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Design and applications of short fibre reinforced rubbers
Design and applications of short fibre reinforced rubbers M C H LEE
8. I
Introduction
O n e of the most important areas in automotive engineering is to isolate the vibration and noise of vehicles effectively. Sources of vibration a n d noise include roadjtyre interaction, aerodynamic/vehicle interaction and power-trainjvehicle interaction. With the trend of making cars smaller, automotive isolation components o r systems become more important in achieving desired customer satisfaction. I t has been estimated that among the currently used isolation components o r systems, over 90% are classified a s passive components o r systems. Typical examples of passive isolation components o r systems for passenger cars a n d trucks are control a r m bushings, engine mounts, shock absorbers, steering linkage bushings, steering ball joint bushings, track bar bushings, strut rod mounts and torque rod bushings. The materials often used in fabricating passive components or systems are elastomer and thermoset composites, because these materials can be formulated and processed to have the required properties (e.g. high damping coefficient and high ultimate elongation) for effectively isolating automotive vibration and noise. Most passive isolation components use materials that have isotropic mechanical properties.' ' In other words, these properties d o not change with respect to the direction o f vibration and/or the component design. The isotropic performance characteristics may generate several application andjor performance deficiencies. For example, in a smaller vehicle, the spring rate of a n elastomer component needs to be reduced i n order to provide the required performance for isolating the vibration and noise of the car. However, the isolation components or systems made of a soft/isotropic elastomer material could lead to undesired yaw, roll and/or pitch motions of the car and consequently, could worsen the overall isolation capability, controllability and driveability. To overcome these concerns, automotive isolation components or systems have to be specially designed to provide the desirable anisotropic dynamic mechanical performance, However, these designs, such as metal insert with special configurations and protective metal shell, often increase the manufactur-
Design and applications of short fibre reinforced rubbers
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Table 8.1. Compositions of unidirectional short fibre reinforced polychloroprene composites Ingredients
Phr
Polychloroprene (Neoprene W) Magnesium oxide Zinc oxide Stearic acid Ethylene thiourea Dioctyl sebacate Sulphur Chopped glass fibre
100 4
5 0.5 0.7 12.5 0.5 0, 5, 10, 20
Table 8.2. Volume and weight concentrations of short fibre in polychloroprene composites Volume concentration (YO)
Weight concentration ( O h )
0 3.83 1.36 13.70
0 4.34 8.32 15.36
ing cost drastically. From the viewpoint of material science, elastomer composites filled with anisotropic fillers, such as short fibres, seem to be a feasible and cost-effective solution. Many researchers5-l have investigated the fracture mechanics of short fibre reinforced rubber composites. Little effort has been put into such research areas as the effects of fibre concentration and fibre orientation on the anisotropic modulus properties of short fibre reinforced elastomer composites. Therefore, in this work, we have investigated the modulus and tensile properties of a unidirectional short fibre reinforced polychloroprene composite system. The anisotropic mechanical properties of this elastomer composite system have also been determined.
8.2 Materials The elastomer used in this work was a polychloroprene(Neoprene W, Du Pont). Theshort fibre used was a chopped glass strand (PPG,Type 3075) with a nominal fibre diameter of 13.2 pm and a cutting length of 12.8 mm. The compositions of the short fibre reinforced polychloroprene composites investigated are shown in Table 8.1; the volume and weight concentrations of the fibres used in each of the elastomer composites are listed in Table 8.2.
8.3
Sample preparation
For each composition, mixing of the ingredients was carried out in a 1.2 kg Banbury internal mixer for 4min at mixing temperatures ranging from 30 to 110 "C. Each masterbatch was then mixed using a 152.4 x 304.8 mm two roll mill for 9 min.The short fibres in the matrix were successfully oriented unidirectionally (parallel to the rolling direction of the mill) by controlling the rotational
I94
Short fibre-polymer composites
force
force
e=oa
longitudinal
e=45*
e=go*
diagonal
transverse
8.1 The angles of fibre orientation in thc uniaxial tensile test.
speeds of the rollers (25 and 34rpm) and the gap distance between the rollers (1-3 mm). These unidirectionally oriented masterbatches were then moulded into standard slabs by compression moulding. The cure temperature and cure time used were 160"C and 25 min, respectively. Tensile specimens with three angles of fibre orientation namely, O", 45" and 90". were prepared by die cutting. A schematic description of the angles for fibre orientation in the tensile specimens is shown in Fig. 8.1.
8.4
Test procedure
Uniaxial tensile tests were conducted at room temperature using an Instron tensile tester. The crosshead speed chosen was 508 mm min- I which corresponds
Design and applications of short fibre reinforced rubbers
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to an initial rate of deformation of 0.33 s- l. Fracture morphology of each tensile specimen was determined using a scanning electron microscope (International Sci. Inst. ISI-DS-130).
8.5
Stress-strain behaviour of unidirectional short fibre reinforced elastomer composites
The stress-strain data of all the compositions at various angles of fibre orientation were analysed using a modified Mooney-Rivlin equation.l2 This equation has the following form: ln[o,/(h -
= ln[G(a))]
+ (l/h).ln[G(O)/G(co)]
C8.11
where oE = engineering stress, h = uniaxial stretch ratio, oJ(A - 1-') = reduced force, G(co) = shear modulus at (l/h) equal to zero, G(0) = shear modulus at (l/h) equal to one.
Equation [8.1] predicts that a plot of In[oJ(h - K 2 ) ]versus (l/A) will exhibit a linear relationship. This line can be extrapolated to intercept (l/A) at the initial shear modulus, G(O), and with (1/1) = 0 at the large strain shear modulus, G(oo), respectively. Equation [8.l] has been successfully applied to predict the isotropic stress-strain behaviour of various crosslinked rubber systems.1 2 * 1 3 In this section, we will show the stress-strain behaviour of the unidirectional short fibre reinforced polychloroprene composites investigated and their deviations from the stress-strain curves predicted using equation C8.11. The plotted results for the stress-strain behaviour of the polychloroprene composites with fibre concentrations of 13.70%, 7.36% and 3.83% (by volume) are shown in Fig. 8.2, 8.3 and 8.4, respectively. As shown in these figures, the stress-strain curves for the three polychloroprene composites with the angle of fibre orientation of 90" (with respect to the direction of uniaxial tensile deformation) exhibit linear relationships and can be described by equation C8.11. In each case, the data points deviate positively from the linear relationships (equation C8.11) at large values of stretch ratio, 1. This behaviour can be characterized by the mechanisms of strain-induced crystallization and/or nonGaussian network deformation of elastomers. 12-14 The stress-strain curves for the polychloroprene composites with the angles of fibre orientation of 45" and 0" clearly show the piecewise linear relationships at low and medium values of stretch ratio and also exhibit positive deviation from the linear relationships at high values of stretch ratio. The above piecewise linear relationships for the stress-strain data shown in Fig. 8.2-8.4 comprise two distinct regimes. In the first regime (at low values of stretch ratio), the value of o J [ ( h - h-')I is nearly constant with respect to the change in the uniaxial ratio. However, the value of aJ[(h - X -')I in the second regime (at medium values of
I96
Short fibrepolymer composites
m
P
Z
cc
0.4
A
N -
I
x I
o .2
x
Y
\
w
b
0.0
/ -0.2
0
0 0'
0
45'
A
I
I
I
I
0.2
0.4
0.6
0.8
90' 1.o
l / s t r e t c h ratio 8.2 The stress-strain curves for the polychloroprenecompositeswith a fibre concentrationof 13.7% (by volume)and at various angles of fibre orientation.
stretch ratio) decreases with increasing stretch ratio and can also be described by equation [S. 1). The unique stress-strain behaviour for the unidirectional short fibre reinforced elastomer composites can be attributed to the oriented fibres in the elastomer matrix. The deformation mechanisms of this unique behaviour were determined with the aid of the fracture morphology of the specimens, and the results will be discussed in the next section.
8.6
Fracture morphology, fibre configuration and deformation mechanism
The fracture surfaces of the tensile specimens for all the fibre reinforced polychloroprene composites were examined by scanning electron microscopy. Figures 8.5, 8.6 and 8.7 show the fracture morphology of the polychloroprene composite with the fibre concentration of 13.7% at the angles of fibre orientation equal to 90", 45" and 0", respectively. The fracture morphology for each composite clearly shows an adhesional failure between the matrix and the fibres. This adhesional failure mode is typical for composite materials having a soft matrix and hard filler^.'^^^^^' The fracture morphology for the polychloroprene composite with 90" fibre orientation (Fig. 8.5) shows that most of the short fibres (over 80%) are unidirectional and parallel to the fracture surface. This result
Design and applications of short fibre reinforced rubbers
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0.6
0.4
0.2
0.0
-0.2
I
0
I
I
1
0.2
0.4
0.6
I
0.8
I 1 .o
1/stretch ratio 8.3 The stress-strain curves for the polychloroprene composites with a fibre concentrationof 7.36% (by volume) and at various angles of fibre orientation.
suggests that the deformation mechanism of the polychloroprene composites with 90" fibre orientation is the uniaxial stretch of elastomer among the parallel fibres. Consequently, the stress-strain behaviour of the polychloroprene compositions at 90" fibre orientation follows the modified Mooney-Rivlin equation for crosslinked rubbers (see equation [8.1] and Fig. 8.2-8.4 at the angle of fibre orientation equal to 90"). Above the value of critical stretch ratio of 3.0 (or the reciprocal value equal to 0.313) for the polychloroprenecomposites with different fibre concentrations, the stress-strain data for all the polychloroprene composites deviate pwitively '2-14 from the linear relationships described by equation
[S.l].
For the polychloroprene composite with the angle of fibre orientation equal to 0",the fracture morphology shows (Fig. 8.7) that most of the short fibres (over 80%) are perpendicular to the fracture surface. The deformation mechanisms for this case comprised two portions. The first deformation mechanism includes two steps, namely, the deformation of fibres (predominantly parallel to one another) and the deformation of elastomer matrix located among the ends of parallel fibres, and then followed by fibre pull-out/fibre fracture in the matrix. In this deformation mechanism the stress-strain behaviour shows a nearly constant value of oJ[(k - A-2)] at low values of stretch rstio (see Fig. 8.2-8.4). A critical
Short fibre-polymer composites
0.6
I
0.4 -
_ -
0.0
I
0'
d
I A
0
0.2
-I
I
0
I
45O
A 90'
-
E-
0.4
0.6
0.8
1.o
l/stretch ratio 8.4 The stress-strain curves for the polychloroprene composites with the fibre concentration of 3.83% (by volume) and at various angles of fibre
orientation.
stretch ratio is therefore defined as the value of stretch ratio below which the first deformation mechanism is the controlling mechanism. Values for the critical stretch ratio of the polychloroprene composites with 0" fibre orientation range from 1.6 to 2.2 (or in terms of engineering strain from 60% to 120%) as the fibre volume concentration decreases from 13.7% to 3.83%. The values of the critical stretch ratio for the polychloroprene composites are much higher than those of the ultimate elongation for the glass fibres (the ultimate elongation being less than 0.050/,).This result is attributed to the deformation of the elastomer matrix among the ends of the parallel fibres before fibre fracture and/or fibre pull-out. The second mechanism is that after fibre fracture and/or fibre pull-out the uniaxial tensile deformation of the elastomer matrix dominates again, and therefore, the stress-strain behaviour of the polychloroprene composite follows that of the modified ivlooney-Rivlin equation (equation C8.11). A critical stretch ratio can also be defined as the value of stretch ratio below which the second deformation mechanism occurs. The values of the second critical stretch ratio for the polychloroprene composites with 0" fibre orientation and different fibre concentrations are about the same and equal to 4.0 (or the reciprocal stretch ratio equal to 0.25, see Fig. 8.2-8.4). Above this critical stretch ratio the stress-strain
Design and applications of short fibre reinforced rubbers
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0.5 mm 8.5 The uniaxial tensile fracture surface of the polychloroprene composite with the fibreconcentrationof 13.7% (byvo1ume)andat 90" fibreorientation.
curves deviate positively' '-14 from the linear relationship predicted by equation C8.11. The average length of fibres in the composite materials is always an important parameter which not only provides information on the reinforcement effectiveness of the fibres in a given matrix, but also provides information on improving the mixing methods for processing the composites. It is noteworthy that the average length of short fibres after mixing and moulding can be determined from the fracture morphology of the specimens with the angle of fibre orientation equal to 90" (Fig. 8.5). The average length of short fibres I,, determined from Fig. 8.5, is 268 pm; the average fibre diameter, d,, measured is 10pm. Based on these values, the average aspect ratio of short fibres lf/df, in the elastomer matrix was determined to be 26.8. As a reminder, the initial cut length of the fibres is 1.28 x 104pm. Using this value, in conjunction with the final fibre length in the matrix, the ratio of initial fibre length to final fibre length is 47.8. Thus, after Banbury mixing, two-roll mixing and compression moulding, the average fibre
200
Short fibre-polymer composites
0.5 mm 8.6 The uniaxial tensile fracture surface of the polychloroprene composite with the fibreconcentrationof 13.7% (byvo1ume)and at 45" fibre orientation.
length is reduced by 47.8 times from its initial fibre length. Even with such a severe reduction in fibre length, the aspect ratio of the short fibres in the polychloroprene matrix (lf/df = 26.8) is still much higher than the critical aspect ratio of the short fibres, lrc/df,required for having a maximum stress value15 l 7 (values of lfc/df being around 515). F o r the polychloroprene composite with 0" fibre orientation, such a high value of fibre aspect ratio also leads to the same deformation mechanism as described in the previous paragraph of this section for the first deformation mechanism of the polychloroprene composite with 0" fibre orientation. F o r the polychloroprene composite with the angle of fibre orientation equal to 45", the fracture morphology (Fig. 8.6) and the stress-strain behaviour (Fig. 8.2-8.4) also show a similar type of deformation mechanism as in the case for the polychloroprene composite with 90" fibre orientation. The value of aJ [(i- i.*)I for the composites with 45" fibre orientation is lower than that for the composites with 0'' fibre orientation. The deformation regime with a constant
Design and applications of short fibre reinforced rubbers
20 I
0.5 mm 8.7 The uniaxial tensile fracture surface of the polychloroprene composite with the fibre concentration of 13.7% (by volume)and at 0" fibre orientation.
value of o J [ ( i . - ;.-')I for the composites with 45" fibre orientation is longer than that for the composites with 0" fibre orientation. These findings can be explained as follows. In the case of 0" (45") fibre orientation the deformation of elastomer chains in the fibre-matrix interfacial regime can be simulated as the 180" (135") peeling deformation m e ~ h a n i s m . ' The ~ local stress (strain) of elastomer matrix in the 180" peeling deformation mechanism is higher (larger) than that in the 135" peeling deformation mechanism and, consequently, the fracture of fibres and the adhesional failure between the elastomer matrix and the fibres for the 180" peeling deformation mechanism are expected to occur earlier than those of the 135" peeling deformation mechanism. As a result, values for the ')I and the regime of stretch ratio with such a constant value constant o J [ ( i - iLof oE/[(iL - k-')] for the composites with 45" fibre orientation are greater than those for the composites with 0" fibre orientation.
Short fibrepolymer composites
202
8.7 Stress-strain equation for unidirectional short fibre reinforced elastomer composites
Based on the results discussed in the previous sections, a general schematic description for the anisotropic stress-strain behaviour of unidirectional short fibre reinforced polychloroprene composites was developed and is shown in Fig, 8.8. The corresponding stress-strain relationships at various angles of fibre orientation are expressed in the following mathematical forms. For 0" fibre orientation: (a) )iCl 2 h 2 1 ln[o,/(iL - >.-')I = ln[G(O,O")] (b) I,, 2 1, 2
[8.2a]
jLcl
ln[o&.
- l L - 2 ) ]= ln[G(co,W)]
+ (lLcI/i.).ln[G(O,O")/G(co,Oo)]
[8.2b]
For 45" fibre orientation: (a) I c 3 2 I 2 1 ln[oJ(i.
-
I-')] = ln[G(O,45")]
[8.3a]
(b) hc4 2 1, 2 h,, ln[aE/(h -
= In[G(co,45")]
+ (h,,/i.)~ln[G(O,45")/G(co,45")]
[8.3b]
For 90" fibre orientation: (a)
A,,
2i 2 1
ln[oJ(I - 1.K2)] = ln[G(co, 90")]
+ (i.c5/iL)4n[C(0,900)/G(co,90°)]
CS.41
The symbols in the above equations represent the same physical meanings as shown in equation [S.l]. The critical stretch ratios, i,,,i.,,, , Ic3, I,, and i.,,,are described in Fig. 8.8. These equations are useful for predicting the stress-strain values of unidirectional short fibre reinforced elastomer composites in automotive engineering design where numerical analyses, such as linear and non-linear FEA (finite element analyses) are required. Using equations [8.2a], [8.3a] and C8.41, we determined the values of initial shear modulus of unidirectional short fibre oriented polychloroprene composites at various angles of fibre orientation. In the next section, we will discuss the anisotropic modulus properties of the polychloroprene composites.
8.8 Modulus properties of unidirectional short fibre reinforced elastomer composites and applications
The values of initial shear modulus of unidirectional short fibre reinforced polychloroprene composites were determined from the stress-strain plots dis-
Design and applications of short fibre reinforced rubbers
-n
I
CI
0.8 I
I
0
0'
0
I
45'
I
1
0.6
0.8
203
A 90'
0.6
2
(u
0.4
I
x
CI
\
b" m
w
-
0.2
0
0
0
0.2
0.4
1 .o
1 /stretch ratio 8.8 The stress-strain curves of unidirectional short fibre reinforced elas-
tomer composites.
cussed in the previous sections; the results are shown in Table 8.3. For all the three angles of fibre orientation investigated, the value of initial shear modulus increases as the fibre concentration increases. The effectivenessoffibre concentration on the reinforcement of the initial shear modulus of the polychloroprene composites is the highest (lowest) at the angle of fibre orientation equal to 0" (90"). Values for the corresponding relative initial shear modulus, G(0, qre1 (defined as the initial shear modulus of the composite with a given angle of fibre orientation, G(O,0),divided by the initial shear modulus of the elastomer gum, G(0)gu,,,)of the polychloroprene composites were also determined and are shown in Table 8.4. The plotted results for the initial shear modulus versus the fibre volume concentration are shown in Fig. 8.9. The results described in Fig. 8.9 clearly show that the modulus-composition equations suggested by Einstein' * and Smalland by Guth and Gold" cannot predict or describe the modulus properties of unidirectional short fibre oriented polychloroprene composites (except for the case of the polychloroprene composite with the fibre concentration of 3.83% and 90" fibre orientation). However, the relative modulus properties of the polychloroprene composites with different angles of fibre orientation can be successfully described by the thermodynamic relationship developed' for the modulus properties of multi-component polymer systems. This relationship is expressed in a general form as shown below:
Short fibre-polymer composites
204
Table 8.3. Initial shear modulus of uniderectional short fibre reinforced polychloroprene composites Initial shear modulus at various angles of fibre orientation (MPa) ~
0”
45”
90”
0.73
0.72 0.93 1.27 1.85
0.72 0.79 1.06 1.50
Fibre concentration ( ~ 0 1 % )
0 3.83 7.36 13.70
1.14
1.72 3.03
Table 8.4. Relative initial shear modulus of unidirectional short fibre reinforced polychloroprene composites Relative initial shear modulus at various angles of fibre orientation 0“
45“
90”
1.00
1.OO
1.00 1.10 I .47 2.08
Fibre concentration (~01%)
0 3.83 1.36 13.70
1.56 2.36
1.29 1.76 2.57
4.15
0
0’
4.0
-
3.5
- -------
3.0
-
2.5
-
1.5 2mo
i
0
A
45’
0
90’
0
Guth-Gold Einstein-Smallwood
0
9 A n
2
4
6
Vf
8
10
12
[%I
8.9 Plots for the relative initial shear modulus versus the volumeconcentration of fibres of the polychloroprene composites at various angles of fibre orientation and predictions from Einstein-Smallwood and Guth-Gold equation.20
14
Design and applications of short fibre reinforced rubbers
205
5.5 v)
2
3
5.0
U
E
4*5
L
4.0
=
3.5
Q
Q)
.-m
3.0
.r
2.5
v)
.-
CI
2.o 1.5 1 .o
0
2
4
6
8
10
12
14
8.10 Plots for the relative initial shear modulus versus the volume concentration of fibres of the polychloroprenecompositesat various angles of fibre orientation and predictions from the thermodynamic mixing equation.2
ln[G(O,8)"']
= +.exp[A(8)(4
- l)].lnK(8)
~8.51
In the above equation, A(8) represents the mixing index of the fibres with the angle of fibre orientation, 8, in the matrix; 4 is the volume concentration of the fibres; lnK(8) is the reinforcement effectiveness of the fibres with the orientation angle, 8; G(0,B)"' is the relative initial shear modulus of the composites with the angle of fibre orientation equal to 8. The value of the mixing index, A, of any type of filler in the matrix is non-negative.2 The higher the value of A is, the worse the degree of mixing of the fillers in the matrix.' The plotted results on the relative initial shear modulus as a function of the volume concentration of the fibres and the predictions frwn equation C8.51 are shown in Fig. 8.10. The values of 1nK and A determined for the polychloroprene composites with various angles of fibre orientation are shown in Table 8.5. Based on the results shown in Table 8.5, it can be concluded that values of reinforcement effectiveness, lnK, for the polychloroprene composites depend on the angle of fibre orientation, 8. The semi-logarithmic plot between the reinforcement effectiveness for the polychloroprene composites and the angles of fibre orientation exhibits a linear relationship (see Fig. 8.1 1).This linear relationship is expressed in the following mathematical form:
206
Short fibre-polymer composites
Table 8.5. Values of reinforcement effectiveness and mixing index for unidirectional short fibre reinforced polychloroprene composites Angle of fibre orientation, 0
Reinforcement effectiveness (InK)
Mixing index ( A )
14.58 9.41 7.12
0.33 0.36 0.33
0"
45"
90"
2.8 2.6
0
Y
2.4
c
2.2 2.0
1.8
'
0
I
I
1
30
60
90
fibre orientation
(degrees)
8.11 Semi-logarithmic plots of the reinforcement effectiveness versus the angle of fibre orientation.
ln[lnK] = 2.68 - 8.49 x 10-3.€l
(90' 2 9 2 Oo)
C8.61
The correlation ratio of the regressional analysis (Fig. 8.1 1) using equation [8.6] is 0.975. Contrary to the results of InK being a function of 9, the values of mixing index for the fibres in the matrix, A, are insensitive to the change in the angle of fibre orientation and are within the range of 0.33 to 0.36. This result means that the fibres are well dispersed in the polychloroprene matrix. As mentioned previously, the value of mixing index for a given filler in its perfect mixing state equals zero.2 In summary, for unidirectional short fibre reinforced polychloroprene composites, the value of 1nK decreases as the angle of fibre orientation, 0, increases. The value of the mixing index, A , on the other hand, is nearly independent of the angle of fibre orientation, 6. (This result is expected,
Design and applications of short fibre reinforced rubbers
207
Table 8.6. Initial shear modulus ratios of unidirectional short fibre reinforced polychloroprene composites Initial shear niodulus ratio Fibre concentration (vol%) ~~
0"/90"
45"/90" ~~
~~~~
0
1.01 1.44
3.83
I .62
7.36 13.70
2.02
~
1
.oo
1.18
I 20 1.23
since the mixing index, A, is a thermodynamic state variable that is only a function of such thermodynamic variables as surface Gibbs free energies for the fillers and matrix, volume fraction of the ingredients, temperature and pressure of the ~ y s t e m . ' ~As) a reminder, the values of both A and 1nK for elastomers filled with particulate filler (such as carbon blacks) are independent of the testing direction (or equivalently, the direction of deformation).2 Combining equation [8.5] with equation C8.61, we obtained the relationship for the initial shear modulus of the polychloroprene composites with various angles of fibre orientation. This relationship can be written in the following form:
+
ln[G(O,O)] = ~I[G(O)~~,,,] @exp[A.(+ - l)]~[lnK(Oo)]~[lnK(900)/lnK(Oo)~~900 [8.7]
In the above equation, all the symbols have the same physical meanings as discussed previously in the text. The range of the angle, 8, of fibre orientation is between 0" (longitudinal) and 90" (transverse) (see Fig. 8.1). The anisotropic characteristics of the initial shear modulus were described by twomodulus ratios as shown in Table 8.6. Each ofthe modulus ratios is defined as the value of 0" (45")modulus divided by that of 90" modulus. Values for both the 0"/90" modulus ratio and the 45"/90" modulus ratio increase with increasing fibre concentration. However, for the same fibre concentration, the value of the45"/90" modulus ratio is lower than that of the 0"/90" modulus ratio. The plotted results for the 0"/90" modulus ratio and the 45"/90" modulus ratio as a function of the volume concentration of the fibres are shown in Fig. 8.12. The above results are attributed to the different fibre orientations in the polychloroprene matrix. 8.9
Concluding remarks
In order to establish rules to assist the design of short fibre reinforced rubbers in various engineering applications, the mechanical properties and fracture morphology of unidirectional short fibre reinforced polychloroprene composites have been determined. Based on the findings, several deformation mechanisms for this composite system have been identified. The constitutive equations and several composition-processing-property relationships for predicting the stress-strain behaviour and the modulus properties of the elastomer composites have also been developed. The modulus properties of the polychloroprene composites with different angles of fibre orientation and various fibre concentra-
208
Short fibre-polymer composites
2.5
2.0
L
Q
1.5
1.o
0
2
4
6
8
10
12
14
8.12 The 0"/90" and the 45"/90" initial shear modulus ratios as a function of the volume concentration of fibres for the polychloroprene composites.
tions can be predicted by a thermodynamic relationship for the modulus properties of multi-component polymer systems. The above mechanisms and relationships are essential to the design and applications of short fibre reinforced rubbers. References 1 Lee M C H, J A p p l Polpi Sci, 29 (1984) 499. Lee M C H, Polyrti Eiig Sci, 25 (1985) 909. Trexler H E and Lee M C H, J Appl P o l p i Sci, 32 (1986) 3899. Lee M C H. J Appl Polyrtt Sci, 33 (1987) 2479. Thomas A G, Kiihher CIicw Techtiol, 48 (1975) 5. 6 Gent A N , Lindley P B and Thomas A G, J Appl PoIyrtt Sci, 8 (1964) 455. 7 Estes G M, Cooper S L a n d Tobolsky A V, J Mncroriiol Sci, Rev kJtrcromol Cherii, 4
2 3 4 5
(1970) 167. 8 Miwa M, Nakayama A, Ohsawa T and Hasegawa A, J .4ppl Polyrn Sci, 23 (1979) 2957. 9 Setua D K and De S K, J Mnier Sci, 20 (1985) 2953. 10 Akhtar S, De P P and De S K, J Mnrer Sci Leit, 5 (1986) 399. 11 Akhtar S, Bhowmick A K, De P P and De S K, J M n t r r Sci, 21 (1986) 41 79. 12 Lee M C H and Williams M C, J Polyrn Sci, Polyrii Phys E d , 23 (1985) 2243. 13 Lee M C H and Shen M, Polyrii J , 12 (1980) 495.
Design and applications of short fibre reinforced rubbers
209
14 Mark J E, Polym Eng Sci, 19(4) (1979) 254. 15 Lee M C H, unpublished research results. 16 Holister G S and Thomas C, Fibre Reinforced Materials, American Elsevier, New York (1966). 17 Kelly A and Tyson W R, ‘Fibre Strengthened Materials’, presented at the Second International Materials Symposium on High-strength Materials, University of California, Berkeley, California, June 17 (1964). 18 Einstein A, Ann Physik, 19 (1906) 289. 19 Smallwood H, J A p p l Phys, 15 (1944) 758. 20 Guth E and Gold 0, Phys Reu, 53 (1938) 322.
8. I
Introduction
O n e of the most important areas in automotive engineering is to isolate the vibration and noise of vehicles effectively. Sources of vibration a n d noise include roadjtyre interaction, aerodynamic/vehicle interaction and power-trainjvehicle interaction. With the trend of making cars smaller, automotive isolation components o r systems become more important in achieving desired customer satisfaction. I t has been estimated that among the currently used isolation components o r systems, over 90% are classified a s passive components o r systems. Typical examples of passive isolation components o r systems for passenger cars a n d trucks are control a r m bushings, engine mounts, shock absorbers, steering linkage bushings, steering ball joint bushings, track bar bushings, strut rod mounts and torque rod bushings. The materials often used in fabricating passive components or systems are elastomer and thermoset composites, because these materials can be formulated and processed to have the required properties (e.g. high damping coefficient and high ultimate elongation) for effectively isolating automotive vibration and noise. Most passive isolation components use materials that have isotropic mechanical properties.' ' In other words, these properties d o not change with respect to the direction o f vibration and/or the component design. The isotropic performance characteristics may generate several application andjor performance deficiencies. For example, in a smaller vehicle, the spring rate of a n elastomer component needs to be reduced i n order to provide the required performance for isolating the vibration and noise of the car. However, the isolation components or systems made of a soft/isotropic elastomer material could lead to undesired yaw, roll and/or pitch motions of the car and consequently, could worsen the overall isolation capability, controllability and driveability. To overcome these concerns, automotive isolation components or systems have to be specially designed to provide the desirable anisotropic dynamic mechanical performance, However, these designs, such as metal insert with special configurations and protective metal shell, often increase the manufactur-
Design and applications of short fibre reinforced rubbers
I93
Table 8.1. Compositions of unidirectional short fibre reinforced polychloroprene composites Ingredients
Phr
Polychloroprene (Neoprene W) Magnesium oxide Zinc oxide Stearic acid Ethylene thiourea Dioctyl sebacate Sulphur Chopped glass fibre
100 4
5 0.5 0.7 12.5 0.5 0, 5, 10, 20
Table 8.2. Volume and weight concentrations of short fibre in polychloroprene composites Volume concentration (YO)
Weight concentration ( O h )
0 3.83 1.36 13.70
0 4.34 8.32 15.36
ing cost drastically. From the viewpoint of material science, elastomer composites filled with anisotropic fillers, such as short fibres, seem to be a feasible and cost-effective solution. Many researchers5-l have investigated the fracture mechanics of short fibre reinforced rubber composites. Little effort has been put into such research areas as the effects of fibre concentration and fibre orientation on the anisotropic modulus properties of short fibre reinforced elastomer composites. Therefore, in this work, we have investigated the modulus and tensile properties of a unidirectional short fibre reinforced polychloroprene composite system. The anisotropic mechanical properties of this elastomer composite system have also been determined.
8.2 Materials The elastomer used in this work was a polychloroprene(Neoprene W, Du Pont). Theshort fibre used was a chopped glass strand (PPG,Type 3075) with a nominal fibre diameter of 13.2 pm and a cutting length of 12.8 mm. The compositions of the short fibre reinforced polychloroprene composites investigated are shown in Table 8.1; the volume and weight concentrations of the fibres used in each of the elastomer composites are listed in Table 8.2.
8.3
Sample preparation
For each composition, mixing of the ingredients was carried out in a 1.2 kg Banbury internal mixer for 4min at mixing temperatures ranging from 30 to 110 "C. Each masterbatch was then mixed using a 152.4 x 304.8 mm two roll mill for 9 min.The short fibres in the matrix were successfully oriented unidirectionally (parallel to the rolling direction of the mill) by controlling the rotational
I94
Short fibre-polymer composites
force
force
e=oa
longitudinal
e=45*
e=go*
diagonal
transverse
8.1 The angles of fibre orientation in thc uniaxial tensile test.
speeds of the rollers (25 and 34rpm) and the gap distance between the rollers (1-3 mm). These unidirectionally oriented masterbatches were then moulded into standard slabs by compression moulding. The cure temperature and cure time used were 160"C and 25 min, respectively. Tensile specimens with three angles of fibre orientation namely, O", 45" and 90". were prepared by die cutting. A schematic description of the angles for fibre orientation in the tensile specimens is shown in Fig. 8.1.
8.4
Test procedure
Uniaxial tensile tests were conducted at room temperature using an Instron tensile tester. The crosshead speed chosen was 508 mm min- I which corresponds
Design and applications of short fibre reinforced rubbers
I95
to an initial rate of deformation of 0.33 s- l. Fracture morphology of each tensile specimen was determined using a scanning electron microscope (International Sci. Inst. ISI-DS-130).
8.5
Stress-strain behaviour of unidirectional short fibre reinforced elastomer composites
The stress-strain data of all the compositions at various angles of fibre orientation were analysed using a modified Mooney-Rivlin equation.l2 This equation has the following form: ln[o,/(h -
= ln[G(a))]
+ (l/h).ln[G(O)/G(co)]
C8.11
where oE = engineering stress, h = uniaxial stretch ratio, oJ(A - 1-') = reduced force, G(co) = shear modulus at (l/h) equal to zero, G(0) = shear modulus at (l/h) equal to one.
Equation [8.1] predicts that a plot of In[oJ(h - K 2 ) ]versus (l/A) will exhibit a linear relationship. This line can be extrapolated to intercept (l/A) at the initial shear modulus, G(O), and with (1/1) = 0 at the large strain shear modulus, G(oo), respectively. Equation [8.l] has been successfully applied to predict the isotropic stress-strain behaviour of various crosslinked rubber systems.1 2 * 1 3 In this section, we will show the stress-strain behaviour of the unidirectional short fibre reinforced polychloroprene composites investigated and their deviations from the stress-strain curves predicted using equation C8.11. The plotted results for the stress-strain behaviour of the polychloroprene composites with fibre concentrations of 13.70%, 7.36% and 3.83% (by volume) are shown in Fig. 8.2, 8.3 and 8.4, respectively. As shown in these figures, the stress-strain curves for the three polychloroprene composites with the angle of fibre orientation of 90" (with respect to the direction of uniaxial tensile deformation) exhibit linear relationships and can be described by equation C8.11. In each case, the data points deviate positively from the linear relationships (equation C8.11) at large values of stretch ratio, 1. This behaviour can be characterized by the mechanisms of strain-induced crystallization and/or nonGaussian network deformation of elastomers. 12-14 The stress-strain curves for the polychloroprene composites with the angles of fibre orientation of 45" and 0" clearly show the piecewise linear relationships at low and medium values of stretch ratio and also exhibit positive deviation from the linear relationships at high values of stretch ratio. The above piecewise linear relationships for the stress-strain data shown in Fig. 8.2-8.4 comprise two distinct regimes. In the first regime (at low values of stretch ratio), the value of o J [ ( h - h-')I is nearly constant with respect to the change in the uniaxial ratio. However, the value of aJ[(h - X -')I in the second regime (at medium values of
I96
Short fibrepolymer composites
m
P
Z
cc
0.4
A
N -
I
x I
o .2
x
Y
\
w
b
0.0
/ -0.2
0
0 0'
0
45'
A
I
I
I
I
0.2
0.4
0.6
0.8
90' 1.o
l / s t r e t c h ratio 8.2 The stress-strain curves for the polychloroprenecompositeswith a fibre concentrationof 13.7% (by volume)and at various angles of fibre orientation.
stretch ratio) decreases with increasing stretch ratio and can also be described by equation [S. 1). The unique stress-strain behaviour for the unidirectional short fibre reinforced elastomer composites can be attributed to the oriented fibres in the elastomer matrix. The deformation mechanisms of this unique behaviour were determined with the aid of the fracture morphology of the specimens, and the results will be discussed in the next section.
8.6
Fracture morphology, fibre configuration and deformation mechanism
The fracture surfaces of the tensile specimens for all the fibre reinforced polychloroprene composites were examined by scanning electron microscopy. Figures 8.5, 8.6 and 8.7 show the fracture morphology of the polychloroprene composite with the fibre concentration of 13.7% at the angles of fibre orientation equal to 90", 45" and 0", respectively. The fracture morphology for each composite clearly shows an adhesional failure between the matrix and the fibres. This adhesional failure mode is typical for composite materials having a soft matrix and hard filler^.'^^^^^' The fracture morphology for the polychloroprene composite with 90" fibre orientation (Fig. 8.5) shows that most of the short fibres (over 80%) are unidirectional and parallel to the fracture surface. This result
Design and applications of short fibre reinforced rubbers
I97
0.6
0.4
0.2
0.0
-0.2
I
0
I
I
1
0.2
0.4
0.6
I
0.8
I 1 .o
1/stretch ratio 8.3 The stress-strain curves for the polychloroprene composites with a fibre concentrationof 7.36% (by volume) and at various angles of fibre orientation.
suggests that the deformation mechanism of the polychloroprene composites with 90" fibre orientation is the uniaxial stretch of elastomer among the parallel fibres. Consequently, the stress-strain behaviour of the polychloroprene compositions at 90" fibre orientation follows the modified Mooney-Rivlin equation for crosslinked rubbers (see equation [8.1] and Fig. 8.2-8.4 at the angle of fibre orientation equal to 90"). Above the value of critical stretch ratio of 3.0 (or the reciprocal value equal to 0.313) for the polychloroprenecomposites with different fibre concentrations, the stress-strain data for all the polychloroprene composites deviate pwitively '2-14 from the linear relationships described by equation
[S.l].
For the polychloroprene composite with the angle of fibre orientation equal to 0",the fracture morphology shows (Fig. 8.7) that most of the short fibres (over 80%) are perpendicular to the fracture surface. The deformation mechanisms for this case comprised two portions. The first deformation mechanism includes two steps, namely, the deformation of fibres (predominantly parallel to one another) and the deformation of elastomer matrix located among the ends of parallel fibres, and then followed by fibre pull-out/fibre fracture in the matrix. In this deformation mechanism the stress-strain behaviour shows a nearly constant value of oJ[(k - A-2)] at low values of stretch rstio (see Fig. 8.2-8.4). A critical
Short fibre-polymer composites
0.6
I
0.4 -
_ -
0.0
I
0'
d
I A
0
0.2
-I
I
0
I
45O
A 90'
-
E-
0.4
0.6
0.8
1.o
l/stretch ratio 8.4 The stress-strain curves for the polychloroprene composites with the fibre concentration of 3.83% (by volume) and at various angles of fibre
orientation.
stretch ratio is therefore defined as the value of stretch ratio below which the first deformation mechanism is the controlling mechanism. Values for the critical stretch ratio of the polychloroprene composites with 0" fibre orientation range from 1.6 to 2.2 (or in terms of engineering strain from 60% to 120%) as the fibre volume concentration decreases from 13.7% to 3.83%. The values of the critical stretch ratio for the polychloroprene composites are much higher than those of the ultimate elongation for the glass fibres (the ultimate elongation being less than 0.050/,).This result is attributed to the deformation of the elastomer matrix among the ends of the parallel fibres before fibre fracture and/or fibre pull-out. The second mechanism is that after fibre fracture and/or fibre pull-out the uniaxial tensile deformation of the elastomer matrix dominates again, and therefore, the stress-strain behaviour of the polychloroprene composite follows that of the modified ivlooney-Rivlin equation (equation C8.11). A critical stretch ratio can also be defined as the value of stretch ratio below which the second deformation mechanism occurs. The values of the second critical stretch ratio for the polychloroprene composites with 0" fibre orientation and different fibre concentrations are about the same and equal to 4.0 (or the reciprocal stretch ratio equal to 0.25, see Fig. 8.2-8.4). Above this critical stretch ratio the stress-strain
Design and applications of short fibre reinforced rubbers
I99
0.5 mm 8.5 The uniaxial tensile fracture surface of the polychloroprene composite with the fibreconcentrationof 13.7% (byvo1ume)andat 90" fibreorientation.
curves deviate positively' '-14 from the linear relationship predicted by equation C8.11. The average length of fibres in the composite materials is always an important parameter which not only provides information on the reinforcement effectiveness of the fibres in a given matrix, but also provides information on improving the mixing methods for processing the composites. It is noteworthy that the average length of short fibres after mixing and moulding can be determined from the fracture morphology of the specimens with the angle of fibre orientation equal to 90" (Fig. 8.5). The average length of short fibres I,, determined from Fig. 8.5, is 268 pm; the average fibre diameter, d,, measured is 10pm. Based on these values, the average aspect ratio of short fibres lf/df, in the elastomer matrix was determined to be 26.8. As a reminder, the initial cut length of the fibres is 1.28 x 104pm. Using this value, in conjunction with the final fibre length in the matrix, the ratio of initial fibre length to final fibre length is 47.8. Thus, after Banbury mixing, two-roll mixing and compression moulding, the average fibre
200
Short fibre-polymer composites
0.5 mm 8.6 The uniaxial tensile fracture surface of the polychloroprene composite with the fibreconcentrationof 13.7% (byvo1ume)and at 45" fibre orientation.
length is reduced by 47.8 times from its initial fibre length. Even with such a severe reduction in fibre length, the aspect ratio of the short fibres in the polychloroprene matrix (lf/df = 26.8) is still much higher than the critical aspect ratio of the short fibres, lrc/df,required for having a maximum stress value15 l 7 (values of lfc/df being around 515). F o r the polychloroprene composite with 0" fibre orientation, such a high value of fibre aspect ratio also leads to the same deformation mechanism as described in the previous paragraph of this section for the first deformation mechanism of the polychloroprene composite with 0" fibre orientation. F o r the polychloroprene composite with the angle of fibre orientation equal to 45", the fracture morphology (Fig. 8.6) and the stress-strain behaviour (Fig. 8.2-8.4) also show a similar type of deformation mechanism as in the case for the polychloroprene composite with 90" fibre orientation. The value of aJ [(i- i.*)I for the composites with 45" fibre orientation is lower than that for the composites with 0'' fibre orientation. The deformation regime with a constant
Design and applications of short fibre reinforced rubbers
20 I
0.5 mm 8.7 The uniaxial tensile fracture surface of the polychloroprene composite with the fibre concentration of 13.7% (by volume)and at 0" fibre orientation.
value of o J [ ( i . - ;.-')I for the composites with 45" fibre orientation is longer than that for the composites with 0" fibre orientation. These findings can be explained as follows. In the case of 0" (45") fibre orientation the deformation of elastomer chains in the fibre-matrix interfacial regime can be simulated as the 180" (135") peeling deformation m e ~ h a n i s m . ' The ~ local stress (strain) of elastomer matrix in the 180" peeling deformation mechanism is higher (larger) than that in the 135" peeling deformation mechanism and, consequently, the fracture of fibres and the adhesional failure between the elastomer matrix and the fibres for the 180" peeling deformation mechanism are expected to occur earlier than those of the 135" peeling deformation mechanism. As a result, values for the ')I and the regime of stretch ratio with such a constant value constant o J [ ( i - iLof oE/[(iL - k-')] for the composites with 45" fibre orientation are greater than those for the composites with 0" fibre orientation.
Short fibrepolymer composites
202
8.7 Stress-strain equation for unidirectional short fibre reinforced elastomer composites
Based on the results discussed in the previous sections, a general schematic description for the anisotropic stress-strain behaviour of unidirectional short fibre reinforced polychloroprene composites was developed and is shown in Fig, 8.8. The corresponding stress-strain relationships at various angles of fibre orientation are expressed in the following mathematical forms. For 0" fibre orientation: (a) )iCl 2 h 2 1 ln[o,/(iL - >.-')I = ln[G(O,O")] (b) I,, 2 1, 2
[8.2a]
jLcl
ln[o&.
- l L - 2 ) ]= ln[G(co,W)]
+ (lLcI/i.).ln[G(O,O")/G(co,Oo)]
[8.2b]
For 45" fibre orientation: (a) I c 3 2 I 2 1 ln[oJ(i.
-
I-')] = ln[G(O,45")]
[8.3a]
(b) hc4 2 1, 2 h,, ln[aE/(h -
= In[G(co,45")]
+ (h,,/i.)~ln[G(O,45")/G(co,45")]
[8.3b]
For 90" fibre orientation: (a)
A,,
2i 2 1
ln[oJ(I - 1.K2)] = ln[G(co, 90")]
+ (i.c5/iL)4n[C(0,900)/G(co,90°)]
CS.41
The symbols in the above equations represent the same physical meanings as shown in equation [S.l]. The critical stretch ratios, i,,,i.,,, , Ic3, I,, and i.,,,are described in Fig. 8.8. These equations are useful for predicting the stress-strain values of unidirectional short fibre reinforced elastomer composites in automotive engineering design where numerical analyses, such as linear and non-linear FEA (finite element analyses) are required. Using equations [8.2a], [8.3a] and C8.41, we determined the values of initial shear modulus of unidirectional short fibre oriented polychloroprene composites at various angles of fibre orientation. In the next section, we will discuss the anisotropic modulus properties of the polychloroprene composites.
8.8 Modulus properties of unidirectional short fibre reinforced elastomer composites and applications
The values of initial shear modulus of unidirectional short fibre reinforced polychloroprene composites were determined from the stress-strain plots dis-
Design and applications of short fibre reinforced rubbers
-n
I
CI
0.8 I
I
0
0'
0
I
45'
I
1
0.6
0.8
203
A 90'
0.6
2
(u
0.4
I
x
CI
\
b" m
w
-
0.2
0
0
0
0.2
0.4
1 .o
1 /stretch ratio 8.8 The stress-strain curves of unidirectional short fibre reinforced elas-
tomer composites.
cussed in the previous sections; the results are shown in Table 8.3. For all the three angles of fibre orientation investigated, the value of initial shear modulus increases as the fibre concentration increases. The effectivenessoffibre concentration on the reinforcement of the initial shear modulus of the polychloroprene composites is the highest (lowest) at the angle of fibre orientation equal to 0" (90"). Values for the corresponding relative initial shear modulus, G(0, qre1 (defined as the initial shear modulus of the composite with a given angle of fibre orientation, G(O,0),divided by the initial shear modulus of the elastomer gum, G(0)gu,,,)of the polychloroprene composites were also determined and are shown in Table 8.4. The plotted results for the initial shear modulus versus the fibre volume concentration are shown in Fig. 8.9. The results described in Fig. 8.9 clearly show that the modulus-composition equations suggested by Einstein' * and Smalland by Guth and Gold" cannot predict or describe the modulus properties of unidirectional short fibre oriented polychloroprene composites (except for the case of the polychloroprene composite with the fibre concentration of 3.83% and 90" fibre orientation). However, the relative modulus properties of the polychloroprene composites with different angles of fibre orientation can be successfully described by the thermodynamic relationship developed' for the modulus properties of multi-component polymer systems. This relationship is expressed in a general form as shown below:
Short fibre-polymer composites
204
Table 8.3. Initial shear modulus of uniderectional short fibre reinforced polychloroprene composites Initial shear modulus at various angles of fibre orientation (MPa) ~
0”
45”
90”
0.73
0.72 0.93 1.27 1.85
0.72 0.79 1.06 1.50
Fibre concentration ( ~ 0 1 % )
0 3.83 7.36 13.70
1.14
1.72 3.03
Table 8.4. Relative initial shear modulus of unidirectional short fibre reinforced polychloroprene composites Relative initial shear modulus at various angles of fibre orientation 0“
45“
90”
1.00
1.OO
1.00 1.10 I .47 2.08
Fibre concentration (~01%)
0 3.83 1.36 13.70
1.56 2.36
1.29 1.76 2.57
4.15
0
0’
4.0
-
3.5
- -------
3.0
-
2.5
-
1.5 2mo
i
0
A
45’
0
90’
0
Guth-Gold Einstein-Smallwood
0
9 A n
2
4
6
Vf
8
10
12
[%I
8.9 Plots for the relative initial shear modulus versus the volumeconcentration of fibres of the polychloroprene composites at various angles of fibre orientation and predictions from Einstein-Smallwood and Guth-Gold equation.20
14
Design and applications of short fibre reinforced rubbers
205
5.5 v)
2
3
5.0
U
E
4*5
L
4.0
=
3.5
Q
Q)
.-m
3.0
.r
2.5
v)
.-
CI
2.o 1.5 1 .o
0
2
4
6
8
10
12
14
8.10 Plots for the relative initial shear modulus versus the volume concentration of fibres of the polychloroprenecompositesat various angles of fibre orientation and predictions from the thermodynamic mixing equation.2
ln[G(O,8)"']
= +.exp[A(8)(4
- l)].lnK(8)
~8.51
In the above equation, A(8) represents the mixing index of the fibres with the angle of fibre orientation, 8, in the matrix; 4 is the volume concentration of the fibres; lnK(8) is the reinforcement effectiveness of the fibres with the orientation angle, 8; G(0,B)"' is the relative initial shear modulus of the composites with the angle of fibre orientation equal to 8. The value of the mixing index, A, of any type of filler in the matrix is non-negative.2 The higher the value of A is, the worse the degree of mixing of the fillers in the matrix.' The plotted results on the relative initial shear modulus as a function of the volume concentration of the fibres and the predictions frwn equation C8.51 are shown in Fig. 8.10. The values of 1nK and A determined for the polychloroprene composites with various angles of fibre orientation are shown in Table 8.5. Based on the results shown in Table 8.5, it can be concluded that values of reinforcement effectiveness, lnK, for the polychloroprene composites depend on the angle of fibre orientation, 8. The semi-logarithmic plot between the reinforcement effectiveness for the polychloroprene composites and the angles of fibre orientation exhibits a linear relationship (see Fig. 8.1 1).This linear relationship is expressed in the following mathematical form:
206
Short fibre-polymer composites
Table 8.5. Values of reinforcement effectiveness and mixing index for unidirectional short fibre reinforced polychloroprene composites Angle of fibre orientation, 0
Reinforcement effectiveness (InK)
Mixing index ( A )
14.58 9.41 7.12
0.33 0.36 0.33
0"
45"
90"
2.8 2.6
0
Y
2.4
c
2.2 2.0
1.8
'
0
I
I
1
30
60
90
fibre orientation
(degrees)
8.11 Semi-logarithmic plots of the reinforcement effectiveness versus the angle of fibre orientation.
ln[lnK] = 2.68 - 8.49 x 10-3.€l
(90' 2 9 2 Oo)
C8.61
The correlation ratio of the regressional analysis (Fig. 8.1 1) using equation [8.6] is 0.975. Contrary to the results of InK being a function of 9, the values of mixing index for the fibres in the matrix, A, are insensitive to the change in the angle of fibre orientation and are within the range of 0.33 to 0.36. This result means that the fibres are well dispersed in the polychloroprene matrix. As mentioned previously, the value of mixing index for a given filler in its perfect mixing state equals zero.2 In summary, for unidirectional short fibre reinforced polychloroprene composites, the value of 1nK decreases as the angle of fibre orientation, 0, increases. The value of the mixing index, A , on the other hand, is nearly independent of the angle of fibre orientation, 6. (This result is expected,
Design and applications of short fibre reinforced rubbers
207
Table 8.6. Initial shear modulus ratios of unidirectional short fibre reinforced polychloroprene composites Initial shear niodulus ratio Fibre concentration (vol%) ~~
0"/90"
45"/90" ~~
~~~~
0
1.01 1.44
3.83
I .62
7.36 13.70
2.02
~
1
.oo
1.18
I 20 1.23
since the mixing index, A, is a thermodynamic state variable that is only a function of such thermodynamic variables as surface Gibbs free energies for the fillers and matrix, volume fraction of the ingredients, temperature and pressure of the ~ y s t e m . ' ~As) a reminder, the values of both A and 1nK for elastomers filled with particulate filler (such as carbon blacks) are independent of the testing direction (or equivalently, the direction of deformation).2 Combining equation [8.5] with equation C8.61, we obtained the relationship for the initial shear modulus of the polychloroprene composites with various angles of fibre orientation. This relationship can be written in the following form:
+
ln[G(O,O)] = ~I[G(O)~~,,,] @exp[A.(+ - l)]~[lnK(Oo)]~[lnK(900)/lnK(Oo)~~900 [8.7]
In the above equation, all the symbols have the same physical meanings as discussed previously in the text. The range of the angle, 8, of fibre orientation is between 0" (longitudinal) and 90" (transverse) (see Fig. 8.1). The anisotropic characteristics of the initial shear modulus were described by twomodulus ratios as shown in Table 8.6. Each ofthe modulus ratios is defined as the value of 0" (45")modulus divided by that of 90" modulus. Values for both the 0"/90" modulus ratio and the 45"/90" modulus ratio increase with increasing fibre concentration. However, for the same fibre concentration, the value of the45"/90" modulus ratio is lower than that of the 0"/90" modulus ratio. The plotted results for the 0"/90" modulus ratio and the 45"/90" modulus ratio as a function of the volume concentration of the fibres are shown in Fig. 8.12. The above results are attributed to the different fibre orientations in the polychloroprene matrix. 8.9
Concluding remarks
In order to establish rules to assist the design of short fibre reinforced rubbers in various engineering applications, the mechanical properties and fracture morphology of unidirectional short fibre reinforced polychloroprene composites have been determined. Based on the findings, several deformation mechanisms for this composite system have been identified. The constitutive equations and several composition-processing-property relationships for predicting the stress-strain behaviour and the modulus properties of the elastomer composites have also been developed. The modulus properties of the polychloroprene composites with different angles of fibre orientation and various fibre concentra-
208
Short fibre-polymer composites
2.5
2.0
L
Q
1.5
1.o
0
2
4
6
8
10
12
14
8.12 The 0"/90" and the 45"/90" initial shear modulus ratios as a function of the volume concentration of fibres for the polychloroprene composites.
tions can be predicted by a thermodynamic relationship for the modulus properties of multi-component polymer systems. The above mechanisms and relationships are essential to the design and applications of short fibre reinforced rubbers. References 1 Lee M C H, J A p p l Polpi Sci, 29 (1984) 499. Lee M C H, Polyrti Eiig Sci, 25 (1985) 909. Trexler H E and Lee M C H, J Appl P o l p i Sci, 32 (1986) 3899. Lee M C H. J Appl Polyrtt Sci, 33 (1987) 2479. Thomas A G, Kiihher CIicw Techtiol, 48 (1975) 5. 6 Gent A N , Lindley P B and Thomas A G, J Appl PoIyrtt Sci, 8 (1964) 455. 7 Estes G M, Cooper S L a n d Tobolsky A V, J Mncroriiol Sci, Rev kJtrcromol Cherii, 4
2 3 4 5
(1970) 167. 8 Miwa M, Nakayama A, Ohsawa T and Hasegawa A, J .4ppl Polyrn Sci, 23 (1979) 2957. 9 Setua D K and De S K, J Mnier Sci, 20 (1985) 2953. 10 Akhtar S, De P P and De S K, J Mnrer Sci Leit, 5 (1986) 399. 11 Akhtar S, Bhowmick A K, De P P and De S K, J M n t r r Sci, 21 (1986) 41 79. 12 Lee M C H and Williams M C, J Polyrn Sci, Polyrii Phys E d , 23 (1985) 2243. 13 Lee M C H and Shen M, Polyrii J , 12 (1980) 495.
Design and applications of short fibre reinforced rubbers
209
14 Mark J E, Polym Eng Sci, 19(4) (1979) 254. 15 Lee M C H, unpublished research results. 16 Holister G S and Thomas C, Fibre Reinforced Materials, American Elsevier, New York (1966). 17 Kelly A and Tyson W R, ‘Fibre Strengthened Materials’, presented at the Second International Materials Symposium on High-strength Materials, University of California, Berkeley, California, June 17 (1964). 18 Einstein A, Ann Physik, 19 (1906) 289. 19 Smallwood H, J A p p l Phys, 15 (1944) 758. 20 Guth E and Gold 0, Phys Reu, 53 (1938) 322.