Anisotropic shear flow in continuous fibre composites

Anisotropic shear f l o w in continuous fibre composites R.S. JONES and R.W. ROBERTS (University of Wales, UK) Received 12 May 1993; revised 1 July 1993 An experimental investigation of the dynamic behaviour of an oriented assembly of aligned continuous fibres suspended in a viscous fluid matrix has been conducted using a purpose-built linear oscillator. The material has been characterized both along and transverse to the fibre direction for different fibre volume concentrations, and the results are compared with analytical predictions. Key w o r d s : continuous fibre-reinforced composites; dynamic behaviour; longitudinal and transverse viscosities

A linear oscillator has been designed and constructed by Jones and Wheeler ~ to measure the viscoelastic response of continuous anisotropic fibre-reinforced composite materials in their molten state. The instrument is illustrated in Fig. 1, and details of the construction and mode of operation were given by the authors. The instrument was tested using isotropic materials and gave data that were in excellent agreement with that given by two commercial instruments.

investigation. The carbon fibre-reinforced Golden Syrup used by Jones and Wheeler was not considered a suitable material for this investigation due to the difficulty of producing identical samples, the misalignment of the fibres and the difficulty of controlling the fibre volume concentration. Instead, a composite was constructed of Golden Syrup reinforced with aligned straight fibres of nylon.

The device was employed ~ to investigate the dynamic behaviour of carbon fibre-reinforced Golden Syrup, a model composite system supplied by ICI containing 60% by volume of virtually inextensible carbon fibres, each fibre having a diameter of approximately 7 ~tm. The model system was considered to be advantageous to the study of the flow of thermoplastic-based composites in that all experimental work could be conducted at room temperature. The composite was regarded as being transversely isotropic with different responses to longitudinal and transverse shear. The measurements of Jones and Wheeler showed little if any distinction between the longitudinal and transverse dynamic data. However, a large scatter in results was observed between identical experiments, which raised doubts as to whether any meaningful measurements could be obtained for this material.

FIBRE AND MATRIX PROPERTIES

An analytical model that predicts the longitudinal and transverse steady shear viscosities of an aligned fibre composite has recently been proposed by Christensen 2. In his analysis, Christensen assumes the composite to be an array of straight and rigid continuous cylinders suspended in a viscous fluid matrix, and expressions are derived which relate both the longitudinal and transverse shear viscosities of the material to the fibre volume concentration. Relatively little corresponding experimental work appears to have been reported in the literature and in view of this it was decided to conduct the present

Nylon fibres Two important properties of the fibres that required estimating were the average fibre diameter and average fibre density. To obtain these estimates a sample of 50 fibres was randomly chosen, and each fibre was cut to a length of 39 mm.

1. Average fibre diameter The diameter of each fibre was measured using a conventional optical microscope and an estimate of the average diameter D was calculated to be 0.21 + 0.003 mm. It was found that 94% of the fibres were within ± 0.03 mm of the average estimate. A slight variation in diameter was also observed along the length of the fibres, but this was assumed to be negligible.

2. Average fibre density The total mass of the fibres was 0.08 g and hence we could deduce Estimated average density of fibres Total mass (g) Total volume (cm 3) 0.08 50~D/2) 2 × 3.9

001 0-4361/94/030171-06 © 1994 Butterworth- Heinemann ktd COMPOSITES. VOLUME 25. NUMBER 3. 1994

171

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the coating process so that any sample contamination would be negligible and good contact was ensured between the sample and the plates. In each experiment the material was characterized both

Golden Syrup matrix The Golden Syrup used as the matrix is Newtonian in behaviour with a viscosity of 70 Pa s at 20°C. It was chosen in preference to a silicone oil, which has less sensitivity to changes in temperature and humidity, because of its better adherence to the fibres; Christensen 2 models a no-slip condition at the fibre/matrix interface. The strong dependence o f the dynamic moduli of Golden Syrup on temperature (Fig. 2) can be used to advantage as a means of comparing variations in the dynamic properties of the composite with those of the matrix.

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EXPERIMENTS A series of experiments was conducted to measure the dynamic response of nylon fibre-reinforced Golden Syrup to small amplitude sinusoidal oscillation at different fibre volume concentrations. In all experiments we employed plates of dimensions 39 × 39 mm.

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A sample was prepared by evenly coating a calculated mass of 39 mm nylon fibres with Golden Syrup before carefully arranging the assembly on the lower plate of the linear oscillator so that it was of uniform thickness and free from any fibre misalignments. The upper plate of the linear oscillator was then lowered until the sample was fully contained in a gap of 1 mm. The mass of fibres required for a volume concentration f was calculated from the estimated average fibre density (see Equation (1)). Every effort was made to minimize the time scale of

172

COMPOSITES. NUMBER 3. 1994

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D y n a m i c v i s c o s i t y and r i g i d i t y vs. f r e q u e n c y for: (a) f = 0.3; (b) f = 0.4; (c) f = 0.5; (d) f = 0.6; (e) f = 0.7; (f) f = 0.8

along and transverse to the fibre direction. A facility to rotate the sample in situ has been incorporated into the design of the oscillator. For each sample four readings were taken by successively rotating the sample through 90 °, giving two alternate longitudinal and transverse readings. A typical set of data is shown in Fig. 3, showing good agreement between each pair of readings and indicating little sample degradation. In subsequent figures the average of each pair of readings is used. Input and output waveforms were monitored by computer and only data from visually good waveforms were accepted.

RESUL TS Sample response to changes in frequency Frequency sweeps from 4.98 to 99.34 rad s-~ were conducted f o r f = 0.3, 0.4, 0.5, 0.6, 0.7 and 0.8 at a temperature of 20°C and amplitude of 0.36 mm. The results are given in Figs 4(a)-4(f). At high fibre concentrations the longitudinal dynamic viscosity r/[ is less than the transverse dynamic viscosity rh, whereas at low concentrations q[ is greater than r/~. Figs 4(c) and 4(d) are particularly interesting since they suggest that at some

COMPOSITES. NUMBER 3 . 1994

173

value o f f between 0.5 and 0.6 we have q'L = q'T.This was confirmed in a separate experiment where f was chosen to be 0.55; the results are shown in Fig. 5. In all cases it was observed that the longitudinal dynamic rigidity GL was less than the transverse dynamic rigidity G~r.

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Effects of changes in amplitude An amplitude range of 0.18 to 0.72 mm was employed and the results f o r f = 0.4, 0.55 and 0.7 at a temperature of 20°C and frequency of 31.42 rad s-~ are shown in Figs 6(a)-6(c). It can be seen that at the lower fibre concentration (0.4) there is little variation of the dynamic moduli with amplitude. However, at the highest concentration (0.7) both qL and q'v decrease with increasing amplitude, with q'v being most affected.

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Temperature effects As stated earlier, the dynamic moduli of the matrix, /"I'm and Gm, have a strong temperature dependence (Fig. 2). Although no temperature-controlling facility has been incorporated into the linear oscillator, we were able to achieve a narrow temperature range of 19 to 21°C. Over this range q'm decreases by 23% and G'm by 26%. Similar temperature sweeps for the composite at fibre concentrations f = 0.4, 0.55 and 0.7 were carried out at a frequency of 31.42 rad s- ~and amplitude of 0.36 mm; the results are illustrated in Figs 7(a)-7(c). For each concentration the percentage decreases in the longitudinal and transverse dynamic moduli over the temperature range are shown in Table 1.

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has also been investigated by Scobbo and Nakajima 4. a Their measurements showed r/L to be approximately 10% greater than rl~. However, the frequency range employed was between 60 and 380 rad s-~ which is outside the frequency range used in our experiments.

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An alternative method of characterizing anisotropic materials in their longitudinal and transverse directions is by off-centred torsion testing. This technique has been applied by Groves e t al. 3 to study the dynamic behaviour of the following fibre and polymer systems at their melt temperatures: (1) 60% carbon fibres in a polyetheretherketone matrix (CFRP) and (2) 35% glass fibres in polypropylene (GFRP).

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174

COMPOSITES. NUMBER 3. 1994

An analytical prediction of the longitudinal and transverse steady shear viscosities r/L and rH for an aligned fibre composite has been put forward by Christensen 2. In his analysis, Christensen assumes the composite to be an array of equally spaced straight and rigid continuous

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cylinders suspended in a viscous fluid matrix, and formulae for r/L and rh are derived in terms of the volume concentr a t i o n f o f the cylinders. Christensen pays particular attention to concentrated suspensions of cylinders so that his main results are only valid at the high concentration range. However, by making use of the classical results for dilute suspensions 5 he derives empirical forms for rh and rh for the entire concentration range. Similar work for discontinuous cylinders has been carried out by Pipes 6. For a hexagonal array of cylinders, which best approximates the fibre arrangement in our experiments, the results of the authors can be summarized as follows: r/L _ 1 + 0.873f qm (1 -- 0.8815[)'"2(1 -- f ) ' : qT _ (l -- 0.193]) 3 (Christensen) r/m (l -- 0.5952f)3/2(1 -.1~)3:2

(2)

and

Table 1. Decreases in d y n a m i c moduli for n y l o n / G o l d e n Syrup composites over t e m p e r a ture range of 19-21°C i

0

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COMPOSITES. NUMBER 3. 1994

175

that the dependence of the dynamic viscosities on fibre volume concentration is the same as that for the steady shear viscosities. Denoting q'm as the dynamic viscosity of o t Golden Syrup (70 Pa s at 20 C), the ratios r/L/r/m and rh/ r/m were calculated for each of the results shown in Figs 4(a)~(f). The values of q[ and r/~ were taken at a middle range frequency of 31.42 rad s 1. A comparison of the ratios with those obtained by Christensen and Pipes is shown in Fig. 8(a). Both analytical predictions show r/L to be less than qT for all fibre volume concentrations, which is contrary to our experimental results. Christensen's formulae, relations (2), for r/L/qm and qv/ r/m are empirical full-range forms which have the correct behaviour for large and small concentrations. It is possible to modify those forms while retaining the asymptotic behaviour such that r/L ( r/T f o r f > 0.55 and r/L ~ r/T f o r f < 0.55. For example, it is seen from Fig. 8(a) that Christensen's formula for r/T/rlm fits our experimental data reasonably well while r/L/r/mdoes not. So, retaining the formula for r/T/r/m, the following alternative formula for r/L/rlm can be constructed: r/L -- [l + fZ(4.763f2 -- 10.193f + 4.43)] Tim

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This has the correct asymptotic behaviour for both concentrated suspensions 0r ~ 1) and dilute suspensions (f -~0) and is such that r/L < r/T f o r f > 0.55 and r/L > r/x f o r f < 0.55. It is seen from Fig. 8(b) that this alternative form gives a better fit to the experimental points. It should be emphasized that the forms for r/L and rh in relations (2) and (4) are examples of an infinite number of possible empirical full-range formulae that have the correct asymptotic behaviour.

176

COMPOSITES. NUMBER 3 . 1994

SUMMARY A continuous fibre composite has been characterized rheologically in both its axial and transverse directions for different fibre volume concentrations. The results show consistency with the work of Groves et al. 3, and a comparison has been made with the analytical predictions of Christensen 2 and Pipes 6. By modifying one of Christensen's formulae good agreement between theory and experimental data has been attained. REFERENCES 1 Jones, R.S. and Wheeler, A.B. 'A characterization of anisotropic shear flow in continuous fibre composite materials' Composites Manufacturing2 (1991) pp 192 196 2 Christensen, R.M. 'Effective viscous flow properties for fibre suspensions under concentrated conditions' J Rheology 37 (1993) pp 103 121 3 Groves, D.J., Stocks, D.M. and Bellamy, A.M. 'Isotropic and anisotropic shear flow in continuous fibre thermoplastic composites" Proc Golden Jubilee Meeting of the British Society of Rheology and Third European Rheology Conference, Edinburgh. UK, 1990 pp 190-192 4 Scobbo, J.J. and Nakajima, N. 'Dynamic mechanical analysis of molten thermoplastic/continuous graphite fiber composites in simple shear deformation' Proc 21st Int SAMPE Technical Conf (1989) pp 730-743 5 Eshelby, J.D. "The determination of the elastic field of an ellipsoidal inclusion and related problems' Proc Royal Soc London A241 (1957) pp 376-396 6 Pipes, R.B. 'Anisotropic viscosities of an oriented fibre composite with a power-law matrix' J Composite Mater 26 (1992) pp 15361552

AUTHORS The authors are with the Department of Applied Mathematics, University of Wales, Aberystwyth, Dyfed SY23 3BZ, UK. Correspondence should be addressed to Dr Jones.