1080 (99.8%) SiC
100 Stress (MPa)
the interrelationship between tensile strength and macro-indentation hardness. Kozola and Shen [18] showed that the indentation hardness can not scale with the overall strength of a discontinuously reinforced aluminum due to increasing particle concentration or particle crowding effect in the region underneath the indenter although the indenter size is much greater than the reinforcement particle size. Shen and Guo [19] determined the stress–strain behavior of a compact material system composed of a soft and elastic–plastic matrix and linearly elastic hard particles using the non-linear finite element method, and then used this stress–strain diagram in the indentation model behaving the metal matrix composite like a homogeneous material. The homogeneous material and two-phase composite models differed significantly due to the increased particle concentration underneath the indenter in the two-phase composite model. Pereyra and Shen [7] observed a particle concentration enhancement in post-indented metal–ceramic composite specimens using a large indenter size via quantitative metallography. They performed quantitative metallography on the post-indented metal matrix composite specimens and observed an evident increase in particle concentration due to the relatively large negative dilatational strain in metal matrix in comparison with ceramic particles [8]. Ege and Shen [20] pointed that a material containing internal pores exhibited an indentation behavior opposite to two-phase composites since local pore crushing occurred underneath the indenter, leading to the underestimated overall mechanical strength of composite material. Micro- or nano-scale indentation can be performed to investigate the local indentation behavior of heterogeneous particle reinforced metal matrix composites. Rosenberger et al [21] used the micro-indentation to understand the effect of the depth and diameter of the reinforcement in the hardness of MMC model with one particle at its centroid, and showed that the hardness measurements might be overestimated by 15–74% depending on the method employed and an ideal measurement might be achieved by an indenter diameter at least twice the reinforcement diameter. Pramanik et al. [22] investigated micro-indentation behavior of PRMMCs based on the stress–strain fields underneath a spherical indenter during the loading and unloading stages of the indenter. Durst et al. [23] presented the finite element simulations of the nano-scale indentation to determine the influence of the shape and aspect ratio of particles on the single-phase indentation behavior in particle-matrix systems. They observed a transitional indentation behavior from particle to matrix which is observed experimentally in precipitation-hardened nickel-based super-alloys. Olivas et al. [24] investigated the thermal residual stresses in SiC particle reinforced Al matrix composites via the nano-indentation. Their experimental results were in good agreement with the finite element analysis and proved the general credibility of applying spherical nano-indentation in characterizing the local surface residual stresses in the ductile matrix of MMCs. Mussert et al. [25] used the nano-indentation experimentally to measure the hardness and elastic modulus of aluminum alloy 6061 reinforced with Al2O3 in three different heat treatment conditions. However, the reinforcement particles have a random dispersion in the metal matrix. In general, this random distribution can affect the indentation response of particle reinforced metal matrix composites. The present study addresses the effects of reinforcement size and volume fraction in random geometric arrangements of reinforcements on the indentation behavior of Al 1080/SiC PRMMCs under a spherical indenter. Our methodology assumes a random particle arrangement in a certain size and volume fraction in the composite structure, which is analogous with real random particulate composite structure instead of a composite structure having arrayed particles in an order [7,8,15–22]. A model of periodic arrays may represent the microstructure of fiber-reinforced
50
0 0
0.05
0.1
0.15 Strain
0.2
0.25
Fig. 1. The true stress–strain diagram of Al 1080 (elastic–plastic) [28] and SiC (elastic) particles [19].
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R. Ekici et al. / Materials and Design 31 (2010) 2818–2833
RP
RP
2
3
2
1
3
1
RP
RP
2
2
3
3
1
1
Fig. 2. Sample FEM models showing the random distributions of SiC particles with different sizes: (a) 20, (b) 53, (c) 167 and (d) 478 lm in a volume fraction of 20%.
Table 2 SiC particle sizes and volume fractions of PRMMCs in FEM models. Particle size P s ðlmÞ in experiments Particle size P s ðlmÞ in FEM models
20
53
20
167
60
478
160
480
Aimed volume fraction V f (%)
Necessary element number
Vf (%)
Achieved element number
Vf (%)
Achieved element number
Vf (%)
Achieved element number
Vf (%)
Achieved element number
10 20 30
2250 4500 6750
10 20 30
2250 4500 6750
10 20 30
2250 4500 6750
9.99 19.91 29.87
2240 4480 6720
7.68 17.92 28.16
1728 4032 6336
2821
R. Ekici et al. / Materials and Design 31 (2010) 2818–2833 Table 3 The chemical composition (Wt. %) of the matrix material Al 1080 [27]. Material
% Al
% Cu
% Fe
% Mg
% Ga
% Si
% Mn
% Ti
% Zn
%V
Al 1080
Min 99.8
Max 0.03
Max 0.15
Max 0.02
Max 0.03
Max 0.15
Max 0.02
Max 0.03
Max 0.03
Max 0.05
Fig. 3. Sample SEM micrographs showing the random distributions of SiC particles with different sizes: (a) 20, (b) 53, (c) 167 and (d) 478 lm in a volume fraction of 20% before the indentation.
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R. Ekici et al. / Materials and Design 31 (2010) 2818–2833
cate particles in larger sizes (53, 167 and 478 lm) than 20 lm these particles are generated approximately using the base mesh element size ð20 lmÞ. Consequently, the actual particle sizes of 53, 167 and 478 lm are approximated to 60, 160 and 480 lm in the finite element models, respectively. Table 2 shows that the particle sizes as well as overall volume fractions in the finite element models are very close to those of the specimens used in the experiments. Since SiC particles are randomly distributed in each finite element model, ten random base models are considered for each of volume fractions 10%, 20% and 30% and each of particle sizes 53, 167 and 478 lm leading to 120 models. However, 30,000 random models for each particle size and each volume fraction are generated in order to determine the effect of increasing particle concentration underneath the indenter. A region of 1 1 mm2 in size in composite structure underneath the indenter is considered to evaluate the increase of particle concentration, and then the first ten models among ones with the densest concentration are chosen for the stress analyses for each particle size and volume fraction. All calculations were performed in an AMD Opteron Server with 4 CPUs in 2.4 GHz and 8 Gb Ram.
form. The three-dimensional model of this actual structure brings some computational difficulties. A region of 6 6 3 mm in size requires 13,500,000 three-dimensional solid finite elements with an edge length of 20 lm because the minimum particle size in the study is 20 lm. The total number of degrees of freedom in the model is extensive for a statistical study. Al 1080 (aluminum alloy in 99.8% purity) is an elastic-plastic matrix material whereas SiC (Silicon Carbide) particles are elastic. Mechanical and physical properties of Al 1080 and SiC particles are given in Table 1. Fig. 1 shows true stress–strain diagrams of Al 1080 and SiC. The yield stress of Al matrix was determined from its stress–strain curve based on the offset rule (0.2% offset). The aluminum has a yield stress of 24 MPa and a yield strain of 0.007. SiC particles were assumed to be perfectly bonded with the Al 1080 matrix and particle fracture was not considered. Quasi-static indentation was performed by pressing a rigid axisymmetric circular indenter onto the top surface of the composite structure. The right half of indenter and composite structure was considered. The symmetry conditions were applied to all nodes along the symmetry axis of the half-region whereas the bottom edge was fixed. The degrees of freedom of the indenter with a radius of 0.794 mm were represented with only a reference point whose horizontal displacement and rotation about the axis normal to the problem plane were fixed. The indenter was meshed using fifty rigid two-noded shell (RAX2) finite elements. The finite element models were considered for the volume fractions V f ¼ 10%; 20% and 30% for each of particle sizes Ps ¼ 20; 53; 167 and 478 lm (Fig. 2). The same particle sizes in the experiments were used for comparison. The simulations conform to the experimental requirements for the Rockwell T-scale hardness test. The direct indentation depth (in lm) instead of hardness number is considered since our objective is simply to define a reasonable numerical measurement of hardness indentation so as to facilitate a direct but qualitative comparison with the experimental results. A pressure load of 15 kg (150 N), that Rockwell T-scale hardness test requires is used in the finite element models. A flexible code was developed in Python language [30] in order to implement all variables representing the geometric and material properties of composite material to each of excessive number of finite element models, and the generated input file was evaluated by ABAQUS/Standard finite element software. The ceramic particles in a specific volume fraction are distributed randomly through the metal matrix the volume fraction of SiC particles is adjusted as a percentage of fixed finite element number (22,500), thus a volume fraction of 10% for SiC particles in the matrix corresponds to 2250 finite elements which were defined as SiC particles. SiC particles are selected randomly and saved in an element set. For each new analysis this element set was changed completely. In order to lo-
3. Experimental study Specimens were prepared using 99.8% pure aluminum (Al 1080) and 99.5% pure silicon carbide (SiC) powders. The chemical composition of the matrix material Al 1080 alloy is given in Table 3. The Al 1080-powder has a mean particle size of 44 lm whereas SiC powder has four different average sizes P s of 20, 53, 167 and 478 lm. All metal matrix composite specimens were produced using the powder metallurgy method in the reinforcement volume fractions V f of 10%, 20% and 30% for each reinforcement particle size. This method requires some processes, such as cold pressing and sintering, or hot pressing. Thus, the matrix (Al 1080) and the reinforcement (SiC) powders were blended by a motorized mixer to produce a homogeneous particle distribution, and were cold pressed. Finally, the compacted powder mixtures were hot pressed uniaxially in a single-end circular die made of hot-work tool steel under a pressure of 350 MPa inside a protective argon atmosphere at a temperature of 610–615 °C for a sintering time of 30 min. The cylindrical specimens are of 3 mm in height and 8 mm in radius. The standard Rockwell T-scale test was employed succesfully to the hardness indentation of unhardened materials, such as metals softer than hardened steel or hard alloys [31]. The hardness tests were performed by pressing a spherical steel indenter with a diameter of 1.588 mm into both the top or bottom at free surfaces and cross-sections perpendicular to hot pressing direction of the specimens at a minor and major load of 30 and 150 N, respectively. Six readings (at least) were taken from these sections of the specimens
Table 4 Experimental indentation results obtained from Rockwell T-scale hardness test. Indentation depth on the specimen cross-sections ðlmÞ
Indentation depth on the specimen surfaces ðlmÞ
1
2
3
4
5
6
1
2
3
4
5
6
10 20 30
66.08 48.96 39.68
67.44 49.52 40.56
67.60 49.28 37.92
67.20 49.36 40.24
67.76 47.08 38.48
66.76 50.61 42.68
66.76 50.88 39.48
66.64 51.92 39.60
65.08 49.12 43.32
66.64 47.04 41.04
64.84 50.12 42.52
64.44 48.44 42.74
66.44 49.37 40.69
53
10 20 30
68.96 53.24 44.16
66.64 49.16 46.32
70.32 54.84 45.44
67.52 52.64 45.24
69.56 53.16 45.80
68.40 52.86 46.16
68.92 50.48 50.40
69.16 51.96 51.80
67.12 52.04 48.76
67.96 51.04 51.46
67.44 53.48 51.04
68.64 52.24 50.56
68.39 52.26 48.09
167
10 20 30
70.60 60.00 47.76
69.40 57.76 51.28
67.12 59.12 52.40
68.08 58.80 51.80
70.50 59.58 51.20
70.22 60.08 52.00
70.64 59.68 48.08
70.96 59.72 50.84
70.40 61.20 50.00
72.24 62.00 50.24
69.56 60.14 51.42
69.84 59.82 50.38
69.97 59.83 50.62
478
10 20 30
72.52 59.20 49.40
73.60 62.56 53.64
69.44 59.52 49.92
70.20 63.36 49.76
70.06 62.28 52.08
72.44 59.86 53.72
73.84 63.44 52.18
76.45 63.52 51.88
72.24 66.44 54.72
71.00 64.52 48.56
70.68 62.32 48.92
72.50 61.12 52.56
72.09 62.35 51.45
Particle size P s ðlm
Volume fraction V f (%)
20
Mean indentation depth ðlmÞ
Table 5 Numerical indentation depths for low local particle volume fractions. Volume fraction Vf , %
20
10 20 30
10.08 20.13 29.49
62.42 33.74 17.55
10.04 18.57 29.81
64.06 37.42 22.42
10.00 20.00 30.25
60.53 34.89 22.90
9.96 20.97 30.17
65.78 34.17 15.90
10.28 19.57 30.37
51.26 36.33 12.90
9.20 19.37 29.93
60.90 36.49 20.62
8.60 21.41 28.77
61.39 32.32 19.53
10.04 19.93 29.45
58.71 30.81 16.78
10.12 21.25 30.41
54.78 34.43 23.00
9.80 20.37 29.53
59.94 33.18 21.90
59.98 34.38 19.35
53ð 60Þ
10 20 30
11.28 20.53 31.21
84.35 70.07 41.26
9.72 19.09 30.85
82.39 70.67 41.74
10.92 15.61 28.93
82.80 71.72 42.62
9.36 19.45 30.37
82.09 71.87 39.74
8.44 22.32 31.45
97.67 62.06 46.40
11.28 20.53 29.77
84.39 66.38 41.33
11.76 18.37 28.93
91.73 68.42 37.99
10.56 20.88 30.61
89.09 68.65 48.14
8.28 21.37 29.05
96.00 65.36 46.77
9.60 18.13 30.21
83.81 63.38 41.77
87.43 67.86 42.78
167ð 160Þ
9.99 19.91 29.87
6.00 17.61 28.49
134.39 106.28 74.68
12.48 24.25 31.37
134.09 104.70 63.42
11.64 14.73 23.37
132.43 103.72 73.92
7.68 13.69 24.00
134.34 104.28 72.42
10.24 17.29 21.77
135.81 107.12 74.51
14.57 21.77 26.25
117.80 100.39 68.99
10.80 29.77 21.45
136.64 92.13 68.30
2.56 20.97 35.53
141.43 101.52 76.74
10.24 11.85 32.97
134.43 96.61 79.84
13.29 25.61 35.21
137.66 108.30 74.64
133.90 102.51 72.75
478ð 480Þ
7:68 17.92 28.16
0.00 5.76 36.49
150.41 131.78 115.05
0.00 16.33 30.73
150.68 133.96 117.67
0.00 23.77 30.73
149.74 131.23 111.43
3.20 3.96 20.17
149.01 132.82 118.53
0.00 24.00 26.65
149.81 138.36 118.40
0.00 23.05 24.97
150.13 136.09 117.18
0.00 21.12 27.33
147.56 138.70 107.85
0.00 1.92 25.73
151.31 136.95 108.63
0.00 1.92 18.25
152.20 137.06 107.64
0.00 23.05 30.65
150.45 135.60 117.74
150.13 135.26 114.01
Numerical indentation depth, a
1
a
2
a
3
a
4
a
5
a
6
a
7
a
8
a
9
a
Mean indentation depth ðlmÞ
10
Local particle volume fraction in a region of 1 1 mm2 underneath the indenter.
Table 6 Numerical indentation depths for high local particle volume fractions.
a
Numerical indentation depth,
lm
Particle size P s ; lm
Volume fraction Vf , %
a
1
a
2
a
a
4
a
5
a
6
a
a
8
a
9
a
10
Mean indentation depth ðlmÞ
20
10 20 30
12.44 22.81 32.73
53.96 29.83 14.94
12.28 22.77 32.85
57.82 36.05 20.33
12.04 22.73 32.65
58.57 29.99 15.59
12.00 22.77 32.81
56.28 33.15 18.22
11.96 22.73 32.73
57.11 37.94 14.61
12.12 22.73 32.69
56.23 33.13 22.44
12.04 22.69 33.73
53.95 40.84 15.36
12.00 23.05 33.25
55.80 36.88 18.78
12.40 22.93 32.69
58.02 32.58 17.74
12.04 22.89 32.73
60.88 40.34 19.30
56.86 35.07 17.73
ð53ð 60Þ
10 20 30
16.57 27.01 36.61
56.91 58.76 46.42
15.25 26.49 36.49
70.29 55.29 47.52
15.37 26.29 37.33
70.40 58.20 24.44
15.29 26.41 36.37
62.19 68.07 28.67
15.21 27.13 36.33
72.52 50.20 40.73
15.09 26.77 37.58
95.02 52.29 25.31
15.85 26.17 36.45
71.90 46.71 48.10
15.37 27.01 36.45
73.27 48.17 33.15
15.73 26.65 36.45
80.02 55.64 20.74
15.37 26.21 36.33
68.92 52.77 50.12
72.14 54.61 36.52
167ð 160Þ
9.99 19.91 29.87
23.05 33.29 42.25
76.80 54.52 33.76
23.37 34.25 44.82
73.52 58.29 38.61
23.37 34.09 42.90
71.25 52.24 47.85
22.73 33.93 42.26
92.66 65.19 50.88
23.05 33.29 41.30
72.33 66.10 47.83
25.93 34.57 43.18
77.26 50.05 31.55
22.09 35.17 43.82
82.84 68.48 38.73
23.37 33.29 42.26
81.24 54.29 50.88
23.37 33.29 41.94
85.72 57.43 33.38
22.41 33.61 41.94
89.12 66.25 36.11
80.27 59.28 40.96
478ð 480Þ
17.68 17.92 28.16
45.13 53.78 62.42
84.86 64.05 73.33
45.13 57.62 65.31
76.72 65.95 66.89
45.13 55.70 63.39
105.63 81.75 76.35
45.13 58.58 58.58
73.04 47.60 75.19
44.18 67.23 77.19
76.67 50.47 66.46
49.74 57.62 58.58
92.76 59.30 50.90
43.22 56.90 63.71
100.94 73.00 44.94
46.10 53.78 64.35
79.55 45.45 66.95
45.13 53.74 66.75
79.10 69.00 40.14
44.18 66.59 59.54
69.90 82.52 48.60
83.92 63.91 60.98
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R. Ekici et al. / Materials and Design 31 (2010) 2818–2833
a
lm
Particle size P s ; lm
Local particle volume fraction in a region of 1 1mm2 underneath the indenter. 2823
R. Ekici et al. / Materials and Design 31 (2010) 2818–2833
to improve the reliability of the readings. In order to achieve a suitable positioning on the partitioned specimens during the hardness tests the specimens cut into two pieces were hot mounted into an acrylic hot mounting resin, and a free surface of 3 16 mm2 on the specimens was grinded, cleaned and polished before the hardness tests. The standard metallography was implemented on all samples [32]. The specimens were first hand-ground with SiC grinding papers through the sequence: 180, 240, 320, 400, 600, 1200 and 4000 grit and polished with a diamond paste to obtain a surface finish of 1 lm on an automatic polisher. Scanning electron microscopy (Leo Ò 440 SEM) and macroscopy (Nikon Stereozoom S-800) were used for photographic studies of indented and unindented sample surfaces. Fig. 3 shows SEM micrographs of the metal matrix composites with SiC particles of Ps ¼ 20; 53; 167 and 478 lm in size and a volume fraction of 20% in the Al matrix. These micrographs were taken at a magnification scale of 70 zoom (200 lm).
4. The effects of particle size and random particle dispersion
Indentation depth (µm)
In order to determine the effects of both particle size and volume fraction of the randomly dispersed reinforcement particles in the matrix on the indentation depth the non-linear stress analyses were carried out for PMMCs with 20, 53, 167 and 478 lm in particle size and 10%, 20% and 30% in volume fractions. Fig. 3
80 70 60 50 40 478
0.1
shows the SEM micrographs of the specimen sections with 20, 53, 167 and 478 lm in particle size and 20% in volume fraction. After the indenter was removed completely from the indentation region the six indentation depths taken from both cross-sections and free surfaces of specimens were compared in Table 4. The measurements of the indentation depth are very close on both free surfaces and sample cross-sections. As the particle size is increased the indentation depth is increased. This increase becomes evident as the volume fraction is increased. As the volume fraction is increased the region underneath the indenter behaves stiffer and the indentation depth decreases for all particle sizes. However, the elasto-plastic matrix deforms considerably in comparison with the elastic particles as the particle size is increased for a certain volume fraction, and the indentation depth increases relatively. Tables 5 and 6 show numerical indentation depths based on the non-linear finite element analyses for particle sizes ðP s Þ of 20, 53, 167 and 478 lm and volume fractions ðV f Þ of 10%, 20% and 30%. In order to show the change in the local volume fraction underneath the indenter the reinforcement particles were randomly distributed and the local volume fractions were calculated in a region of 1 1 mm2 for each of particle sizes and volume fractions. The ten numerical indentation depths and local volume fractions were tabulated in Tables 5 and 6, respectively, considering the local lower and higher particle volume fractions underneath the indenter than the overall volume fractions. Table 5 shows the indentations depths of the random particle dispersions in which the local vol-
Indentation depth (µm)
2824
150 100 50 478
0.1
0.2
0.2
167
167 53
Volume fraction (Vf)
20 0.3
Indentation depth (µm)
Particle size (Ps, µm)
53
Particle size (Ps, µm)
20 0.3
Volume fraction (Vf)
100 80 60 40 20 478
0.1
0.2 167 Particle size (P , µm) s
53 20 0.3
Volume fraction (Vf)
Fig. 4. Couple effect of both particle size (20, 53, 167 and 478 lm) and volume fraction (10%, 20% and 30%) on: (a) the experimental (Table 4), and numerical mean peak indentation depths (lm), (b) Table 5, and (c) Table 6.
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R. Ekici et al. / Materials and Design 31 (2010) 2818–2833
ume fractions are close to the overall volume fractions. The indentation depth increases with increasing particle size. However, the indentation depth decreases considerably with increasing volume. The numerical indentation depths exhibit similar trends to the experimental ones, but the numerical indentation depths deviate from the experimental indentation depths as the particle is increased. The random particle dispersion, especially underneath the indenter affects evidently the indentation depth. Table 6 also shows the numerical indentation depths in which the local volume fractions are considerably larger than the overall volume fractions. Similarly, the indentation depth increases with increasing particle size whereas increasing the volume fraction results in considerable decreases in the indentation depth. The numerical indentation depths exhibit a similar behavior to those of the experimental indentation depths. However, a considerable increase is observed in the local particle volume fraction underneath the indenter, which is causing evident decreases in the indentation depths in comparison with those in Table 5. Therefore, the numerical indentation depths approach to the experimental ones. The randomness of the ceramic particle distribution through the metal matrix af-
fects considerably the indentation depth; therefore, the numerical and experimental indentation depths can be expected to converge only if the random particle distribution and both particle geometry and size are similar in the sections of both the produced specimen and the numerical model. Fig. 4 shows the couple effect of both particle size and volume fraction on the mean peak indentation depth based on the hardness tests (Table 4) and numerical analyses (Tables 5 and 6). The experimental and numerical indentation depths show similar trends; thus, the indentation depth increases with increasing particle size but decreases with increasing volume fraction. Figs. 4b and c are plotted based on the random particle distributions with a close/larger local particle volume fraction to/than the overall particle volume fraction, respectively. Fig. 4c exhibits similar indentation depths to the experimental ones (Fig. 4a) on the contrary to Fig. 4b. It is evident that the local particle volume fraction, consequently, the random particle dispersion in the local region underneath the indenter as well as through the whole structure affects considerable the numerical and experimental indentation measurements.
200
110
Experimental Numerical
180
140
← Vf=0.20
120
← Vf=0.30
100 80
← Vf=0.10 ← Vf=0.20 ← Vf=0.30
60
90 Indentation depth (μm)
Indentation depth (μm)
160 ← Vf=0.10
Experimental Numerical
100
←
80
←
70
V =0.10 f
← ← Vf=0.20 ← V =0.30 ← f
60 50 40 30
40
20 20 20 53
167
10
478
20 53
Particle size (Ps, μm)
167
478 Particle size (Ps, μm)
90 Experimental Numerical
120
← Ps=478 μm
100 80
← Ps=167 μm Ps=478 μm ← P =167 μm ← s ← P =53 μm ←
60
Experimental Numerical
80
Indentation depth (μm)
Indentation depth (μm)
140
70 ←
60
Ps=478 μm ← ← P =167 μm ← s P =53 μm s ← Ps=167 μm ← P ← s=20 μm Ps=53 μm
50 40 30
s
40
Ps=20 μm
20
← P =20 μm s
←
←
20 0.1
0.2 Volume fraction (Vf)
0.3
10
0.1
0.2
0.3
Volume fraction (Vf)
Fig. 5. Individual effects of a) particle size and b) volume fraction on the mean peak indentation depths (lm) based on both the experiments and numerical analyses.
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Figs. 5a and b show individual effect of each particle size and volume fraction on the mean peak indentation depth based on the experimental and numerical analyses, respectively. As the particle volume fraction is increased from 10% to 30% for a particle size of 20 lm the mean indentation depth decreases by 39% and 68% based on the experimental and numerical results, respectively. This decrease appears as 69% in the numerical results for the high local particle volume fractions. As the particle size is increased from 20 to 478 lm for a volume fraction of 30% the mean indentation depth increases by 26% and 489% based on the experimental and numerical results, respectively and this corresponds to 244% in the numerical results for high local particle volume fractions. In case of the lower local particle concentrations (Tables 4 and 5, Fig. 5) the error levels between the experimental and numerical indentation depths are relatively less for small particle sizes (20– 53 lm), and the error levels increase with increasing particle size and volume fraction. The error level becomes minimal (9.7%) for a particle size of 20 lm and a volume fraction of 10% and maximal (122%) for a particle size of 478 lm and a volume fraction of 30%. In case of the higher local particle concentrations (Tables 4–6, and Fig. 5) the error level minimizes to 0.92% for the particle size of 167 lm and a volume fraction of 20% and maximizes to 56% for a particle size of 20 lm and a volume fraction of 30%. The local particle concentration underneath the indenter affects considerably the indentation depths. As the local particle concentration increases underneath the indenter this limited region behaves stiffer; therefore, and the indentation depth decreases. In practice, the composite has three-dimensional random particle size and dispersion on the contrary to the two-dimensional axisymmetric structure and constant square element geometry. In addition, the actual structure has particles having highly irregular shape and sharp corners and random local particle volume fractions depending on the overall particle volume concentration. The present theoretical model considers the elasto-plastic behavior of the matrix material and geometrical non-linearity occurring during the local
deformations of the indentation surface, and can predict accurately the general effect of both particle volume fraction and particle size. If the actual three-dimensional structure of the specimen can be transferred to the finite element model the error levels between the experimental and numerical indentation depths could be decreased evidently. However, this study shows that the random particle dispersion affects obviously the indentation behavior of the structure even for the same particle volume fraction and size. In addition, some cracks occurred around the indentation regions for the larger particle sizes whereas the elastic properties are assumed for SiC particles and the matrix damage is not considered in the theoretical models. Fig. 6 shows indentation regions of specimens having a volume fraction of 30% and particle sizes 20, 53, 167 and 478 lm. The particle cracks are observed especially for particle sizes of 167 and 478 lm. Therefore, the particle cracking contributes the permanent indentation depth to reduce; hence a lower indentation depth is measured than the predicted value. The particle cracking has an increasing effect of the estimation error. The experimental and numerical indentation depths decrease evidently as the particle size increases for a certain volume fraction. Thus, the inter-particle distance increases as the particle size increases for a certain volume fraction and the particle number decreases (Figs. 2 and 3). The small particles result in a higher stiffness. However, the large particles make the microstructure to be more ductile and to exhibit a lower resistance to the indentation deformation. Fig. 7 shows the effect of the particle size for a volume fraction of 20% on the equivalent residual stress reqv and plastic strain eeqv distributions in the matrix after the load is removed completely. The elastic ceramic particles are removed in the residual stress and strain distributions. The blank elements are ceramic particles. A transverse stress band is formed around the ceramic particles underneath the indenter, and enlarges laterally due to increasing indentation deformation in the aluminum matrix as the particle size is increased. As the volume fraction is kept con-
Fig. 6. Indentation surfaces of the PRMMC specimens with a volume fraction of 30% and particle size: (a) 20, (b) 53, (c) 167 and (d) 478 lm.
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Fig. 7. Effect of particle size on the residual von Mises stress and equivalent plastic strain distributions in the region underneath the indenter: (a) P s ¼ 20 lm ðV f ¼ 20%Þ, (b) P s ¼ 53 lm ðV f ¼ 20%Þ, (c) P s ¼ 167 lm ðV f ¼ 19:9%Þ and (d) P s ¼ 478 lm ðV f ¼ 17:9%Þ (see Table 5).
stant (20%) the mean residual stress level reduces with increasing particle size since most of the indentation load is transferred to the matrix and less number of ceramic particles. The residual stress levels decrease, the local stress concentration region enlarges and the indentation depth increases with increasing particle size. In addition, the residual stress and strain levels in the indentation region are dependent on the random particle distribution. The plastic
strains eeqv concentrate underneath the indenter and decay away from the indentation region. The particle size affects markedly the residual strain distributions through the aluminum matrix. A thin transverse strain band is formed for a microstructure with small particles in size (Fig. 7a) and the residual strains spread over a large region for larger particles in size (Fig. 7d). The random particle distribution also affects the residual strain distributions of the
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Fig. 8. Effect of particle volume fraction V f for a particle size of 167 lm on the residual von Mises stress and equivalent plastic strain distributions in the region underneath the indenter: (a) V f ¼ 0:0, (b) V f ¼ 10% (9.9%), (c) V f ¼ 20% (19.9%) and (d) V f ¼ 30% (29.9%) (see Table 5).
matrix surrounding these particles. Thus, the residual strain distribution is highly non-uniform for smaller particles ð20 lmÞ and becomes more uniform for larger particles ð478 lmÞ. The indentation depth decreases with increasing volume fraction of the particles. This becomes more evident for the large particle sizes. Fig. 8 shows the effect of the particle volume fraction for a certain particle size (167 lm) on the residual von Mises stress reqv and residual strain eeqv distributions in the limited region
underneath the indenter. The unreinforced Al 1080 (without particles) has continuous residual stress and strain distributions. However, the residual stress and strains concentrate in the metal matrix around the ceramic particles having a particle size of 167 lm for the particle volume fractions 10 (9.99 exactly), 20 (19.9 exactly) and 30 (29.9 exactly) per percent. The stress and strain distributions are uniform for the unreinforced Al 1080, but they become discontinuous as the particle volume fraction is in-
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creased. In addition, the stress and strain distributions are dependent on the random particle dispersion; thus, they are formed around the elastic particles with respect to the random particle arrangement. A transverse stress band appears in the metal matrix around the ceramic particles underneath the indenter. The residual stresses spreads over a large region in the matrix for a lower particle volume fraction and concentrates in a narrow region underneath the indenter as the particle volume fraction is increased. The mean stress levels also reduce. The residual strain eeqv regions are localized underneath the indenter and the peak strain levels decay away from the indentation region. The random particle dispersion affects the residual strain levels and distributions around the ceramic particles in case the local particle volume fraction gets higher. Apalak et al. [33] showed that the local particle concentration increased in the limited region underneath the indenter. The hydrostatic pressure results in a volumetric compression in soft matrix than those in reinforced stiffer matrix and a small increase in the particle concentration is also observed. Figs. 7 and 8 show this volumetric change in the region under the indenter. This re-
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quires a larger indentation load to achieve a certain indentation depth. The enhancement of local particle concentration is observed in the SEM micrographs taken from the cross-sections of the indentation regions of the specimens having the particle volume fractions of 10%, 20% and 30% and a particle size of 167 lm (Fig. 9). The indentation depth is decreased and more ceramic particles concentrate around the free specimen surfaces as the volume fraction is increased. In addition, a limited matrix concentration results in the applied load to be carried by the ceramic particles rather than the metal matrix, consequently, the ceramic particles are observed to be cracked for the high particle volume fractions. Fig. 10 shows the effect of the particle size on the local particle concentration in the SEM micrographs taken from the cross-sections of the indentation regions of the specimens having particle sizes 20, 53, 167, 478 lm for a particle volume fraction of 20%. The enhancement in the local particle concentration is more evident for the small particle sizes (20 and 53 lm) than the large particle sizes (167 and 478 lm). The high particle volume fraction and the small particle sizes affect the local particle volume fraction during the indentation test. The randomness of the particle dispersion espe-
Fig. 9. SEM micrographs of the cross-sections of the indentation regions of PRMMC specimens having a particle size of 167 lm and particle volume fractions V f : (a) 10%, (b) 20% and (c) 30%.
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cially under the indenter affects both residual stress and strain distributions as well as the indentation depth. Figs. 11 and 12 show the effects of particle size, particle volume fraction and random particle dispersion on the deformed surface profiles and the indentation depths for each particle volume fraction V f ¼ 0:10; 0:20; 0:30 and for each the particle size P s ¼ 20;
53; 167; 478 lm based on ten random particle distributions for each case. The random ceramic particle distribution affects slightly the deformed surface profiles of indentation region for the large particle sizes (Ps ¼ 167 and 478 lm) and for the small volume fractions (V f ¼ 0:10 and 0.20). A random particle distribution affects evidently the deformed surface profiles for a small particle size
Fig. 10. SEM micrographs of cross-sections of the indentation regions of PRMMC specimens having a volume fraction of 20% and particle sizes P s : (a) 20, (b) 53, (c) 167 and (d) 478 lm.
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20 µm 53 µm 167 µm 478 µm
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Fig. 11. The effects of random particle distributions on the surface profiles and the indentation depths of PRMMCs having particle sizes P s ¼ 20; 53; 167 and 478 lm and the particle volume fractions a) V f ¼ 10%, (b) 20% and (c) 30% (see Table 5).
ðPs ¼ 20 and 53 lmÞ and a large volume fraction ðV f ¼ 0:30Þ and results in small fluctuations in the deformed surface profiles corresponding to the ceramic particles. The smooth deformed indentation surface is degenerated with increasing particle volume fraction and decreasing particle size since more ceramic particles are located near the material free surface. Furthermore, the peak indentation depth is affected evidently by the random particle distribution especially in the small particle sizes and in the large volume fractions.
5. Conclusions This study investigates the effects of particle size, particle volume fraction, particle random dispersion and local particle concentration on both the indentation depth and the residual stress and strain distributions of an Al 1080/SiC particle reinforced metal matrix. The indentation depth decreased with increasing particle volume fraction but increased with increasing particle size. The experimental and numerical indentation depths were in good agreement if the changes in local particle concentration are considered. The random local particle concentration underneath the indenter appeared as an important parameter affecting the indentation depth. In case the random particle distribution is ignored the error levels between the experimental and numerical
indentation depths increase with increasing particle size rather than the particle volume fraction depending on the random particle distribution. The deformed surface profiles and the peak indentation depths are considerably affected by the random particle distribution, especially for small particle sizes and high volume fractions. The deformed surface profile is degenerated with increasing particle volume fraction and decreasing particle size since more ceramic particles are located around the free surface. The random particle dispersion also effects on the residual stress and strain distributions and levels. The residual stress concentrates underneath the indenter for small particle size and spreads over a large zone for large particle sizes. The residual strains only concentrate underneath the indenter and spreads over a slightly large region for large particle sizes. As the volume fraction is increased the residual strains and stresses concentrate in a limited region underneath the indenter by forming a stress band form. The random particle locations affect the formation of stress and strain distributions.
Acknowledgements Authors would like to thank for the financial support of the Sci_ entific and Technological Research Council of Turkey (TÜBITAK) under the contract: 106M020 and the Scientific Research Project Division of Erciyes University under the contract: FBT-06-30.
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Fig. 12. The effects of random particle distributions on the surface profiles and the indentation depths of PRMMCs having volume fractions V f ¼ 10%; 20% and 30% in the particle sizes a) P s ¼ 20, (b) 53, (c) 167 and (d) 478 lm (see Table 5).
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