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A three point bend test for fibre-reinforced composites
A THREE POINT BEND TEST FOR FIBRE-REINFORCED COMPOSITES A. W. CHRISTIANSEN,J. LILLEYand J. B. SHORTALL
Department of Metallurgy and Materials Science,
University of Liverpool, Liverpool, L69 3BX (Great Britain) (Received: 15 December, 1972)
SUMMARY
The effect of fabrication and testing variables on the three point bend testing of glass fibre-reinforced polyester resin composites has been investigated. The volume fraction of fibres in the composites, the specimen span-to-depth ratio and the overhang of the specimen beyond the outer loading nose were varied. At low fibre loadings only tensile (flexural) failure was observed, while, at high fibre loadings, indentation of the specimen by the loading nose preceded shear failure. At fibre loadings of 30 and 45 volume per cent either shear or flexure failure could be obtained, depending on the span to depth ratio used. The flexure strengths were found to obey a simple law of mixtures relationship with fibre loading but the shear strengths were independent of fibre loading. Variation in the amount of overhang had no effect on the shear strength of the composites. INTRODUCTION
The ultimate properties, including tensile strength, Young's modulus, bending stiffness, compressive strength and fracture toughness, of fibre-reinforced composites are greatly affected by the properties of the interface. Consequently, the interlaminar shear strength may be considered an important design variable and a test is required which can give a realistic interpretation of the interlaminar shear strength in a reproducible manner. One such is the horizontal shear test using a short beam specimen in three point bending. This is illustrated in Fig. 1. This test appears suitable as a general, simple method of evaluating shear strength in composites but, before interpretation, it is necessary to determine the importance of events observed on the load-deformation diagram and in the test specimen itself, and how these events are to be interpreted and related to failure stress. 1
Fibre Science and Technology (7) (1974)---© Applied Science Publishers Ltd, England, 1974 Printed in Great Britain
2
A . W . CHR1STIANSEN, J. LILLEY, J. B. SHORTALL
The experimental requirements for such a test on a fibre-reinforced composite are simpler than those for a tensile test, since the effect of flaws and geometrical stress concentrations are less severe. In addition, a rectangular cross-section specimen can be used and this leads to ease of sample preparation. Also, there is no need to provide end tabs on a reduced cross-section to ensure failure away from the grips. At small span-to-depth (L/d) ratios an orthotropic beam of low shear strength is expected to fail by shear at the neutral axis. 1 At progressively large L/d ratios the mode of failure has been shown to become flexural. 2 In this situation the outer fibres fail in tension if, as is usual, the tensile strength is less than the compressive strength. There is an intermediate range of L/d ratios in which the behaviour is transitional and the mode of failure may vary from sample to sample or assume aspects of both modes as deformation proceeds.
L b__. t
P front v~ew Fig. 1.
e n d v~ew
Pertinent features of a beam specimen in three point bending.
It has been suggested 9 that, when testing for tensile (flexural) failure of unidirectional glass fibre-reinforced polymer composites, an L/d of 40:1 should be used since materials of this type have been known to fail by interlaminar shear at L/d as large as 16:1. However, the greater the span, the greater the horizontal thrust at the supports and the consequent corrections necessary to the data. 5,9 In a general review of materials evaluation by bend tests, Mullin and Knoelt 4 discussed the theoretical origins of L/d ratios, and the effect of material variables and specimen defects such as voids, and Westwater 5 observed that samples with small L/d ratios often fail by cracks running out to, or past, the support noses and also that the amount of overhang may effect the mode of failure. Daniels et al. 3 have demonstrated representative failure modes of carbon fibre/epoxy resin composites in the short beam test but indicate that the same behaviour will not necessarily occur for other combinations of materials. To establish three-point bend testing as a meaningful test on fibre-reinforced
A THREE POINT BEND TEST FOR FIBRE-REINFORCED COMPOSITES
3
materials, therefore, several variables need to be evaluated, including the Lid ratio effects and limits, overhang effects (which are expected to be a more severe limitation for short beams) and the particular fibre-matrix system being studied. To study these variables in some detail and also to serve as a useful apparatus for subsequent investigations on interlaminar shear strength, a bend rig has been developed which has the additional facility of providing for photographic recording of deformation and failure of specimens from a choice of side, end or tensile surface views: further, by designing the bend rig to operate over a large range of Lid ratios, the same apparatus can be used to gather several types of information, from short beam interlaminar shear strengths to large Lid ratio flexure strengths. In this paper we present the results of studies using this rig and of the effects of Lid ratios and overhang for polyester resins containing different volume fractions of reinforcing fibres. MATERIALS
The polyester resin used was Filabond 8000, supplied by Synthetic Resins Ltd. This was crosslinked using 0.5 or 1.0 volume per cent of a cobalt naphthenate accelerator and 1.0 volume per cent of a MEK peroxide catalyst. The mould release agent used was Silicone Releasil 2540 using curing agent Catalyst N2541. The glass fibres used were supplied by Pilkington Brothers Limited in the form of rovings containing fibres with a nominal diameter of 12/~m. The fibres had a size coating containing a silane coupling agent reactive towards the glass surface and the polyester resin. EXPERIMENTAL
Equipment The equipment used included an Instron testing machine, a Zeiss Tessovar Photomacrographic system and an Isomet diamond cutting saw.
Bend rig construction and use The bend rig was constructed throughout from gauge plate steel (specification AISI-OI) and all members were fastened together by screws. The dimensions of the rig are as shown in Fig. 2. The maximum span length of 56 mm allowed for variation of L/dratios up to 17 at a beam depth of 3.2 ram. The 3.2 mm radius of the loading and support noses is one quoted in the appropriate British Standards Specification 7 and is in the range advised in the appropriate ASTM specification. 8 To prevent the horizontal thrust of the bending specimen from moving the support noses outward, a screw was inserted from each end of the jig which holds the noses in place. To obtain different span settings the support noses were arranged to run in channels in the horizontal side members. Centreline marks on the upper
4
A . W . CHRISTIANSEN, J. LILLEY, J. B. SHORTALL
:~
l!I
!
"\
.1
'
......
0
20
40
60
80
100
SCALE: MILLIMETRES
Fig. 2.
Exploded-view schematic drawing of the three point bend rig.
ends of the noses were used to align them with the required distance markings which were every 2 mm on these cross members. The bend rig was used in conjunction with an Instron testing machine and was easily fitted into place by alignment of four bolt holes in the rig with those in the crosshead. Since all flexural failures are expected to occur at midspan on the surface of maximum tensile stress (opposite the central loading nose) the rig was designed so that this surface faced upwards and could be viewed through the top of the rig. The loading nose was thus below the specimen, supported on a column which passed through a hole in the centre o f the cross-head and which rested upon a
A THREEPOINT BEND TEST FOR FIBRE-REINFORCEDCOMPOSITES
5
compression loading cell. Supporting members of the frame were positioned to allow easy observation of the specimen ends and sides, including pertinent overhang regions. Figure 3 shows the bend rig and Zeiss Tessovar Photomicrographic recording system in position on the Instron testing machine. For pictures taken from above, the recording system was supported and positioned by two vertical columns rising from the photographic platform. For horizontal views the bend rig was
Fig. 3. Bend rig and photographic apparatus in place on the testing machine.
6
A . W . CHRISTIANSEN, J. LILLEY, J. B. SHORTALL
placed upon a spacer to raise it to the height of the camera on its stand. The stand was designed to allow small vertical movements during a test in the event that a specimen is to be followed to extreme deflection. The Tessovar system itself allowed focal length adjustments via a rack and pinion mechanism. For optimum photographic contrast, various backgrounds were tested. For the more transparent specimens reflection of light off a background and through the specimen provided visual observation of events inside the specimen not otherwise noticeable at the surface facing the camera.
Specimen preparation The cured polyester resin was prepared by adding the required amount of accelerator to 100 parts of resin with low speed stirring, followed by the addition of one part of catalyst, with continued stirring. A length of pre-weighed glass fibres was gathered and held together at one end while being pre-soaked with the resin which had a gel time of about 30 min at room temperature. Two such bundles were placed in a two-channel leaky mould coated with mould release agent containing a layer of resin. A light tension was established to keep the fibres aligned. Additional resin was then added, the upper part of the mould containing two plungers pushed down into place and the whole assembly put into an oven pre-set to the required cure temperature. The curing time was five hours and the cure temperature 120°C. Specimens were cut to length from these composites, using the slow speed Isomer saw, and used directly for the bend tests.
RESULTS
Effect of Lid ratio and volumefraction A series of specimens with Lid ratios between 5 and 12 and fibre volume fractions (V:) of 0.15, 0.30, 0.45 and 0.60 were tested in bending to determine the strengths and modes of failure. A nominal overhang of 2 mm was used in each case. The interlaminar shear stress, which is at a maximum at the neutral axis, was calculated with the aid of the standard equation: 3P =
-
- -
4 bd
(1)
where ~ is the interlaminar shear stress at the neutral axis, P is the load, b the width, and d the depth, of the specimen. The load was that measured at the first major maximum in the load deflection curve. This is shown in Fig. 4 which shows the load deflection curve for a 0.45 V: specimen which failed in shear at an L/d of 4.3. The results obtained on the complete range o f volume fraction samples at various ratios of L/d are illustrated in Fig. 5. The curved lines represent where specimens
7
A THREE POINT BEND TEST FOR FIBRE-REINFORCED COMPOSITES
I ~t L~:43 /
L/0=7.,
/
STRAIN
Fig. 4.
Stress-strain curves for samples with Vf = 0-45 : interlaminar shear failure for and flexure failure for L/d = 7'4.
Lid =
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cr "r co
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+X
,SPAN TO ~P'I"H RATIO
Fig. 5. Interlaminar shear stress at failure as a function of the s p a n to depth ratio for various fibre loadings: unreinforced resin ( × ) ; fibre volume fractions of O"15 ( + ) , 0-30 ( 0 ) , 0"45 (A) and 0'60 (©).
8
A . W . CHRISTIANSEN~ J. LILLEY, J. B. SHORTALL
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0 8
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SPAN T O DEPTH R A T I O
Fig. 6. Flexure stress at failure as a function of the span to depth ratio for various fibre loadings: unreinforced resin ( x ) ; fibre volume fractions of 0.15 ( + ) , 0"30 (O), 0-45 (A) and 0.60 (©).
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.
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1 / I
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-x
0 0 ~5 VOLUME
0.30 FRACTION
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0.60
OF FIBRES
Fig. 7. Flexure strength and interlaminar shear strength as a function of fibre loading. Circles (O) correspond to the horizontal straight lines in Fig. 6. The line through the flexure strength data is for the law of mixtures relationship with af = 1900 M N m -2 and am = 70 M N m -2.
A THREE POINT BEND TEST FOR FIBRE-REINFORCED COMPOSITES
9
failed in flexure and the straight line is the region where specimens generally failed in shear. Figure 8(b) shows an example o f normal shear failure with the crack extending up to the end o f the overhang, while Fig. 8(c) shows an example of normal tensile failure. The tensile, or compressive, stress calculated for the outer fibres (where it is a maximum) is given by the expression 1 =
(2)
The two stresses are related such that:
so that, where the shear stress, ~, is a constant, the flexure stress will vary linearly with L/d, and where the flexure stress is a constant the interlaminar shear stress will vary as an hyperbolic function of L/d. The flexure strength results, obtained over a range of volume fractions and at various ratios of L/d are illustrated in Fig. 6. The horizontal straight lines represent the region in which the specimens failed in flexure. The effects of volume fraction on shear strengths and flexure strengths are summarised in Fig. 7. The composite flexure strength was calculated using the rule of mixtures: o~ = o rV: + or=(1 - V:) (4/ where ~c, o : and cr,, are the strengths of the composite, fibres and matrix respectively. By us!ng a value of 1900 M N / m 2 for a : and a value of 70 MN/m 2 for the polyester resin (extrapolated value, Fig. 7) and plotting them (Fig. 7) it can be seen that the experimentally-obtained values fit the rule of mixtures curve. A complicating factor in interpreting the results was that, with the highest fibre volume fractions and L/d ratios of 5 and more, the effect of indentation by the central loading nose was to cause a compressive failure zone; this preceded shear failure and, in some cases, appeared to initiate the shear failure. This can be seen from Fig. 8(a); also illustrated is an example of shear failure showing shear at newly-created neutral axes, d. The phenomenon of compressive damage leading to shear failure extended up to samples of V: = 0-60 with L/d of 12; in this case no tensile failure was visible although it should otherwise lie within the range of data grouped with tensile failure (Fig. 6).
Effect of overhang A range of specimens of V: = 0.45 and Lid of 5.5, which were conditions under which interlaminar shear failure always occurred, were prepared with end overhangs of from 8 per cent to 50 per cent of the span. These specimens were tested to
l0
A. W. CHRISTIANSEN, J. LILLEY, J. B. SHORTALL
I Fig. 8. Examples of failure modes: (a) compressive damage followed by shear failure; (b) normal interlaminar shear to the end of the beam (50 per cent overhang specimen); (c) tensile failure; (d) secondary shears at neutral axes of pieces resulting from the initial shear failure.
11
A THREE POINT BEND TEST FOR FIBRE-REINFORCED COMPOSITES
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PERCENTAGE OVERHANG
Interlaminar shear strength for specimens with Vf = proportions of overhang.
= 5'5
for various
failure, as described earlier, and the resulting interlaminar shear strengths are shown in Fig. 9. DISCUSSION
Effect of L/d and volumefraction The importance of fibre volume fraction in these tests is very apparent. The initial tests on V~r = 0.15 specimens showed a flexure, or tensile, failure mode down to the smallest Lid of 3, and the variation of ~, the interlaminar shear stress, and or, the flexure strength, follow the appropriate relations for flexure failure. At higher fibre loadings, V~r > 0.30 shear failure occurred for L/d ratios of 4 and below. As the volume fraction increased, the flexure strength also increased, as can be seen most easily from Figs. 6 and 7. The relationship appears essentially linear (Fig. 7) and can be extrapolated back to a value close to that for the resin alone (70 MN/m2). The flexure strength values for the 0.60 Vy specimens at different high Lid ratios do not show the straight line relationship observed at lower volume fractions and a transition Lid ratio did not occur. This could be accounted for by compressive failure at the central loading nose which gave rise to a shear failure (Fig. 8(a)). The interlaminar shear strength appears to be essentially independent of volume fraction (Fig. 7), indicating that, at the plane of shear, the presence of proportionately more fibres nearby does not affect the strength for shear failure. The average value of To, the interlaminar shear strength, for the composites is seen to almost equal cro for the resin. Zo should be a reflection of the interfacial bond between matrix and fibre, since that is expected to be the weakest bond. Other workers in the writers' Department measuring the shear bond strength of systems which consisted of a single glass fibre embedded in a block of Filabond 8000 resin yielded values comparable with the interlaminar shear strength values reported here. 1o
]2
A . W . CHRISTIANSEN, J. LILLEY, J. B. SHORTALL
The shear failures in the specimens tested occurred with the plane of shear on, or near, the neutral axis, i.e. at d/2, and exceptions to this were due to the specimen preparation procedure. In preparing the specimens glass rovings were used, and these tended to cling together, leaving resin-rich areas between. 3' 11 Often, very soon after the initial shear failure, one or more additional shear failures occurred at approximately d/4 and 3d/4, i.e. at the neutral axes of the pieces resulting from the original failure (Fig. 8(d)).
Effect of overhang The interlaminar shear strength of a sample designed to fail in shear showed no dependence on overhang, the failures being all of the shear type with shear often occurring all the way out to the ends of the specimens past the loading nose, even for the large overhang specimens (Fig. 8(b)). Visual observations showed that failure was initiated near the midspan of the specimens and propagated toward the ends of the beams. Consequently, the effect of overhang is not a restriction on the interlaminar shear strength. CONCLUSIONS
It has been demonstrated that, in three-point bend testing of composites, as the
Lid ratio is decreased from large values failure will occur, at first at a constant flexure strength, Cro, until the interlaminar shear stress in the sample eventually reaches the interlaminar shear strength, %. At smaller Lid values the material fails by shear (at the neutral plane) at a constant value of Zo, and tr decreases as L/d decreases. The theoretical transition point for shear to flexure failure in unidirectional fibrereinforced composites 4 was only observed in the systems studied here for volume fractions of about 0.30 to 0-45 and it is suggested that, for the testing of composites for interlaminar shear properties, the restriction of a transition L/d which is a function of fibre volume fraction must be observed. Failures which have a shear appearance may actually be in a much more complex stress state and the resultant strength value misleading. The interlaminar shear strength of the glass fibre polyester resin system studied here, when tested using the appropriate volume fraction and specimen geometry, was 70 M N / m 2 and this value was constant for all volume fractions when the specimens failed by shear. ACKNOWLEDGEMENTS
The results reported in this paper are part of a research programme on fibrereinforced materials being conducted in this Department. The writers wish to thank the Science Research Council for the award of a Research Fellowship (AWC).
A THREE POINT BEND TEST FOR FIBRE-REINFORCED COMPOSITES
13
REFERENCES 1. S. TIMOSHENKO,Strength of Materials, Part 1, Van Nostrand, Princeton, 3rd edn, 1955. 2. W. N. REYNOLDSand N. L. HANCOX, Seventh International Reinforced Plastics Conference, British Plastics Federation, Reinforced Plastics Group, Brighton, 1970. Paper 12. 3. B. K. DANIELS,lq. K. HARAKASand R. C. JACKSON,Fibre Sci. and Technol., 3 (1971) p. 187. 4. J. V. MULLIN and A. C. KNOELL, Mater. Res. Std., 10(12) (1970) p. 16. 5. J. W. WESTWATI~R,.4m. Soe. Testing Mater., Proc., 49 (1949) p. 1092. 6. Apparent Horizontal Shear Strength of Reinforced Plastics by Short-Beam Method, ASTM D 2344-65T, 1965. 7. Testing of Plastics, Cross-breaking Strength (Flexure Strength) BS 2782: Part 3 : 1970, Methods 304A-E, 1970. 8. Flexural Properties of Plastics, ASTM D 790-66, 1966. 9. H. S. LOVELESS, Chap. 10, Testing of Plastics, Vol. 2, edited by J. V. Sehmitz, WileyInterscience, London, 1966. 10. H. W. C. YIp and J. B. SI-IORTALL(in press), J. Physics. 11. P. HANCOCKand R. C. CtYrnERBERTSON,J. Mater. Sci., 5 (1970) p. 762.
Department of Metallurgy and Materials Science,
University of Liverpool, Liverpool, L69 3BX (Great Britain) (Received: 15 December, 1972)
SUMMARY
The effect of fabrication and testing variables on the three point bend testing of glass fibre-reinforced polyester resin composites has been investigated. The volume fraction of fibres in the composites, the specimen span-to-depth ratio and the overhang of the specimen beyond the outer loading nose were varied. At low fibre loadings only tensile (flexural) failure was observed, while, at high fibre loadings, indentation of the specimen by the loading nose preceded shear failure. At fibre loadings of 30 and 45 volume per cent either shear or flexure failure could be obtained, depending on the span to depth ratio used. The flexure strengths were found to obey a simple law of mixtures relationship with fibre loading but the shear strengths were independent of fibre loading. Variation in the amount of overhang had no effect on the shear strength of the composites. INTRODUCTION
The ultimate properties, including tensile strength, Young's modulus, bending stiffness, compressive strength and fracture toughness, of fibre-reinforced composites are greatly affected by the properties of the interface. Consequently, the interlaminar shear strength may be considered an important design variable and a test is required which can give a realistic interpretation of the interlaminar shear strength in a reproducible manner. One such is the horizontal shear test using a short beam specimen in three point bending. This is illustrated in Fig. 1. This test appears suitable as a general, simple method of evaluating shear strength in composites but, before interpretation, it is necessary to determine the importance of events observed on the load-deformation diagram and in the test specimen itself, and how these events are to be interpreted and related to failure stress. 1
Fibre Science and Technology (7) (1974)---© Applied Science Publishers Ltd, England, 1974 Printed in Great Britain
2
A . W . CHR1STIANSEN, J. LILLEY, J. B. SHORTALL
The experimental requirements for such a test on a fibre-reinforced composite are simpler than those for a tensile test, since the effect of flaws and geometrical stress concentrations are less severe. In addition, a rectangular cross-section specimen can be used and this leads to ease of sample preparation. Also, there is no need to provide end tabs on a reduced cross-section to ensure failure away from the grips. At small span-to-depth (L/d) ratios an orthotropic beam of low shear strength is expected to fail by shear at the neutral axis. 1 At progressively large L/d ratios the mode of failure has been shown to become flexural. 2 In this situation the outer fibres fail in tension if, as is usual, the tensile strength is less than the compressive strength. There is an intermediate range of L/d ratios in which the behaviour is transitional and the mode of failure may vary from sample to sample or assume aspects of both modes as deformation proceeds.
L b__. t
P front v~ew Fig. 1.
e n d v~ew
Pertinent features of a beam specimen in three point bending.
It has been suggested 9 that, when testing for tensile (flexural) failure of unidirectional glass fibre-reinforced polymer composites, an L/d of 40:1 should be used since materials of this type have been known to fail by interlaminar shear at L/d as large as 16:1. However, the greater the span, the greater the horizontal thrust at the supports and the consequent corrections necessary to the data. 5,9 In a general review of materials evaluation by bend tests, Mullin and Knoelt 4 discussed the theoretical origins of L/d ratios, and the effect of material variables and specimen defects such as voids, and Westwater 5 observed that samples with small L/d ratios often fail by cracks running out to, or past, the support noses and also that the amount of overhang may effect the mode of failure. Daniels et al. 3 have demonstrated representative failure modes of carbon fibre/epoxy resin composites in the short beam test but indicate that the same behaviour will not necessarily occur for other combinations of materials. To establish three-point bend testing as a meaningful test on fibre-reinforced
A THREE POINT BEND TEST FOR FIBRE-REINFORCED COMPOSITES
3
materials, therefore, several variables need to be evaluated, including the Lid ratio effects and limits, overhang effects (which are expected to be a more severe limitation for short beams) and the particular fibre-matrix system being studied. To study these variables in some detail and also to serve as a useful apparatus for subsequent investigations on interlaminar shear strength, a bend rig has been developed which has the additional facility of providing for photographic recording of deformation and failure of specimens from a choice of side, end or tensile surface views: further, by designing the bend rig to operate over a large range of Lid ratios, the same apparatus can be used to gather several types of information, from short beam interlaminar shear strengths to large Lid ratio flexure strengths. In this paper we present the results of studies using this rig and of the effects of Lid ratios and overhang for polyester resins containing different volume fractions of reinforcing fibres. MATERIALS
The polyester resin used was Filabond 8000, supplied by Synthetic Resins Ltd. This was crosslinked using 0.5 or 1.0 volume per cent of a cobalt naphthenate accelerator and 1.0 volume per cent of a MEK peroxide catalyst. The mould release agent used was Silicone Releasil 2540 using curing agent Catalyst N2541. The glass fibres used were supplied by Pilkington Brothers Limited in the form of rovings containing fibres with a nominal diameter of 12/~m. The fibres had a size coating containing a silane coupling agent reactive towards the glass surface and the polyester resin. EXPERIMENTAL
Equipment The equipment used included an Instron testing machine, a Zeiss Tessovar Photomacrographic system and an Isomet diamond cutting saw.
Bend rig construction and use The bend rig was constructed throughout from gauge plate steel (specification AISI-OI) and all members were fastened together by screws. The dimensions of the rig are as shown in Fig. 2. The maximum span length of 56 mm allowed for variation of L/dratios up to 17 at a beam depth of 3.2 ram. The 3.2 mm radius of the loading and support noses is one quoted in the appropriate British Standards Specification 7 and is in the range advised in the appropriate ASTM specification. 8 To prevent the horizontal thrust of the bending specimen from moving the support noses outward, a screw was inserted from each end of the jig which holds the noses in place. To obtain different span settings the support noses were arranged to run in channels in the horizontal side members. Centreline marks on the upper
4
A . W . CHRISTIANSEN, J. LILLEY, J. B. SHORTALL
:~
l!I
!
"\
.1
'
......
0
20
40
60
80
100
SCALE: MILLIMETRES
Fig. 2.
Exploded-view schematic drawing of the three point bend rig.
ends of the noses were used to align them with the required distance markings which were every 2 mm on these cross members. The bend rig was used in conjunction with an Instron testing machine and was easily fitted into place by alignment of four bolt holes in the rig with those in the crosshead. Since all flexural failures are expected to occur at midspan on the surface of maximum tensile stress (opposite the central loading nose) the rig was designed so that this surface faced upwards and could be viewed through the top of the rig. The loading nose was thus below the specimen, supported on a column which passed through a hole in the centre o f the cross-head and which rested upon a
A THREEPOINT BEND TEST FOR FIBRE-REINFORCEDCOMPOSITES
5
compression loading cell. Supporting members of the frame were positioned to allow easy observation of the specimen ends and sides, including pertinent overhang regions. Figure 3 shows the bend rig and Zeiss Tessovar Photomicrographic recording system in position on the Instron testing machine. For pictures taken from above, the recording system was supported and positioned by two vertical columns rising from the photographic platform. For horizontal views the bend rig was
Fig. 3. Bend rig and photographic apparatus in place on the testing machine.
6
A . W . CHRISTIANSEN, J. LILLEY, J. B. SHORTALL
placed upon a spacer to raise it to the height of the camera on its stand. The stand was designed to allow small vertical movements during a test in the event that a specimen is to be followed to extreme deflection. The Tessovar system itself allowed focal length adjustments via a rack and pinion mechanism. For optimum photographic contrast, various backgrounds were tested. For the more transparent specimens reflection of light off a background and through the specimen provided visual observation of events inside the specimen not otherwise noticeable at the surface facing the camera.
Specimen preparation The cured polyester resin was prepared by adding the required amount of accelerator to 100 parts of resin with low speed stirring, followed by the addition of one part of catalyst, with continued stirring. A length of pre-weighed glass fibres was gathered and held together at one end while being pre-soaked with the resin which had a gel time of about 30 min at room temperature. Two such bundles were placed in a two-channel leaky mould coated with mould release agent containing a layer of resin. A light tension was established to keep the fibres aligned. Additional resin was then added, the upper part of the mould containing two plungers pushed down into place and the whole assembly put into an oven pre-set to the required cure temperature. The curing time was five hours and the cure temperature 120°C. Specimens were cut to length from these composites, using the slow speed Isomer saw, and used directly for the bend tests.
RESULTS
Effect of Lid ratio and volumefraction A series of specimens with Lid ratios between 5 and 12 and fibre volume fractions (V:) of 0.15, 0.30, 0.45 and 0.60 were tested in bending to determine the strengths and modes of failure. A nominal overhang of 2 mm was used in each case. The interlaminar shear stress, which is at a maximum at the neutral axis, was calculated with the aid of the standard equation: 3P =
-
- -
4 bd
(1)
where ~ is the interlaminar shear stress at the neutral axis, P is the load, b the width, and d the depth, of the specimen. The load was that measured at the first major maximum in the load deflection curve. This is shown in Fig. 4 which shows the load deflection curve for a 0.45 V: specimen which failed in shear at an L/d of 4.3. The results obtained on the complete range o f volume fraction samples at various ratios of L/d are illustrated in Fig. 5. The curved lines represent where specimens
7
A THREE POINT BEND TEST FOR FIBRE-REINFORCED COMPOSITES
I ~t L~:43 /
L/0=7.,
/
STRAIN
Fig. 4.
Stress-strain curves for samples with Vf = 0-45 : interlaminar shear failure for and flexure failure for L/d = 7'4.
Lid =
4.3
go
8o
,0
o
\o
o
6
A
,+\-.\ n
~
6
n
r; z
m
50
if)
cr "r co
~
~o
< ._j - 113
+
Z
+X
,SPAN TO ~P'I"H RATIO
Fig. 5. Interlaminar shear stress at failure as a function of the s p a n to depth ratio for various fibre loadings: unreinforced resin ( × ) ; fibre volume fractions of O"15 ( + ) , 0-30 ( 0 ) , 0"45 (A) and 0'60 (©).
8
A . W . CHRISTIANSEN~ J. LILLEY, J. B. SHORTALL
14
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o
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9
10
11
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SPAN T O DEPTH R A T I O
Fig. 6. Flexure stress at failure as a function of the span to depth ratio for various fibre loadings: unreinforced resin ( x ) ; fibre volume fractions of 0.15 ( + ) , 0"30 (O), 0-45 (A) and 0.60 (©).
12r
.
.
.
.
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1 / I
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-
-x
0 0 ~5 VOLUME
0.30 FRACTION
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OF FIBRES
Fig. 7. Flexure strength and interlaminar shear strength as a function of fibre loading. Circles (O) correspond to the horizontal straight lines in Fig. 6. The line through the flexure strength data is for the law of mixtures relationship with af = 1900 M N m -2 and am = 70 M N m -2.
A THREE POINT BEND TEST FOR FIBRE-REINFORCED COMPOSITES
9
failed in flexure and the straight line is the region where specimens generally failed in shear. Figure 8(b) shows an example o f normal shear failure with the crack extending up to the end o f the overhang, while Fig. 8(c) shows an example of normal tensile failure. The tensile, or compressive, stress calculated for the outer fibres (where it is a maximum) is given by the expression 1 =
(2)
The two stresses are related such that:
so that, where the shear stress, ~, is a constant, the flexure stress will vary linearly with L/d, and where the flexure stress is a constant the interlaminar shear stress will vary as an hyperbolic function of L/d. The flexure strength results, obtained over a range of volume fractions and at various ratios of L/d are illustrated in Fig. 6. The horizontal straight lines represent the region in which the specimens failed in flexure. The effects of volume fraction on shear strengths and flexure strengths are summarised in Fig. 7. The composite flexure strength was calculated using the rule of mixtures: o~ = o rV: + or=(1 - V:) (4/ where ~c, o : and cr,, are the strengths of the composite, fibres and matrix respectively. By us!ng a value of 1900 M N / m 2 for a : and a value of 70 MN/m 2 for the polyester resin (extrapolated value, Fig. 7) and plotting them (Fig. 7) it can be seen that the experimentally-obtained values fit the rule of mixtures curve. A complicating factor in interpreting the results was that, with the highest fibre volume fractions and L/d ratios of 5 and more, the effect of indentation by the central loading nose was to cause a compressive failure zone; this preceded shear failure and, in some cases, appeared to initiate the shear failure. This can be seen from Fig. 8(a); also illustrated is an example of shear failure showing shear at newly-created neutral axes, d. The phenomenon of compressive damage leading to shear failure extended up to samples of V: = 0-60 with L/d of 12; in this case no tensile failure was visible although it should otherwise lie within the range of data grouped with tensile failure (Fig. 6).
Effect of overhang A range of specimens of V: = 0.45 and Lid of 5.5, which were conditions under which interlaminar shear failure always occurred, were prepared with end overhangs of from 8 per cent to 50 per cent of the span. These specimens were tested to
l0
A. W. CHRISTIANSEN, J. LILLEY, J. B. SHORTALL
I Fig. 8. Examples of failure modes: (a) compressive damage followed by shear failure; (b) normal interlaminar shear to the end of the beam (50 per cent overhang specimen); (c) tensile failure; (d) secondary shears at neutral axes of pieces resulting from the initial shear failure.
11
A THREE POINT BEND TEST FOR FIBRE-REINFORCED COMPOSITES
Z
go
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80
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w T ~
60
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rr
w I-Z
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n
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'
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PERCENTAGE OVERHANG
Interlaminar shear strength for specimens with Vf = proportions of overhang.
= 5'5
for various
failure, as described earlier, and the resulting interlaminar shear strengths are shown in Fig. 9. DISCUSSION
Effect of L/d and volumefraction The importance of fibre volume fraction in these tests is very apparent. The initial tests on V~r = 0.15 specimens showed a flexure, or tensile, failure mode down to the smallest Lid of 3, and the variation of ~, the interlaminar shear stress, and or, the flexure strength, follow the appropriate relations for flexure failure. At higher fibre loadings, V~r > 0.30 shear failure occurred for L/d ratios of 4 and below. As the volume fraction increased, the flexure strength also increased, as can be seen most easily from Figs. 6 and 7. The relationship appears essentially linear (Fig. 7) and can be extrapolated back to a value close to that for the resin alone (70 MN/m2). The flexure strength values for the 0.60 Vy specimens at different high Lid ratios do not show the straight line relationship observed at lower volume fractions and a transition Lid ratio did not occur. This could be accounted for by compressive failure at the central loading nose which gave rise to a shear failure (Fig. 8(a)). The interlaminar shear strength appears to be essentially independent of volume fraction (Fig. 7), indicating that, at the plane of shear, the presence of proportionately more fibres nearby does not affect the strength for shear failure. The average value of To, the interlaminar shear strength, for the composites is seen to almost equal cro for the resin. Zo should be a reflection of the interfacial bond between matrix and fibre, since that is expected to be the weakest bond. Other workers in the writers' Department measuring the shear bond strength of systems which consisted of a single glass fibre embedded in a block of Filabond 8000 resin yielded values comparable with the interlaminar shear strength values reported here. 1o
]2
A . W . CHRISTIANSEN, J. LILLEY, J. B. SHORTALL
The shear failures in the specimens tested occurred with the plane of shear on, or near, the neutral axis, i.e. at d/2, and exceptions to this were due to the specimen preparation procedure. In preparing the specimens glass rovings were used, and these tended to cling together, leaving resin-rich areas between. 3' 11 Often, very soon after the initial shear failure, one or more additional shear failures occurred at approximately d/4 and 3d/4, i.e. at the neutral axes of the pieces resulting from the original failure (Fig. 8(d)).
Effect of overhang The interlaminar shear strength of a sample designed to fail in shear showed no dependence on overhang, the failures being all of the shear type with shear often occurring all the way out to the ends of the specimens past the loading nose, even for the large overhang specimens (Fig. 8(b)). Visual observations showed that failure was initiated near the midspan of the specimens and propagated toward the ends of the beams. Consequently, the effect of overhang is not a restriction on the interlaminar shear strength. CONCLUSIONS
It has been demonstrated that, in three-point bend testing of composites, as the
Lid ratio is decreased from large values failure will occur, at first at a constant flexure strength, Cro, until the interlaminar shear stress in the sample eventually reaches the interlaminar shear strength, %. At smaller Lid values the material fails by shear (at the neutral plane) at a constant value of Zo, and tr decreases as L/d decreases. The theoretical transition point for shear to flexure failure in unidirectional fibrereinforced composites 4 was only observed in the systems studied here for volume fractions of about 0.30 to 0-45 and it is suggested that, for the testing of composites for interlaminar shear properties, the restriction of a transition L/d which is a function of fibre volume fraction must be observed. Failures which have a shear appearance may actually be in a much more complex stress state and the resultant strength value misleading. The interlaminar shear strength of the glass fibre polyester resin system studied here, when tested using the appropriate volume fraction and specimen geometry, was 70 M N / m 2 and this value was constant for all volume fractions when the specimens failed by shear. ACKNOWLEDGEMENTS
The results reported in this paper are part of a research programme on fibrereinforced materials being conducted in this Department. The writers wish to thank the Science Research Council for the award of a Research Fellowship (AWC).
A THREE POINT BEND TEST FOR FIBRE-REINFORCED COMPOSITES
13
REFERENCES 1. S. TIMOSHENKO,Strength of Materials, Part 1, Van Nostrand, Princeton, 3rd edn, 1955. 2. W. N. REYNOLDSand N. L. HANCOX, Seventh International Reinforced Plastics Conference, British Plastics Federation, Reinforced Plastics Group, Brighton, 1970. Paper 12. 3. B. K. DANIELS,lq. K. HARAKASand R. C. JACKSON,Fibre Sci. and Technol., 3 (1971) p. 187. 4. J. V. MULLIN and A. C. KNOELL, Mater. Res. Std., 10(12) (1970) p. 16. 5. J. W. WESTWATI~R,.4m. Soe. Testing Mater., Proc., 49 (1949) p. 1092. 6. Apparent Horizontal Shear Strength of Reinforced Plastics by Short-Beam Method, ASTM D 2344-65T, 1965. 7. Testing of Plastics, Cross-breaking Strength (Flexure Strength) BS 2782: Part 3 : 1970, Methods 304A-E, 1970. 8. Flexural Properties of Plastics, ASTM D 790-66, 1966. 9. H. S. LOVELESS, Chap. 10, Testing of Plastics, Vol. 2, edited by J. V. Sehmitz, WileyInterscience, London, 1966. 10. H. W. C. YIp and J. B. SI-IORTALL(in press), J. Physics. 11. P. HANCOCKand R. C. CtYrnERBERTSON,J. Mater. Sci., 5 (1970) p. 762.