The effective thermal conductivity of double-reinforced composites
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ORIGINAL
The effective thermal conductivity of double-reinforced composites 1 · Jan Niedermeyer2 · Claudia Redenbach2 · Nicholas Ecke3 · Alois K. Schlarb3,4,5 · Heiko Andra ¨ ¨1 · Johannes Holler 1 Peter Klein
Received: 31 October 2019 / Accepted: 13 June 2020 © The Author(s) 2020
Abstract Polymer based composite materials have a great potential for applications in tribology as dry lubricants since the components comprising the composition may be chosen to fit to various tribological requirements. It is however well known that heat transfer and thermal effects are important for such systems. Systematic experimental studies of temperature effects are time consuming and expensive. In this work, we use a numerical homogenization approach in order to study the principal influence of key composite descriptors of fiber and particle reinforced PEEK on the homogenized heat conductivity. It turns out that the sensitivity of this key parameter on the descriptors can be nicely fitted to a regression model and thus allows for interpolation in the sense of a structure-property-relationship. Keywords Composites · Homogenization · Heat conduction List of frequently used symbols Homogenized heat conductivity in direction i λhom i λ(x) Locally constant heat conductivity tensor at micro scale l Length of a cubical box x 3D position vector i-component of x xi ∇ Nabla operator Volume fraction of fisbres in composite υf υg Volume fraction of graphite particles
1 Introduction Due to increasing costs for energy and growing environmental awareness, energy and material efficiency are of Peter Klein
[email protected] 1
Fraunhofer Institute for Industrial Mathematics, Kaiserslautern, Germany
2
Dep. Mathematics, TU Kaiserslautern, Kaiserslautern, Germany
3
Lehrstuhl f¨ur Verbundwerkstoffe, TU Kaiserslautern, Kaiserslautern, Germany
4
OPTIMAS-Landesforschungszentrum, TU Kaiserslautern, Kaiserslautern, Germany
5
Qingdao University of Science and Technology, Qingdao, China
ever-increasing importance in product development. One of the main causes for energy and material loss is friction in tribological contacts. In recent years, polymer-based materials have been used for various tribological applications in increasing quantities [9]. These materials combine the potential for lightweight design, dry running capability and cost-effective processing. Typically, a polymer-based tribological composite, produced by compounding, consists of a high-performance polymer which is reinforced with fibres to increase mechanical strength and wear resistance and modified with an internal solid lubricant to reduce friction [22, 30]. Further improvements of both friction and wear behavior can be achieved by the addition of hard microand nano-sized particles which improve the stiffness of the matrix material and interact with the carbon fibres in several ways [5, 6, 17, 29, 30]. The development of these hybrid composites is expensive and time consuming, due to the large number of experiments required to determine the tribological behavi
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