Keywords: metal matrix composites, high reinforcement, thermal expansion coefficient, volume fraction, finite element analysis.

High reinforcement volume fraction Metal Matrix Composites (HR-MMC) are mostly used in electronic packaging applications and appliances, where reinforcement content can be as high as 70% in volume. The main justification for this use is because of the dimensional stability of these materials in different environments. This dimensional stability is essentially dependent on the Thermal Expansion Coefficient (TEC) of the composite material. In the present work, the authors perform a set of numerical studies related to the determination of the effective TEC of high reinforcement volume fraction metal matrix composites.

The metal matrix material used in this work is an aluminium matrix composite with silicon carbide particle reinforcement -- AlSiC_p. Two constitutive laws are used to model this material. The reinforcement is considered to follow a classical thermal-elastic model and the matrix material has a thermoelastic-rate dependent plastic behaviour model [1,2]. These constitutive models are implemented numerically with the finite element method in a three-dimensional program. The program is used to determine the effective thermal expansion coefficient of several AlSiC_p composite materials.

Numerical simulations are performed on representative unit cells with adequate boundary conditions [3] and with reinforcement volume fractions between 20 and 70%. The higher reinforcement content composites, with SiC volume fractions between 50 and 70%, are obtained mixing different sized SiC particles. Two distinct geometrical models were used to represent the MMC unit cells. In the first model -- the self-contained model (SCM) -- the reinforcement particles are all inside the unit cell domain and cannot be cut. In the second model -- the full-space model (FSM) -- some reinforcement particles can be partly cut by the unit cell boundaries. However, each particle that is cut has its complementary part on the opposite unit cell face. Only symmetry boundary conditions were implemented.

Several unit cells are created for each reinforcement volume fraction. SiC particles are randomly positioned in order to avoid errors derived from clustering or other undesirable numerical and/or technological consequences. To measure the thermal expansion coefficient of the AlSiC_p composite material, all unit cells were cooled from C down to room temperature ( C). The cooling rate was Cs. The numerical results obtained with the described models are thoroughly compared with theoretical predictions [4,5,6] and experimental results [7].

The numerically determined TEC values ranged from C, for the 70% reinforcement volume fraction MMC, up to C, for the 20% reinforcement volume fraction MMC. These results are in very good agreement with the values predicted with the rule of mixtures. Relative differences between the results obtained with the SCM and FSM models are all under 4% and, thus, almost neglectable. This fact leads to the conclusion that the results from the SCM and the FSM models are both accurate. However, the full-space model has the advantage of allowing the generation of representative unit cells with higher reinforcement volume fractions (theoretically up to arround 94%).

There is a tendency for an increase in the relative differences for higher reinforcement volume fractions. This can be explained because, the contraction role of the matrix decreases and the higher the reinforcement content the more difficult it is for the matrix to flow around it. Additionally, the effect of not considering reinforcement/matrix damage should be mostly felt in the higher reinforcement volume fraction models as a consequence of the higher reinforcement/matrix interface areas.

1

F. Teixeira-Dias, L.F. Menezes, "Numerical aspects of finite element simulations of residual stresses in metal matrix composites", International Journal for Numerical Methods in Engineering, 50, 629-644, 2001. doi:10.1002/1097-0207(20010130)50:3<629::AID-NME41>3.0.CO;2-7

2

F. Teixeira-Dias, L.F. Menezes, "Numerical determination of the influence of the cooling rate and reinforcement volume fraction on the levels of residual stresses in Al-SiC composites" Computational Materials Science, 21, 26-36, 2001. doi:10.1016/S0927-0256(00)00213-5

3

H.J. Böhm, A. Eckschlager, W. Han, "Multi-inclusion unit cell models for metalic matrix composites with randomly oriented discontinuous reinforcements", Computational Materials Science, 25, 42-53, 2002. doi:10.1016/S0927-0256(02)00248-3

4

L. Geiger, M. Jackson, "Low-expansion MMCs boost avionics", Advanced Materials Processing Technologies, 136, 23-8, 1989.

5

P.S. Turner, "Thermal expansion stresses in reinforced plastics", Journal of Research of the National Institute of Standards and Technology, 37, 239, 1946.

6

E.H. Kerner, "The elastic and thermo-elastic properties of composite media", Proc. Phys. Soc., 69, 808, 1956. doi:10.1088/0370-1301/69/8/305

7

Q. Zhang, G. Wu, G. Chen, L. Jiang, B. Luan, "The thermal expansion and mechanical properties of high reinforcement content SiCp/Al composites fabricated by squeeze casting technology", Composites: Part A, 34, 1023-1027, 2003. doi:10.1016/S1359-835X(03)00253-7

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