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Measuring the fibre orientation and modelling the elastic properties of injection-moulded long-glass-fibre-reinforced nylon
Composites Science and Technology 53 (1995) 125-131 0 1995 Elsevier Science Limited Printed in Northern Ireland. All rights reserved 0266-3538(95)00011-9
0266-3538/95/$09.50
MEASURING THE FIBRE ORIENTATION AND MODELLING THE ELASTIC PROPERTIES OF INJECTION-MOULDED LONG-GLASS-FIBRE-REINFORCED NYLON
P. J. Hine,” N. Davidson,h uIRC
in Polymer Science and Technology,
R. A. Duckett”*
& I. M. Ward
h Instrumentation Group, Physics Department,
University of Leeds,
Leeds, UK, LS2 9JT
(Received 10 December 1993; revised version received 13 April 1994; accepted 15 December 1994) Abstract
the injection process and prediction of the resulting fibre orientation. Folkes’ in his book on short-fibrereinforced thermoplastics gives a good review of this area of study; the thesis of Bay’ describes a model for the prediction of fibre orientation during injection moulding. Other authors who have attempted to predict fibre orientations during flow include Doshi et al.,” Gilver et al4 and McClelland and Gibson.” The second major area of study is the measurement of fibre orientation and composite property modelling. Again there are a large number of papers concerned with area of research including Bay,2 this Truckenmuller,’ Fakirov and Fakirova,’ Darlington,x O’Donnell and White’ and O’Connell and Duckett.“’ In this laboratory we have concentrated on the second area of research examining the links between fibre orientation and composite properties, utilising a unique image analysis facility for obtaining accurate 3D fibre orientation measurement, combined with our innovative models for predicting 3D composite elastic properties. Systems so far studied include aligned short-carbon-fibre-reinforced epoxy manufactured by prepreg methods,‘1.‘2 random-in-plane carbon-fibrereinforced epoxy, again manufactured by prepreg techniques” and hydrostatically extruded short-glassfibre-reinforced polyoxymethylene.‘4 The present paper describes a characterisation of the 3D fibre orientation of an injection-moulded plaque of long-glass-fibre-reinforced Nylon 6.6 and the use of the orientation data for modelling the orthotropic elastic properties. The elastic properties of the composite were measured by the ultrasonic velocity method, and provided a rigorous test of our modelling techniques. Image analysis, working from polished sections taken at various points from the composite, was used to determine the 3D fibre orientation distribution. This was achieved by using a transputer-based image analysis system, developed in-house by our colleagues in the Instrumentation Group in the Department of Physics. 15*IhThis is a unique facility which allows rapid
This paper describes the characterisation of the 30 fibre orientation of a single-gated injection-moulded plaque of short-glass-fibre-reinforced Nylon by image analysis, and the use of this orientation data for the theoretical prediction of the composite elastic properties, Fibre orientations were measured by using a purpose built image analysis facility, which allows 30 data to be obtained. Composite elastic properties were measured by an ultrasonic velocity method and compared with theoretical predictions obtained from the modelling techniques of Wilczynski and Ward. Keywords: composites, fibre orientation, modelling, elastic properties, glass-fibre-reinforced Nylon
1 INTRODUCTION The current trend in fibre-reinforced composites is away from expensive carbon-fibre-reinforced thermoset composites, towards glass-fibre-reinforced thermoplastic composites, often manufactured by injection moulding. The advantages of a thermoplastic-based composite include lower material cost, low cycle time for manufacture and the possibility of recycling after use. There is therefore considerable incentive for understanding the complex links between the composite manufacturing process, the resulting fibre orientations and final composite properties. The long-term aim of this research is to be able to predict the final properties of a composite from details of the manufacturing process and the properties of the constituent phases. Research on short-fibre composites can be divided into two major areas: understanding the effects of the manufacturing process on resulting composite fibre orientation structures and understanding the effects of fibre orientation on mechanical properties. The first involves understanding the complicated rheology involved in the flow of fibre and molten polymer during * To whom correspondence should be addressed. 12s
P. 1. Hine et al.
126
and accurate orientation data to be obtained, analysing typically 40 000 images h-‘. The modelling of the properties of fibre-reinforced composites is undertaken in two stages, as originally proposed by Brody and Ward.” Firstly, the properties of an individual composite unit are calculated, and secondly the effects of a range of orientations are computed. We have followed the recommendations of our previous work,” in using the theory of Wilczynski to determine the unit properties and the full aggregate for modelling the effects of model of Ward” orthotropic anisotropy. 2 EXPERIMENTAL The composite used in this study was long-glass-fibrereinforced Nylon 6.6, from the ‘VERTON’ family of materials manufactured by ICI Ltd. The sample was a rectangular plate (65 mm X 220 mm) with the single fan gate located along the shorter side of the rectangle: the sample was 6 mm thick in the gate section and 3 mm thick in the main section. The fibre volume fraction of the composite was measured by acid digestion (ASTM D3171 (Ref. 20)) as 0.28 f 0.01. Image analysis was used to determine the 3D fibre orientation distribution at various positions across the sample. The chosen analysis points are shown in Fig. 1, along with the sample geometry details. The first section was taken in the gate region, 5 mm from the gate entrance: this section was denoted A and was taken in the 32 plane (see Fig. 2). The remainder of the sections, B to G, were located in the main section of the plate. The first series of samples was taken along the centre line of the plate at 15 mm, 60 mm, 110 mm and 220 mm from the gate entrance (sections B to E, respectively). The second series was taken 110mm from the gate, along the centre line of the plate and at 10mm and 30mm from the centre line (B, F and G, respectively). The sections from the main plate were taken in the 12 plane. When a section is taken through a composite it
G
;
Injection Point +A;B
reveals each fibre as an elliptical image. Measurement of the elliptical parameters of each image allows the angles that specify the 3D orientation of the fibre to be determined. In general only two angles, 13and 4, are needed to specify the 3D orientation (Fig. 2) of each fibre: for this paper 8 is defined as the angle a fibre makes with the 3 axis of the sample, which is the injection direction, and 4 is the angle the projection of the fibre onto the 12 plane makes with the 2 axis. For a material where the properties are orthotropic, it is often more instructive to determine the angle each fibre makes with the three structural axes, defined as Or, &, & (also shown in Fig. 2). Both of these approaches, for defining the 3D fibre position, have been used in this work. One of the major problems with image analysis of polished composite sections are the errors encountered when analysing fibres that are nearly perpendicular to the sectioned surface, and so are supposedly close to circular. Errors introduced by polishing or digitisation cause the fibres to appear elliptical and so they are assigned incorrect values of 8. In fact the fibres may not even be circular in shape to start with, and so even fibres which are perpendicular to the section would be interpreted as being inclined to the section normal. A method for reducing this error is to section at an angle to the main fibre direction.“~‘* The fibres now appear mainly as ellipses and the influence of polishing and digitisation errors on the ellipticity is much reduced. Once the data is collected it can then be transformed back to the main axis system of the sample. ’ ’ For initial investigation of the structure of fibre orientations within the sample the standard transverse section was used, but where accurate orientation distributions were needed for modelling a 70” section angle was used. All the image data collected was corrected for the effects of counting bias. We have followed our previous work by using the simplest form for this correction by dividing the number of fibres counted in each angle increment A8 by cos 8. Modelling was only carried out at one position on
F D
C
E
I 6Chnn1
3
b J
?
1
(.. j 3OmmI 220mm --+
6mm thick
Fig. 1.
1
3mm thick
Details of the injection
moulded image analysis positions.
Injection direction
sample
and the Fig. 2. Sample axis definitions.
%
2
Injection-moulded
long-glass-jibre-reinforced
the plate; 60mm from the gate and along the centre line of the sample (position C). Elastic properties were measured at this point using the ultrasonic velocity method. In this technique the sample is placed in a water bath between two ultrasonic transducers, one a transmitter and one a receiver. The basic measurement is the time of flight for a 2.25 MHz sound pulse to travel between the transducers. By measuring this time with and without the sample in place, the time of flight for the sample can be determined, and from the time of flight, sample thickness and sample density, the velocity of propagation of the sound through the sample is calculated. Rotation of the sample allows both transverse and shear waves to be propagated through the sample, and the form of the relationship of these two sound velocities in the sample, versus angle of rotation of the sample, is related to stiffness constants (C,) in the plane of propagation of the wave (e.g. propagation in the 13 plane of the sample involves Cl,, C&, Cl3 and C&. Computer fitting procedures allow the best estimates for these constants to be calculated. For a transversely isotropic sample (3 axis fibre direction, 1 and 2 axes equivalent) only two experiments are required to determine all the stiffness constants; one experiment with the 3 axis horizontal and a second experiment with the 3 axis vertical. For an orthotropic material a further experiment is necessary to obtain all nine stiffness constants, with the 3 axis in the direction of the sound wave. This is achieved by cutting the sample into strips and then reassembling the strips with their 3 axis pointing along the transducer/receiver axis. This third experiment allows all the nine stiffness constants to be calculated. For a fuller description of this procedure see Refs 22 and 23. 3 THEORY Theoretical modelling of composite elastic properties is composed of two stages. Firstly, the properties of the individual composite unit, envisaged as a cylindrical fibre surrounded by a circular sheath of matrix, are determined using the properties of the two phases and the fibre volume fraction. Following our previous work we use the theory of Wilczynski’8 for this calculation. The second stage in the modelling procedure is to determine the effect of the misorientation of the individual composite units. This is done using the aggregate model described by Ward,” which resolves the properties of each individual unit to the main structural axes of the composite via the measured orientation averages. This approach, for calculating the effects of orientation, is similar to that proposed by Advani and Tucker. 24 In the current work, orthotropic material properties require the full version
127
Nylon
of the aggregate model, which use orientation averages in terms of both 19and 4. For an orthotropic material there are nine independent elastic constants relating applied stresses (a,) and strains (E;) to measured strains (El) and stresses (aj) through the stiffness constants C;j and the compliance constants Sij. These can be stated in terms of the general Hooke’s law as g, = C;j&, E, = S,jO;
The transformation from the axis system of each unit to the axis system of the sample can be defined using the full tensor transformation and leads to equations of the form S, , = (sin4 8 cos4 4){Sj, - 2Si3 + S;, - Si,}
+ (sin2 8 ~0s’ $){2S;, - 2Si3 - S;,} + (sin4 0 ~0s’ +){-2S;,
+ 4S;, - 2S& + 2Si,}
+ (sin4 f3>{S;,- 2Si3 + S;, - SA,} + (sin2 B){-2S;, + 2S& + SA,} + {s;,)
(2)
where Sg are the unit compliance constants, 8 and 4 are as shown in Fig. 2, and ( ) are orientation averages. Analogous equations can be determined for the other composite compliance constants in terms of the unit compliance constants and the appropriate orientation averages. A similar set of equations can be derived for the stiffness constants C,. Averaging in terms of the compliance constants of the unit (Sb) produces one bound on the composite elastic properties while averaging in terms of the stiffness constants (Cg) produces a second bound. Bishop and Hi112’ showed that averaging the compliance constants produces a lower bound (Voigt) while averaging the stiffness constants (Reuss) produces an upper bound. 4 RESULTS 4.1 Characterisation of the fibre orientation Figure 3 shows an analysis of the fibre orientation at position A on the sample, which is 5 mm from the gate (see Fig. 1). At the top of the figure there is a pictorial representation of the scanned area which is created by the computer after scanning has finished. Information on the X, Y position of each image, along with its orientation, are stored on disc during scanning and these are used to recreate the scanned area. All the pictorial scans shown in this paper were produced in this way. Figure 3 also shows these data analysed in terms of the orientation averages along the three main axes, (co? e,), sample (~0s~ 0,) and (~0s~ 8,): (cos2 0,) = 1 would mean perfect alignment along that
P. J. Hine et al.
128 3
the sample, although there is some out of plane orientation (2 axis), particularly in the core region. The core region occupies approximately 50% of the sample thickness, in this fan-gate region of the specimen. More detailed structures within the scanned area could be investigated by splitting the data into smaller strips, although this has not been presented here. Figure 4 shows scanned areas from within the main body of the sample, at positions D, F and G: 110 mm from the gate and across the sample width. Three different structures are seen at these three sample positions. At the centre (D) there is a well defined skin/core/skin orientation. By 10 mm from the centre line (F) this has almost disappeared and towards the edge of the sample (G) there is no evidence of a core. These data are displayed in terms of orientation averages in Fig. 5. At position D the core is now only
t
0.80
0.60
aI “a 8
0.40 1 .oo
0.20
0.80 CD “m
0.60
s
0.40
0.00 0
20
40
60
a0
100
0.20
Sample
Thickness
(%) 0.00
Fig. 3. Image data and orientation
averages at position A.
0
20
40
60
80
100
‘.O” -
axis. For this graph the sample was split into ten equal strips parallel to the 3 axis and the orientation data were analysed in each strip. Analysing the data in this way gives information on how fibre orientation varies through the sample thickness. The mouldings have the well documented skin/core/skin structure, with the fibres in the core aligned preferentially perpendicular to the injection direction (parallel to the 1 axis), and the fibres in the skins aligned more parallel to the injection direction. The fibres lie mainly in the 31 plane, i.e. the plane of particular
0
F
20
40
60
80
100
1.00 0.80
0.60 0.40
2 1 * .~u_*__~_I--~~-c-._.+,~
0.20 0.00 0
20
40
Sample D
F
80
thickness
80
100
(%I
2
G T
3-1 Fig. 4. Scanned areas at positions D, F and G.
\ Fig. 5. Orientation
averages across the sample positions D, F and G.
J width at
Injection-moulded
long-glass-fibre-reinforced
20% of the sample thickness compared to 50% at position A at the gate entrance. The in-plane orientation (31 plane) has increased at this position with (cos’ 9,) low throughout the sample thickness. The in-plane orientation also dominates at positions F and G. By section F the core has almost disappeared and at G the fibres are preferentially aligned along the injection direction (3 axis) throughout the thickness. Finally Fig. 6 shows orientation data for positions B, D and E, which were along the centre line of the sample, in the 3 mm thick region. A well defined skin/core/skin orientation is seen along the centre line, although there is evidence that the core is narrower at further distances from the gate: at position B the core is 30% of the sample thickness, whereas at E it is 24%. For all sections the transition between core and skin has been determined from the point where the orientation averages (cos’ 0,) and
‘.OO I
0
20
B
40
60
80
100
129
Nylon
(cos’ 0,) are equal. It is certainly clear that the skin region at position B is not as well aligned as at D and E and that the transition between skin and core is also more gradual at position B (nearest to the gate). The structures seen above have been reported many times before (for example, Refs l-3 and 5-10) and are a result of the interaction of the flow front of the polymer during injection with the fibres. Immediately on exiting the gate the polymer flow is diverging and this tends to align fibres perpendicular to the flow front. Fibres in the core region travel down the length of the sample in this configuration due to the constant velocity profile at the mould centre. Away from the centre the velocity profile falls off parabolically to reach zero at the mould walls. This parabolic velocity profile, often termed fountain flow, has the effect of realigning fibres parallel to the injection direction. The image analysis system allows good 3D information on these orientation structures to be accurately and rapidly obtained, although a more detailed discussion is outside the scope of this paper, which is primarily concerned with the use of the measured orientation data for elastic property modelling. Under the conditions where the fibres are predominantly perpendicular to the sectioned surface, i.e. in section G, it is possible to use image analysis to measure any volume fraction differences across the sample. At this position the fibre volume fraction was 0.28 at the sample centre and 0.22 at the sample edge. For modelling use, the fibre orientation was measured from a 70” section taken at position C. As discussed above, a 70” section was used in order to reduce sectioning and digitisation errors. Figure 7 shows the 8 distribution obtained from scanning the 70” section compared to that of a transverse section taken previously. It is seen that the data from the transverse section contains less fibres at low values of
250
1
I
0.60 0.60 0.40 0.20 0.00
Sample thickness
(%I
0
15
30
45
60
75
90
/7[ Theta .
70
cut
Transformed
Fig. 6. Orientation averages along the sample centre line at positions B, D and E.
.
TrSflSVSK3S cut
Fig. 7. Histograms for 8, at position C, from a transverse and a 70” section.
P. J. Hine et al.
130 Table 1. Orientation (sin4 0) (sin’ 0) (cos4 4) (co? 4) (sin4 8 cos’ $J) (sir? 8 cos* 4) (sin4 0 cos’ 4) (sin* 8 cos4 4)
averages O-286 0.399 0.386 0.303 0.031 0.083 0.043 0.040
8, due to problems
with imaging near perpendicular fibres. Orientation averages, needed for modelling, are therefore determined from the 70” section and are shown below in Table 1. 4.2 Modelling the composite elastic properties Theoretical predictions of a fully oriented ideal composite unit were calculated first. The properties of the two component phases were taken to be, E = 78 GPa, Y = 0.25 for the ‘E’ glass fibre, and for the unfilled Nylon matrix material (measured using ultrasonics to ensure consistency) E = 3.70 GPa and Y = 0.4. The volume fraction of fibres was 0.28 f 0.03. Using these phase properties and the theory of Wilczynski, the computed elastic properties of the composite unit are shown below in Table 2. Theoretical predictions for the elastic properties of the composite were determined by combining the unit constants, the measured orientation averages and the aggregate model. The elastic properties at position C, needed for comparison with the theoretical predictions, were measured using the ultrasonic velocity method. The results are shown in Table 3 where the axes are defined as shown in Fig. 2, in comparison with the predicted theoretical bounds; an upper bound from averaging stiffness constants and a lower bound from averaging compliance constants. The three Young’s moduli, E3?, Ez2 and El,, all lie within the theoretical bounds when the errors in measurement and prediction are taken into account. The predictions for the Poisson’s ratios are also in excellent agreement with the theoretical bounds,
Table 2. Computed perties
of
the
elastic
composite
prounit
(k2%)” E,, EII
24.5 8.09
between theoretical bounds and experimental values”
Table 3. Comparison
predicted
Theoretical
Theoretical
Experimental
lower bound (*5%)
upper bound (+5%)
(ultrasonics) (*2%)
12.0 7.83 8.34 0.35 0.36 0.39 2.55 2.45 2.68
17.5 8.56 10.5 0.33 0.37 0.44 3.21 2.71 2.93
E72 ED E,, VI3 v22 VI2
G13 G23
G,z
14.5 7.3 9.6 0.37 0.39 0.39 3.65 2.42 2.23
UE,,, Young’s modulus in GPa; G,,, shear modulus in GPa; and v,,, Poisson’s ratio. although in the case of Y17 the lower bound is greater than the upper bound. Although most of the individual measured stiffness and compliance constants should be bounded by the theoretical predictions, the calculated values for the Poisson’s ratios are not rigorously bounded. For the shear moduli, GZ3 lies between the predicted bounds while G,3 and Glz lie just outside the theoretical bounds. It is currently not clear whether the comparatively small discrepancy with these two constants is due to a problem in the experimental measurements or to some subtleties in modelling which have not so far been included in our relatively simple approach. For example fibre/fibre interactions and interfibre distances have so far not been considered and it could be that the shear moduli are very sensitive to these small differences.
5 CONCLUSIONS The image analysis system is able to give accurate and rapid 3D fibre orientation data which can be used for both understanding the effects of the injection process, and for theoretical modelling. The preferred orientation of fibres resulting from the injection moulding of a rectangular plaque produces considerable mechanical anisotropy. The agreement between the measured elastic properties and the theoretical predictions, based on the measured 3D fibre orientations, was excellent using the full aggregate model. ACKNOWLEDGEMENT
VI2
0.35 0.48
The Verton injection moulded sample was kindly supplied by Dr Rob Bailey of ICI plc, Wilton, UK.
G,,
2.24
REFERENCES
VI3
u E,, Young’s modulus in GPa; G,, shear modulus in GPa; and v,,, Poisson’s ratio.
1. Folkes, M. J., Short Fibre Reinforced Thermoplastics. Research Studies Press, John Wiley, Chichester, 1982. 2. Bay, R. S., Fibre orientation in injection moulded
Injection-moulded
long-glass-jibre-reinforced
composites: A comparison of theory and experiment. PhD thesis, University of Illinois at Urbana-Champaign, USA, 1990. 3. Doshi, S. R., Dealy, J. M. & Charrier, J. M., Flow induced fibre orientations in an expanding channel tubing die. Polym. Comp., 7 (1986) 323. 4. Gilver, R. C., Crochet, M. J. & Pipes, R. B., Numerical prediction of fibre orientation in dilute suspension. J. Comp. Mater., 17 (1983) 330. 5. McClelland, A. N. & Gibson, A. G., Rheology and fibre
6.
7.
8.
9.
10.
orientation in the injection moulding of long fibre reinforced nylon 66 composites. Cornp. Manufact., 1 (1990) 15. Truckenmuller, F. 62 Fritz, H. G., Injection moulding of long fibre reinforced thermoplastics. Polym. Engng Sci., 31 (1991) 1316. Fakirov, S. & Fakirova, C., Direct determination of the orientation of short glass fibres in an injection moulded PET system. Pofym. Comp., 6 (1985) 41. Darlington, M. W. & McGinley, P. L., Fibre orientation distribution in short fibre reinforced composites. J. Mater. Sci., 10 (1975) 906. O’Donnell, B. & White, J. R., Young’s modulus variation within glass fibre filled Nylon 6.6 injection mouldings. Proc 1st International Conference on Deformation and Fracture of Composites, Plastics and Rubber Institute, London, 1991, 24/l. O’Connell, P. A. & Duckett, R. A., Measurements of fibre orientation in short fibre reinforced thermoplastics. Comp. Sci. Technol., 42 (1991) 329.
11. Hine, P. J., Duckett, R. A., Davidson, N. & Clarke, A. R., Modelling the elastic properties of fibre reinforced composites: I Orientation measurement. Comp. Sci. Technol., 47 (1993) 65. 12. Hine, P. J., Duckett, R. A. & Ward, I. M., Modelling the elastic properties of fibre reinforced composites: II Theoretical modelling. Comp. Sci. Technol., 49 (1993) 13. 13. Gong, X. A., Hine, P. J. Duckett,
The elastic properties
R. A. & Ward, I. M., of random-in-plane short fibre
131
Nylon
reinforced composites. Polym. Camp., 15 (1994) 74. 14. Hine, P. J., Davidson, N., Duckett, R. A., Clarke, A. R. & Ward, I. M., Orientation measurement and modelling the elastic properties of hydrostatically extruded glass fibre reinforced POM. Proc. 2nd International Conference
on Deformation
and Fracture
of Composites.
Manchester, UK, 1993. 15. Clarke, A. R., Davidson, N. & Archenhold, G., A multitransputer image analyser for 3D fibre orientation studies in composites. Trans. Royal Microscopical Sot., 1 (1990) 305. 16. Clarke, A. R.,
Davidson, N. & Archenhold, G., Determining the spatial distribution of carbon fibres in composites. Proc. Transputing ‘91 (Vol 1). Adam Hilger Ltd, Boston, MA, USA, 1991, p. 31. 17. Brody, H. & Ward, I. M., Modulus of short carbon and glass fibre reinforced composites. Polym. Engng Sci., 11 (1971) 139. 18. Wilczynski, A. P., A basic theory of reinforcement for unidirectional fibrous composites. Comp. Sci. Technol.,
38 (1990) 327. 19. Ward, I. M., Optical and mechanical anisotropy in crystalline polymers. Proc. Phys. Sot., 80 (1962) 1176. 20. ASTM, Annual Book of Testing Standards 1991, ed. R.
A. Storer. ASTM, Philadelphia, PA, USA. 21. Yurgartis, S. W., Measurement of small angle fibre misalignments in continuous fibre composites. Comp. Sci. Technol., 30 (1987) 279. 22. Read, B. E. & Dean, G. D., The Determination of the Dynamic Properties of Polymers and Composites. Adam
Hilger Ltd. Bristol, UK, 1978. 23. Lord, D., The determination of the elastic constants of fibre reinforced composites by an ultrasonic method. PhD thesis, University of Leeds, Leeds. UK, 1978. 24. Advani, S. G. & Tucker, C. L., The use of tensors to describe and predict fiber orientations in short fiber composites. J. Rheol., 31 (1987) 751. 25. Bishop, J. & Hill, R., A theory of the plastic distortion of a polycrystalline aggregate under combined stress. Phil. Mug., 42 (1951) 414.
0266-3538/95/$09.50
MEASURING THE FIBRE ORIENTATION AND MODELLING THE ELASTIC PROPERTIES OF INJECTION-MOULDED LONG-GLASS-FIBRE-REINFORCED NYLON
P. J. Hine,” N. Davidson,h uIRC
in Polymer Science and Technology,
R. A. Duckett”*
& I. M. Ward
h Instrumentation Group, Physics Department,
University of Leeds,
Leeds, UK, LS2 9JT
(Received 10 December 1993; revised version received 13 April 1994; accepted 15 December 1994) Abstract
the injection process and prediction of the resulting fibre orientation. Folkes’ in his book on short-fibrereinforced thermoplastics gives a good review of this area of study; the thesis of Bay’ describes a model for the prediction of fibre orientation during injection moulding. Other authors who have attempted to predict fibre orientations during flow include Doshi et al.,” Gilver et al4 and McClelland and Gibson.” The second major area of study is the measurement of fibre orientation and composite property modelling. Again there are a large number of papers concerned with area of research including Bay,2 this Truckenmuller,’ Fakirov and Fakirova,’ Darlington,x O’Donnell and White’ and O’Connell and Duckett.“’ In this laboratory we have concentrated on the second area of research examining the links between fibre orientation and composite properties, utilising a unique image analysis facility for obtaining accurate 3D fibre orientation measurement, combined with our innovative models for predicting 3D composite elastic properties. Systems so far studied include aligned short-carbon-fibre-reinforced epoxy manufactured by prepreg methods,‘1.‘2 random-in-plane carbon-fibrereinforced epoxy, again manufactured by prepreg techniques” and hydrostatically extruded short-glassfibre-reinforced polyoxymethylene.‘4 The present paper describes a characterisation of the 3D fibre orientation of an injection-moulded plaque of long-glass-fibre-reinforced Nylon 6.6 and the use of the orientation data for modelling the orthotropic elastic properties. The elastic properties of the composite were measured by the ultrasonic velocity method, and provided a rigorous test of our modelling techniques. Image analysis, working from polished sections taken at various points from the composite, was used to determine the 3D fibre orientation distribution. This was achieved by using a transputer-based image analysis system, developed in-house by our colleagues in the Instrumentation Group in the Department of Physics. 15*IhThis is a unique facility which allows rapid
This paper describes the characterisation of the 30 fibre orientation of a single-gated injection-moulded plaque of short-glass-fibre-reinforced Nylon by image analysis, and the use of this orientation data for the theoretical prediction of the composite elastic properties, Fibre orientations were measured by using a purpose built image analysis facility, which allows 30 data to be obtained. Composite elastic properties were measured by an ultrasonic velocity method and compared with theoretical predictions obtained from the modelling techniques of Wilczynski and Ward. Keywords: composites, fibre orientation, modelling, elastic properties, glass-fibre-reinforced Nylon
1 INTRODUCTION The current trend in fibre-reinforced composites is away from expensive carbon-fibre-reinforced thermoset composites, towards glass-fibre-reinforced thermoplastic composites, often manufactured by injection moulding. The advantages of a thermoplastic-based composite include lower material cost, low cycle time for manufacture and the possibility of recycling after use. There is therefore considerable incentive for understanding the complex links between the composite manufacturing process, the resulting fibre orientations and final composite properties. The long-term aim of this research is to be able to predict the final properties of a composite from details of the manufacturing process and the properties of the constituent phases. Research on short-fibre composites can be divided into two major areas: understanding the effects of the manufacturing process on resulting composite fibre orientation structures and understanding the effects of fibre orientation on mechanical properties. The first involves understanding the complicated rheology involved in the flow of fibre and molten polymer during * To whom correspondence should be addressed. 12s
P. 1. Hine et al.
126
and accurate orientation data to be obtained, analysing typically 40 000 images h-‘. The modelling of the properties of fibre-reinforced composites is undertaken in two stages, as originally proposed by Brody and Ward.” Firstly, the properties of an individual composite unit are calculated, and secondly the effects of a range of orientations are computed. We have followed the recommendations of our previous work,” in using the theory of Wilczynski to determine the unit properties and the full aggregate for modelling the effects of model of Ward” orthotropic anisotropy. 2 EXPERIMENTAL The composite used in this study was long-glass-fibrereinforced Nylon 6.6, from the ‘VERTON’ family of materials manufactured by ICI Ltd. The sample was a rectangular plate (65 mm X 220 mm) with the single fan gate located along the shorter side of the rectangle: the sample was 6 mm thick in the gate section and 3 mm thick in the main section. The fibre volume fraction of the composite was measured by acid digestion (ASTM D3171 (Ref. 20)) as 0.28 f 0.01. Image analysis was used to determine the 3D fibre orientation distribution at various positions across the sample. The chosen analysis points are shown in Fig. 1, along with the sample geometry details. The first section was taken in the gate region, 5 mm from the gate entrance: this section was denoted A and was taken in the 32 plane (see Fig. 2). The remainder of the sections, B to G, were located in the main section of the plate. The first series of samples was taken along the centre line of the plate at 15 mm, 60 mm, 110 mm and 220 mm from the gate entrance (sections B to E, respectively). The second series was taken 110mm from the gate, along the centre line of the plate and at 10mm and 30mm from the centre line (B, F and G, respectively). The sections from the main plate were taken in the 12 plane. When a section is taken through a composite it
G
;
Injection Point +A;B
reveals each fibre as an elliptical image. Measurement of the elliptical parameters of each image allows the angles that specify the 3D orientation of the fibre to be determined. In general only two angles, 13and 4, are needed to specify the 3D orientation (Fig. 2) of each fibre: for this paper 8 is defined as the angle a fibre makes with the 3 axis of the sample, which is the injection direction, and 4 is the angle the projection of the fibre onto the 12 plane makes with the 2 axis. For a material where the properties are orthotropic, it is often more instructive to determine the angle each fibre makes with the three structural axes, defined as Or, &, & (also shown in Fig. 2). Both of these approaches, for defining the 3D fibre position, have been used in this work. One of the major problems with image analysis of polished composite sections are the errors encountered when analysing fibres that are nearly perpendicular to the sectioned surface, and so are supposedly close to circular. Errors introduced by polishing or digitisation cause the fibres to appear elliptical and so they are assigned incorrect values of 8. In fact the fibres may not even be circular in shape to start with, and so even fibres which are perpendicular to the section would be interpreted as being inclined to the section normal. A method for reducing this error is to section at an angle to the main fibre direction.“~‘* The fibres now appear mainly as ellipses and the influence of polishing and digitisation errors on the ellipticity is much reduced. Once the data is collected it can then be transformed back to the main axis system of the sample. ’ ’ For initial investigation of the structure of fibre orientations within the sample the standard transverse section was used, but where accurate orientation distributions were needed for modelling a 70” section angle was used. All the image data collected was corrected for the effects of counting bias. We have followed our previous work by using the simplest form for this correction by dividing the number of fibres counted in each angle increment A8 by cos 8. Modelling was only carried out at one position on
F D
C
E
I 6Chnn1
3
b J
?
1
(.. j 3OmmI 220mm --+
6mm thick
Fig. 1.
1
3mm thick
Details of the injection
moulded image analysis positions.
Injection direction
sample
and the Fig. 2. Sample axis definitions.
%
2
Injection-moulded
long-glass-jibre-reinforced
the plate; 60mm from the gate and along the centre line of the sample (position C). Elastic properties were measured at this point using the ultrasonic velocity method. In this technique the sample is placed in a water bath between two ultrasonic transducers, one a transmitter and one a receiver. The basic measurement is the time of flight for a 2.25 MHz sound pulse to travel between the transducers. By measuring this time with and without the sample in place, the time of flight for the sample can be determined, and from the time of flight, sample thickness and sample density, the velocity of propagation of the sound through the sample is calculated. Rotation of the sample allows both transverse and shear waves to be propagated through the sample, and the form of the relationship of these two sound velocities in the sample, versus angle of rotation of the sample, is related to stiffness constants (C,) in the plane of propagation of the wave (e.g. propagation in the 13 plane of the sample involves Cl,, C&, Cl3 and C&. Computer fitting procedures allow the best estimates for these constants to be calculated. For a transversely isotropic sample (3 axis fibre direction, 1 and 2 axes equivalent) only two experiments are required to determine all the stiffness constants; one experiment with the 3 axis horizontal and a second experiment with the 3 axis vertical. For an orthotropic material a further experiment is necessary to obtain all nine stiffness constants, with the 3 axis in the direction of the sound wave. This is achieved by cutting the sample into strips and then reassembling the strips with their 3 axis pointing along the transducer/receiver axis. This third experiment allows all the nine stiffness constants to be calculated. For a fuller description of this procedure see Refs 22 and 23. 3 THEORY Theoretical modelling of composite elastic properties is composed of two stages. Firstly, the properties of the individual composite unit, envisaged as a cylindrical fibre surrounded by a circular sheath of matrix, are determined using the properties of the two phases and the fibre volume fraction. Following our previous work we use the theory of Wilczynski’8 for this calculation. The second stage in the modelling procedure is to determine the effect of the misorientation of the individual composite units. This is done using the aggregate model described by Ward,” which resolves the properties of each individual unit to the main structural axes of the composite via the measured orientation averages. This approach, for calculating the effects of orientation, is similar to that proposed by Advani and Tucker. 24 In the current work, orthotropic material properties require the full version
127
Nylon
of the aggregate model, which use orientation averages in terms of both 19and 4. For an orthotropic material there are nine independent elastic constants relating applied stresses (a,) and strains (E;) to measured strains (El) and stresses (aj) through the stiffness constants C;j and the compliance constants Sij. These can be stated in terms of the general Hooke’s law as g, = C;j&, E, = S,jO;
The transformation from the axis system of each unit to the axis system of the sample can be defined using the full tensor transformation and leads to equations of the form S, , = (sin4 8 cos4 4){Sj, - 2Si3 + S;, - Si,}
+ (sin2 8 ~0s’ $){2S;, - 2Si3 - S;,} + (sin4 0 ~0s’ +){-2S;,
+ 4S;, - 2S& + 2Si,}
+ (sin4 f3>{S;,- 2Si3 + S;, - SA,} + (sin2 B){-2S;, + 2S& + SA,} + {s;,)
(2)
where Sg are the unit compliance constants, 8 and 4 are as shown in Fig. 2, and ( ) are orientation averages. Analogous equations can be determined for the other composite compliance constants in terms of the unit compliance constants and the appropriate orientation averages. A similar set of equations can be derived for the stiffness constants C,. Averaging in terms of the compliance constants of the unit (Sb) produces one bound on the composite elastic properties while averaging in terms of the stiffness constants (Cg) produces a second bound. Bishop and Hi112’ showed that averaging the compliance constants produces a lower bound (Voigt) while averaging the stiffness constants (Reuss) produces an upper bound. 4 RESULTS 4.1 Characterisation of the fibre orientation Figure 3 shows an analysis of the fibre orientation at position A on the sample, which is 5 mm from the gate (see Fig. 1). At the top of the figure there is a pictorial representation of the scanned area which is created by the computer after scanning has finished. Information on the X, Y position of each image, along with its orientation, are stored on disc during scanning and these are used to recreate the scanned area. All the pictorial scans shown in this paper were produced in this way. Figure 3 also shows these data analysed in terms of the orientation averages along the three main axes, (co? e,), sample (~0s~ 0,) and (~0s~ 8,): (cos2 0,) = 1 would mean perfect alignment along that
P. J. Hine et al.
128 3
the sample, although there is some out of plane orientation (2 axis), particularly in the core region. The core region occupies approximately 50% of the sample thickness, in this fan-gate region of the specimen. More detailed structures within the scanned area could be investigated by splitting the data into smaller strips, although this has not been presented here. Figure 4 shows scanned areas from within the main body of the sample, at positions D, F and G: 110 mm from the gate and across the sample width. Three different structures are seen at these three sample positions. At the centre (D) there is a well defined skin/core/skin orientation. By 10 mm from the centre line (F) this has almost disappeared and towards the edge of the sample (G) there is no evidence of a core. These data are displayed in terms of orientation averages in Fig. 5. At position D the core is now only
t
0.80
0.60
aI “a 8
0.40 1 .oo
0.20
0.80 CD “m
0.60
s
0.40
0.00 0
20
40
60
a0
100
0.20
Sample
Thickness
(%) 0.00
Fig. 3. Image data and orientation
averages at position A.
0
20
40
60
80
100
‘.O” -
axis. For this graph the sample was split into ten equal strips parallel to the 3 axis and the orientation data were analysed in each strip. Analysing the data in this way gives information on how fibre orientation varies through the sample thickness. The mouldings have the well documented skin/core/skin structure, with the fibres in the core aligned preferentially perpendicular to the injection direction (parallel to the 1 axis), and the fibres in the skins aligned more parallel to the injection direction. The fibres lie mainly in the 31 plane, i.e. the plane of particular
0
F
20
40
60
80
100
1.00 0.80
0.60 0.40
2 1 * .~u_*__~_I--~~-c-._.+,~
0.20 0.00 0
20
40
Sample D
F
80
thickness
80
100
(%I
2
G T
3-1 Fig. 4. Scanned areas at positions D, F and G.
\ Fig. 5. Orientation
averages across the sample positions D, F and G.
J width at
Injection-moulded
long-glass-fibre-reinforced
20% of the sample thickness compared to 50% at position A at the gate entrance. The in-plane orientation (31 plane) has increased at this position with (cos’ 9,) low throughout the sample thickness. The in-plane orientation also dominates at positions F and G. By section F the core has almost disappeared and at G the fibres are preferentially aligned along the injection direction (3 axis) throughout the thickness. Finally Fig. 6 shows orientation data for positions B, D and E, which were along the centre line of the sample, in the 3 mm thick region. A well defined skin/core/skin orientation is seen along the centre line, although there is evidence that the core is narrower at further distances from the gate: at position B the core is 30% of the sample thickness, whereas at E it is 24%. For all sections the transition between core and skin has been determined from the point where the orientation averages (cos’ 0,) and
‘.OO I
0
20
B
40
60
80
100
129
Nylon
(cos’ 0,) are equal. It is certainly clear that the skin region at position B is not as well aligned as at D and E and that the transition between skin and core is also more gradual at position B (nearest to the gate). The structures seen above have been reported many times before (for example, Refs l-3 and 5-10) and are a result of the interaction of the flow front of the polymer during injection with the fibres. Immediately on exiting the gate the polymer flow is diverging and this tends to align fibres perpendicular to the flow front. Fibres in the core region travel down the length of the sample in this configuration due to the constant velocity profile at the mould centre. Away from the centre the velocity profile falls off parabolically to reach zero at the mould walls. This parabolic velocity profile, often termed fountain flow, has the effect of realigning fibres parallel to the injection direction. The image analysis system allows good 3D information on these orientation structures to be accurately and rapidly obtained, although a more detailed discussion is outside the scope of this paper, which is primarily concerned with the use of the measured orientation data for elastic property modelling. Under the conditions where the fibres are predominantly perpendicular to the sectioned surface, i.e. in section G, it is possible to use image analysis to measure any volume fraction differences across the sample. At this position the fibre volume fraction was 0.28 at the sample centre and 0.22 at the sample edge. For modelling use, the fibre orientation was measured from a 70” section taken at position C. As discussed above, a 70” section was used in order to reduce sectioning and digitisation errors. Figure 7 shows the 8 distribution obtained from scanning the 70” section compared to that of a transverse section taken previously. It is seen that the data from the transverse section contains less fibres at low values of
250
1
I
0.60 0.60 0.40 0.20 0.00
Sample thickness
(%I
0
15
30
45
60
75
90
/7[ Theta .
70
cut
Transformed
Fig. 6. Orientation averages along the sample centre line at positions B, D and E.
.
TrSflSVSK3S cut
Fig. 7. Histograms for 8, at position C, from a transverse and a 70” section.
P. J. Hine et al.
130 Table 1. Orientation (sin4 0) (sin’ 0) (cos4 4) (co? 4) (sin4 8 cos’ $J) (sir? 8 cos* 4) (sin4 0 cos’ 4) (sin* 8 cos4 4)
averages O-286 0.399 0.386 0.303 0.031 0.083 0.043 0.040
8, due to problems
with imaging near perpendicular fibres. Orientation averages, needed for modelling, are therefore determined from the 70” section and are shown below in Table 1. 4.2 Modelling the composite elastic properties Theoretical predictions of a fully oriented ideal composite unit were calculated first. The properties of the two component phases were taken to be, E = 78 GPa, Y = 0.25 for the ‘E’ glass fibre, and for the unfilled Nylon matrix material (measured using ultrasonics to ensure consistency) E = 3.70 GPa and Y = 0.4. The volume fraction of fibres was 0.28 f 0.03. Using these phase properties and the theory of Wilczynski, the computed elastic properties of the composite unit are shown below in Table 2. Theoretical predictions for the elastic properties of the composite were determined by combining the unit constants, the measured orientation averages and the aggregate model. The elastic properties at position C, needed for comparison with the theoretical predictions, were measured using the ultrasonic velocity method. The results are shown in Table 3 where the axes are defined as shown in Fig. 2, in comparison with the predicted theoretical bounds; an upper bound from averaging stiffness constants and a lower bound from averaging compliance constants. The three Young’s moduli, E3?, Ez2 and El,, all lie within the theoretical bounds when the errors in measurement and prediction are taken into account. The predictions for the Poisson’s ratios are also in excellent agreement with the theoretical bounds,
Table 2. Computed perties
of
the
elastic
composite
prounit
(k2%)” E,, EII
24.5 8.09
between theoretical bounds and experimental values”
Table 3. Comparison
predicted
Theoretical
Theoretical
Experimental
lower bound (*5%)
upper bound (+5%)
(ultrasonics) (*2%)
12.0 7.83 8.34 0.35 0.36 0.39 2.55 2.45 2.68
17.5 8.56 10.5 0.33 0.37 0.44 3.21 2.71 2.93
E72 ED E,, VI3 v22 VI2
G13 G23
G,z
14.5 7.3 9.6 0.37 0.39 0.39 3.65 2.42 2.23
UE,,, Young’s modulus in GPa; G,,, shear modulus in GPa; and v,,, Poisson’s ratio. although in the case of Y17 the lower bound is greater than the upper bound. Although most of the individual measured stiffness and compliance constants should be bounded by the theoretical predictions, the calculated values for the Poisson’s ratios are not rigorously bounded. For the shear moduli, GZ3 lies between the predicted bounds while G,3 and Glz lie just outside the theoretical bounds. It is currently not clear whether the comparatively small discrepancy with these two constants is due to a problem in the experimental measurements or to some subtleties in modelling which have not so far been included in our relatively simple approach. For example fibre/fibre interactions and interfibre distances have so far not been considered and it could be that the shear moduli are very sensitive to these small differences.
5 CONCLUSIONS The image analysis system is able to give accurate and rapid 3D fibre orientation data which can be used for both understanding the effects of the injection process, and for theoretical modelling. The preferred orientation of fibres resulting from the injection moulding of a rectangular plaque produces considerable mechanical anisotropy. The agreement between the measured elastic properties and the theoretical predictions, based on the measured 3D fibre orientations, was excellent using the full aggregate model. ACKNOWLEDGEMENT
VI2
0.35 0.48
The Verton injection moulded sample was kindly supplied by Dr Rob Bailey of ICI plc, Wilton, UK.
G,,
2.24
REFERENCES
VI3
u E,, Young’s modulus in GPa; G,, shear modulus in GPa; and v,,, Poisson’s ratio.
1. Folkes, M. J., Short Fibre Reinforced Thermoplastics. Research Studies Press, John Wiley, Chichester, 1982. 2. Bay, R. S., Fibre orientation in injection moulded
Injection-moulded
long-glass-jibre-reinforced
composites: A comparison of theory and experiment. PhD thesis, University of Illinois at Urbana-Champaign, USA, 1990. 3. Doshi, S. R., Dealy, J. M. & Charrier, J. M., Flow induced fibre orientations in an expanding channel tubing die. Polym. Comp., 7 (1986) 323. 4. Gilver, R. C., Crochet, M. J. & Pipes, R. B., Numerical prediction of fibre orientation in dilute suspension. J. Comp. Mater., 17 (1983) 330. 5. McClelland, A. N. & Gibson, A. G., Rheology and fibre
6.
7.
8.
9.
10.
orientation in the injection moulding of long fibre reinforced nylon 66 composites. Cornp. Manufact., 1 (1990) 15. Truckenmuller, F. 62 Fritz, H. G., Injection moulding of long fibre reinforced thermoplastics. Polym. Engng Sci., 31 (1991) 1316. Fakirov, S. & Fakirova, C., Direct determination of the orientation of short glass fibres in an injection moulded PET system. Pofym. Comp., 6 (1985) 41. Darlington, M. W. & McGinley, P. L., Fibre orientation distribution in short fibre reinforced composites. J. Mater. Sci., 10 (1975) 906. O’Donnell, B. & White, J. R., Young’s modulus variation within glass fibre filled Nylon 6.6 injection mouldings. Proc 1st International Conference on Deformation and Fracture of Composites, Plastics and Rubber Institute, London, 1991, 24/l. O’Connell, P. A. & Duckett, R. A., Measurements of fibre orientation in short fibre reinforced thermoplastics. Comp. Sci. Technol., 42 (1991) 329.
11. Hine, P. J., Duckett, R. A., Davidson, N. & Clarke, A. R., Modelling the elastic properties of fibre reinforced composites: I Orientation measurement. Comp. Sci. Technol., 47 (1993) 65. 12. Hine, P. J., Duckett, R. A. & Ward, I. M., Modelling the elastic properties of fibre reinforced composites: II Theoretical modelling. Comp. Sci. Technol., 49 (1993) 13. 13. Gong, X. A., Hine, P. J. Duckett,
The elastic properties
R. A. & Ward, I. M., of random-in-plane short fibre
131
Nylon
reinforced composites. Polym. Camp., 15 (1994) 74. 14. Hine, P. J., Davidson, N., Duckett, R. A., Clarke, A. R. & Ward, I. M., Orientation measurement and modelling the elastic properties of hydrostatically extruded glass fibre reinforced POM. Proc. 2nd International Conference
on Deformation
and Fracture
of Composites.
Manchester, UK, 1993. 15. Clarke, A. R., Davidson, N. & Archenhold, G., A multitransputer image analyser for 3D fibre orientation studies in composites. Trans. Royal Microscopical Sot., 1 (1990) 305. 16. Clarke, A. R.,
Davidson, N. & Archenhold, G., Determining the spatial distribution of carbon fibres in composites. Proc. Transputing ‘91 (Vol 1). Adam Hilger Ltd, Boston, MA, USA, 1991, p. 31. 17. Brody, H. & Ward, I. M., Modulus of short carbon and glass fibre reinforced composites. Polym. Engng Sci., 11 (1971) 139. 18. Wilczynski, A. P., A basic theory of reinforcement for unidirectional fibrous composites. Comp. Sci. Technol.,
38 (1990) 327. 19. Ward, I. M., Optical and mechanical anisotropy in crystalline polymers. Proc. Phys. Sot., 80 (1962) 1176. 20. ASTM, Annual Book of Testing Standards 1991, ed. R.
A. Storer. ASTM, Philadelphia, PA, USA. 21. Yurgartis, S. W., Measurement of small angle fibre misalignments in continuous fibre composites. Comp. Sci. Technol., 30 (1987) 279. 22. Read, B. E. & Dean, G. D., The Determination of the Dynamic Properties of Polymers and Composites. Adam
Hilger Ltd. Bristol, UK, 1978. 23. Lord, D., The determination of the elastic constants of fibre reinforced composites by an ultrasonic method. PhD thesis, University of Leeds, Leeds. UK, 1978. 24. Advani, S. G. & Tucker, C. L., The use of tensors to describe and predict fiber orientations in short fiber composites. J. Rheol., 31 (1987) 751. 25. Bishop, J. & Hill, R., A theory of the plastic distortion of a polycrystalline aggregate under combined stress. Phil. Mug., 42 (1951) 414.