Micro-scale prediction of effective thermal conductivity of CNT/Al composites by finite element method
Introduction
Rapid developments in the electronic industry require thermal management materials with higher thermal conductivity and lower coefficient of thermal expansion, so as to minimize the thermal stress during the operation of the device [1,2]. Aluminium has a lower thermal conductivity (237 W/mK) and larger coefficient of thermal expansion (23 ppmK-1) than copper, but it is lighter, cheaper, and has good machinability, making it more attractive option when producing high thermal conductivity composites [3,4]. It is well known that the multi-walled carbon nanotubes (MWCNTs) have ultra-high theoretical thermal conductivity (2000–3000 W/mK) and a low coefficient of thermal expansion (−2.5 ppmK-1 at room temperature) [5,6]. This makes CNT an excellent reinforcement to manufacture Al matrix composites with ultra-high thermal conductivity and adjustable coefficient of thermal expansion.
Up to now, a lot of studies focused on the microstructures and the mechanical properties of CNT/Al composites. Many experimental investigations showed that the enhancement efficiency of CNTs in the Al matrix composites was much lower than the theoretical expectation if CNT content over some threshold value, which was attributed to the weak interfacial bonding and poor dispersion of CNTs in the Al matrix. Recently, with improving the fabricating methods, CNTs can be uniformly dispersed in the Al matrix and no obvious defects or voids appeared at the CNT-Al interfaces, and the mechanical properties, such as hardness, tensile strength of CNT/Al composites were significantly improved with a very low content of CNT addition [[7], [8], [9], [10]]. Furthermore, the experimental results showed that the CNT/Al composites with directionally aligned CNTs exhibited much higher strength, ductility, and modulus values than those with randomly distributed CNTs [11].
Compared with the studies on the mechanical properties, only a few reports focused on the thermal properties of CNT/Al composites. Wu et al. [11] reported that the thermal conductivity increased from 185 to 199 W/mK with 0.5 wt% CNT addition, and the enhanced thermal properties were ascribed to CNT bridging. However, when 5 wt% CNT were added, the thermal conductivity decreased to value substantially below that of the matrix. This was attributed to inhomogeneous dispersion of CNTs and the formation of bundles with increased CNT content. Yamanaka et al. [12] investigated the thermal conductivity of CNT/Al composites reinforced with up to 5 vol% CNT, and the experimental results showed that the thermal conductivity increased with the CNTs when the CNT content was lower than 4 vol%. Moreover, the effect of considerable improvement in the thermal conductivity of composites at low CNT content is not just restricted to CNT/Al composites, but for many composites, even CNT/polymer composites [13] and CNT/fiber/polymer composites [[14], [15], [16]]. Generally, a small increase in the CNT content is thought to have a large effect on the thermal conductivity of the composites. Experimental investigation by Shin et al. [17] indicated that with 4 wt% CNT addition, for individually dispersed CNTs, the thermal conductivity of CNT/Al composites (103 W/mK) was lower than that of the Al matrix (156 W/mK), however, if the composites exhibited a network structure of CNTs, it reveals much enhanced thermal conductivity of 172 W/m K. Recently, Ujah et al. [18,19] reported that for the addition of 8 wt% CNT, the thermal conductivity of the composite was improved by 44 %, and this was attributed to that a high mass fraction of atoms precipitated from the solid solution, thereby having more free electrons and phonons required for thermal conductivity.
Complex microstructure of CNT/Al composites leads to scattered experimental data available in the literature, and there is no general rule for estimating the thermal conductivity of the CNT/Al composites. Therefore, the simulation is the most cost-effective alternatives for prediction of the thermal behavior of complex structural composites [20]. The multi-scale object oriented finite element method was utilized to compute the thermal conductivity of 10 wt% CNT/Al composite [21], and the effect of CNT dispersion on thermal conductivity was investigated. The calculation results showed that the thermal conductivity of CNT/Al composites was improved by 81 % with good dispersion of CNTs in the matrix, while the presence of CNT clusters led to drastic decrease in thermal conductivity of CNT/Al composite. The enhanced thermal conductivity of CNT/Al composite was attributed to that the CNTs served as high thermal flux pathways, and the CNT aligned structure and morphology, as well as the interface thermal resistance can significantly affect the overall heat conducting behavior of composites [[21], [22], [23]].
So far, most of the researches were dedicated to the influence of CNT volume fraction on thermal properties, in which CNTs were distributed randomly. Few reports focus on the influence of CNT microstructure, such as configuration, interface etc. on thermal properties of CNT/Al composites. Therefore, a thorough understanding of the heat conducting behavior of CNT/Al composites at microscale is important for optimizing the thermal properties, as well as the manufacturing process.
In this work, a multi-scale finite element model was used to study the effective thermal conductivity of CNT/Al composites. In order to offer an accurate representation of real micro-structures, the configuration, interface and inclusions were taken into account, and then compared the effective thermal conductivity calculated with the experimental data in the literature.
Section snippets
Microstructure reconstruction
In this work, the multi-scale finite element software ABAQUS was used to build models for the thermal calculation of CNT/Al composites. A 3D representative volume element (RVE) with five typical CNT configurations, namely randomly arranged, evenly oriented, layered, bundled and networked were established, seen in Fig. 1. From a microscopic viewpoint, the RVE consists of CNTs, matrix, inclusions and the interface between CNTs and matrix. In these models, the CNT is simulated as a transversely
Results and discussions
To characterize the thermal flux transfer, the Fourier's law [35] was used. If the heat flow is along the y direction, the relationship between the heat flux and the effective thermal conductivity is:where is the average heat flux of CNT/Al composites, is the effective thermal conductivity, is the temperature gradient along the y direction. The heat flux can be calculated by:where is the total volume of CNT/Al composites, , ,
Conclusions
In this study, the microscale RVE was employed to analyze the effective thermal conductivity of CNT/Al composites. The influences of the CNT configuration, heat transfer direction, interfacial thermal resistance and volume fraction were investigated in detail. The main conclusions are as follows.
- (1)
Due to the difference of thermal conductivities between matrix and CNTs, the temperature contour lines are non-parallel at the end of the CNTs aligned along the load direction, and the influences of
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work is supported by (a) Key Research Program of Frontier Sciences, CAS (No. QYZDJ-SSW-JSC015); (b) National Natural Science Foundation of China (No. 51931009, 51871214 and 51871215); (c) National Key R&D Program of China (No. 2017YFB0703104).
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