The compressive strength of highly-aligned carbon-fibre/epoxy composites produced by pultrusion
Introduction
Composites usually fail under compressive loading parallel to the fibre axis at appreciably lower stresses than when the same material is loaded in tension. This is of major concern, since there are many important applications in which such materials are subjected to high compressive stresses. Most models for compressive failure focus on shear failure parallel to the fibre axis, which occurs more readily with increasing misalignment between this direction and the loading axis. The presence of a region in which the fibres are misoriented with respect to the loading axis by an angle φ leads to failure by the formation of a kink band (sometimes termed a microbuckle) at an applied stress, , which can be related to a critical interfacial shear stress on planes parallel to the fibre axis, . The value of should be measured experimentally on the composite material concerned, although it may be close to the matrix shear yield stress in some cases. Writing φ as the sum of an original misorientation φ0 and the elastic shear strain, γ12, arising from the shear stress leads, after some rearrangement, to the following expression for the compressive strength.where G12c is the shear modulus of the composite.
An analysis of this type has been presented by Budiansky and Fleck [1]. The above equation reduces to expressions derived earlier by Argon [2] and by Rosen [3] for the respective limiting cases of a rigid-plastic material (G12c→∞) and no initial fibre misalignment (φ0→0). The equation predicts a value for which falls sharply with increasing φ0 from G12c (typically several GPa for a polymer-matrix composite) at φ0=0° to about 1–2 GPa at φ0 ≈ 2–3°, for a composite shear strength, , of around 50–100 MPa. This model has in general given fairly good quantitative agreement between prediction and measurement when applied to a range of polymer composites [4], [5], [6], [7], [8], [9], [10], although it should be mentioned that there is usually a large degree of uncertainty surrounding the experimental characterisation of fibre misalignment in a composite. There have also been several studies [11], [12], [13] in which the basic principles involved in prediction of this type of shear instability have been incorporated into numerical models, allowing investigation of the effects of variables such as the size and shape of the initially misoriented region.
A few researchers [5], [14], [15], [16], [17], [18] have considered the possibility of the failure behaviour being affected by the strength of the fibres. In a recent study [18] of monofilament-reinforced titanium, for which low values of φ0 are readily attainable and the shear strength is relatively high (∼300 MPa), it was shown that there is a range of φ0 (up to about 3°) for which failure occurs by a fibre crushing mechanism, such that the composite compressive strength is approximately constant and is given by the following equationwhere f is the fibre volume fraction, is the fibre crushing strength and σmY is the matrix yield strength. Since for the monofilaments used in the study was ∼9 GPa, σmY for the matrix was ∼1.3 GPa and the value of f was ∼35%, the strength of well-aligned material (φ0 ∼ 1°) was predicted (and measured) to be ∼4 GPa, whereas application of Eq.(1) suggests a value >10 GPa. A consequence of the relatively low shear strengths and shear moduli of polymer composites is that the compressive strength indicated by Eq. (1) is normally well below that given by Eq. (2) for these materials, although, in view of uncertainties about the compressive strength of many fibres, it is conceivable that this might not be true in cases of very good fibre alignment (φ0 <1°) and/or relatively low fibre volume fraction.
In the current paper, an investigation is presented into the compressive failure strength of carbon-fibre/epoxy composite material produced by a pultrusion technique which generates very high degrees of fibre alignment within relatively small diameter rods. There is very little published information on the compressive strength of such material, although some recent work has covered the use of such rods in composite assemblies [19], the development of test methods [20] for slender specimens of this type and some preliminary mechanical property measurements [21]. These suggested compressive strengths of about 1.8 GPa for 1.7 mm diameter rods and 2.4 GPa for 0.74 mm rods, but there was considerable scatter in the data and no clear explanation for a dependence of the strength on the specimen diameter. In the current work, measured strengths are examined both in terms of expected failure mechanisms, and the effect on these of pores which were present in some of the material studied, and from the point of view of how the testing geometry might influence the stress field in the specimen, and hence the apparent strength.
Section snippets
Material production
‘Graphlite®' rod, supplied by Neptco Incorporated, was fabricated using a pultrusion technique. The composite comprises 67 vol% of IM7 carbon fibres, in an “Epon” range epoxy resin matrix. The rod was formed in a continuous length with a nominal diameter of 1.7 mm. Two grades of material were supplied, termed grade A and grade B. These were produced under different pultrusion conditions. Although the processing details are not available, grade B was produced under conditions allowing a more
Compressive failure behaviour
A typical stress–strain plot is presented in Fig. 5, which also shows the transverse (hoop) strain as a function of axial strain, indicating how the instantaneous Poisson ratio was changing as the test progressed. It can be seen that no significant divergence occurred between the readings of the two axial gauges. This indicates that little or no long range bending of the specimen occurred up to the point of failure. In fact, bending in the plane normal to that defined by the two gauges would
FEM analysis
Finite element modelling, using ABAQUS v.5.7, was employed to determine elastic stress distributions within the specimen and around individual pores. Meshes were composed of isoparametric 8-noded quadrilateral elements, specially designed for the ABAQUS solver to model axisymmetric systems. The composite material was treated as an anisotropic continuum and the other constituents as isotropic continua. (The effect of any local variations in fibre alignment in the vicinity of the holes was
Conclusions
The following conclusions may be drawn from this work.
(a) Two grades (A & B) of pultruded composite rod have been studied. Grade B, which was produced using different pultrusion conditions from those of grade A, exhibited extensive fibre fracture, and associated elongated pores, whereas grade A was free of these defects. Grade B material exhibited a thin pore-free region near the periphery of the pultruded rod.
(b) The degree of fibre alignment was characterised using the fibre sectioning method
Acknowledgements
This work was carried out as part of a studentship supported by the EPSRC, within a programme involving Hexcel Composites, British Aerospace, DERA and Neptco. The authors are grateful for useful discussions with P.M. McClellan and S. O'Meara, of Neptco, with Dr. J. Ball, of British Aerospace, and with Prof. N.A. Fleck and Dr. M.P.F. Sutcliffe, of Cambridge University.
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