Keywords: composites, representative volume elements, statistical microstructure, multi-scale modelling, random point fields, carbon fibre.

Failure in composite materials results from microscopic damage accumulation in both the fibre and/or the matrix, leading to a multitude of macroscopic failure modes. In an attempt to predict such phenomena, multi-scale modelling techniques, where micromechanical models are coupled to macroscopic models, have begun to emerge [1,2]. Micromechanical models represent the fibre and matrix phases discretely in the form of a representative volume element (RVE), which is of finite size and is statistically representative of the material as a whole. A previous representation of an RVE used a periodic arrangement of fibres, in the form of a unit cell [3] and this is quite common in the published literature. However, in reality the micro-structure can contain fibre rich (clusters) and fibre denuded regions causing an irregular stress distribution to exist across the microstructure, which allows microscopic damage mechanisms to occur more easily [4].

This paper highlights the development of an RVE which is statistically equivalent to the micro-structure of the carbon fibre composite material. The microstructure is examined using image analysis software and a large bank of data is generated and then used to create statistical models of the fibre diameter, radial and nearest neighbour distributions. An algorithm is then developed in Matlab, where it is possible to generate random representations of the microstructure, the spatial arrangements of which are defined by a hard-core random field. It was found that the fibre volume fraction of these generated microstructures was less than the actual microstructure and consequently the pitch distribution and radial distribution functions differed somewhat. It was thus found that the microstructure of composite materials with a high volume fractions cannot be modelled using a hard-core random field and so in order to arrive at a statistically equivalent microstructure, a new approach is required.

1

Y.W. Kwon, D.H. Kim, T. Chu, "Multi-Scale Modeling of Refractory Woven Fabric Composites", Journal of Materials Science, 41(20): 6647-6654, 2006. doi:10.1007/s10853-006-0195-4

2

C.H. Wang, "Progressive Multi-Scale Modelling of Composite Laminates", in "Progressive Multi-Scale Modelling of Composite Laminates", P.B. C. Soutis, (Editor). Woodhead Publishing: Cambridge., Chapter 8, 259-277, 2005.

3

C.T. Sun, R.S. Vaidya, "Prediction of Composite Properties, from a Representative Volume Element", Composites Science and Technology, 56(2): 171-179, 1996. doi:10.1016/0266-3538(95)00141-7

4

T. Matsuda, N. Ohno, H. Tanaka, T. Shimizu, "Effects of Fiber Distribution on Elastic-Viscoplastic Behavior of Long Fiber-Reinforced Laminates", International Journal of Mechanical Sciences, 45(10): 1583-1598, 2003. doi:10.1016/j.ijmecsci.2003.09.021

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