Carbon Fibre Composites: Deformation Micromechanics Analysed using Raman Spectroscopy
In the quest to understand reinforcement by high performance fibres, such as carbon fibres, the development of the subject of composite micromechanics is traced from its earliest roots. It is shown first how, employing concepts introduced by Kelly, it is
- PDF / 1,493,304 Bytes
- 22 Pages / 439.37 x 666.142 pts Page_size
- 83 Downloads / 236 Views
Carbon Fibre Composites: Deformation Micromechanics Analysed using Raman Spectroscopy Robert J Young School of Materials, University of Manchester, Manchester, M13 9PL, UK
2.1. Introduction In the quest to understand reinforcement by high performance fibres, such as carbon fibres, the development of the subject of composite micromechanics is traced from its earliest roots. It is shown first how, employing concepts introduced by Kelly, it is possible through the use of shear-lag theory to predict the distribution of stress and strain in a single discontinuous fibre in a low-modulus matrix. For a number of years the shear-lag approach could only be used theoretically as there were no techniques available to monitor the stresses within a fibre in a resin. It is then shown that the advent of Raman spectroscopy and the discovery of stress-induced Raman bands shifts in reinforcing fibres, has enabled us to map out the stresses in individual fibres in a transparent resin matrix, and thereby both test and develop Kelly’s pioneering analytical approach.
2.2. Fibre Reinforcement – Theory 2.2.1. Composite micromechanics Interest in the mechanics of fibre reinforcement can be traced back to the first uses of high-modulus fibres to reinforce a low modulus matrix. A useful relationship developed to describe this reinforcement is the so-called ‘rule of mixtures’ in which, for stress parallel to the fibre direction, the Young’s modulus of a composite Ec consisting of infinitely-long aligned fibres is given by an equation of the form Ec
Ef Vf EmV m
(2.1)
where Ef and Em are the Young’s modulus of the fibre and matrix and Vf and Vm are the volume fraction of the fibre and matrix respectively (Young and Lovell, 2011). This equation captures the essence of fibre reinforcement and is found to work well in the specific conditions outlined above when high modulus fibres are incorporated into low modulus matrix materials. Since the strain in the fibre and matrix are the same, the stress in the fibres is much higher than that in the matrix - hence the fibres take most of the load and so reinforce the polymer matrix. O. Paris (Ed.), Structure and Multiscale Mechanics of Carbon Nanomaterials, CISM International Centre for Mechanical Sciences DOI 10.1007/ 978-3-7091-1887-0_2 © CISM Udine 2016
30
R. J. Young
In reality, however, composites do not consist of infinitely-long aligned fibres and are not always stressed parallel to the fibre direction. The full analysis of the situation in reality is the subject of many composites textbooks (Hull and Clyne, 1996; Gibson, 2012). The deformation of composites containing fibres of finite length deformed axially has been considered by a number of authors including Krenchel (1964). In addition he also analysed the situation with fibres aligned randomly in plane and also randomly in three dimensions (Krenchel, 1964). The problem of transfer of stress from the matrix to a fibre and the subsequent variation of stress along a fibre of finite length in a matrix was first tackled properly by Kelly
Data Loading...
