- Email: [email protected]
On the achievement of uniform particle distribution in metal matrix composites fabricated by accumulative roll bonding
Materials Letters 91 (2013) 59–62
Contents lists available at SciVerse ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
On the achievement of uniform particle distribution in metal matrix composites fabricated by accumulative roll bonding M. Reihanian a,n, E. Bagherpour b, M.H. Paydar c a
Department of Materials Science and Engineering, Faculty of Engineering, Shahid Chamran University, Ahvaz, Iran Department of Materials Science and Engineering, Faculty of Engineering, Semnan University, Semnan, Iran c Department of Materials Science and Engineering, School of Engineering, Shiraz University, Shiraz, Iran b
a r t i c l e i n f o
abstract
Article history: Received 1 September 2012 Accepted 14 September 2012 Available online 23 September 2012
A model to attain a homogeneous particle distribution in bi-modal and tri-modal metal matrix composites produced by accumulative roll bonding is presented. Three cubic models, including simple, face-centered and body-centered cubic models, are considered for uniform distribution of particles in the matrix. Results show that the critical reduction to get a uniform distribution of particles rises with increasing volume fraction, decreasing particle size and raising initial layer thickness. The validity of the model is verified by accumulative roll bonded-metal matrix composites reported in literatures. Good agreement is observed between the model and the experimental data. & 2012 Elsevier B.V. All rights reserved.
Keywords: Composite materials Metal forming and shaping Accumulative roll bonding Particle distribution Modeling
1. Introduction Metal matrix composites (MMCs) are promising materials in specific industries due to their excellent properties such as high strength and thermal stability. Manufacturing techniques for MMCs can be classified into liquid- and solid-state processing. During the most recent years, accumulative roll bonding (ARB) has been employed, as a new solid-state process, for producing particulate MMCs [1–13]. Accumulative roll bonding is a kind of severe plastic deformation that can produce high strength metals with ultra-fine grained microstructure [14]. The basic ceramic particles used as reinforcement in accumulative roll bonding process are Al2O3 [1–3], B4C [3–9] and SiC [10–13]. Reinforcement size and volume fraction are two key factors that control the mechanical properties of MMCs. To attain a composite with good combination of strength and ductility, reinforcements with small size and large volume fractions are required. However, these requirements usually lead to a non-homogenous distribution of particles, degrading the mechanical properties of the composite. Recently, a model for volume fraction and particle size selection in particle-reinforced MMCs via powder metallurgy routes has been proposed [15]. More recently, the present authors proposed a model to predict the critical strain to get a uniform distribution of particles in metal matrix composites produced by ARB [16]. The model
considered only simple cubic arrangement of particles and minimum particle size in calculations. In the present work, to simulate more accurately the particle distribution, three cubic models are developed for uniform particle distribution in the matrix. Particularly, the model considers the mean particle size for calculations. Among all the distribution models, the most effective is determined by verifying the experimental data reported in literatures.
2. Modeling The term bi-modal is defined for composites that consist of two constituents: a matrix and reinforcement. The tri-modal term stands for composites that contain three constituents: a matrix and two different types of reinforcements. Fig. 1 shows schematically the ARB process for fabricating MMCs. The particles are distributed between the layer interfaces (Fig. 1a). Assume that the particles are rigid spheres and dispersed as packed as possible between the layers. The assumption of the model is that the particles have single size. In the case that the particles have a size distribution, a particle size independent mean value is supposed. According to the model, the criterion to get a uniform distribution is that the minimum inter-particle spacing l becomes equal to or higher than the layer thickness tn after n cycles, that is
l Ztn n
Corresponding author. Tel.: þ98 611 3330010 19x5684; fax: þ 98 611 3336642. E-mail address: [email protected] (M. Reihanian). 0167-577X/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matlet.2012.09.043
ð1Þ
In simple cubic (SC) arrangement (Fig. 1b), each corner particle contributes one-eighth to the total volume; the eight corner particles together count as one. The constant of the unit cell is
60
M. Reihanian et al. / Materials Letters 91 (2013) 59–62
Fig. 1. (a) Schematic illustration of fabricating metal matrix composites through ARB process, (b) simple cubic, (c) face-centered cubic and (d) body-centered cubic models of particle distribution.
the particles A and B are obtained by
a ¼ l. The volume fraction f of the particles is determined as 3
pd =6
ð2Þ
fA ¼
where d is the particle diameter. Assuming a plane strain condition, the layer thickness after imposing a total reduction Rt is given by
fB ¼
f¼
3
l
t n ¼ t 1 ð1Rt Þ Combining Eqs. (1)–(3) yields 1=3 p d Rt Z1 ¼ RSC bi t1 6f
ð3Þ
ð4Þ
where RSC bi is the critical total reduction needed to achieve a homogeneous SC distribution of particles in the matrix. At this time, consider that the particles distribute uniformly in the matrix and form a face-centered cubic (FCC) or base-centered (BCC) distribution. The ideal unit cells are schematically illustrated in Fig. pffiffiffi 1c and d, correspondingly. pffiffiffi The constant of the unit cell is a ¼ 2l for FCC and a ¼ 2l= 3 for BCC. Using the same procedure as for the SC model, we can get !1=3 p d ð5Þ ¼ RFCC Rt Z1 pffiffiffi bi t 1 3 2f pffiffiffi !1=3 d 3p Rt Z1 ¼ RBCC bi t1 8f
pd3A =6 l
pd3B =6 3
l
BCC are the critical total reductions required to get where RFCC bi and Rbi homogeneous FCC and BCC distribution of particles, respectively. Now, consider a tri-modal composite in which two kinds of particles A and B distribute uniformly and randomly in the matrix and form a SC distribution. The size of the particles A and B are denoted as dA and dB, respectively. The reinforcements distribute spatially with a number ratio a ¼nA/nB, where nA and nB are the number of particles A and B in each volume element. The probabilities of a unit position to be particles A and B are pA ¼nA/(nA þnB) and pB ¼nB/(nA þnB), respectively. In terms of the number ratio a, these probabilities can be expressed as pA ¼ a/(1 þ a) and pB ¼1/(1þ a). The constant of the SC unit cell is a ¼ l and there is one particle in each cell. Thus, the volume fractions of
pA ¼
pB ¼
pd3A =6
a
l3
ð1 þ aÞ
pd3B =6
1 ð1 þ aÞ
l3
ð7aÞ
ð7bÞ
Dividing Eq. (7a) by Eq. (7b) gives 3 f dB a¼ A fB dA
ð8Þ
Incorporating Eqs. (1), (3), and (8) in Eqs. (7a) or (7b) gives " #1=3 p dA dB ð9Þ ¼ RSC Rt Z1 tr 3 3 t1 6ðf A d þ f B d Þ B
A
where RSC tr is the critical total reduction needed to achieve a uniform SC distribution of particles A and B in a tri-modal composite. Using the same procedure for FCC and BCC arrangement of particles results in " #1=3 p dA dB Rt Z1 pffiffiffi ð10Þ ¼ RFCC tr 3 3 t1 3 2ðf A d þf B d Þ B
" Rt Z1
ð6Þ
3
pffiffiffi 3p
A
#1=3
3 3 8ðf A dB þ f B dA Þ
dA dB t1
¼ RBCC tr
ð11Þ
and RBCC are the critical total reductions required to where RFCC tr tr get a homogeneous FCC and BCC distribution of particles A and B in a tri-modal composite. It is obvious that when dA ¼dB and fB ¼0, criteria (9), (10) and (11) change into criteria (4), (5) and (6), respectively, and the tri-modal models change into the bi-modal models.
3. Results and discussion Briefly, the model predicts that the critical reduction to get a uniform distribution of particles rises with increasing volume fraction, decreasing particle size and raising initial layer thickness. Fig. 2 shows the variation of critical reduction in a bi-modal composite as a function of particle volume fraction for SC, FCC and
M. Reihanian et al. / Materials Letters 91 (2013) 59–62
BCC models. The same trend is observed for all three models. However, for the same volume fraction, the critical reduction predicted by SC model is larger than that of the others. The least critical reduction is predicted by FCC model. The reason comes from the fact that the FCC arrangement represents a close-packed structure. The SC has the most open structure. Accordingly, the
Fig. 2. Variation in critical reduction with particle volume fraction for SC, FCC and BCC models.
61
particles require going a long distance to form a uniform SC distribution that leads to the highest critical reduction. According to the model, the critical reduction is increased as the volume fraction is raised. The reason is that for a given particle diameter, the number of particles increases with increasing volume fraction. Thus, higher reductions are needed to homogenize the microstructure. It is noted that at large volume fractions the critical reduction approaches one that dictates very large strains or high number of ARB cycles. At these conditions, the volume fraction has no significant effect on the critical reduction. Variation of critical reduction with particle size is illustrated in Fig. 3. The larger the particle size, the lower the critical reduction to distribute uniformly the particles in the matrix. At a given volume fraction, the number of particles decreases with increasing particle size. Therefore, lower reduction is needed to distribute the particles in the matrix. The critical reduction predicted by all models converged to one as the particle size approached zero. To evaluate the effectiveness of the SC, FCC and BCC models, the experimental results extracted from literatures are employed and summarized in Table 1. It is observed that the predicted results are in good agreement with the experiments. The consistency of the models to the experimental data is denoted as good, fair and poor. When the difference between the predicted and experimental values of critical reduction is less than 0.01, the conformity of the model is supposed to be good. For the differences in the range of 0.01–0.02, the consistency is assumed to be fair. For the differences higher than 0.02, the compatibility is considered as poor. According to this criterion, the percentage of the published papers that exhibit good agreement is 57% for BCC and FCC, while it is 71% for SC model. As a result, the SC prediction is closer to experimental data.
4. Conclusions
Fig. 3. Variation in critical reduction with particle size for SC, FCC and BCC models.
1. The critical reduction rises with increasing volume fraction, decreasing particle size and raising initial layer thickness. 2. The critical reduction predicted by SC model is the largest. The least is predicted by FCC model. 3. The predicted results show good agreement with the results of the literature. 4. Among all cubic models, the SC model is more effective to predict the critical reduction.
Table 1 Effectiveness of the SC, FCC and BCC models in MMCs fabricated by ARB. Material
Pure AlþAl2O3 Pure AlþAl2O3 Pure Cuþ Al2O3 Al 1100þ B4C Al 1100þ B4C Al 1050þ B4C Al 1100þ B4C Al 1100þ B4C Al 1050þ B4C Al 1050þ SiC Al 1050þ SiC Al 1050þ SiC Al 1050þ SiC Al 1050þ SiC Al 1050þ SiC a
Not reported.
Process parameters
Models’ Predicted
f (%)
d (mm)
t0 (mm)
No. of cycles
R
RSC bi
15 3 15 7.5 8 10 8 7.7 0 28 7 10 10 7 7
50 0.47 2 2.5 3 3 3 3 2 5 5 2 40 5 5
1.5 0.5 1.5 0.4 0.4 0.4 0.4 0.4 NRa 0.5 0.4 1.5 1.5 0.4 1
13 8 9 8 8 7 8 8 7 7 8 13 9 8 8
0.999 0.996 0.998 0.996 0.996 0.992 0.996 0.996 0.992 0.992 0.996 0.999 0.998 0.996 0.996
0.95 0.999 0.998 0.994 0.986 0.987 0.993 0.986 – 0.988 0.976 0.998 0.954 0.976 0.99
Models’ Compatibility
Ref.
RFCC bi
RBCC bi
SC
FCC
BCC
0.944 0.999 0.998 0.994 0.984 0.985 0.993 0.984 – 0.986 0.973 0.997 0.948 0.973 0.989
0.945 0.999 0.998 0.994 0.985 0.986 0.993 0.985 – 0.987 0.974 0.997 0.95 0.974 0.989
Poor Good Good Good Good Good Good Good – Good Fair Good Poor Fair Good
Poor Good Good Good Fair Good Good Fair – Good Poor Good Poor Poor Good
Poor Good Good Good Fair Good Good Fair – Good Poor Good Poor Poor Good
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [12] [13] [16]
62
M. Reihanian et al. / Materials Letters 91 (2013) 59–62
References [1] Jamaati R, Toroghinejad MR. Manufacturing of high-strength aluminum/ alumina composite by accumulative roll bonding. Mater Sci Eng A 2010; 527:4146–51. [2] Rezayat M, Akbarzadeh A, Owhadi A. Production of high strength Al–Al2O3 composite by accumulative roll bonding. Composites: Part A 2012;43:261–7. [3] Jamaati R, Toroghinejad MR. Application of ARB process for manufacturing high-strength, finely dispersed and highly uniform Cu/Al2O3 composite. Mater Sci Eng A 2010;527:7430–5. [4] Alizadeh M. Comparison of nanostructured Al/B4C composite produced by ARB and Al/B4C composite produced by RRB process. Mater Sci Eng A 2010;528:578–82. [5] Alizadeh M. Processing of Al/B4C composites by cross-roll accumulative roll bonding. Mater Lett 2010;64:2641–3. [6] Yazdani A, Salahinejad E. Evolution of reinforcement distribution in Al–B4C composites during accumulative roll bonding. Mater Des 2011;32:3137–42. [7] Alizadeh M, Paydar MH. High-strength nanostructured Al/B4C composite processed by cross-roll accumulative roll bonding. Mater Sci Eng A 2012; 538:14–9. [8] Alizadeh M, Paydar MH, Sharifian Jazi F. Structural evaluation and mechanical properties of nanostructured Al/B4C composite fabricated by ARB process. Composites: Part B, in press; http://dx.doi.org/10.1016/j.compositesb.2012. 04.069.
[9] Yazdani A, Salahinejad E, Moradgholi J, Hosseini M. A new consideration on reinforcement distribution in the different planes of nanostructured metal matrix composite sheets prepared by accumulative roll bonding (ARB). J Alloys Compd 2011;509:9562–4. [10] Alizadeh M, Paydar M. Fabrication of Al/SiCP composite strips by repeated roll-bonding (RRB) process. J Alloys Compd 2009;477:811–6. [11] Alizadeh M, Paydar MH. Fabrication of nanostructure Al/SiCP composite by accumulative roll-bonding (ARB) process. J Alloys Compd 2010;492:231–5. [12] Jamaati R, Amirkhanlou S, Toroghinejad MR, Niroumand B. Effect of particle size on microstructure and mechanical properties of composites produced by ARB process. Mater Sci Eng A 2011;528:2143–8. [13] Alizadeha M, Paydar MH, Terada D, Tsuji N. Effect of SiC particles on the microstructure evolution and mechanical properties of aluminum during ARB process. Mater Sci Eng A 2012;540:13–23. [14] Saito Y, Utsunomiya H, Tsuji N, Sakai T. Novel ultra-high straining process for bulk materials—development of the accumulative roll-bonding (ARB) process. Acta Mater 1999;47:579–83. [15] Reihanian M, Bagherpour E, Paydar MH. A model for volume fraction and particle size selection in tri-modal metal matrix composites. Mater Sci Eng A 2009;513–514:172–5. [16] Reihanian M, Bagherpour E, Paydar MH. Particle distribution in metal matrix composites fabricated by accumulative roll bonding. Mater Sci Technol 2012;28:103–8.
Contents lists available at SciVerse ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
On the achievement of uniform particle distribution in metal matrix composites fabricated by accumulative roll bonding M. Reihanian a,n, E. Bagherpour b, M.H. Paydar c a
Department of Materials Science and Engineering, Faculty of Engineering, Shahid Chamran University, Ahvaz, Iran Department of Materials Science and Engineering, Faculty of Engineering, Semnan University, Semnan, Iran c Department of Materials Science and Engineering, School of Engineering, Shiraz University, Shiraz, Iran b
a r t i c l e i n f o
abstract
Article history: Received 1 September 2012 Accepted 14 September 2012 Available online 23 September 2012
A model to attain a homogeneous particle distribution in bi-modal and tri-modal metal matrix composites produced by accumulative roll bonding is presented. Three cubic models, including simple, face-centered and body-centered cubic models, are considered for uniform distribution of particles in the matrix. Results show that the critical reduction to get a uniform distribution of particles rises with increasing volume fraction, decreasing particle size and raising initial layer thickness. The validity of the model is verified by accumulative roll bonded-metal matrix composites reported in literatures. Good agreement is observed between the model and the experimental data. & 2012 Elsevier B.V. All rights reserved.
Keywords: Composite materials Metal forming and shaping Accumulative roll bonding Particle distribution Modeling
1. Introduction Metal matrix composites (MMCs) are promising materials in specific industries due to their excellent properties such as high strength and thermal stability. Manufacturing techniques for MMCs can be classified into liquid- and solid-state processing. During the most recent years, accumulative roll bonding (ARB) has been employed, as a new solid-state process, for producing particulate MMCs [1–13]. Accumulative roll bonding is a kind of severe plastic deformation that can produce high strength metals with ultra-fine grained microstructure [14]. The basic ceramic particles used as reinforcement in accumulative roll bonding process are Al2O3 [1–3], B4C [3–9] and SiC [10–13]. Reinforcement size and volume fraction are two key factors that control the mechanical properties of MMCs. To attain a composite with good combination of strength and ductility, reinforcements with small size and large volume fractions are required. However, these requirements usually lead to a non-homogenous distribution of particles, degrading the mechanical properties of the composite. Recently, a model for volume fraction and particle size selection in particle-reinforced MMCs via powder metallurgy routes has been proposed [15]. More recently, the present authors proposed a model to predict the critical strain to get a uniform distribution of particles in metal matrix composites produced by ARB [16]. The model
considered only simple cubic arrangement of particles and minimum particle size in calculations. In the present work, to simulate more accurately the particle distribution, three cubic models are developed for uniform particle distribution in the matrix. Particularly, the model considers the mean particle size for calculations. Among all the distribution models, the most effective is determined by verifying the experimental data reported in literatures.
2. Modeling The term bi-modal is defined for composites that consist of two constituents: a matrix and reinforcement. The tri-modal term stands for composites that contain three constituents: a matrix and two different types of reinforcements. Fig. 1 shows schematically the ARB process for fabricating MMCs. The particles are distributed between the layer interfaces (Fig. 1a). Assume that the particles are rigid spheres and dispersed as packed as possible between the layers. The assumption of the model is that the particles have single size. In the case that the particles have a size distribution, a particle size independent mean value is supposed. According to the model, the criterion to get a uniform distribution is that the minimum inter-particle spacing l becomes equal to or higher than the layer thickness tn after n cycles, that is
l Ztn n
Corresponding author. Tel.: þ98 611 3330010 19x5684; fax: þ 98 611 3336642. E-mail address: [email protected] (M. Reihanian). 0167-577X/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.matlet.2012.09.043
ð1Þ
In simple cubic (SC) arrangement (Fig. 1b), each corner particle contributes one-eighth to the total volume; the eight corner particles together count as one. The constant of the unit cell is
60
M. Reihanian et al. / Materials Letters 91 (2013) 59–62
Fig. 1. (a) Schematic illustration of fabricating metal matrix composites through ARB process, (b) simple cubic, (c) face-centered cubic and (d) body-centered cubic models of particle distribution.
the particles A and B are obtained by
a ¼ l. The volume fraction f of the particles is determined as 3
pd =6
ð2Þ
fA ¼
where d is the particle diameter. Assuming a plane strain condition, the layer thickness after imposing a total reduction Rt is given by
fB ¼
f¼
3
l
t n ¼ t 1 ð1Rt Þ Combining Eqs. (1)–(3) yields 1=3 p d Rt Z1 ¼ RSC bi t1 6f
ð3Þ
ð4Þ
where RSC bi is the critical total reduction needed to achieve a homogeneous SC distribution of particles in the matrix. At this time, consider that the particles distribute uniformly in the matrix and form a face-centered cubic (FCC) or base-centered (BCC) distribution. The ideal unit cells are schematically illustrated in Fig. pffiffiffi 1c and d, correspondingly. pffiffiffi The constant of the unit cell is a ¼ 2l for FCC and a ¼ 2l= 3 for BCC. Using the same procedure as for the SC model, we can get !1=3 p d ð5Þ ¼ RFCC Rt Z1 pffiffiffi bi t 1 3 2f pffiffiffi !1=3 d 3p Rt Z1 ¼ RBCC bi t1 8f
pd3A =6 l
pd3B =6 3
l
BCC are the critical total reductions required to get where RFCC bi and Rbi homogeneous FCC and BCC distribution of particles, respectively. Now, consider a tri-modal composite in which two kinds of particles A and B distribute uniformly and randomly in the matrix and form a SC distribution. The size of the particles A and B are denoted as dA and dB, respectively. The reinforcements distribute spatially with a number ratio a ¼nA/nB, where nA and nB are the number of particles A and B in each volume element. The probabilities of a unit position to be particles A and B are pA ¼nA/(nA þnB) and pB ¼nB/(nA þnB), respectively. In terms of the number ratio a, these probabilities can be expressed as pA ¼ a/(1 þ a) and pB ¼1/(1þ a). The constant of the SC unit cell is a ¼ l and there is one particle in each cell. Thus, the volume fractions of
pA ¼
pB ¼
pd3A =6
a
l3
ð1 þ aÞ
pd3B =6
1 ð1 þ aÞ
l3
ð7aÞ
ð7bÞ
Dividing Eq. (7a) by Eq. (7b) gives 3 f dB a¼ A fB dA
ð8Þ
Incorporating Eqs. (1), (3), and (8) in Eqs. (7a) or (7b) gives " #1=3 p dA dB ð9Þ ¼ RSC Rt Z1 tr 3 3 t1 6ðf A d þ f B d Þ B
A
where RSC tr is the critical total reduction needed to achieve a uniform SC distribution of particles A and B in a tri-modal composite. Using the same procedure for FCC and BCC arrangement of particles results in " #1=3 p dA dB Rt Z1 pffiffiffi ð10Þ ¼ RFCC tr 3 3 t1 3 2ðf A d þf B d Þ B
" Rt Z1
ð6Þ
3
pffiffiffi 3p
A
#1=3
3 3 8ðf A dB þ f B dA Þ
dA dB t1
¼ RBCC tr
ð11Þ
and RBCC are the critical total reductions required to where RFCC tr tr get a homogeneous FCC and BCC distribution of particles A and B in a tri-modal composite. It is obvious that when dA ¼dB and fB ¼0, criteria (9), (10) and (11) change into criteria (4), (5) and (6), respectively, and the tri-modal models change into the bi-modal models.
3. Results and discussion Briefly, the model predicts that the critical reduction to get a uniform distribution of particles rises with increasing volume fraction, decreasing particle size and raising initial layer thickness. Fig. 2 shows the variation of critical reduction in a bi-modal composite as a function of particle volume fraction for SC, FCC and
M. Reihanian et al. / Materials Letters 91 (2013) 59–62
BCC models. The same trend is observed for all three models. However, for the same volume fraction, the critical reduction predicted by SC model is larger than that of the others. The least critical reduction is predicted by FCC model. The reason comes from the fact that the FCC arrangement represents a close-packed structure. The SC has the most open structure. Accordingly, the
Fig. 2. Variation in critical reduction with particle volume fraction for SC, FCC and BCC models.
61
particles require going a long distance to form a uniform SC distribution that leads to the highest critical reduction. According to the model, the critical reduction is increased as the volume fraction is raised. The reason is that for a given particle diameter, the number of particles increases with increasing volume fraction. Thus, higher reductions are needed to homogenize the microstructure. It is noted that at large volume fractions the critical reduction approaches one that dictates very large strains or high number of ARB cycles. At these conditions, the volume fraction has no significant effect on the critical reduction. Variation of critical reduction with particle size is illustrated in Fig. 3. The larger the particle size, the lower the critical reduction to distribute uniformly the particles in the matrix. At a given volume fraction, the number of particles decreases with increasing particle size. Therefore, lower reduction is needed to distribute the particles in the matrix. The critical reduction predicted by all models converged to one as the particle size approached zero. To evaluate the effectiveness of the SC, FCC and BCC models, the experimental results extracted from literatures are employed and summarized in Table 1. It is observed that the predicted results are in good agreement with the experiments. The consistency of the models to the experimental data is denoted as good, fair and poor. When the difference between the predicted and experimental values of critical reduction is less than 0.01, the conformity of the model is supposed to be good. For the differences in the range of 0.01–0.02, the consistency is assumed to be fair. For the differences higher than 0.02, the compatibility is considered as poor. According to this criterion, the percentage of the published papers that exhibit good agreement is 57% for BCC and FCC, while it is 71% for SC model. As a result, the SC prediction is closer to experimental data.
4. Conclusions
Fig. 3. Variation in critical reduction with particle size for SC, FCC and BCC models.
1. The critical reduction rises with increasing volume fraction, decreasing particle size and raising initial layer thickness. 2. The critical reduction predicted by SC model is the largest. The least is predicted by FCC model. 3. The predicted results show good agreement with the results of the literature. 4. Among all cubic models, the SC model is more effective to predict the critical reduction.
Table 1 Effectiveness of the SC, FCC and BCC models in MMCs fabricated by ARB. Material
Pure AlþAl2O3 Pure AlþAl2O3 Pure Cuþ Al2O3 Al 1100þ B4C Al 1100þ B4C Al 1050þ B4C Al 1100þ B4C Al 1100þ B4C Al 1050þ B4C Al 1050þ SiC Al 1050þ SiC Al 1050þ SiC Al 1050þ SiC Al 1050þ SiC Al 1050þ SiC a
Not reported.
Process parameters
Models’ Predicted
f (%)
d (mm)
t0 (mm)
No. of cycles
R
RSC bi
15 3 15 7.5 8 10 8 7.7 0 28 7 10 10 7 7
50 0.47 2 2.5 3 3 3 3 2 5 5 2 40 5 5
1.5 0.5 1.5 0.4 0.4 0.4 0.4 0.4 NRa 0.5 0.4 1.5 1.5 0.4 1
13 8 9 8 8 7 8 8 7 7 8 13 9 8 8
0.999 0.996 0.998 0.996 0.996 0.992 0.996 0.996 0.992 0.992 0.996 0.999 0.998 0.996 0.996
0.95 0.999 0.998 0.994 0.986 0.987 0.993 0.986 – 0.988 0.976 0.998 0.954 0.976 0.99
Models’ Compatibility
Ref.
RFCC bi
RBCC bi
SC
FCC
BCC
0.944 0.999 0.998 0.994 0.984 0.985 0.993 0.984 – 0.986 0.973 0.997 0.948 0.973 0.989
0.945 0.999 0.998 0.994 0.985 0.986 0.993 0.985 – 0.987 0.974 0.997 0.95 0.974 0.989
Poor Good Good Good Good Good Good Good – Good Fair Good Poor Fair Good
Poor Good Good Good Fair Good Good Fair – Good Poor Good Poor Poor Good
Poor Good Good Good Fair Good Good Fair – Good Poor Good Poor Poor Good
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [12] [13] [16]
62
M. Reihanian et al. / Materials Letters 91 (2013) 59–62
References [1] Jamaati R, Toroghinejad MR. Manufacturing of high-strength aluminum/ alumina composite by accumulative roll bonding. Mater Sci Eng A 2010; 527:4146–51. [2] Rezayat M, Akbarzadeh A, Owhadi A. Production of high strength Al–Al2O3 composite by accumulative roll bonding. Composites: Part A 2012;43:261–7. [3] Jamaati R, Toroghinejad MR. Application of ARB process for manufacturing high-strength, finely dispersed and highly uniform Cu/Al2O3 composite. Mater Sci Eng A 2010;527:7430–5. [4] Alizadeh M. Comparison of nanostructured Al/B4C composite produced by ARB and Al/B4C composite produced by RRB process. Mater Sci Eng A 2010;528:578–82. [5] Alizadeh M. Processing of Al/B4C composites by cross-roll accumulative roll bonding. Mater Lett 2010;64:2641–3. [6] Yazdani A, Salahinejad E. Evolution of reinforcement distribution in Al–B4C composites during accumulative roll bonding. Mater Des 2011;32:3137–42. [7] Alizadeh M, Paydar MH. High-strength nanostructured Al/B4C composite processed by cross-roll accumulative roll bonding. Mater Sci Eng A 2012; 538:14–9. [8] Alizadeh M, Paydar MH, Sharifian Jazi F. Structural evaluation and mechanical properties of nanostructured Al/B4C composite fabricated by ARB process. Composites: Part B, in press; http://dx.doi.org/10.1016/j.compositesb.2012. 04.069.
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