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The influence of fibre diameter on the tensile behaviour of short-glass-fibre reinforced polymers
Composites Science and Technology 2,4 (1985) 231-240
The Influence of Fibre Diameter on the Tensile Behaviour of Short-glass-fibre Reinforced Polymers
F. R a m s t e i n e r a n d R. T h e y s o h n Kunststofflaboratorium, BASF Aktiengesellschaft, D-6700, Ludwigshafenam Rhein (Federal Republic of Germany)
SUMMARY The tensile behaviour of short-fibre reinforced polymers depends on many factors. The extent to which the radius of the fibres and their aspect ratio must be regarded as separate geometric parameters is studied in this work. Young's modulus is completely described by the aspect ratio, but both the absolute value of the failure strength and the impact strength are influenced by the detrimental effect of higher stress concentrations at thick fibres compared to thin ones.
INTRODUCTION The outstanding chemical, physical and processing properties of thermoplastics cannot be utilised when the polymer is not sufficiently stiff and strong for an intended application. To meet this occasional shortcoming polymers are often reinforced with short fibres. The efficiency of these particles in improving the mechanical properties depends on several parameters, e.g. on the matrix properties, bonding conditions between matrix and particle, the nature of the fibres, and the shape of the reinforcing fibre. In this paper we shall concentrate on the influence of fibre diameter on the tensile behaviour of short-glass-fibre reinforced thermoplastics. 231 Composites Science and Technology 0266-3538/85/$03"30 © Elsevier Applied Science Publishers Ltd, England, 1985. Printed in Great Britain
F. Ramsteiner, R. Theysohn
232
EXPERIMENTAL Injection-moulded test pieces were used to study the elasticity (Young's modulus), the failure strength and the impact strength of glass-fibre reinforced polyamide. The tensile testing direction was chosen to coincide with the injection direction. For work at different temperatures the testing machines were equipped with environmental chambers. The fibre length distributions were determined by measuring 500 fibres under the microscope after the matrix had been burnt off. From these frequency distribution functions the number average length or the median length, which is the characteristic length at 50 ~o fibre population, were determined. Further experimental details are described elsewhere. 1
RESULTS AND DISCUSSION
Young's modulus The influence of the fibre diameter on the Young's modulus of short-fibre reinforced polyamide has been investigated. The aspect ratios of fibres with four different diameters are shown in Fig. 1 for composites with a lower (10~o) and a higher (40~) fibre concentration. With increasing concentration the fibres become shorter as a consequence of
90.
70
D=1Opm 131.~n
17pm
~
50
2/.pro
conc.,~o;;on (w~gh~%)
~ e -x"
30
x
x
,'5
Io x ~0
;5
D
Fig. 1. Median length divided by the radius of the fibres as a function of the diameter of the fibres in polyamide-based composites at two concentrations ( 1 0 ~ by weight = 0-05 volume fraction, 40 ~o by weight = 0.24 volume fraction).
Role of fibre diameter in short-glass-fibre reinforcedpolymers
/
12000 j
"/
E
tl.I
10000
8000
6000
4000
j/
233
,,o' !
--x~O --O~D --O--D: --&--O:
= lOom : 13pro 17pro 2/..p m
0'.2 v, Fig. 2. Young's modulus of short-glass-fibre reinforced polyamide (D ---diameter of fibres). the enhanced mutual attrition of the fibres during the processing of the product. At the lower concentration of fibres (10 % by weight) the aspect ratio seems to decrease with increasing fibre diameter. Figure 2 shows the Young's modulus of short-glass-fibre reinforced polyamide as a function of fibre volume fraction for different fibre diameters, ranging from 10 to 24 #m, each type of fibre being coated with the same sizing/coupling agent system. As can be seen from Fig. 2, the diameter of the fibres obviously does not play an important role in determining the Young's modulus as long as the aspect ratio of the fibres is not too different. Furthermore, the increase in Young's modulus is nearly linear with volume fraction. This linearity is also often reported in the literature for other systems, but it is at first sight contrary to micromechanical predictions which imply an increasing efficiency with increasing fibre volume fraction. 2'3 The progressive increase of Young's modulus with fibre concentration is probably counterbalanced by the decreasing aspect ratio of the fibres and some misalignment of the fibres in injection-moulded specimens. 4
F. Ramsteiner, R.
234
Theysohn
Our system of Fig. 2 behaves, quantitatively, as expected when the modulus is related to the aspect ratio (LID= 30) for lower fibre concentration, as has already been shown for other systems. In conclusion, the influence of the shape of the fibres on stiffness enhancement is ge.ometrically completely described by the aspect ratio, the fibre diameter being without influence. This finding is in accordance with predictions of micromechanics, where only the aspect ratio, and not the radius, is a controlling geometrical factor. Failure strength In Fig. 3 the failure strength of the same short-glass-fibre reinforced polyamide is plotted as a function of the volume fraction of fibres with three different diameters. At the test temperature of 50 °C, where the polyamide matrix is very ductile, the extrapolated values from the reinforced products to the plain matrix coincide, whereas in the less tough state of the matrix at low temperature ( - 20 °C) thick fibres seem to entail locally higher stress concentrations than thin ones, markedly reducing the 0fm-.N/mm21
/
/e"
10pro / 17 pm
2t.O
-20*C
2/-. pm
o/
200
160
,•,jlOpm 17pm
• / ~ o
120
+50oC
~ 2/..pro
80
~o I
o
Fig. 3.
6.~
6.2
o:3
Failure strength of polyamide reinforced with fibres of different diameter. Test temperatures, - 20 °C and + 50 °C.
Role of fibre diameter in short-glass-fibre reinforced polymers
235
extrapolated failure strength of the matrix. The failure strength of plain polyamide at - 2 0 °C has previously been measured' to be 114 M Pa. This value is very similar to that extrapolated from the thin fibre system (10 gm). At 50°C, the failure strength of 50 MPa has been reported for polyamide in a preceding paper. 1 It is probable that stress intensities at the fibres can be reduced by local flow processes in a ductile matrix much better than in a brittle one. Kelly's model 6 has proved to be very fruitful for describing the fibre reinforcement: ¢Tfm=
zil i -- G
m)
l)f -F G m
(1)
where 6fm=failure strength of composite; Zfm=interfacial shear strength; ~ zilJD = aspect ratio, approximated in this paper by lso/D; zi = number of fibres with length li; D = diameter of fibres; a" = stress in the matrix at the onset of failure; and vf = fibre volume fraction. Rearranging eqn (1) leads to the expression for evaluating the interfacial shear strength from increase of failure strength with the fibre volume fraction: ~Tfm= ~
)
~ dvf + O'm
(2)
The values, evaluated by using aspect ratio and reinforcement at lower concentrations (vf _<0.15), are compiled in Table 1 for the products with thin and thick fibres. From this table it is concluded that: (a) in our reinforced systems thick and thin fibres yield the same interfacial shear strength, "l~fm, at the same temperature; (b) the interfacial shear strength falls with rising temperature; (c) the fibre reinforcement is more efficient at low temperature; (d) the matrix shear strength given by the von Mises criterion (a~/x/~) amounts to 60 MPa and 25 MPa at - 2 0 °C and 50 °C, respectively. At higher temperature, where the matrix is ductile, the interfacial shear strength becomes comparable to the matrix shear strength, indicating the fibres to be well bonded to the matrix. This conclusion is confirmed by scanning electron microscopy (Fig. 4), showing the fibres protruding from the fracture surface to be completely coated with matrix. At their ends the fibres are surrounded by a torus, probably the recoiled matrix after fracture of the highly stressed matrix material in this region. In the more
F. Ramsteiner, R. Theysohn
236
TABLE 1 Characteristic D a t a for Fibre Reinforced Polyamide
Diameter Temperature lso/D of fibres (°C) (kLm) 10
-20 +50 --20 +50
24
27 20
a'm
"cfro
Oem/V/3
ddfm/dvf
(MPa)
(MPa)
(MPa)
(Mea)
105 43 77 43
40 21 39 23
60 25
1000 540 710 410
brittle state of the matrix at - 2 0 °C, the adhesion is lower than the matrix shear strength and the fibres are bare. In conclusion, the rate of change of failure strength with fibre volume fraction is mainly determined by the aspect ratio of the fibres, provided other parameters (matrix, interface, fibre orientation) are kept constant. In materials of modest toughness, the fibre radius influences the stress
-20*C
,~
~'."
i~
~
+50*C
0=10 prn
Fig. 4.
O--2/.lain
Fibres on the fracture surface of polyamide (various fibre diameters and test temperatures).
Role of fibre diameter in short-glass-fibre reinforced polymers
237
concentration factor of the fibres, lowering the matrix failure strength with increasing fibre radius. The non-linear behaviour of failure strength with fibre concentration at high fibre concentrations has been discussed elsewhere.4
Impact strength The influence of fibre diameter on the impact strength (Charpy bending test, DIN 53 453 unnotched specimens) of glass-fibre reinforced polyamide is illustrated in Fig. 5. At 50 °C, where the matrix polymer is ductile, the impact strength falls with increasing volume fraction, but is nearly independent of fibre diameter. This embrittlement is caused by the fibres suppressing the energy-dissipating deformation processes characteristic of the parent polymer, either by restricting deformation processes as a result of the reinforcing effect or by premature fracture initiation at the stress concentrations introduced by the fibres. In the less ductile state of polyamide at - 20 °C, where the fibre stress concentration factor plays a major role, impact strength is reduced by thick fibres more markedly on |kJ/m2] • t ~\ = '~~ 1 ~ ~
100
• A x o
10pm 13pro 17pm 2/-dJm
\\ -
.50oC 60 ~\
o,," /
ix 1.0
\9%\\ / ." \~V
t~ i
2O
~_.":--.-2o-c
//;I
/
=/ / i /
J
/
o d.~ d~ 0:3 ~" Fig. 5. Impact strength of tlass-fibre reinforced ~lyamide (unnoich~ specimens).
238
F. Ramsteiner, R. Theysohn
,230C
-2~C
.SO~C
force
lOpm
241am
c
Fig. 6.
~
10%
10%
40%
40%
10%
x.0%
Force/deflection diagrams obtained during Charpy impact testing of glass-fibre reinforced polyamide (unnotched specimens).
ok IkJtn¢l • 10 iJm Z.O-
a 13 IJm
x 17pm o 24pm
30
~:><~A. .,50°C
'~/ /
-~o.c
x
IO
I,
o Fig. 7.
;.,
~.2
0.3 v,
Notched impact strength of glass-fibre reinforced polyamide.
Role of fibre diameter in short-glass-fibre reinforced polymers
239
than by thin fibres. This strong inhibition of the deformation processes and the lower elevated strength brought about by employing thick instead of thin fibres is obvious from the force/deflection diagrams recorded during testing at - 2 0 °C and 23 °C (Fig. 6). At 50°C, by contrast, the consequences of different stress concentration factors are less pronounced than at - 20 °C. The notched impact strength is generally reduced by fillers because they encourage crack propagation. Fibres, however, impede crack propagation perpendicular to their orientation, thus raising the notched impact strength or critical stress intensity factor, Klc, independently of the test temperature. As can be seen from Fig. 7, the notched impact strength is scarcely influenced by fibre diameter in the case of the less tough matrix at - 2 0 °C. However, at higher temperature, where polyamide is tough, thin fibres (lower stress concentration) seem to be preferable at low fibre volume fraction. At higher concentration thick fibres seem to be a little more advantageous, probably because of the higher possibilities for deformation processes in the matrix between fibres with larger separation, as is the situation when thick fibres are used. In summarizing, the effect of fibre diameter on the notched impact strength has been shown to be small in polyamide, whereas the impact strength of unnotched specimens is reduced with increasing fibre diameter if the matrix is brittle.
ACKNOWLEDGEMENT The authors are indebted to Dr W. Heckmann for the scanning electron microscopy.
REFERENCES 1. F. Ramsteiner and R. Theysohn, Tensile and impact strengths of unidirectional, short-fibre-reinforced thermoplastics, Composites, 10 (1979) p. l l l . 2. T. S. Chow, The effect of particle shape on the mechanical properties of filled polymers, J. Mat. Sci., 15 (1980) p. 1873. 3. J.C. Halpin and J. L. Kardos, The Halpin-Tsai equations: A review, Polym. Eng. Sci., 16 (1976) p. 344. 4. W. Heckmann, F. Ramsteiner and R. Theysohn, Effects influencing the fibre
240
F. Ramsteiner, R. Theysohn
concentration dependence of tensile strength of unidirectional, short glass fibre reinforced thermoplastics, Advances in Composite Materials, Proe. 3rd Int. Conf. on Composite Materials, Paris, 1980, p. 95. 5. F. Ramsteiner, Elastic behaviour of unidirectional short fibre reinforced thermoplastics, Composites, 12 (1981) p. 65. 6. A. Kelly, The strengthening of metals by dispersed particles, Proc. Roy. Soc. Lond., A282 (1964) p. 63.
The Influence of Fibre Diameter on the Tensile Behaviour of Short-glass-fibre Reinforced Polymers
F. R a m s t e i n e r a n d R. T h e y s o h n Kunststofflaboratorium, BASF Aktiengesellschaft, D-6700, Ludwigshafenam Rhein (Federal Republic of Germany)
SUMMARY The tensile behaviour of short-fibre reinforced polymers depends on many factors. The extent to which the radius of the fibres and their aspect ratio must be regarded as separate geometric parameters is studied in this work. Young's modulus is completely described by the aspect ratio, but both the absolute value of the failure strength and the impact strength are influenced by the detrimental effect of higher stress concentrations at thick fibres compared to thin ones.
INTRODUCTION The outstanding chemical, physical and processing properties of thermoplastics cannot be utilised when the polymer is not sufficiently stiff and strong for an intended application. To meet this occasional shortcoming polymers are often reinforced with short fibres. The efficiency of these particles in improving the mechanical properties depends on several parameters, e.g. on the matrix properties, bonding conditions between matrix and particle, the nature of the fibres, and the shape of the reinforcing fibre. In this paper we shall concentrate on the influence of fibre diameter on the tensile behaviour of short-glass-fibre reinforced thermoplastics. 231 Composites Science and Technology 0266-3538/85/$03"30 © Elsevier Applied Science Publishers Ltd, England, 1985. Printed in Great Britain
F. Ramsteiner, R. Theysohn
232
EXPERIMENTAL Injection-moulded test pieces were used to study the elasticity (Young's modulus), the failure strength and the impact strength of glass-fibre reinforced polyamide. The tensile testing direction was chosen to coincide with the injection direction. For work at different temperatures the testing machines were equipped with environmental chambers. The fibre length distributions were determined by measuring 500 fibres under the microscope after the matrix had been burnt off. From these frequency distribution functions the number average length or the median length, which is the characteristic length at 50 ~o fibre population, were determined. Further experimental details are described elsewhere. 1
RESULTS AND DISCUSSION
Young's modulus The influence of the fibre diameter on the Young's modulus of short-fibre reinforced polyamide has been investigated. The aspect ratios of fibres with four different diameters are shown in Fig. 1 for composites with a lower (10~o) and a higher (40~) fibre concentration. With increasing concentration the fibres become shorter as a consequence of
90.
70
D=1Opm 131.~n
17pm
~
50
2/.pro
conc.,~o;;on (w~gh~%)
~ e -x"
30
x
x
,'5
Io x ~0
;5
D
Fig. 1. Median length divided by the radius of the fibres as a function of the diameter of the fibres in polyamide-based composites at two concentrations ( 1 0 ~ by weight = 0-05 volume fraction, 40 ~o by weight = 0.24 volume fraction).
Role of fibre diameter in short-glass-fibre reinforcedpolymers
/
12000 j
"/
E
tl.I
10000
8000
6000
4000
j/
233
,,o' !
--x~O --O~D --O--D: --&--O:
= lOom : 13pro 17pro 2/..p m
0'.2 v, Fig. 2. Young's modulus of short-glass-fibre reinforced polyamide (D ---diameter of fibres). the enhanced mutual attrition of the fibres during the processing of the product. At the lower concentration of fibres (10 % by weight) the aspect ratio seems to decrease with increasing fibre diameter. Figure 2 shows the Young's modulus of short-glass-fibre reinforced polyamide as a function of fibre volume fraction for different fibre diameters, ranging from 10 to 24 #m, each type of fibre being coated with the same sizing/coupling agent system. As can be seen from Fig. 2, the diameter of the fibres obviously does not play an important role in determining the Young's modulus as long as the aspect ratio of the fibres is not too different. Furthermore, the increase in Young's modulus is nearly linear with volume fraction. This linearity is also often reported in the literature for other systems, but it is at first sight contrary to micromechanical predictions which imply an increasing efficiency with increasing fibre volume fraction. 2'3 The progressive increase of Young's modulus with fibre concentration is probably counterbalanced by the decreasing aspect ratio of the fibres and some misalignment of the fibres in injection-moulded specimens. 4
F. Ramsteiner, R.
234
Theysohn
Our system of Fig. 2 behaves, quantitatively, as expected when the modulus is related to the aspect ratio (LID= 30) for lower fibre concentration, as has already been shown for other systems. In conclusion, the influence of the shape of the fibres on stiffness enhancement is ge.ometrically completely described by the aspect ratio, the fibre diameter being without influence. This finding is in accordance with predictions of micromechanics, where only the aspect ratio, and not the radius, is a controlling geometrical factor. Failure strength In Fig. 3 the failure strength of the same short-glass-fibre reinforced polyamide is plotted as a function of the volume fraction of fibres with three different diameters. At the test temperature of 50 °C, where the polyamide matrix is very ductile, the extrapolated values from the reinforced products to the plain matrix coincide, whereas in the less tough state of the matrix at low temperature ( - 20 °C) thick fibres seem to entail locally higher stress concentrations than thin ones, markedly reducing the 0fm-.N/mm21
/
/e"
10pro / 17 pm
2t.O
-20*C
2/-. pm
o/
200
160
,•,jlOpm 17pm
• / ~ o
120
+50oC
~ 2/..pro
80
~o I
o
Fig. 3.
6.~
6.2
o:3
Failure strength of polyamide reinforced with fibres of different diameter. Test temperatures, - 20 °C and + 50 °C.
Role of fibre diameter in short-glass-fibre reinforced polymers
235
extrapolated failure strength of the matrix. The failure strength of plain polyamide at - 2 0 °C has previously been measured' to be 114 M Pa. This value is very similar to that extrapolated from the thin fibre system (10 gm). At 50°C, the failure strength of 50 MPa has been reported for polyamide in a preceding paper. 1 It is probable that stress intensities at the fibres can be reduced by local flow processes in a ductile matrix much better than in a brittle one. Kelly's model 6 has proved to be very fruitful for describing the fibre reinforcement: ¢Tfm=
zil i -- G
m)
l)f -F G m
(1)
where 6fm=failure strength of composite; Zfm=interfacial shear strength; ~ zilJD = aspect ratio, approximated in this paper by lso/D; zi = number of fibres with length li; D = diameter of fibres; a" = stress in the matrix at the onset of failure; and vf = fibre volume fraction. Rearranging eqn (1) leads to the expression for evaluating the interfacial shear strength from increase of failure strength with the fibre volume fraction: ~Tfm= ~
)
~ dvf + O'm
(2)
The values, evaluated by using aspect ratio and reinforcement at lower concentrations (vf _<0.15), are compiled in Table 1 for the products with thin and thick fibres. From this table it is concluded that: (a) in our reinforced systems thick and thin fibres yield the same interfacial shear strength, "l~fm, at the same temperature; (b) the interfacial shear strength falls with rising temperature; (c) the fibre reinforcement is more efficient at low temperature; (d) the matrix shear strength given by the von Mises criterion (a~/x/~) amounts to 60 MPa and 25 MPa at - 2 0 °C and 50 °C, respectively. At higher temperature, where the matrix is ductile, the interfacial shear strength becomes comparable to the matrix shear strength, indicating the fibres to be well bonded to the matrix. This conclusion is confirmed by scanning electron microscopy (Fig. 4), showing the fibres protruding from the fracture surface to be completely coated with matrix. At their ends the fibres are surrounded by a torus, probably the recoiled matrix after fracture of the highly stressed matrix material in this region. In the more
F. Ramsteiner, R. Theysohn
236
TABLE 1 Characteristic D a t a for Fibre Reinforced Polyamide
Diameter Temperature lso/D of fibres (°C) (kLm) 10
-20 +50 --20 +50
24
27 20
a'm
"cfro
Oem/V/3
ddfm/dvf
(MPa)
(MPa)
(MPa)
(Mea)
105 43 77 43
40 21 39 23
60 25
1000 540 710 410
brittle state of the matrix at - 2 0 °C, the adhesion is lower than the matrix shear strength and the fibres are bare. In conclusion, the rate of change of failure strength with fibre volume fraction is mainly determined by the aspect ratio of the fibres, provided other parameters (matrix, interface, fibre orientation) are kept constant. In materials of modest toughness, the fibre radius influences the stress
-20*C
,~
~'."
i~
~
+50*C
0=10 prn
Fig. 4.
O--2/.lain
Fibres on the fracture surface of polyamide (various fibre diameters and test temperatures).
Role of fibre diameter in short-glass-fibre reinforced polymers
237
concentration factor of the fibres, lowering the matrix failure strength with increasing fibre radius. The non-linear behaviour of failure strength with fibre concentration at high fibre concentrations has been discussed elsewhere.4
Impact strength The influence of fibre diameter on the impact strength (Charpy bending test, DIN 53 453 unnotched specimens) of glass-fibre reinforced polyamide is illustrated in Fig. 5. At 50 °C, where the matrix polymer is ductile, the impact strength falls with increasing volume fraction, but is nearly independent of fibre diameter. This embrittlement is caused by the fibres suppressing the energy-dissipating deformation processes characteristic of the parent polymer, either by restricting deformation processes as a result of the reinforcing effect or by premature fracture initiation at the stress concentrations introduced by the fibres. In the less ductile state of polyamide at - 20 °C, where the fibre stress concentration factor plays a major role, impact strength is reduced by thick fibres more markedly on |kJ/m2] • t ~\ = '~~ 1 ~ ~
100
• A x o
10pm 13pro 17pm 2/-dJm
\\ -
.50oC 60 ~\
o,," /
ix 1.0
\9%\\ / ." \~V
t~ i
2O
~_.":--.-2o-c
//;I
/
=/ / i /
J
/
o d.~ d~ 0:3 ~" Fig. 5. Impact strength of tlass-fibre reinforced ~lyamide (unnoich~ specimens).
238
F. Ramsteiner, R. Theysohn
,230C
-2~C
.SO~C
force
lOpm
241am
c
Fig. 6.
~
10%
10%
40%
40%
10%
x.0%
Force/deflection diagrams obtained during Charpy impact testing of glass-fibre reinforced polyamide (unnotched specimens).
ok IkJtn¢l • 10 iJm Z.O-
a 13 IJm
x 17pm o 24pm
30
~:><~A. .,50°C
'~/ /
-~o.c
x
IO
I,
o Fig. 7.
;.,
~.2
0.3 v,
Notched impact strength of glass-fibre reinforced polyamide.
Role of fibre diameter in short-glass-fibre reinforced polymers
239
than by thin fibres. This strong inhibition of the deformation processes and the lower elevated strength brought about by employing thick instead of thin fibres is obvious from the force/deflection diagrams recorded during testing at - 2 0 °C and 23 °C (Fig. 6). At 50°C, by contrast, the consequences of different stress concentration factors are less pronounced than at - 20 °C. The notched impact strength is generally reduced by fillers because they encourage crack propagation. Fibres, however, impede crack propagation perpendicular to their orientation, thus raising the notched impact strength or critical stress intensity factor, Klc, independently of the test temperature. As can be seen from Fig. 7, the notched impact strength is scarcely influenced by fibre diameter in the case of the less tough matrix at - 2 0 °C. However, at higher temperature, where polyamide is tough, thin fibres (lower stress concentration) seem to be preferable at low fibre volume fraction. At higher concentration thick fibres seem to be a little more advantageous, probably because of the higher possibilities for deformation processes in the matrix between fibres with larger separation, as is the situation when thick fibres are used. In summarizing, the effect of fibre diameter on the notched impact strength has been shown to be small in polyamide, whereas the impact strength of unnotched specimens is reduced with increasing fibre diameter if the matrix is brittle.
ACKNOWLEDGEMENT The authors are indebted to Dr W. Heckmann for the scanning electron microscopy.
REFERENCES 1. F. Ramsteiner and R. Theysohn, Tensile and impact strengths of unidirectional, short-fibre-reinforced thermoplastics, Composites, 10 (1979) p. l l l . 2. T. S. Chow, The effect of particle shape on the mechanical properties of filled polymers, J. Mat. Sci., 15 (1980) p. 1873. 3. J.C. Halpin and J. L. Kardos, The Halpin-Tsai equations: A review, Polym. Eng. Sci., 16 (1976) p. 344. 4. W. Heckmann, F. Ramsteiner and R. Theysohn, Effects influencing the fibre
240
F. Ramsteiner, R. Theysohn
concentration dependence of tensile strength of unidirectional, short glass fibre reinforced thermoplastics, Advances in Composite Materials, Proe. 3rd Int. Conf. on Composite Materials, Paris, 1980, p. 95. 5. F. Ramsteiner, Elastic behaviour of unidirectional short fibre reinforced thermoplastics, Composites, 12 (1981) p. 65. 6. A. Kelly, The strengthening of metals by dispersed particles, Proc. Roy. Soc. Lond., A282 (1964) p. 63.