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The effect of shear deformation on the processing and mechanical properties of aligned reinforcements
Composites Science and Technology 57 (1997) 327-344 0 1997 Elsevier Science Limited Printed ELSEVIER
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THE EFFECT OF SHEAR DEFORMATION ON THE PROCESSING AND MECHANICAL PROPERTIES OF ALIGNED REINFORCEMENTS P. Smith,
C. D. Rudd
& A. C. Long*
Department of Mechanical Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, UK
(Received 29 May 1996; revised 5 September 1996; accepted 19 September 1996)
so
Abstract The growth of liquid moulding processes for the production of structural and semi-structural components has been eased by the development of computer-aided engineering tools for structural analysis and process modelling. However, the accuracy of these tools is dependent on the available material property data. These are usually obtained from experimental or theoretical analysis of flat plaques. These methods do not take into account reinforcement deformation during the preforming process. Deformation, caused by forming two-dimensional reinforcements over threedimensional surfaces, can result in local fibre reorientations and volume fraction changes within the preform. In this study the major deformation mode, simple shear, is isolated. The effects of simple shear deformation on permeability and elastic properties of engineered and woven glass fabrics are investigated. Predictions of elastic properties are made by using established methods and compared with experimental data for a range of fabric architectures. A semiempirical method is applied to characterise the effects of shear on reinforcement permeability. 0 1997 Elsevier Science Limited. All rights reserved Keywords: preforming, shear deformation, reinforcement, in-plane permeability, properties
t V
% ;I Y P
Fabric superficial density Cavity thickness Volume fraction Fibre angle with respect to applied load Krenchel efficiency factor Ply angle Poisson’s ratio Density
Subscripts
E i m X,Y I,2
Property of composite Property of fibre Property of unidirectional layer Property of matrix Principal axes of bi-directional reinforcement Principal axes of unidirectional reinforcement
laminate/ laminate/
1 INTRODUCTION Liquid moulding processes are being increasingly used for the production of structural and semi-structural components from composite materials. The use of reinforcement preforms allows separation of the reinforcement preparation and the moulding cycle to reduce cycle times. The most common method of preform manufacture involves forming the reinforcement between matched moulds. Structural components demand the use of aligned fibre reinforcements to provide the required mechanical properties. Typical aligned fibre reinforcements are woven or braided, with stitch-bonded or ‘engineered’ fabrics becoming popular. These consist of stitched unidirectional layers at various orientations and generally provide improved in-plane mechanical properties over woven or braided fabrics due to the elimination of crimp. Preforms are usually designed to achieve the required component mechanical performance. The mechanical performance can be assessed by the rule of mixtures, which returns a useful initial estimate, or
aligned tensile
NOMENCLATURE Proportion of fibres at angle (Y,, to applied load E Elastic modulus G Shear modulus k Permeability k “OrIll Normalised permeability k undef Permeability of undeformed fabric Permeability of fabric at ply angle 8 k, n Number of fabric layers R Fibre radius a,
* To whom correspondence should be addressed. 327
328
P. Smith et al.
classical laminate analysis, which gives more accurate predictions. Processing considerations are equally important, and determine whether component production is feasible and economic. A number of models have been developed to simulate the impregnation phase of liquid moulding (see, for example, Refs. l-4). The accuracy of these models is dependent on the accuracy of the input data. Property measurements are usually taken from flat plaque data and input into processing and mechanical property models. Mechanical property data are determined from unidirectional flat plaques for input into classical laminate analysis. Plaques are tested to determine shear and tensile moduli and Poisson’s ratio, although initial estimates can be made by using a simple rule of mixtures and the well known Halpin-Tsai equations.’ Processing models require fabric permeability inputs. These can be measured by applying Darcy’s law for flow through a radial or rectilinear mould cavity to obtain the principal fabric permeabilities. During preform manufacture, the two-dimensional reinforcement is required to conform to threedimensional shapes. The reinforcement deforms to accommodate the preform shape and the fibre geometry is forced to adjust. Several models have been developed to simulate the draping of fabric over a three-dimensional surface. Mack and Taylor6 established a draping algorithm for the fitting of a textile garment to the human body. Adaptations of the model were directly applicable to preforming: Robertson et al.‘.’ developed a simple drape model for a hemispherical surface. More recently, Van West et al.” and Bergsmar have developed kinematic draping algorithms to drape fabric over an arbitrary three-dimensional surface. The models are based on a pin-jointed fibre mesh and require iterative solutions. Long” developed a PC-based drape model which describes the surface using flat patches, allowing the solutions to be calculated directly as opposed to iteratively. The fibre deformation caused during the preforming process may result in a significant departure from anticipated processing and mechanical characteristics. Initial investigations by Rudd et cd.‘* have demonstrated the changes in longitudinal modulus and permeability. Further works by Long and Rudd13 and BickertonI have demonstrated the effect of reinforcement deformation on fluid flow through the deformed fabric. The assumption of flat plaque properties and principal permeabilities based on undeformed fabrics may therefore be inaccurate and the effect of reinforcement deformation on the preform has to be considered. This study aims to demonstrate the effect of reinforcement deformation on the processing and mechanical properties of a range of bi-directional fabrics and suggests reliable methods of predicting the property changes arising from the deformation.
2 REINFORCEMENT
DEFORMATION
Aligned fibre reinforcements have differing on- and off-axis properties. However, deformation caused during preform manufacture results in considerable changes in both the principal axis orientation and fibre volume fraction. Long et ~1.‘~ suggested that aligned reinforcement deformation can be split into two major mechanisms, simple shear and shear-slip at the fibre cross-overs. These are demonstrated in Fig. 1. PotterI suggested that simple shear is the dominant mode of deformation for most bi-directional reinforcements. In this case, the reinforcement behaves as a pin-jointed mesh, and the fibres rotate around the cross-over points to produce the deformation. In order to measure the effects of shear on fabrics, simple shear deformation was isolated from any other deformation mode. This was achieved by using a four-bar linkage, shown in Fig. 2, which clamped the reinforcement along two edges. One edge of the linkage was connected to a laboratory bench and a force was applied to the opposite edge. A parallelogram was formed, forcing the reinforcement to shear. The change in ply angle 8 (the angle between the major principal axis and the fibre axis) was monitored via two perpendicular lines marked on the undeformed reinforcement. Five commercially available glass-fibre fabrics, typical of those used in liquid composite moulding,
Fibre rotation or shear
Fibre slip
Fig. 1. Major reinforcement
deformation
mechanisms. Sheared rig posltion T :r ........... I
Force Applied
Reinforcement
” FIxed Bar
Fig. 2. Four-bar
linkage
inter-fibre
shear isolation
rig.
Shear deformation and aligned reinforcements
329
Table 1. Fabric architecture data (from manufacturers’ data) Manufacturer
Type
Architecture
Tech Textiles
ELT 850 (1036)
0°/900 engineered
Tech Textiles
E-BX hd 936 (3074)
Chomarat Chomarat JPS
8OOT 830s Conform 3793
~t45” engineered, high drape Plain-weave 2:2 Twill-weave 4-Harness satin-weave, high drape
Tow tex (g km-‘)
Superficial density (g m-‘)
Minimum ply angle (“)
0”: 1800 90”: 1200 600”
850
*27
936
*27
2450 2450 140
790 820 532
+25” +26 *22”
“Measured values.
were sheared using the four-bar linkage. These are described in Table 1 and illustrated in Figs 3-7. Figure 3(a,b) shows the 0”/90” engineered fabric. The fibres are stitched to form distinct tows, and are locked in position by the stitches. This may be compared with the &45” engineered fabric, shown in Fig. 4(a,b), where the fibres form a more homogeneous fabric. The stitch pattern allows the fabric to deform by shear-slip, resulting in a more drapeable fabric. The plain-weave and twill-weave fabrics (Figs 5 and 6) are woven with heavy warp and weft tows. The combination of the plain- or twill-weave pattern and tow size adds a large quantity of crimp to the fabrics, which affects the processing and mechanical properties. The fabric illustrated in Fig. 7 uses light warp and weft tows tightly woven into a 4-harness satin pattern, forming a highly drapeable, low-crimp fabric. The minimum ply angle coincided with the point at which wrinkles appeared in the simply sheared fabric. The angle was measured using a protractor while the fabric was clamped in the shearing rig, and was found to be different for each fabric. This depended on a number of factors. Tow dimensions and the stitch or weave pattern may have influenced the minimum ply angle attainable. When simple shear reduced the tow spacing to zero, adjacent tows contacted each other. Any further simple shear deformation caused little change in the ply angle, and forced the reinforcement to increase in thickness, as spacing between individual fibres decreased to a minimum. In practice, any fabric thickness increase is limited by the preforming process and deformation beyond the point of tow contact would cause an increase in fibre volume fraction as the fibre packing becomes tighter. It is suggested that the reinforcement would deform along the path of least resistance, and it is at the point of tow contact where the reinforcement will experience a secondary deformation mode such as relative fibre slip, followed by wrinkling or folding. Shearing of aligned reinforcement up to the locking angle, the point where adjacent tows came into contact, resulted in two changes in fabric architecture. First, the orientation of the fibres was altered, the ply
angle reducing with increased shear. The second effect was a decrease in tow spacing which resulted in an increase in superficial density, hence an increase in fibre volume fraction, where:12 I$=
n& tp sin 219
This effect is shown in Fig. 8. The fibre volume fraction was measured by burn-off tests conducted on flat plaques and predicted using eqn (1). A minimum of five samples was used to obtain experimental data at each ply angle. The flat plaques were manufactured using resin-transfer moulding (RTM). Preforms were produced using the four-bar linkage, described earlier, to shear the reinforcements to give ply angles ranging from &22” to *68”. Three or four layers, depending on original fabric superficial density, were then compacted to give unsheared target fibre volume fractions of around 0.30. Resin was injected at a pressure of 1 bar into a 3.5 mm cavity tool with a temperature of 70°C. Dow Derakane 8084 vinylester resin (with 1% by mass Interox TBPEH initiator) was used with the 0”/90” engineered fabric and Cray Valley Total 6345.001 unsaturated polyester resin (with 2% by mass Akzo Perkadox 16 initiator) was used with the other fabrics. The plaques were allowed to cure for 20 min before being post-cured at 115°C for 24 h. The fibre volume fraction increased as the ply angle decreased. This relates to the decrease in tow spacing observed during the shearing process. A comparison of experimental and predicted volume fractions in Fig. 8 shows a good correlation for ply angles between ~t35” and &45”. For ply angles lower than &35” the predicted volume fraction is higher than the experimental volume fraction. This is due to relaxation of the fabric that occurred during transfer from the shearing rig to the flat plaque mould. This effect is more noticeable at higher volume fractions where the tow spacing is smaller and the fibre packing is tighter. The same effect was seen for all of the fabrics tested.
330
P. Smith et al.
Fig. 3. 0”/90” Engineered
31 N-PLANE
PERMEABILITY
3.1Measurement Pei -meability is usually determined using a simple ex1 jeriment within a thin cavity. Flow experiments
flow use
fabric: (a) front; (b) rear.
either a radial flow rig with central fluid injection or a rectilinear flow rig with end injection. The radial flow rig, which was used in this work, consists of a thin radial cavity with a Newtonian test fluid injc:cted through a central port. The method allows both
Shear deformation and aligned reinforcements
Fig. 4. f 45” Engineered
princi ipal permeabilities to be measured in one exper iment and removes any errors caused by racetl racking of the fluid, but it requires a complex result s analysis method. The rectilinear approach is simpl er, but involves more experiments and potentially larger errors. A Newtonian test fluid is injected
fabric: (a) front; (b) rear.
from one end of the rig at a constant pressure and analysis is performed using Darcy’s law. Hirt et al.” and Adams and Rebenfeld18 developed a radial flow technique which involved injecting oil at a con stant pressure. Equations linked the permeability ta I the rate of change of flow-front position, measure’ d by
332
P. Smith et al.
Fig. 5. Plain-weave
fabric.
Fig. 6. 2:2 Twill-weave
fabric.
333
Shear deformation and aligned reinforcements
Fig. 7. 4-Harness
satin-weave
developed by Chick et al.‘” which used a fixed flow-rate injection. The permeability is related to the pressure differences at fixed points in the cavity, measured using a series of pressure transducer ‘s. The method allows a metal lid to be used, as obser vation
Ok lservation
of the advancing flow front during imIpregnation. Flow rates and pressures are equivalent to the RTM process but are limited by a necessarily tri msparent cavity lid which is susceptible to deflection An alternative method was at high pressures.
l
fabric.
(Burn Off) -Predicted
Experimental
(Equation 1)
40 38 .36 -34 --
26 --
I__\:_ i
0
24 -22 -20 1 25
27
29
31
33
35
37
39
41
Ply Angle (Degrees) Fig. 8. Fibre volume
fraction
versus ply angle for o”/90° fabric.
43
45
P. Smith et al.
334
of the advancing flow front is unnecessary. Consequently, the fixed flow-rate approach allows higher flow rates and pressures to be achieved. In this study a constant flow-rate radial test rig and the method described by Chick et al.‘” were used to determine in-plane permeability of simply sheared fabrics. SAE 30 oil was injected into a 4 mm cavity at room temperature, at approximately 7 ml s-‘. Four layers of reinforcement were used for each experiment, giving deformed fibre volume fractions ranging from 0.30 to 0.45. The injection time and pressures along the principal fabric axes were monitored. The principal permeabilities were then calculated from the pressure distribution in the cavity. 3.2 Prediction 3.2.1 Unidirectional reinforcements Several models exist for predicting the permeability of a unidirectional reinforcement from the fibre architecture. The most common is the Kozeny-Carman equation,‘““’ which models the variation of permeability with volume fraction and was originally developed for granular beds:
k=R’(l-w 4c
v:
where c is a constant dependent on the geometric form of the bed. The predicted permeability is isotropic, which is not true for a unidirectional reinforcement. The model is therefore limited when considering transverse flow. It does not account for the transverse flow being more constricted than the longitudinal flow, or the flow stopping in the transverse direction when the fibre volume fraction reaches its maximum. Further difficulties arise when choosing a value for the Kozeny constant, c. Values of between 0.38 and 0.68 have been suggested20.22-‘5 for flow through homogeneous graphite-fibre beds. Gutowski et ~1.~’ showed that eqn (2) did not hold for high fibre volume fractions and suggested an improved empirical model for transverse permeability. Cai2h compared the Kozeny-Carman equation and the Gutowski adaption with experimental measurements and concluded that both can be applied to unidirectional reinforcement with volume fractions below 0.55. A typical aligned fibre reinforcement formed from fibre tows is a heterogeneous structure. During fluid impregnation the flow can be split into two parts, macroscopic flow around the tows and microscopic flow within the tows. Gebart27 has suggested the use of an ‘effective fibre radius’ in the Kozeny-Carman equation to account for the heterogeneous fibre structure. The effective fibre radius is an averaged value falling between the filament and tow radii.
The permeability models based on the KozenyCarman equation relate to idealised unidirectional fibre structures that are rarely encountered in practice. The reinforcement structure is included by the use of a fibre radius term. When the technique is applied to more complex reinforcement structures, empirical terms are used to determine permeability. 3.2.2 Biaxial reinforcements The simplest prediction of biaxial permeability is made by splitting the fabric into unidirectional layers. Flow between layers is disregarded, so the bulk fabric permeability can be determined using a simple addition rule.28 This assumption only applies when the ply group thickness is small, as is the case for most laminates. A further model has been developed by Bruschke et a1.2Yto account for flow between layers that occurs close to the flow front. The accuracy of the Kozeny-Carman unidirectional permeability model and bulk fabric permeability models may be limited by the structure of the fabric. The use of tows to produce heterogeneous plies, through-thickness stitching present in engineered fabrics, or the intermingling of layers and resulting crimp in woven fabrics is not considered in the models, and may limit the accuracy of the permeability predictions. Little previous work has been carried out on the permeability of deformed reinforcements. Hammani et a1.30determined the permeability of a simply sheared engineered fabric. The experimental results showed variations in both the magnitude and direction of the principal permeabilities due to the fabric deformation. The volume fraction increase caused by simple shear was identified as the major cause of permeability variation. Ueda and Gutowski”’ investigated the permeability of a deformed woven fabric. A reasonable correlation was obtained between a permeability model based on crimp and experimental results for a deformed satin-weave fabric. A further investigation by Smi?’ compared an empirical permeability model based on eqn (2) with experimental results for simply sheared woven and engineered fabrics. A good agreement between predicted and experimental permeabilities was found for the fabrics. The approach used to calculate permeability for the sheared fabrics in this work is based on the Kozeny-Carman method described above. Figure 9 shows the notation used for the permeability theory described below. For a reinforcement with ply angle &te, the fibre volume fraction can be calculated from eqn (1). For each layer, permeability along the fibres, from the Kozeny-Carman k,> was determined equation (eqn (2)). It should be possible to determine the Kozeny constant c experimentally for unidirectional (UD) layers, but in practice it is difficult to conduct flow experiments with truly UD reinforce-
Shear deformation and aligned reinforcements Unidirectional
f bidirectional
Fig. 9. Permeability
theory
nomenclature.
ment. In this case, the Kozeny constant was found for each reinforcement by a least-squares method. This provided a good correlation between the experimental and theoretical permeabilities of each deformed, bi-directional reinforcement. The values of R and c used for each fabric can be found in Table 2. This approach was applied to both engineered and woven fabrics. Bulmer33 showed that transverse permeability (kJ of a quasi-UD layer is approximately 1/20th of the longitudinal value. This work was based on a stitched quasi-UD fabric containing 10% transverse reinforcement. The estimation of intermediate, in-plane permeabilities has therefore been simplified by assuming k2 to be zero. The principal permeabilities (flow along the semi-major and semi-minor axes) of the bi-directional reinforcement can then be approximated by applying a transformation to the axial values and using a simple addition rule, assuming zero flow between layers. This gives the following for flow parallel to the major axis of the fabric (corresponding to the bisector of the two fibre axes): k, = k, cos* 0
(3)
Note that this is based on a simplified version of the expression proposed by Advani et al.:34 k, = k, co? 8 + k2 sin’ 8 -
(kZ - k,)2 sin’ 8 cos* 8 k, sin2 + Bkz cos’ B
(4)
Equation (3) is developed by disregarding the final term in eqn (4). The permeability method described above can then be used to generate values for k, and k,; eqn (4) should be used if experimentally Table 2. Permeability
constants
Reinforcement
Fibre radius (/*ml
Q”/9Q0 engineered + 45” engineered Plain-weave 2:2 Twill-weave
7.5 7.5 6.5 6.5
Kozeny
constant
0.0404 0.0146 0.0018 0~0069
335
determined permeability values are used for the unidirectional principal permeabilities kl and k2. In the method of prediction described above, the Kozeny constant c is found by a least-squares fit to experimental data. This process is analogous to the effective fibre radius term used in the Gebart The process takes the variation in method.*’ reinforcement structure between different fabrics into account and allows the Kozeny-Carman equation to be applied to fabrics with different heterogeneous structures. The predictions of in-plane permeability are compared with experimental results in Figs 10-13. In all cases there is an excellent agreement between experimental and theoretical permeabilities over the range of ply angles tested. Although the magnitudes of the permeabilities vary for the reinforcements, a similar trend can be seen in each. The permeability decreases at ply angles above ~t45” due to the combined effect of fibre orientation and increased volume fraction. At ply angles between &38” and +45” there is an increase in permeability. This is due to the fibres becoming aligned with the direction of flow. However, as the ply angle decreases further the increasing volume fraction is the dominant effect and the permeability reduces. A similar effect is seen for both woven and engineered reinforcements. The permeabilities for both types of fabric rise as the ply angle drops below *45”. The permeability of the engineered fabrics (Figs 10 and 11) then begins to fall away at a ply angle of *40” and reduces quickly as the volume fraction increases. The woven fabrics (Figs 12 and 13) do not exhibit a drop in permeability until the ply angle reduces to *36”. The subsequent fall in permeability is then less severe than for the engineered fabrics. A further difference to note is a generally higher permeability for the woven fabrics over all ply angles measured. These differences can only be due to fabric architecture. Possible causes are the effect of crimp channels in the woven fabrics,“.35 or a reduction in engineered fabric permeability caused by the polyester stitching. There is also a notable difference in the permeabilities of the 0”/90” and *45” stitch-bonded fabrics. The permeabilities measured for the 0”/90 fabric are lower than those of the &45” fabric, despite the former having a lower fibre volume fraction. This effect can only be due to differences in the fibre architecture and stitch pattern in each fabric. The fibres in each layer of the V/90” fabric are stitched into distinct tows, forming a heterogeneous reinforcement (Fig. 3(a,b)). The layers in the *45” fabric approximate to a more homogeneous structure (Fig. 4(a,b)). This difference in structure, and the subsequent fluid flow patterns, may account for the increased in-plane permeability found in the +45” fabric.
P. Smith et al.
336 1
l
Kx Experimental - - - Kx Kozeny Carman j
0.70 l l
7
/
0.50
0 r K rng
l
l
0.60
0.40 /
.* = Q 0.30
/
/
/
I l
/
c 0. 0.20
0.10
0.00 25
30
35
40
45
50
55
60
65
Ply Angle (Degrees) Fig. 10. Principal permeability:
l
0”/90” engineered
+ l
l
,--+---•-w,
/
/
/
/
/
/
/
/
/
/ /*
l
‘.
l
\
l\,* ‘\
l
\
‘?
4
A,
l l
volume fraction.
Kx Experimental - - - Kx Kozeny Carman
+
1.20 --
fabric, 0.32 unsheared
l l
l
\\
l
\ \* \\ \\ \\ \*\ l \
0.20 --
l l
\\
0.00 4 25
30
35
40
45
50
55
60
Ply Angle (Degrees) Fig. 11. Principal permeability:
+45” engineered
fabric, 0.36 unsheared
volume fraction.
65
337
Shear deformation and aligned reinforcements Kx ExDerimental - - - Kx Kozeny Carman 1
1 + 16.00,
25
30
35
40
45
50
55
60
65
Ply Angie (Degrees)
Fig. 12. Principal
permeability:
1 +
plain-weave
fabric, 0.26 unsheared
volume
fraction.
Kx ExDerimental - - - Kx Kozenv Carrnanl
4.50 l
4.00 3.50 B g
3.00
X -g
2.50
1: z 2.00 t E $ L
1.50 1.00
0.50
-I
25
30
35
40
45
50
55
60
Ply Angle (Degrees) Fig. 13. Principal
permeability:
2:2 twill-weave
fabric, 0.27 unsheared
volume
fraction.
65
338
P. Smith et al.
Experimental results for stitch-bonded and woven fabrics arising from this study have been compared with the results of Ueda and Gutowski3’ and Smit3’ in Fig. 14(a,b). The permeability values have been normalised to account for the differing fibre volume fractions of undeformed fabric, where: ke k norm=k undef
by the rule of mixtures: E, = E,V, + E,(l
- 6,)
Y,2 = YfVf + v&l - Vf)
(84 (8b)
Transverse and shear moduli were calculated from the relationships:
(5)
(1+‘9V,)
MEM
Results show good correlation across all ply angles for woven and engineered fabrics. In Fig. 14(a), Ueda and Gutowski’s data show a higher normalised permeability at all ply angles. These data are for a 7-harness satin-weave fabric and are compared with data for plain- and twill-weave fabrics. The presence of crimp channels in the sheared satin-weave fabric used by Ueda and Gutowski may account for the higher normalised permeabilities.
4 MECHANICAL
matrix properties
“(l-
hvf)
where: Wf-MJ
h=
Wf
5Mn)
+
in which M is the appropriate modulus and 5 is an empirically determined constant. Halpin suggests the use of 5 = 2-O for transverse modulus EZ, and 5 = 1.0 for shear modulus G,2. These are then converted to the on-axis compliance matrix:
PROPERTIES
Permeability is affected by both volume fraction and ply angle changes associated with simple shear, but in Section 3 it has been shown that these effects may work in opposition. This is not the case for mechanical properties. Ply angle and volume fraction changes caused by simple shear may complement each other, producing more marked variations in the modulus and Poisson’s ratio of the deformed laminate. At the simplest level, the analysis suggested by KrencheP6 for angle-ply laminates can be used to estimate the mechanical properties of a sheared reinforcement. An efficiency factor can be calculated: 7 = 2 a, cos4 (Y,
- V,) + EfVfv
The on-axis compliance matrix was converted to an off-axis compliance matrix for the UD ply by applying a strain transformation based on an angle 8. The longitudinal modulus, E,, and Poisson’s ratio, vXY, were then calculated for the bidirectional laminate using:38 _
_“’
E, = _
s, Shh- %6
(6)
This, along with the volume fraction calculated from eqn (l), is then substituted into a modified form of the rule of mixtures to give an estimate of the longitudinal modulus, E,: E, = E,(l
where:
(7)
This method accounts for the change in volume fraction and the fibre reorientation effects. The main limitation is the omission of the Poisson effect in the technique. A more robust approach is to use classical laminate theory37 to predict laminate properties. This approach considers the laminate to be formed of unidirectional plies. The properties of each ply are usually based on experimental data, although in this case it was more convenient to use empirical expressions such as the Halpin-Tsai equations.” On-axis longitudinal modulus and Poisson’s ratio were estimated from fibre and
(124
I
Y ry=
s,&6 -
-
%6s,6
3,,366-
ST6
Wb)
where: S,, = Sr, cos4 8 + S,, sin4 8 + (2S,, + S,,) cos* 8 sin* 8 Sr2 = (ST1+ $2 - Se,) cos2 8 sin’ 8 + S,,(c0s4 8 + sin4 e) $6,= 2(2S,,+ 2Sz2- 4S12- &)COS* 8 Sin*8 + S,,(c0s4 8 + sin4 e) S,,= (2S11- 2S,, - SG6)cos3 e sin 8
- (2S2, - 2S12- S,,) sin3 8 cos 8 S,,= (2S,, - 2S,, - S,,) sin” 8 cos 8 - (2& - 2S12-&)cos3
8 sin 8
Shear deformation and aligned reinforcements
339
‘.’ (a) A
1.2
A
A
t
.2 = .a
l-_l AKX 0 Kx Smit
A
A
1 --
l A A
g
E
0.8 --
A
OX
ii
A A
0
A
$
A
A
i! 2
A
A
A
A
A
A
0
A
A
zb
0.4 --
A
A
A
20
25
30
40
35
50
45
60
55
65
Ply Angle (Degrees)
1.4 -Jb) A
1.2 -f .c z8
A--
E b a
0.8 --
n Q fv)
:
A
t
X X
X 0.6 --
f
E b 2
a
O
2
X
x
A 0
0.4 --
0 0
A
0-l 20
A
I 25
30
35
40
45
50
55
60
65
70
Ply Angle (Degrees) Fig. 14.
Normalised permeability for: (a) simply sheared engineered fabrics; (b) simply sheared woven fabrics.
The Krenchel-modified rule of mixtures and the classical laminate analysis are based on laminates formed from unidirectional plies. Both approaches neglect the effect of crimp39 present in woven fabrics. Both the Krenchel-modified rule of mixtures and the classical laminate analysis approach were used to estimate the laminate stiffness for sheared laminates. The effect of crimp in the woven fabrics was neglected. The material properties used in the analyses can be found in Table 3. Elastic property tests were conducted on laminates
with sheared woven and engineered fabrics. Flat plaque mouldings were produced by RTM, as described previously. The elastic properties were measured using an Instron 1195 universal testing machine to a method encompassing BS 2782. Figures 15-18 compare the experimental data with the modulus predicted using the Krenchel-modified rule of mixtures and classical laminate analysis approaches. For all materials tested the values predicted by the classical laminate analysis approach are reasonably accurate. The predictions made using
340
P. Smith et al.
Table 3. Fibre and matrix properties (from manufacturers’ data and Ref. 40)
Material
Tensile modulus (GPa)
Shear modulus (GPa)
Poisson’s ratio
Density (kg m-3)
Glass fibre Cray Valley 6345.001 polyester resin Dow Derakane 8084 vinylester resin
73.0 4.47
29-9 1.62
o-22 0.38
2605 1211h
3.3
1.2
0.38
1088*
5 SUMMARY
El
y From: G,, = ~ 2(1+ Y) ’ Measured values taken from cured resin samples.
the Krenchel-modified rule-of-mixtures method are only accurate for ply angles below +45”. At ply angles above &45” the predicted modulus is lower than the experimental values. Krenchel neglected the Poisson effect in his analysis, assuming there was no transverse deformation. This becomes increasingly important as the fibres become more transverse to the load. Figures 19-20 show the experimentally determined Poisson’s ratio values for an engineered and a woven fabric. Poisson’s ratio reaches a peak at a ply angle of around *to”, and then reduces as the ply angle is increased.
Tangent Modulus -
1 +
The experimental values are compared with predictions made using the classical laminate theory, which correspond reasonably well.
Simple shear has been isolated as a mode of fabric deformation. Fibre reorientation and volume fraction changes have been established as effects of shear. A brief analysis of the shear mechanism has identified a point where wrinkles and folds may begin to form. A four-bar shearing rig was developed and used to shear a variety of engineered and woven fabrics. The effect of shear on the processing properties of the fabric and the mechanical properties of the laminate have been investigated. Shear deformation was found to have a considerable effect on the principal permeabilities of the reinforcement. A semi-empirical expression, based on the Kozeny-Carman equation, relating permeability to the ply angle has been found for each of the fabrics tested. The mechanical properties of laminates formed from sheared reinforcement were also affected by the shear deformation. Elastic stiffness was predicted by the simple Krenchel/rule-of-mixtures approach, which yielded large discrepancies at high ply angles, and the classical laminate theory, which gave improved and reasonably accurate predictions. This work has shown that inter-fibre shear and reinforcement deformation occurring during the
ROM - - - - -. Classical Laminate Theory 1
25
Q 15
-I
2
3
B
IO--
B
5 t
20
25
30
35
40
45
50
55
60
Ply Angle (Degrees) Fig. 15. Longitudinal
modulus: 0”/90” engineered
fabric/polyester
resin.
65
70
341
Shear deformation and aligned reinforcements 1 +
0
Tanaent Modulus -
ROM - - - - -. Classical Laminate Theorv 1
I
25
20
30
35
40
45
50
55
60
70
65
Ply Angle (Degrees) Fig. 16.
Longitudinal modulus: *45” engineered fabric/polyester resin.
preforming process should be considered. Folds and wrinkles caused by deforming a reinforcement beyond its locking angle have the potential to cause numerous processing and potential strength problems.41 Localised changes in permeability may cause processing
I
l
Tanaent Modulus -
problems such as dry spots and an unexpected flow pattern. Shear has also been shown to affect the mechanical properties significantly, and failure to take account of this is likely to lead to inaccuracies in structural analyses.
ROM - - - - -. Classical Laminate Theotv 1
25
I --
, --
--
t
20
25
30
35
40
45
50
55
60
Ply Angle (Degrees)
Fig. 17. Longitudinal modulus: plain-weave fabric/polyester resin.
65
70
342
P. Smith et al. l
04 20
25
Tangent Modulus -RoM
30
35
40
_..__. Classical Laminate Theory
45
50
55
60
65
70
Ply Angle (Degrees) Fig. 18. Longitudinal
modulus: 4-harness satin-weave fabric/polyester
ACKNOWLEDGEMENTS
resin.
authors would like to thank Chris Price (AMM) and Chadwick (Chomarat) for the supply of glass reinforcement. Dan Morris, Roger Smith, Andrew Kingham and Geoff Tomlinson are also thanked for their assistance with experimental work. Ivan
This work was funded by Motor Company and the authors are indebted to Ken Kendall and Carl Johnson for their advice and encouragement. The
-Classical
Laminate Theory
l
Experimental
1.1 1 -0.9 --
0.8 -0 t;; u c” % .E :
0.7 -~ 0.6 -0.5 -~ 0.4 -0.3 -0.2 -0.1 -Oi
20
25
30
35
40
45
50
55
60
Ply Angie (Degrees)
Fig. 19. Poisson’s ratio: 0”/90” engineered fabric/vinylester
resin.
343
Shear deformation and aligned reinforcements l
20
25
30
Experimental -Classical
35
40
45
Laminate Theory 1
50
Ply Angle (Degrees) Fig. 20. Poisson’s ratio: 4-harness satin-weave fabric/polyester
REFERENCES 1. Advani,
S. G. & Bruschke, element/control volume approach anisotropic porous media. Polym. 398-405. 2. Rudd, C. D., Rice, E. V., Bulmer, Process modelling and design moulding. Plast. Rubb. Compos.
M. V., A finite to mold filling in Compos., 11 (1990) L. J. & Long, A. C., for resin transfer
resin.
11. Long, A. C., Preform design for liquid moulding processes. PhD thesis, University of Nottingham, 1994. 12. Rudd, C. D., Middleton, V., Owen, M. J., Long, A. C. & McGeehin, P., Design, processing and performance of structural preforms. In Proc. CANCOM ‘93, 2nd Int. Conf on Composite Structures and Materials, Ottawa, 1993, pp. 139-152. 13. Long, A. C. & Rudd, C. D., Computer integrated design of structural preforms for liquid moulding processes. In
20
Proc. 27th ISATA-New and Alternative Materials for the Transportation Industries, Aachen, 1994, pp.
3. Chan, A. W., & Morgan, R. J., Computer modeling of liquid composite molding for 3-dimensional complex shaped structures. In Proc. 10th Annual ASMIESD Advanced Composites Conference, Dearborn, MI, 1994, pp. 341-345. 4. Lee, L. J., Young, W. B. & Lin, R. J., Mold filling and cure modelling of RTM and SRIM processes. Compos.
381-390. 14. Bickerton, S., Effect of draping of fibre preforms on process parameters during manufacturing with resin transfer molding. In Proc. 11th ESD Advanced Composites Conference and Exposition, Dearborn, MI, November 1995, pp. 213-220. 15. Long, A. C., Rudd, C. D., Blagdon, M. & Smith, P., Characterising the processing and performance of aligned reinforcements during preform manufacture. Composites Part A (in press). 16. Potter, K. D., The influence of accurate stretch data for reinforcements on the production of complex structural mouldings. Composites, 11 (1979) 161-167. 17. Hirt, D. E., Adams, K. L., Prud’homme, R. K. & Rebenfeld, L., In-plane radial fluid flow characterization of fibrous materials. J. Thermal Insulation, 10 (1987) 153-172. 18. Adams, K. L. & Rebenfeld, L., In-plane flow of fluids in fabrics: Structure/flow characterization. Text. Res. J., 57 (1987) 647-654. 19. Chick, J. P., Rudd, C. D., van Leeuwen, P. A. & Frenay, T. I. Material characterisation for flow modelling in structural reaction injection moulding.
(1993) 67-76.
Process. Applic.,
Struct., 27 (1994) 109-120.
5. Halpin, J. C., Primer on Composite Materials: Analysis. Technomic, Lancaster, PA, 1984. 6. Mack, C. & Taylor, H. M., The fitting of woven cloth to surfaces. J. Text. Inst. (Trans.), 57 (1956) 447-488. 7. Robertson, R. E., Hsiue, E. S., Sickafus, E. N. & Yeh, G. S. Y., Fiber rearrangements during the moulding of continuous fiber composites: 1. Flat cloth to a hemisphere. Polym. Compos., 53 (1984) 126-131. 8. Robertson, R. E., Hsiue, E. S. & Yeh, G. S. Y., Continuous fiber rearrangements during the moulding of fiber composites: 2. Flat cloth to a rounded cone. Polym. Compos., 53 (1984) 191-197. 9. Van West, B. P., Pipes, R. B. & Keefe, M., A simulation of the draping of bidirectional fabrics over arbitrary surfaces. J. Text. Inst., 4 (1990) 448-460. 10. Bergsma, 0. K., Computer simulation of 3D forming processes of fabric reinforced plastics. In Proc. 9th Znt. Con& on Composite Materials, ICCMI9, Madrid, 1993, pp. 560-567.
Polym. Compos., 171 (1996) 124-135.
20. Williams, J. G., Morris, C. E. M. & Ennis, B. C., Liquid flow through aligned fibre beds. Polym. Eng. Sci., 14.6 (1974) 413-419.
P. Smith et al.
21. Summerscales, J., A model for the effect of fibre clustering on the flow rate in resin transfer moulding. Compos. Manuf, 41 (1993) 27-31. 22. Gutowski, T. G., Cai, Z., Bauer, S., Boucher, D., Kingery, J. & Wineman, S., Consolidation experiments for laminate composites. J. Cornpos. Mater., 21 (1987) 650-669. 23. Lam, R. C. & Kardos, J. L., The permeability of aligned and cross-plied fiber beds during processing of continuous fiber composites. In Proc. American Society for Composites, Third Tech. Conf, Seattle, WA, 1988, pp. 3-11. 24. Lam, R. C. & Kardos, J. L., The permeability and compressibility of aligned and cross-plied carbon fiber beds during processing of composites. In Proc. 47th Ann. Tech. Conf (ANTEC ‘89), SPE, New York, 1989, pp. 1408-1412. 25. Skartsis, L. & Kardos, J. L., The Newtonian permeability and consolidation of oriented carbon fiber beds. In Proc. American Society for Composites, Fifth Tech. Conf, East Lansing, MI, 1990, pp. 548-556. 26. Cai, Z., Estimation of permeability of fibrous preforms for resin transfer moulding processes. Compos. Man@,
31. Ueda, S. & Gutowski, T. G., Anisotropic permeability of deformed woven fabrics. Composites Part A (submitted). 32. Smit, A., The effect of shear deformation on the permeability of reinforcement fabrics for resin transfer moulding. MSc thesis, Delft University of Technology, April 1995. 33. Bulmer, L. J., In-plane permeability of reinforcements for liquid moulding processes. PhD thesis, University of Nottingham, 1993. 34. Advani, S. G., Brushke, M. V. & Parnas, R. S., Resin transfer moulding flow phenomena in polymeric composites. In Flow and Rheology in Polymer Composites Manufacturing, ed. S. G. Advani. Elsevier Science BV, Amsterdam, 1994, pp. 465-515. 35. Salem, A. J. & Parnas, R. S., The unidirectional and radial in-plane flow of fluids through woven composite reinforcements. In Proc. 6th ASC Tech. ConfComposite Materials, Mechanics
36. 37.
34 (1993) 251-257. 27. Gebart,
ments
B. R., Permeability of unidirectional reinforcefor RTM. /. Compos. Mater., 268 (1992)
1100-1133. 28. Rudd, C. D., Rice, E. V., Bulmer, L. J. & Long, A. C.,
Process modelling and design for resin transfer moulding. Plast. Rubb. Compos. Process. Applic., 20 (1993) 67-76. 29. Bruschke, M. V., Lute, T. L. & Advani,
S. G., Effective RTM preforms.
in-plane permeability of multi-layered In Proc. American Society for Composites, Seventh Tech. Conf, University Park, PA, 1992, pp. 103-112. 30. Hammani, A., Trochu, F., Gauvin, R. & Wirth, S., Directional permeability measurement of deformed reinforcement. In Proc. ENERCOMP ‘95, Montreal, Quebec, May 1995, pp. 552-562.
38.
39.
and Processing,
New
York, 1991, pp. 1012-1021. Krenchel, H., Fibre Reinforcement. Akademisk Forlag, Copenhagen, 1964. Tsai, S. W. & Hahn, H. T., introduction to Composite Materials. Technomic, Lancaster, PA, 1980. Jones, I. A., Finite element modelling and testing of filament wound orthotropic components. PhD thesis, University of Nottingham, 1993. Zweben, C., Mechanics of composite materials. In Delaware Behaviour
Design Encyclopedia Vol. 1: Mechanical and Properties of Composite Materials.
Technomic, Lancaster, PA, 1989. 40. Cauthier, M. M. (ed.), Engineered Materials Handbook: Desk Edition. ASM International, Metals Park, OH, 1995. 41. Arndt, R. D., Fabric preforming for structural reaction injection molding. In Advanced Composite Materials: New
Developments
and
Applications
Detroit, MI, 1991, pp. 35-40.
Conf
Proc.,
PII:
in Northern
SO266-3538(96)00132-7
Ireland.
All rights resewed 0266-3538/97/$17.00
THE EFFECT OF SHEAR DEFORMATION ON THE PROCESSING AND MECHANICAL PROPERTIES OF ALIGNED REINFORCEMENTS P. Smith,
C. D. Rudd
& A. C. Long*
Department of Mechanical Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, UK
(Received 29 May 1996; revised 5 September 1996; accepted 19 September 1996)
so
Abstract The growth of liquid moulding processes for the production of structural and semi-structural components has been eased by the development of computer-aided engineering tools for structural analysis and process modelling. However, the accuracy of these tools is dependent on the available material property data. These are usually obtained from experimental or theoretical analysis of flat plaques. These methods do not take into account reinforcement deformation during the preforming process. Deformation, caused by forming two-dimensional reinforcements over threedimensional surfaces, can result in local fibre reorientations and volume fraction changes within the preform. In this study the major deformation mode, simple shear, is isolated. The effects of simple shear deformation on permeability and elastic properties of engineered and woven glass fabrics are investigated. Predictions of elastic properties are made by using established methods and compared with experimental data for a range of fabric architectures. A semiempirical method is applied to characterise the effects of shear on reinforcement permeability. 0 1997 Elsevier Science Limited. All rights reserved Keywords: preforming, shear deformation, reinforcement, in-plane permeability, properties
t V
% ;I Y P
Fabric superficial density Cavity thickness Volume fraction Fibre angle with respect to applied load Krenchel efficiency factor Ply angle Poisson’s ratio Density
Subscripts
E i m X,Y I,2
Property of composite Property of fibre Property of unidirectional layer Property of matrix Principal axes of bi-directional reinforcement Principal axes of unidirectional reinforcement
laminate/ laminate/
1 INTRODUCTION Liquid moulding processes are being increasingly used for the production of structural and semi-structural components from composite materials. The use of reinforcement preforms allows separation of the reinforcement preparation and the moulding cycle to reduce cycle times. The most common method of preform manufacture involves forming the reinforcement between matched moulds. Structural components demand the use of aligned fibre reinforcements to provide the required mechanical properties. Typical aligned fibre reinforcements are woven or braided, with stitch-bonded or ‘engineered’ fabrics becoming popular. These consist of stitched unidirectional layers at various orientations and generally provide improved in-plane mechanical properties over woven or braided fabrics due to the elimination of crimp. Preforms are usually designed to achieve the required component mechanical performance. The mechanical performance can be assessed by the rule of mixtures, which returns a useful initial estimate, or
aligned tensile
NOMENCLATURE Proportion of fibres at angle (Y,, to applied load E Elastic modulus G Shear modulus k Permeability k “OrIll Normalised permeability k undef Permeability of undeformed fabric Permeability of fabric at ply angle 8 k, n Number of fabric layers R Fibre radius a,
* To whom correspondence should be addressed. 327
328
P. Smith et al.
classical laminate analysis, which gives more accurate predictions. Processing considerations are equally important, and determine whether component production is feasible and economic. A number of models have been developed to simulate the impregnation phase of liquid moulding (see, for example, Refs. l-4). The accuracy of these models is dependent on the accuracy of the input data. Property measurements are usually taken from flat plaque data and input into processing and mechanical property models. Mechanical property data are determined from unidirectional flat plaques for input into classical laminate analysis. Plaques are tested to determine shear and tensile moduli and Poisson’s ratio, although initial estimates can be made by using a simple rule of mixtures and the well known Halpin-Tsai equations.’ Processing models require fabric permeability inputs. These can be measured by applying Darcy’s law for flow through a radial or rectilinear mould cavity to obtain the principal fabric permeabilities. During preform manufacture, the two-dimensional reinforcement is required to conform to threedimensional shapes. The reinforcement deforms to accommodate the preform shape and the fibre geometry is forced to adjust. Several models have been developed to simulate the draping of fabric over a three-dimensional surface. Mack and Taylor6 established a draping algorithm for the fitting of a textile garment to the human body. Adaptations of the model were directly applicable to preforming: Robertson et al.‘.’ developed a simple drape model for a hemispherical surface. More recently, Van West et al.” and Bergsmar have developed kinematic draping algorithms to drape fabric over an arbitrary three-dimensional surface. The models are based on a pin-jointed fibre mesh and require iterative solutions. Long” developed a PC-based drape model which describes the surface using flat patches, allowing the solutions to be calculated directly as opposed to iteratively. The fibre deformation caused during the preforming process may result in a significant departure from anticipated processing and mechanical characteristics. Initial investigations by Rudd et cd.‘* have demonstrated the changes in longitudinal modulus and permeability. Further works by Long and Rudd13 and BickertonI have demonstrated the effect of reinforcement deformation on fluid flow through the deformed fabric. The assumption of flat plaque properties and principal permeabilities based on undeformed fabrics may therefore be inaccurate and the effect of reinforcement deformation on the preform has to be considered. This study aims to demonstrate the effect of reinforcement deformation on the processing and mechanical properties of a range of bi-directional fabrics and suggests reliable methods of predicting the property changes arising from the deformation.
2 REINFORCEMENT
DEFORMATION
Aligned fibre reinforcements have differing on- and off-axis properties. However, deformation caused during preform manufacture results in considerable changes in both the principal axis orientation and fibre volume fraction. Long et ~1.‘~ suggested that aligned reinforcement deformation can be split into two major mechanisms, simple shear and shear-slip at the fibre cross-overs. These are demonstrated in Fig. 1. PotterI suggested that simple shear is the dominant mode of deformation for most bi-directional reinforcements. In this case, the reinforcement behaves as a pin-jointed mesh, and the fibres rotate around the cross-over points to produce the deformation. In order to measure the effects of shear on fabrics, simple shear deformation was isolated from any other deformation mode. This was achieved by using a four-bar linkage, shown in Fig. 2, which clamped the reinforcement along two edges. One edge of the linkage was connected to a laboratory bench and a force was applied to the opposite edge. A parallelogram was formed, forcing the reinforcement to shear. The change in ply angle 8 (the angle between the major principal axis and the fibre axis) was monitored via two perpendicular lines marked on the undeformed reinforcement. Five commercially available glass-fibre fabrics, typical of those used in liquid composite moulding,
Fibre rotation or shear
Fibre slip
Fig. 1. Major reinforcement
deformation
mechanisms. Sheared rig posltion T :r ........... I
Force Applied
Reinforcement
” FIxed Bar
Fig. 2. Four-bar
linkage
inter-fibre
shear isolation
rig.
Shear deformation and aligned reinforcements
329
Table 1. Fabric architecture data (from manufacturers’ data) Manufacturer
Type
Architecture
Tech Textiles
ELT 850 (1036)
0°/900 engineered
Tech Textiles
E-BX hd 936 (3074)
Chomarat Chomarat JPS
8OOT 830s Conform 3793
~t45” engineered, high drape Plain-weave 2:2 Twill-weave 4-Harness satin-weave, high drape
Tow tex (g km-‘)
Superficial density (g m-‘)
Minimum ply angle (“)
0”: 1800 90”: 1200 600”
850
*27
936
*27
2450 2450 140
790 820 532
+25” +26 *22”
“Measured values.
were sheared using the four-bar linkage. These are described in Table 1 and illustrated in Figs 3-7. Figure 3(a,b) shows the 0”/90” engineered fabric. The fibres are stitched to form distinct tows, and are locked in position by the stitches. This may be compared with the &45” engineered fabric, shown in Fig. 4(a,b), where the fibres form a more homogeneous fabric. The stitch pattern allows the fabric to deform by shear-slip, resulting in a more drapeable fabric. The plain-weave and twill-weave fabrics (Figs 5 and 6) are woven with heavy warp and weft tows. The combination of the plain- or twill-weave pattern and tow size adds a large quantity of crimp to the fabrics, which affects the processing and mechanical properties. The fabric illustrated in Fig. 7 uses light warp and weft tows tightly woven into a 4-harness satin pattern, forming a highly drapeable, low-crimp fabric. The minimum ply angle coincided with the point at which wrinkles appeared in the simply sheared fabric. The angle was measured using a protractor while the fabric was clamped in the shearing rig, and was found to be different for each fabric. This depended on a number of factors. Tow dimensions and the stitch or weave pattern may have influenced the minimum ply angle attainable. When simple shear reduced the tow spacing to zero, adjacent tows contacted each other. Any further simple shear deformation caused little change in the ply angle, and forced the reinforcement to increase in thickness, as spacing between individual fibres decreased to a minimum. In practice, any fabric thickness increase is limited by the preforming process and deformation beyond the point of tow contact would cause an increase in fibre volume fraction as the fibre packing becomes tighter. It is suggested that the reinforcement would deform along the path of least resistance, and it is at the point of tow contact where the reinforcement will experience a secondary deformation mode such as relative fibre slip, followed by wrinkling or folding. Shearing of aligned reinforcement up to the locking angle, the point where adjacent tows came into contact, resulted in two changes in fabric architecture. First, the orientation of the fibres was altered, the ply
angle reducing with increased shear. The second effect was a decrease in tow spacing which resulted in an increase in superficial density, hence an increase in fibre volume fraction, where:12 I$=
n& tp sin 219
This effect is shown in Fig. 8. The fibre volume fraction was measured by burn-off tests conducted on flat plaques and predicted using eqn (1). A minimum of five samples was used to obtain experimental data at each ply angle. The flat plaques were manufactured using resin-transfer moulding (RTM). Preforms were produced using the four-bar linkage, described earlier, to shear the reinforcements to give ply angles ranging from &22” to *68”. Three or four layers, depending on original fabric superficial density, were then compacted to give unsheared target fibre volume fractions of around 0.30. Resin was injected at a pressure of 1 bar into a 3.5 mm cavity tool with a temperature of 70°C. Dow Derakane 8084 vinylester resin (with 1% by mass Interox TBPEH initiator) was used with the 0”/90” engineered fabric and Cray Valley Total 6345.001 unsaturated polyester resin (with 2% by mass Akzo Perkadox 16 initiator) was used with the other fabrics. The plaques were allowed to cure for 20 min before being post-cured at 115°C for 24 h. The fibre volume fraction increased as the ply angle decreased. This relates to the decrease in tow spacing observed during the shearing process. A comparison of experimental and predicted volume fractions in Fig. 8 shows a good correlation for ply angles between ~t35” and &45”. For ply angles lower than &35” the predicted volume fraction is higher than the experimental volume fraction. This is due to relaxation of the fabric that occurred during transfer from the shearing rig to the flat plaque mould. This effect is more noticeable at higher volume fractions where the tow spacing is smaller and the fibre packing is tighter. The same effect was seen for all of the fabrics tested.
330
P. Smith et al.
Fig. 3. 0”/90” Engineered
31 N-PLANE
PERMEABILITY
3.1Measurement Pei -meability is usually determined using a simple ex1 jeriment within a thin cavity. Flow experiments
flow use
fabric: (a) front; (b) rear.
either a radial flow rig with central fluid injection or a rectilinear flow rig with end injection. The radial flow rig, which was used in this work, consists of a thin radial cavity with a Newtonian test fluid injc:cted through a central port. The method allows both
Shear deformation and aligned reinforcements
Fig. 4. f 45” Engineered
princi ipal permeabilities to be measured in one exper iment and removes any errors caused by racetl racking of the fluid, but it requires a complex result s analysis method. The rectilinear approach is simpl er, but involves more experiments and potentially larger errors. A Newtonian test fluid is injected
fabric: (a) front; (b) rear.
from one end of the rig at a constant pressure and analysis is performed using Darcy’s law. Hirt et al.” and Adams and Rebenfeld18 developed a radial flow technique which involved injecting oil at a con stant pressure. Equations linked the permeability ta I the rate of change of flow-front position, measure’ d by
332
P. Smith et al.
Fig. 5. Plain-weave
fabric.
Fig. 6. 2:2 Twill-weave
fabric.
333
Shear deformation and aligned reinforcements
Fig. 7. 4-Harness
satin-weave
developed by Chick et al.‘” which used a fixed flow-rate injection. The permeability is related to the pressure differences at fixed points in the cavity, measured using a series of pressure transducer ‘s. The method allows a metal lid to be used, as obser vation
Ok lservation
of the advancing flow front during imIpregnation. Flow rates and pressures are equivalent to the RTM process but are limited by a necessarily tri msparent cavity lid which is susceptible to deflection An alternative method was at high pressures.
l
fabric.
(Burn Off) -Predicted
Experimental
(Equation 1)
40 38 .36 -34 --
26 --
I__\:_ i
0
24 -22 -20 1 25
27
29
31
33
35
37
39
41
Ply Angle (Degrees) Fig. 8. Fibre volume
fraction
versus ply angle for o”/90° fabric.
43
45
P. Smith et al.
334
of the advancing flow front is unnecessary. Consequently, the fixed flow-rate approach allows higher flow rates and pressures to be achieved. In this study a constant flow-rate radial test rig and the method described by Chick et al.‘” were used to determine in-plane permeability of simply sheared fabrics. SAE 30 oil was injected into a 4 mm cavity at room temperature, at approximately 7 ml s-‘. Four layers of reinforcement were used for each experiment, giving deformed fibre volume fractions ranging from 0.30 to 0.45. The injection time and pressures along the principal fabric axes were monitored. The principal permeabilities were then calculated from the pressure distribution in the cavity. 3.2 Prediction 3.2.1 Unidirectional reinforcements Several models exist for predicting the permeability of a unidirectional reinforcement from the fibre architecture. The most common is the Kozeny-Carman equation,‘““’ which models the variation of permeability with volume fraction and was originally developed for granular beds:
k=R’(l-w 4c
v:
where c is a constant dependent on the geometric form of the bed. The predicted permeability is isotropic, which is not true for a unidirectional reinforcement. The model is therefore limited when considering transverse flow. It does not account for the transverse flow being more constricted than the longitudinal flow, or the flow stopping in the transverse direction when the fibre volume fraction reaches its maximum. Further difficulties arise when choosing a value for the Kozeny constant, c. Values of between 0.38 and 0.68 have been suggested20.22-‘5 for flow through homogeneous graphite-fibre beds. Gutowski et ~1.~’ showed that eqn (2) did not hold for high fibre volume fractions and suggested an improved empirical model for transverse permeability. Cai2h compared the Kozeny-Carman equation and the Gutowski adaption with experimental measurements and concluded that both can be applied to unidirectional reinforcement with volume fractions below 0.55. A typical aligned fibre reinforcement formed from fibre tows is a heterogeneous structure. During fluid impregnation the flow can be split into two parts, macroscopic flow around the tows and microscopic flow within the tows. Gebart27 has suggested the use of an ‘effective fibre radius’ in the Kozeny-Carman equation to account for the heterogeneous fibre structure. The effective fibre radius is an averaged value falling between the filament and tow radii.
The permeability models based on the KozenyCarman equation relate to idealised unidirectional fibre structures that are rarely encountered in practice. The reinforcement structure is included by the use of a fibre radius term. When the technique is applied to more complex reinforcement structures, empirical terms are used to determine permeability. 3.2.2 Biaxial reinforcements The simplest prediction of biaxial permeability is made by splitting the fabric into unidirectional layers. Flow between layers is disregarded, so the bulk fabric permeability can be determined using a simple addition rule.28 This assumption only applies when the ply group thickness is small, as is the case for most laminates. A further model has been developed by Bruschke et a1.2Yto account for flow between layers that occurs close to the flow front. The accuracy of the Kozeny-Carman unidirectional permeability model and bulk fabric permeability models may be limited by the structure of the fabric. The use of tows to produce heterogeneous plies, through-thickness stitching present in engineered fabrics, or the intermingling of layers and resulting crimp in woven fabrics is not considered in the models, and may limit the accuracy of the permeability predictions. Little previous work has been carried out on the permeability of deformed reinforcements. Hammani et a1.30determined the permeability of a simply sheared engineered fabric. The experimental results showed variations in both the magnitude and direction of the principal permeabilities due to the fabric deformation. The volume fraction increase caused by simple shear was identified as the major cause of permeability variation. Ueda and Gutowski”’ investigated the permeability of a deformed woven fabric. A reasonable correlation was obtained between a permeability model based on crimp and experimental results for a deformed satin-weave fabric. A further investigation by Smi?’ compared an empirical permeability model based on eqn (2) with experimental results for simply sheared woven and engineered fabrics. A good agreement between predicted and experimental permeabilities was found for the fabrics. The approach used to calculate permeability for the sheared fabrics in this work is based on the Kozeny-Carman method described above. Figure 9 shows the notation used for the permeability theory described below. For a reinforcement with ply angle &te, the fibre volume fraction can be calculated from eqn (1). For each layer, permeability along the fibres, from the Kozeny-Carman k,> was determined equation (eqn (2)). It should be possible to determine the Kozeny constant c experimentally for unidirectional (UD) layers, but in practice it is difficult to conduct flow experiments with truly UD reinforce-
Shear deformation and aligned reinforcements Unidirectional
f bidirectional
Fig. 9. Permeability
theory
nomenclature.
ment. In this case, the Kozeny constant was found for each reinforcement by a least-squares method. This provided a good correlation between the experimental and theoretical permeabilities of each deformed, bi-directional reinforcement. The values of R and c used for each fabric can be found in Table 2. This approach was applied to both engineered and woven fabrics. Bulmer33 showed that transverse permeability (kJ of a quasi-UD layer is approximately 1/20th of the longitudinal value. This work was based on a stitched quasi-UD fabric containing 10% transverse reinforcement. The estimation of intermediate, in-plane permeabilities has therefore been simplified by assuming k2 to be zero. The principal permeabilities (flow along the semi-major and semi-minor axes) of the bi-directional reinforcement can then be approximated by applying a transformation to the axial values and using a simple addition rule, assuming zero flow between layers. This gives the following for flow parallel to the major axis of the fabric (corresponding to the bisector of the two fibre axes): k, = k, cos* 0
(3)
Note that this is based on a simplified version of the expression proposed by Advani et al.:34 k, = k, co? 8 + k2 sin’ 8 -
(kZ - k,)2 sin’ 8 cos* 8 k, sin2 + Bkz cos’ B
(4)
Equation (3) is developed by disregarding the final term in eqn (4). The permeability method described above can then be used to generate values for k, and k,; eqn (4) should be used if experimentally Table 2. Permeability
constants
Reinforcement
Fibre radius (/*ml
Q”/9Q0 engineered + 45” engineered Plain-weave 2:2 Twill-weave
7.5 7.5 6.5 6.5
Kozeny
constant
0.0404 0.0146 0.0018 0~0069
335
determined permeability values are used for the unidirectional principal permeabilities kl and k2. In the method of prediction described above, the Kozeny constant c is found by a least-squares fit to experimental data. This process is analogous to the effective fibre radius term used in the Gebart The process takes the variation in method.*’ reinforcement structure between different fabrics into account and allows the Kozeny-Carman equation to be applied to fabrics with different heterogeneous structures. The predictions of in-plane permeability are compared with experimental results in Figs 10-13. In all cases there is an excellent agreement between experimental and theoretical permeabilities over the range of ply angles tested. Although the magnitudes of the permeabilities vary for the reinforcements, a similar trend can be seen in each. The permeability decreases at ply angles above ~t45” due to the combined effect of fibre orientation and increased volume fraction. At ply angles between &38” and +45” there is an increase in permeability. This is due to the fibres becoming aligned with the direction of flow. However, as the ply angle decreases further the increasing volume fraction is the dominant effect and the permeability reduces. A similar effect is seen for both woven and engineered reinforcements. The permeabilities for both types of fabric rise as the ply angle drops below *45”. The permeability of the engineered fabrics (Figs 10 and 11) then begins to fall away at a ply angle of *40” and reduces quickly as the volume fraction increases. The woven fabrics (Figs 12 and 13) do not exhibit a drop in permeability until the ply angle reduces to *36”. The subsequent fall in permeability is then less severe than for the engineered fabrics. A further difference to note is a generally higher permeability for the woven fabrics over all ply angles measured. These differences can only be due to fabric architecture. Possible causes are the effect of crimp channels in the woven fabrics,“.35 or a reduction in engineered fabric permeability caused by the polyester stitching. There is also a notable difference in the permeabilities of the 0”/90” and *45” stitch-bonded fabrics. The permeabilities measured for the 0”/90 fabric are lower than those of the &45” fabric, despite the former having a lower fibre volume fraction. This effect can only be due to differences in the fibre architecture and stitch pattern in each fabric. The fibres in each layer of the V/90” fabric are stitched into distinct tows, forming a heterogeneous reinforcement (Fig. 3(a,b)). The layers in the *45” fabric approximate to a more homogeneous structure (Fig. 4(a,b)). This difference in structure, and the subsequent fluid flow patterns, may account for the increased in-plane permeability found in the +45” fabric.
P. Smith et al.
336 1
l
Kx Experimental - - - Kx Kozeny Carman j
0.70 l l
7
/
0.50
0 r K rng
l
l
0.60
0.40 /
.* = Q 0.30
/
/
/
I l
/
c 0. 0.20
0.10
0.00 25
30
35
40
45
50
55
60
65
Ply Angle (Degrees) Fig. 10. Principal permeability:
l
0”/90” engineered
+ l
l
,--+---•-w,
/
/
/
/
/
/
/
/
/
/ /*
l
‘.
l
\
l\,* ‘\
l
\
‘?
4
A,
l l
volume fraction.
Kx Experimental - - - Kx Kozeny Carman
+
1.20 --
fabric, 0.32 unsheared
l l
l
\\
l
\ \* \\ \\ \\ \*\ l \
0.20 --
l l
\\
0.00 4 25
30
35
40
45
50
55
60
Ply Angle (Degrees) Fig. 11. Principal permeability:
+45” engineered
fabric, 0.36 unsheared
volume fraction.
65
337
Shear deformation and aligned reinforcements Kx ExDerimental - - - Kx Kozeny Carman 1
1 + 16.00,
25
30
35
40
45
50
55
60
65
Ply Angie (Degrees)
Fig. 12. Principal
permeability:
1 +
plain-weave
fabric, 0.26 unsheared
volume
fraction.
Kx ExDerimental - - - Kx Kozenv Carrnanl
4.50 l
4.00 3.50 B g
3.00
X -g
2.50
1: z 2.00 t E $ L
1.50 1.00
0.50
-I
25
30
35
40
45
50
55
60
Ply Angle (Degrees) Fig. 13. Principal
permeability:
2:2 twill-weave
fabric, 0.27 unsheared
volume
fraction.
65
338
P. Smith et al.
Experimental results for stitch-bonded and woven fabrics arising from this study have been compared with the results of Ueda and Gutowski3’ and Smit3’ in Fig. 14(a,b). The permeability values have been normalised to account for the differing fibre volume fractions of undeformed fabric, where: ke k norm=k undef
by the rule of mixtures: E, = E,V, + E,(l
- 6,)
Y,2 = YfVf + v&l - Vf)
(84 (8b)
Transverse and shear moduli were calculated from the relationships:
(5)
(1+‘9V,)
MEM
Results show good correlation across all ply angles for woven and engineered fabrics. In Fig. 14(a), Ueda and Gutowski’s data show a higher normalised permeability at all ply angles. These data are for a 7-harness satin-weave fabric and are compared with data for plain- and twill-weave fabrics. The presence of crimp channels in the sheared satin-weave fabric used by Ueda and Gutowski may account for the higher normalised permeabilities.
4 MECHANICAL
matrix properties
“(l-
hvf)
where: Wf-MJ
h=
Wf
5Mn)
+
in which M is the appropriate modulus and 5 is an empirically determined constant. Halpin suggests the use of 5 = 2-O for transverse modulus EZ, and 5 = 1.0 for shear modulus G,2. These are then converted to the on-axis compliance matrix:
PROPERTIES
Permeability is affected by both volume fraction and ply angle changes associated with simple shear, but in Section 3 it has been shown that these effects may work in opposition. This is not the case for mechanical properties. Ply angle and volume fraction changes caused by simple shear may complement each other, producing more marked variations in the modulus and Poisson’s ratio of the deformed laminate. At the simplest level, the analysis suggested by KrencheP6 for angle-ply laminates can be used to estimate the mechanical properties of a sheared reinforcement. An efficiency factor can be calculated: 7 = 2 a, cos4 (Y,
- V,) + EfVfv
The on-axis compliance matrix was converted to an off-axis compliance matrix for the UD ply by applying a strain transformation based on an angle 8. The longitudinal modulus, E,, and Poisson’s ratio, vXY, were then calculated for the bidirectional laminate using:38 _
_“’
E, = _
s, Shh- %6
(6)
This, along with the volume fraction calculated from eqn (l), is then substituted into a modified form of the rule of mixtures to give an estimate of the longitudinal modulus, E,: E, = E,(l
where:
(7)
This method accounts for the change in volume fraction and the fibre reorientation effects. The main limitation is the omission of the Poisson effect in the technique. A more robust approach is to use classical laminate theory37 to predict laminate properties. This approach considers the laminate to be formed of unidirectional plies. The properties of each ply are usually based on experimental data, although in this case it was more convenient to use empirical expressions such as the Halpin-Tsai equations.” On-axis longitudinal modulus and Poisson’s ratio were estimated from fibre and
(124
I
Y ry=
s,&6 -
-
%6s,6
3,,366-
ST6
Wb)
where: S,, = Sr, cos4 8 + S,, sin4 8 + (2S,, + S,,) cos* 8 sin* 8 Sr2 = (ST1+ $2 - Se,) cos2 8 sin’ 8 + S,,(c0s4 8 + sin4 e) $6,= 2(2S,,+ 2Sz2- 4S12- &)COS* 8 Sin*8 + S,,(c0s4 8 + sin4 e) S,,= (2S11- 2S,, - SG6)cos3 e sin 8
- (2S2, - 2S12- S,,) sin3 8 cos 8 S,,= (2S,, - 2S,, - S,,) sin” 8 cos 8 - (2& - 2S12-&)cos3
8 sin 8
Shear deformation and aligned reinforcements
339
‘.’ (a) A
1.2
A
A
t
.2 = .a
l-_l AKX 0 Kx Smit
A
A
1 --
l A A
g
E
0.8 --
A
OX
ii
A A
0
A
$
A
A
i! 2
A
A
A
A
A
A
0
A
A
zb
0.4 --
A
A
A
20
25
30
40
35
50
45
60
55
65
Ply Angle (Degrees)
1.4 -Jb) A
1.2 -f .c z8
A--
E b a
0.8 --
n Q fv)
:
A
t
X X
X 0.6 --
f
E b 2
a
O
2
X
x
A 0
0.4 --
0 0
A
0-l 20
A
I 25
30
35
40
45
50
55
60
65
70
Ply Angle (Degrees) Fig. 14.
Normalised permeability for: (a) simply sheared engineered fabrics; (b) simply sheared woven fabrics.
The Krenchel-modified rule of mixtures and the classical laminate analysis are based on laminates formed from unidirectional plies. Both approaches neglect the effect of crimp39 present in woven fabrics. Both the Krenchel-modified rule of mixtures and the classical laminate analysis approach were used to estimate the laminate stiffness for sheared laminates. The effect of crimp in the woven fabrics was neglected. The material properties used in the analyses can be found in Table 3. Elastic property tests were conducted on laminates
with sheared woven and engineered fabrics. Flat plaque mouldings were produced by RTM, as described previously. The elastic properties were measured using an Instron 1195 universal testing machine to a method encompassing BS 2782. Figures 15-18 compare the experimental data with the modulus predicted using the Krenchel-modified rule of mixtures and classical laminate analysis approaches. For all materials tested the values predicted by the classical laminate analysis approach are reasonably accurate. The predictions made using
340
P. Smith et al.
Table 3. Fibre and matrix properties (from manufacturers’ data and Ref. 40)
Material
Tensile modulus (GPa)
Shear modulus (GPa)
Poisson’s ratio
Density (kg m-3)
Glass fibre Cray Valley 6345.001 polyester resin Dow Derakane 8084 vinylester resin
73.0 4.47
29-9 1.62
o-22 0.38
2605 1211h
3.3
1.2
0.38
1088*
5 SUMMARY
El
y From: G,, = ~ 2(1+ Y) ’ Measured values taken from cured resin samples.
the Krenchel-modified rule-of-mixtures method are only accurate for ply angles below +45”. At ply angles above &45” the predicted modulus is lower than the experimental values. Krenchel neglected the Poisson effect in his analysis, assuming there was no transverse deformation. This becomes increasingly important as the fibres become more transverse to the load. Figures 19-20 show the experimentally determined Poisson’s ratio values for an engineered and a woven fabric. Poisson’s ratio reaches a peak at a ply angle of around *to”, and then reduces as the ply angle is increased.
Tangent Modulus -
1 +
The experimental values are compared with predictions made using the classical laminate theory, which correspond reasonably well.
Simple shear has been isolated as a mode of fabric deformation. Fibre reorientation and volume fraction changes have been established as effects of shear. A brief analysis of the shear mechanism has identified a point where wrinkles and folds may begin to form. A four-bar shearing rig was developed and used to shear a variety of engineered and woven fabrics. The effect of shear on the processing properties of the fabric and the mechanical properties of the laminate have been investigated. Shear deformation was found to have a considerable effect on the principal permeabilities of the reinforcement. A semi-empirical expression, based on the Kozeny-Carman equation, relating permeability to the ply angle has been found for each of the fabrics tested. The mechanical properties of laminates formed from sheared reinforcement were also affected by the shear deformation. Elastic stiffness was predicted by the simple Krenchel/rule-of-mixtures approach, which yielded large discrepancies at high ply angles, and the classical laminate theory, which gave improved and reasonably accurate predictions. This work has shown that inter-fibre shear and reinforcement deformation occurring during the
ROM - - - - -. Classical Laminate Theory 1
25
Q 15
-I
2
3
B
IO--
B
5 t
20
25
30
35
40
45
50
55
60
Ply Angle (Degrees) Fig. 15. Longitudinal
modulus: 0”/90” engineered
fabric/polyester
resin.
65
70
341
Shear deformation and aligned reinforcements 1 +
0
Tanaent Modulus -
ROM - - - - -. Classical Laminate Theorv 1
I
25
20
30
35
40
45
50
55
60
70
65
Ply Angle (Degrees) Fig. 16.
Longitudinal modulus: *45” engineered fabric/polyester resin.
preforming process should be considered. Folds and wrinkles caused by deforming a reinforcement beyond its locking angle have the potential to cause numerous processing and potential strength problems.41 Localised changes in permeability may cause processing
I
l
Tanaent Modulus -
problems such as dry spots and an unexpected flow pattern. Shear has also been shown to affect the mechanical properties significantly, and failure to take account of this is likely to lead to inaccuracies in structural analyses.
ROM - - - - -. Classical Laminate Theotv 1
25
I --
, --
--
t
20
25
30
35
40
45
50
55
60
Ply Angle (Degrees)
Fig. 17. Longitudinal modulus: plain-weave fabric/polyester resin.
65
70
342
P. Smith et al. l
04 20
25
Tangent Modulus -RoM
30
35
40
_..__. Classical Laminate Theory
45
50
55
60
65
70
Ply Angle (Degrees) Fig. 18. Longitudinal
modulus: 4-harness satin-weave fabric/polyester
ACKNOWLEDGEMENTS
resin.
authors would like to thank Chris Price (AMM) and Chadwick (Chomarat) for the supply of glass reinforcement. Dan Morris, Roger Smith, Andrew Kingham and Geoff Tomlinson are also thanked for their assistance with experimental work. Ivan
This work was funded by Motor Company and the authors are indebted to Ken Kendall and Carl Johnson for their advice and encouragement. The
-Classical
Laminate Theory
l
Experimental
1.1 1 -0.9 --
0.8 -0 t;; u c” % .E :
0.7 -~ 0.6 -0.5 -~ 0.4 -0.3 -0.2 -0.1 -Oi
20
25
30
35
40
45
50
55
60
Ply Angie (Degrees)
Fig. 19. Poisson’s ratio: 0”/90” engineered fabric/vinylester
resin.
343
Shear deformation and aligned reinforcements l
20
25
30
Experimental -Classical
35
40
45
Laminate Theory 1
50
Ply Angle (Degrees) Fig. 20. Poisson’s ratio: 4-harness satin-weave fabric/polyester
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S. G. & Bruschke, element/control volume approach anisotropic porous media. Polym. 398-405. 2. Rudd, C. D., Rice, E. V., Bulmer, Process modelling and design moulding. Plast. Rubb. Compos.
M. V., A finite to mold filling in Compos., 11 (1990) L. J. & Long, A. C., for resin transfer
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11. Long, A. C., Preform design for liquid moulding processes. PhD thesis, University of Nottingham, 1994. 12. Rudd, C. D., Middleton, V., Owen, M. J., Long, A. C. & McGeehin, P., Design, processing and performance of structural preforms. In Proc. CANCOM ‘93, 2nd Int. Conf on Composite Structures and Materials, Ottawa, 1993, pp. 139-152. 13. Long, A. C. & Rudd, C. D., Computer integrated design of structural preforms for liquid moulding processes. In
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Proc. 27th ISATA-New and Alternative Materials for the Transportation Industries, Aachen, 1994, pp.
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381-390. 14. Bickerton, S., Effect of draping of fibre preforms on process parameters during manufacturing with resin transfer molding. In Proc. 11th ESD Advanced Composites Conference and Exposition, Dearborn, MI, November 1995, pp. 213-220. 15. Long, A. C., Rudd, C. D., Blagdon, M. & Smith, P., Characterising the processing and performance of aligned reinforcements during preform manufacture. Composites Part A (in press). 16. Potter, K. D., The influence of accurate stretch data for reinforcements on the production of complex structural mouldings. Composites, 11 (1979) 161-167. 17. Hirt, D. E., Adams, K. L., Prud’homme, R. K. & Rebenfeld, L., In-plane radial fluid flow characterization of fibrous materials. J. Thermal Insulation, 10 (1987) 153-172. 18. Adams, K. L. & Rebenfeld, L., In-plane flow of fluids in fabrics: Structure/flow characterization. Text. Res. J., 57 (1987) 647-654. 19. Chick, J. P., Rudd, C. D., van Leeuwen, P. A. & Frenay, T. I. Material characterisation for flow modelling in structural reaction injection moulding.
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