Conduction in Composites with Highly Conductive Short Fibres: Comparison between Experiments, Discrete Element Simulation and Analytical Solution

Increasing thermal or electrical conductivity of polymer composites by using a high content (i.e. largely above the percolation threshold) of highly conductive particles such as short carbon fibres, carbone nanotubes or short metallic fibres can be a potentially very interesting technological solution to replace metallic parts. However, an important limitation in the development of these composites is ascribed to the difficulty to predict accurately their effective conductivity. • The first reason is the lack of analytical conductivity models. Indeed, if numerous analytical models have been proposed to estimate thermal conductivity in dilute suspensions or near the percolation threshold, they are generally not adapted to the high volume fraction of fibres of industrial materials. To the best of our knowledge, the unique analytical model dedicated to highly concentrated composites with highly conductive fibres has been proposed in [1]. However, this model is restricted to 2D microstructures and some of its fitting parameters are hard to get from the microstructure. More recently, by extending concepts initially introduced for granular materials [2], 3D analytical conductivity models for highly concentrated fibrous media with fibre-fibre interfacial barriers have been proposed from an upscaling process [3] and from discrete element simulations [4,5]. However, these models have not been compared to reliable experimental data yet. • Model predictions are usually compared with experimental data coming from samples that have been produced under industrial processing conditions, e.g. injection moulding. Firstly, induced fibrous microstructures are difficult to observe and quantify due to the opaque nature of polymers that are generally used. Secondly, they are also very difficult to control and may exhibit very strong heterogeneities [6] which can induced high experimental scattering. In order to circumvent the above experimental difficulties, we have processed a model composites made of a PMMA matrix reinforced with short copper fibres. The transparent matrix allows direct observation of fibrous microstructures. The processing route [7] allows to produce samples were produced with homogeneous various fibre content, aspect ratios and orientation (see figure 1). Samples were then subjected to transient unidirectional thermal loading with a specially designed testing apparatus and an inverse modelling technique was used in order to compute their effective in-plane conductivity from experiments. Results underline the role of the fibre content aspect ratio and orientation. Experimental trends are then compared (i) with discrete element simulation performed on Representative Elementary Volumes (REV’s) of the considered fibrous microstructures (see figure 1), (ii) with the analytical model developed in [4,5].