Design rules for optimising microstructures of composite for thermal management Tomasz Boguszewski*, Lukasz Ciupinski, Krzysztof Kurzydlowski Faculty of Materials Science and Engineering, Warsaw University of Technology, ul. Woloska 141, 02-501 Warsaw, Poland *
[email protected], tel: +48 22 234 87 24, fax: 022 234 87 50
Abstract Metal matrix (aluminium, silver or copper) ceramic filler (SiC, diamond or graphite) composites are considered for thermal management applications as candidate materials. Properties of such composite depend strongly on their microstructure. In particular, particles content, shape size and spatial distribution can be used to tailor strength and heat conductivity of these composites. Properties of metal matrix composites are also influenced by interface between the constituents. Such interface might be formed un-intentionally, during the fabrication or designed to meet additional requirement, such as reduction of residual stresses and high heat conductance. With this abundance of factors shaping property of composites for thermal management, modelling, for example using finite element method (FEM) is needed to optimize their structure. The paper describes a series of FEM models which can be used for designing composites. Their applicability is demonstrated on the example of copper diamond composites. Keywords: composite, finite element method, heat sink Introduction Analytical solution which could be used during design process are valid only for very simply cases. Hasselman and Johnson [1] presented equation for coefficient of thermal conductivity in composite with spherical particle surround by bigger sphere. This model is appropriate for composite with very low particles volume fractions. In similar paper [2] Thomas and Hasselman considered particle which is in contact in one point with matrix. Assumption concerning direction of the heat transfer and conductivity of the interface layer, were also proposed.
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Analytical solution for anisotropic composite exists but only in the case of one direction, which could be modeled in two dimension. Islam and
Pramila [3] had good agreement heat flow modelling and
experiment’s results in case of fibre composite with interface layer. Some analytical and experimental results for anisotropic composite are presented by Gogol and Furmanski [4] where authors prove that conductivity in composite depend on direction of heat transfer and distribution of fibres. These examples indicate that analytical solution are limited. Numerical method give better opportunity to design composite in optimum way. Model and method A commercial FEM code Ansys was used to develop composite models. Three types of finite elements available in Ansys library were used. SOLID95, PLANE55 for thermal calculations and SOLID45 for mechanical calculations. Model had some restriction which simplify the analysis. Temperature load was applied to two opposite walls at the top and bottom of the model. It was assumed that only conductive heat transfer is effective. No convection or radiation was considered. Contact between the phases was assumed to be ideal and the contact resistance was not taken into consideration. Materials properties used were those of isotropic copper and diamond properties was taken for modelling. The thermal conductivity was equal to 370 W/(K*m) for copper and 2000 W/(K*m) for diamond. Calculation were made in three-phase models were the interface between filler (diamond) and the matrix (copper) was considered. Analysis concentrated on influence of the volumetric contribution of diamond, thermal conductivity and interface thickness on the composite thermal conductivity. The model with dense packed particles was considered. The results show that the conductivity of composite with interface layer depends on the conductivity of the layer material rather than its thickness. Discontinuity in the interface layer has noticeable influence when the volume contribution of particles is high but the main parameter which changes the conductivity of composite is the volume fraction of particles.
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Summary The influence of VvD – diamond volume fraction, LSW/LD – distance between particles and VvP/VvFP – volume fraction of interface discontinuity on thermal conductivity of the composite is displayed in Fig. 1. This graph can be considered as a design tool for copper –diamond based composite produces. One can use this graph either to estimate e.g. amount of the interface discontinuity in the composite with known thermal conductivity, VvD and LSW/LD or to estimate the composite expected thermal conductivity for given microstructure. In the first case parameters of the structure could be defined with some tolerance. But in second case it is possible to define quite accurately the structure parameters required. Figure 1 plots the changes of the composite effective thermal conductivity, K eff, normalized to the matrix conductivity KCu as a function of VvD, LSW/LD and VvP/VvFP. The example Fig. 1 assumes the known volumetric contribution of particles of 24% which gives the Keff/KCu=1,9 – point (1). Setting the second parameter the average distance between particles, LSW/LD equal 43% one should increase the conductivity of composite by roughly +∆Keff/KCu=0,4 – point (2). The third parameter is volumetric contribution of discontinuities in interface layer. For VvP/VvFP=23% the decrease in the composite conductivity will be roughly -∆Keff/KCu=0,3 – point (3). As a results one should expect that the composite with such structure should have the thermal conductivity twice as that of the matrix.
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Figure Captions
Fig. 1 Example of prediction composite material properties References [1] D.P.H. Hasselman and Lloyd F. Johnson. Effective Thermal Conductivity of Composites with Interfacial Thermal Barrier Resistance, Journal of Composite Materials 1987; 21; 508. [2] J. R. Thomas and D. P. H. Hasselman. Effective thermal Conductivity of Continuous Matrixspherical Dispersed Phase Composite with Single-point Interfacial Thermal Contact: Continuum Regime Gas Conduction In the Gap, Journal of Composite Materials, vol. 40, No. 11/2006. [3] MD. R. Islam and A. Pramila. Thermal conductivity of Fiber Reinforced Composite by the FEM, Journal of Composite Materials, Vol. 33, No. 18/1999. [4] W. Gogół, P. Furmański. Some Investigations of Effective Thermal Conductivity of Undirectional Fiber-Reinforced Composites, Journal of Composite Materials Supplement, Vol. 14 (1980), p. 167. [5] Wikipedia: http://pl.wikipedia.org/wiki/Mied%C5%BA
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