Analysis of stress concentrations in multi-fibre microcomposites by means of Raman spectroscopy

Abstract

Many theories have been developed to predict the strength of unidirectional fibre-reinforced composites [1-4]. Over the years it has been recognized that knowledge of the stress concentrations in fibres adjacent to a broken fibre is of major importance in these theories. Since such stress concentrations cannot normally be measured directly, many analytical theories have been proposed for the calculation of this stress concentration factor [5 7]. Recently, also the finite element method has been used to calculate the stress concentration factor in fibres adjacent to a fibre break [8]. Because of the complexity of the problem, all these calculations contain great simplifications with respect to, for example, the fibre arrangement and material properties. Using a simple shear lag theory in which only the fibre is assumed to carry the tensile stress, Hedgepeth and Van Dyke [5] calculated a stress concentration factor of 1.333 for a planar array of fibres, independent of the inter-fibre spacing and the physical properties of the fibre and the matrix. More complicated theories for the stress concentration factor include, for example, the fibre content and the modulus of the fibre (El) and of the matrix (Ere) [6, 7]. Ochiai et al. [6], for instance, proposed a theory for the stress concentration factor in a planar array of elastic fibres in an elastic matrix in which, in contrast to Hedgepeth and Van Dyke [5], both the fibres and the matrix are assumed to carry tensile stress and act as media for stress transfer. At an inter-fibre spacing of 1 fibre diameter (@) this theory yields a stress concentration factor of approximately 1.25 for Ef = 350 GPa and Em = 3.5 GPa. Unfortunately, until now experimental verification of calculated stress concentration factors had not been possible. In this letter, we present preliminary results showing that Raman spectroscopy makes it possible to measure stress concentration factors in fibres adjacent to a fibre break. With Raman spectroscopy, strain profiles of a large variety of fibres can be measured in situ, i.e. inside a composite [9-11]. In our experiments use is made of a carbordepoxy multi-fibre microcomposite, in which five continuous carbon fibres are aligned parallel in a planar array at a predefined inter-fibre spacing in a dumbbell-shape tensile bar (see Fig. 1). Such a microcomposite has shown to be very useful in investigations into the effects of stress concentration factors due to an