A characterization of shear flow in continuous fibre thermoplastic laminates

A characterization of shear flow in continuous fibre thermoplastic laminates D. J. GROVES (ICI Wilton Materials Research Centre, UK)

The viscoelastic response of some continuous fibre thermoplastic composites has been investigated dynamically. The contribution of the number and direction of laminate ply layers and fibre type, together with the geometry, have been explored in relation to the matrix polymer. An interpretation in terms of an apparent Maxwell viscosity is in agreement with steady shear flow viscosity, and approximates to a large strain dynamic viscosity. A yield stress of the order of 1 kPa is implied by the Maxwell interpretation together with a high stress viscosity more than 10 times the viscosity of the matrix polymer. The use of model laminates leads to the prediction of both interply and intraply polymer flow in continuous fibre thermoplastic composites.

Key words: shear flow; viscoelastic response; model laminates; continuous fibre thermoplastic composites

The use of continuous fibre composite materials has been developing rapidly, with glass fibre and particularly with the introduction of carbon fibres. For many years these materials were based on thermosetting resins, used in the fluid state to impregnate fibre systems and then cured thermally to form a cross-linked structure. With the introduction of continuous fibre-reinforced thermoplastic structural composite, new concepts of rapid fibre composite fabrication were established, depending only on effective heat transfer. This general concept of composite thermoforming brings with it the need to characterize and understand the rheology of these thermoplastic based systems. Little has been reported on the melt flow in such composites and the viscoelastic characterization of composite materials up to the present time appears to be restricted to the solid phase. 1 Initially the material is in the form of a thermoplastic tape or prepreg 0.125 mm thick, and containing about 60% by volume of continuous fibre uniaxially aligned along its length. Subsequently tapes are usually laminated together with the ply orientation chosen according to the application. The forming of laminates and associated shaping processes which are performed essentially in the molten state with consequential reorganization of fibre orientation have been reviewed by Cogswell. 2 Some aspects of metal forming

technology are also involved. 3 It follows that materials are available in essentially planar form and rheological characterization is therefore restricted to a planar or parallel plate geometry. A high performance composite requires a high performance, high temperature thermoplastic such as the linear chain polyetheretherketone, which is normally processed at temperatures close to 400°C. Depending on composition and molecular weight, the viscosity has a range between 102 and 104 Pa s. In the context of polymer melt flow, the composite fibres are inextensible and the rheological characterization is therefore restricted to shear deformation. Even so, the system is rheologically complex. To simplify analysis, the two materials characterized here are fabricated witl~ a nominally Newtonian resin, one containing 17 ~tm diameter glass fibre and the other containing 7 I~m diameter carbon fibre. The effect of different resin viscosities and the links between shear rheology and processing are reported separately. 4

EXPERIMENTAL PROCEDURE All measurements were made at 380°C using a Rheometrics Dynamic Spectrometer. Parallel disc platens were used to avoid disturbing the fibre alignment in the planar specimens. When a laminate o f

0010-4361/89/010028-05 $3.00(~)1989 Butterworth & Co (Publishers) Ltd 28

COMPOSITES. VOLUME 20. NUMBER 1. JANUARY 1989

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relaxation to be achieved. An inert nitrogen atmosphere was used throughout to ensure good polymer stability during the time of measurement.

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prepreg plies is sheared in the plane of lamination, the initial ply orientation will change. It follows that in steady shear experiments there is uncertainty in defining the interply orientation after the varying times of shear necessary to achieve equilibrium stress at different shear rates. The primary characterization was therefore made in small strain oscillation about the cylindrical axis of symmetry to obtain the complex modulus and phase angle, from which the dynamic viscosity and modulus were calculated. The test sample geometry is shown in Fig. 1.

Sample preparation Single layers of prepreg were cut approximately to platen size in the octagonal form shown in Fig. 1. The prepreg was laminated together between the rheometer platens, in either an all parallel or cross-ply (alternate 0* and 90 °) orientation. The pressing force between platens was approximately 1 kg. This simple specimen preparation has been shown to give identical data to ;high pressure press laminated samples, and offers total rversatdlty m the number and onentaUon of plies. platen diameters between 10 mm and 50 mm have been used with 25 mm adopted as the standard for most measurements.

Measurements The rheometer test temperature is measured at the centre of the lower disc platen. As the matrix polymer melts through the laminate thickness and reaches the set temperature, the normal laminating force drops. A dwell time of between 3 and 5 min after reaching the test temperature was sufficient to allow a uniform temperature distribution to develop and stress

COMPOSITES. JANUARY 1989

1) Dynamic measurements The complex modulus (G*) was calculated from the maximum shear stress and shear strain (obtained from the measured torque and strain amplitude vectors). Using the phase angle (6), the in phase and quadrature components, storage modulus (G') and loss modulus(G") respectively, were calculated assuming linear viscoelasticity for an isotropic sample with sinusoidal response. The moduli, G' and G " , were expressed as functions of angular frequency (to) to characterize the dynamic response and strain amplitude to establish linearity of strain response. Complex viscosity (11" = G*/to) and dynamic viscosity (~1' = ~1" sin 6) were calculated following the same assumptions. The input and output sinusoidal waveforms were monitored during all measurements by an oscilloscope. Only data from visually good waveforms have been included. In addition, a frequency spectrum analyser was used to make a detailed analysis of waveform harmonic content. Only odd harmonics were present, the number and amplitude increasing at low frequency. These waveform harmonics together with a diverging strain amplitude dependence of modulus confirm non-linear viscoelasticity at the lowest frequencies. However, at higher frequencies and larger amplitudes of deformation, a pure sine wave response and diminishing strain dependence of modulus demonstrate that these composites then approximate to linear viscoelastic behaviour.

2) Steady shear measurements A triangular wave was used to provide unidirectional steady shear over 1 radian of angular displacement (+0.5 rad). A steady torque for the shear stress was obtainable up to a maximum shear rate of 0.5 s -1. The angular displacement or strain needed to establish a steady torque increased with shear rate, imposing the limit of usable shear rate.

RESULTS AND DISCUSSION Firstly, the thermal stability of the composite samples was examined by monitoring dynamic viscosity at 1 rad s-1 over a timescale of 1 hour. There was no measurable change. Secondly, the number of laminate plies, between 5 and 19, was found to have little effect on the moduli and complex viscosity as shown in Fig. 2 for carbon fibres in crossed ply orientation. The frequency and strain dependence show small differences between crossed and parallel plies of carbon fibre for dynamic viscosity in Fig. 3 and dynamic modulus in Fig. 4. The maximum strain amplitude dependence is clearly at the lower frequencies and strains. While the matrix polymers themselves are almost Newtonian and have a strain independent linear viscoelastic response, Figs 3 and 4 show the composites

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to be very non-Newtonian. There is also non-linear viscoelastic behaviour, at low frequencies. A simple relationship between the dynamic response and steady shear flow would not therefore be expected. However, the treatment as a Maxwell fluid, following Benbow, Cogswell and Cross 5 leads to some unexpected results in Fig. 5 for carbon fibre composite and Fig. 6 for glass fibre composite. By applying the relationships:

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for apparent Maxwell viscosity (tiM) and shear rate (9), the strain dependence is largely eliminated. At larger strain amplitudes and higher angular frequencies, the dynamic viscosity approximates more closely to the apparent Maxwell viscosity. This is the converse of normal expectation with a polymer melt. It is evident from the dependence of tan 6 on angular frequency shown in Fig. 7 that tan 8 increases with strain amplitude, and that the viscoelastic response of these composites becomes closer to a simple viscous fluid at larger shear strains. Equation (1) states that when tan 6 is large, as would be the case for a Newtonian fluid, tiM---->ti'. 30

Fig. 5 Comparison of, dynamic, steady shear and apparent Maxwell viscosities for carbon fibre composite

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COMPOSITES.

J A N U A R Y 1989

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fibres. When the Maxwell viscosity is presented as a function of shear stress in Fig. 8, there is a limiting stress of about 1 kPa which appears to be dependent on the nature of the reinforcing fibre. The contribution of the fibre may also be inferred from the dependence of the dynamic moduli on platen diameter and fibre length. Since the approximate maximum shear strain (%) is given by:

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for a fixed sample thickness h, the angular displacement 0 must increase as the platen radius R decreases. Thus as the fibres are deformed through a greater angular displacement as their length is decreased with the smaller platens, the dynamic modulus and viscosity increase, as shown in Fig. 9.

Strain d e p e n d e n c e of tan b for c a r b o n fibre and glass

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Shear flow distribution Although the use of apparent Maxwell viscosity seems to reduce or eliminate strain dependence, it is only by steady shear measurement that a true steady flow viscosity can be established with certainty. Reference to Figs 5 and 6 shows that the steady shear and apparent Maxwell viscosities are in reasonable agreement. It should be noted that steady flow viscosity measurement is subject to strain hardening at shear rates above about 0.1 s-1. For data above that shear rate, an inflexion prior to the strain hardening has been taken to represent equilibrium stress, and these values are in agreement with the computed Maxwell viscosity. However, very high shear strains above 2.5 are involved, and the fibre ply orientation may be changed, although with qualitatively similar shear flow rheology for cross-ply and parallel ply composites, that may not represent a serious problem. At low shear rates, or low angular frequency and low strain amplitude, these thermoplastic composites are clearly non-Newtonian and non-linear in viscoelasticity. It is speculated that this small strain hindrance is caused by the elastic contribution of the

When the prepreg tapes are laminated together a resin rich layer of approximately 5 ~m thickness is formed at the interply boundaries. The possibility of flow occurring only in this interply layer must be examined. In steady shear flow, the stress appears to be related to low shear rates by an approximate Power Law with an index of about 0.5. Clearly the flow is neither Newtonian nor an entirely wall shear regimen. To investigate this problem, model laminates of thermoplastic polymer with rigid sheets of different density were evaluated by dynamic viscoelastic response. In three experiments, the laminates contained 9 layers of polyimide sheet, aluminium sheet and brass sheet respectively, placed alternately with 10 layers of a polyetheretherketone sheet. Polyetheretherketone (PEEK)sheets were 0.1 mm thick, the polyimide and aluminium 0.15 mm and the brass was 0.13 mm thick. In each case, only the PEEKis fluid at 380°C. The dynamic viscosity was calculated firstly, for the total laminate and secondly, for a sample thickness equivalent to the 10 matrix resin layers alone. Each is expressed as a ratio of the matrix resin viscosity in Fig. 10. It is seen that in the latter case the viscosity ratio approaches unity for the polyimidee laminate with

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C O M P O S I T E S . J A N U A R Y 1989

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inconsistent with the model laminate results, it implies that there must be intraply mobility of the thermoplastic matrix resin. This view is supported by the non-Newtonian response which confirms an interaction between the Newtonian matrix resin and fibres.

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CONCLUSlONS

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an increasing magnitude, probably due to inertia, for aluminium and brass. Unlike the fibre composite, all three laminates remain almost Newtonian. A similar analysis, taking account of the matrix resin thickness only was then applied to the carbon fibre composite. In calculating the dynamic viscosity, two cases were considered. Firstly, the sample thickness was taken as the sum of the interply resin rich layers only with the viscosity ratio shown as curve A of Fig. 11. Secondly, the intraply resin was included by taking the total platen separation minus the sample thickness contribution of the fibres themselves, the viscosity ratio being shown as curve B in Fig. 11. With a ratio less than unity the apparent matrix viscosity in curve A is less than for the free resin. Since this is unlikely, and Carbon fibre composite

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32

ACKNOWLEDGEMENT The Author acknowledges the helpful experimental contribution of Mr R. C. Young.

1 Vallance, M. A. and Tomkin~n, G. D. 'Linear viscoelastic response of high performance thermoplastic composites' Antec 86 44th Annual Technical Conf (1986) p 562 2 Cogswell, F. N. 'The processing science of thermoplastic structural composites' Int Polym Process 1 No 4 (1987) p 157 3 Cattanach, J. B. and Cogswell, F. N. in: Developments in Reinforced Plastics 5, Edited by G. Pritchard (Elsevier Applied Science, 1986) 4 Cogswell, F. N. and Groves, D. J. 'The melt rheology of continuous fibre reinforced structural composite materials', Proc lOth Int Congress Rheol. Sydney, 1988 (to be published) 5 Benbow, J. J., Cogswell, F. N. and Cross, M. M. 'On the dynamic response of viscoelastic fluids' Rheol Acta 15 (1976) p 231

o Resin rich interlayer only o Composite thickness minus fibre

10 -1

A study of model laminates leads to the prediction of intraply flow of the matrix polymer as well as interply flow in the resin rich layers.

REFERENCES

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composite, determined from oscillatory shear is nonlinear at low frequencies. An interpretation of the dynamic viscosity using the concept of apparent Maxwell viscosity and maximum shear rate is independent of strain amplitude, and in qualitative agreement with steady shear flow viscosity. The dynamic viscosity approximates to the Maxwell viscosity at increasing strain amplitude as tan 6 increases and elastic constraint decreases. However, strain hardening occurs at larger strains in steady shear. Conversely, the Maxwell viscosity interpretation predicts a limiting stress or yield at low shear rate which depends on the fibre type and its arrangement. A very small platen size and fibre length may increase the predicted composite viscosity and should be avoided.

103

A U THOR

The author is with ICI Wilton Materials Research Centre, PO Box No 90, Wilton, Middlesbrough, Cleveland T56 8JE, UK

COMPOSITES.

JANUARY

19891