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The effect of transverse compressive stresses on tensile failure of glass fibre-epoxy
Composite Structures 32 (1995) 621-626 0 1995 Elsevier Science Limited Printed in Great Britain. All rights reserved 0263-8223/95/$9.50 0263-8223(95)00057-7
The effect of transverse compressive stresses on tensile failure of glass fibre-epoxy Michael R. Wisnom Department of Aerospace Engineering Universityof Bristol, Brktol BS8 1 TR, UK
Four point bending tests were carried out on 32-ply glass fibre-epoxy specimens with 0” plies on the surface. Different combinations of 0” and +45” interior plies allowed the transverse stresses at the surface to be varied. All specimens failed by fibre tension, and the strength was relatively insensitive to transverse compressive strengths. The maximum stress failure criterion was found to provide a reasonable fit to the experimental data, and is recommended for design purposes.
own failure envelope in the area of the 45” cut-off.’ There is a need for further experimental evidence to help to resolve this controversy. The objective of the present study was to carry out a series of carefully controlled tests to assess the degree to which transverse compressive stresses influence the fibre direction tensile strength, and provide data for comparing the various failure criteria.
1 INTRODUCTION Knowledge of the strength of fibre reinforced composites under combined states of stress is important for the reliable design of composite structures. Many failure criteria have been proposed over the years. The most commonly used are the simple maximum stress or strain criteria, and interactive ones such as the Tsai-Hill and Tsai-Wu criteria. Despite the importance of the topic, there is still considerable disagreement about which criteria are best. The problems of carrying out satisfactory tests and the consequent paucity of good experimental data has made it difficult to resolve this issue. One particularly problematic area is in the tension-compression quadrant, concerning the effect of transverse compression stresses on fibre direction tensile strength. Hart Smith has proposed a strain based maximum shear stress failure criterion which implies a 45” cut off between longitudinal tensile strain and transverse compressive strain.’ Tests by Swanson and coworkers on laminated cylinders under internal pressure and axial compression have suggested that the maximum strain and maximum stress criteria give satisfactory results in the tension-compression quadrant.2-4 However, the results show considerable scatter, and Hart Smith states that the data in Ref. 2 gives good agreement with his
2 DESIGN OF TESTS Design of a good specimen to investigate the effect of transverse compressive stresses is a challenging task. Ideally there should be a uniform stress field with no stress concentrations and no components of stress present other than tension and transverse compression. As many factors as possible should be kept constant between different specimens to avoid other possible influences on the results apart from the transverse stresses. It was decided to use four point bending tests since these enable tensile failure to be obtained in an area with uniform loading and no significant stress concentrations. Direct tension tests are much more difficult because failure often occurs near the grips where there are stress concentrations and in-plane and interla621
M. R. Whom
622
minar shear and normal stresses arise. Previous work had shown that very good repeatability could be achieved with flexural tests, which is important in investigating effects which may not be all that large. Tensile failure under bending may give a higher strength than under pure tension due to the effect of the stress gradient,576 but on a comparative basis this is still valid provided the stress gradient remains the same. 0” plies were always placed on the surface where the maximum stress arises and where failure was expected to occur. In order to generate transverse compressive stresses, + 45” plies were introduced into the layup. By altering the ratio of +45” to 0” plies the amount of transverse stress could be varied. Another important factor was the avoidance of premature failure due to delamination at the free edge. Laminates with +45” plies have the advantage of not being particularly susceptible to this type of damage. Three different types of specimen were selected, all with the same total number of plies. This is important in order to keep the stress gradient the same for the same surface stress. The layups adopted were 032, [04/( +45/-45)6]s and [O/(+45/-45),/+45],. Laminated plate analysis was carried out using the properties for 60% volume fraction E glass/913 epoxy given in Table 1 and with a ply thickness of 0.127 mm. Pure bending was applied with moments to give a fibre direction stress of 1500 MPa in the surface ply, close to the expected tensile failure stress for the material. Results are given in Table 2 for the stresses at the centre of the surface 0” ply and at the centre of the outermost 45” ply. Stresses are in Table 1. Material properties for glass fibre-epoxy
Fibre direction modulus, E 1 Transverse modulus, Ez Poisson’s ratio, v12 Shear modulus, G12
43.9 GPa 15.4 GPa 0.29 4.34 GPa
the ply coordinate system, with g1 being the fibre direction stress, c2 the transverse stress and r12 the in-plane shear stress. It can be seen that the [O/(+45/-45)7/+45], layup generates a very substantial transverse compressive stress in the surface 0” ply, with the [04/( + 45/ -45)& layup producing an intermediate value. Fibre direction stresses in the outermost 45” plies are relatively low. There are high shear and transverse tensile stresses which could present a risk of transverse cracking in the 45” plies, but this is minimised by having only single adjacent plies with the same orientation. The layups with +45” plies are not balanced under bending due to the different positions of the + 45” and -45” relative to the neutral axis, and due to the extra +45” plies in the [O/(+45/-45),/+45], layup. This gives rise to a small amount of torsion which produces some shear stresses in the surface plies. However as can be seen in Table 2, the magnitudes of these stresses are very small, and they are not likely to have any significant influence on failure. It is important to keep the stressed volume the same between different specimens since there can be significant size effects on tensile strength in bending.7 This was achieved by using the same dimensions for all specimens. There could also be an effect due to the different number of 0” plies in each specimen. This would not be expected to be a large effect since failure should be mainly controlled by the surface ply where the stress is highest, and this is a 0” ply for all specimens. Calculations based on Weibull statistical strength theory confirmed this effect to be negligible. The centre span was selected to have a reasonably large volume subject to the maximum stress without the deflections becoming excessive. The outer span was sized to avoid the possibility of shear failure. The choice of width was a difficult compromise. A wide specimen is required to ensure
Table 2. Laminated plate theory stresses at centre of outer plies (MPa)
Outer 0” ply LayuP
0 [(c/C+45/-45)&
[O/(+45/-45)7/+45],
61
1500 1500 1500
02
-86q6 - 151.3
Outer 45” ply z12
01
-:.o -3.5
3G2 344.3
62
167 152.0
712
161.9 - 222.9
Tensilefailure of glass Jibre-epoxy
that the free edge region does not unduly affect the results. On the other hand a narrow specimen is necessary in order to reduce effects due to restriction of anticlastic curvature. A width of 20 mm was chosen, which was considered satisfactory in terms of minimising free edge effects. However, there were anticlastic curvature effects present, which will be discussed later. The radius of the loading and support noses was chosen to avoid local failure at the contact points. Figure 1 shows the final configuration chosen.
3 EXPERIMENTAL RESULTS
PROCEDURE
AND
Three panels were laid up from Ciba E glass/ 913 prepreg. All the prepreg was from the same batch, and the panels were cured according to the manufacturer‘s instructions using the same cure cycles. Specimens were cut out with a diaCombined longitudinal and mond saw. transverse strain gauges were attached to the centre of each surface of each specimen. Six specimens of each type were tested in a servo-hydraulic test machine. Fixed loading and support noses were used, with thin greased rubber pads placed between them and the specimens to redistribute loads at the contact points. Tests were carried out under displacement control at a nominal rate of 5 mm/min. Values of load, cross-head displacement and strain gauge readings were logged on a computer. All specimens failed in tension, with very similar appearance. Initially a few small bundles of fibres broke and split off from the tensile surface, followed by more extensive fibre fracture accompanied by splitting and delamination. Crosshead displacements at initiation of failure were about 26, 24 and 21 mm for the Oj2,
Fig. 1.
Test
623
and [O/( +45/-45)7/+45], [04/( +45/-45)& specimens respectively. Complete fracture did not occur, but failure propagated through the thickness with increasing deflection until the test was stopped because the displacements were excessive. Fibre fracture initiated near the centre of the span, with no apparent tendency for it to start closer to the loading noses. There were no indications of edge delamination preceding fibre failure for any of the specimens. For the 032 and [04/( + 45/- 45),], specimens no damage occurred on the compression side except for a few small splits apparently initiating from cut fibres at the edge. However, most of the [O/( + 45/ - 45)7/ + 451, specimens showed a small amount of splitting, delamination and fibre failure on the compression surface. The damage occurred in the centre span, away from the edges, presumably as a result of the high transverse tensile stresses induced in the 0” plies by the underlying +45” plies. On one specimen the damage was more extensive, and the overall appearance was very similar to that on the tension side. In all cases failure was predominantly on the tension surface, and the presence of some damage on the compression surface should not have had a significant influence on the tensile failure. Failure was taken as the strain at which the longitudinal strain gauge on the tension side broke. This normally occurred when a large area of fibres on the surface fractured, and therefore is a reasonably accurate measure of the tensile strain at failure. For three of the OS2 specimens this happened at or very close to the maximum load. However for the other three, and for all of the specimens with +45” plies the load reached a peak, started to drop and then gauge failure occurred. This suggests that tensile failure may have initiated away from the central area where the gauge was attached. In a few cases the strain gauge reading accelerated just before it stopped working. The last reading
dimensions (mm, not to scale).
M. R. Wisnom
624
Table 3. Strain gauge readings on tensile surface at failure (microstrain) 0 32
Tensile 34570 38 460 37 300 38 830 37 900 40 360 37 900 5.1
Mean C.V. (%)
[W(
+
49 - 45)&
LO/(+45/-45),/+45],
Transverse - 8790 - 8240 - 8240* -9210 - 8480 - 9660”
Tensile 35 170 37 260 33 880 36 100 34 860 35 450
Transverse - 17 360 - 19 160 - 16570 -18510 - 18700 - 17 770
Tensile 34 670 38 180 32350 36050 33 560 37 630
Transverse - 24 540* -24220* - 21890 -23560 - 22 860 -25 740*
- 8770 6.5
35 450 3.2
- 18010 5.3
35 410 6.5
- 23 800 5.7
* Estimated. Transverse strain (microstrain) 0
-1oaxl
-20000
0
10,000
moo0
3%~
4woo
Fibre direction strain (microstrain) Fig. 2.
Measured
strains at failure.
corresponding to steady increase in the strain was taken. Table 3 summarises the results, and they are plotted in Fig. 2. In most cases transverse strains were taken at the same instant as the longitudinal strains. Some transverse gauges broke slightly earlier than the longitudinal ones, and it was necessary to estimate the final strain. This was done by linear extrapolation based on the last transverse gauge reading. Checks on specimens where no premature gauge failure occurred showed that for the unidirectional specimens it was best to base the extrapolation on the transverse gauge on the compression surface. For the specimens with _+45” plies use of the longitudinal tensile strain readings was found to be more accurate.
4 INTERPRETATION OF RESULTS IN TERMS OF STRESSES The experimental results can be converted into stresses using the stress-strain equations.
Results based on the mean strains from Table 3 and the linear elastic properties from Table 1 are shown in Table 4, and plotted in Fig. 3. The calculated transverse compressive stresses are very high, in the most severe case even greater than the measured transverse compressive strength of the material of 199 MPa. This is explained by the significant non-linearity of the transverse stress-strain response, which should be taken into account. Based on data from Ref. 8, the following relations for the transverse compression secant modulus E2 (MPa) in terms of the stress c2 (MPa) were used: E,=17000+68(50+02)
02< -50
E,=l7000
022 -50
(1)
The response in the fibre direction is dominated by the fibres, and linear elasticity is a good assumption. Mean stresses calculated using (1) and the other properties from Table 1 are also shown in Table 4. These results for stresses at failure based on the non-linear calculations are plotted in Fig. 4.
5 DISCUSSION The results for the unidirectional specimens show that there are transverse tensile as well as longitudinal tensile stresses present at the centre of the tensile surface. The reason for this is restriction of anticlastic curvature due to the large deflections and the relatively wide specimen. The transverse stresses must go to zero at the edges, but vary across the width with a maximum at the centre where the strain gauges were located. The anticlastic curvature also causes a variation of fibre direction stress across the width due to the differences in distance
Tensilefailure of glass fibre-epoxy
625
Table 4. Average stresses at failure (MPa) Transverse
response
0 32
Linear
1674 35.2 1675 39.0
61 62
Non-linear
[W(
01 62
+
45/ - 45),],
[W( + 45/- 45)d + 451S
1521 - 122.7 1526 - 10.5 1
1492 - 214.7 1512 - 145.3
Transverse stress (MPa) 50
Transverse stress (MPa) 50
Tsai_Hill
\
,,.....
.
).....
,,,,.... .,”
MEW stress
/
...’
‘..
,,,,....
....
”
-200 t .~r._:-';'~~_-..______.____________-______.__ 1 ___I j
I
Best fit to data -
Best fit to data -
-250 0
-250 2nOO FTre
Fig. 3.
Comparison
direct~Ktress
0
2,~
&E)
of failure criteria, response.
linear
transverse
from the neutral axis at the centre and edge of the specimen. Large deflection finite element analysis indicated that the magnitude of this variation at failure would be about lo%, with the fibre direction tensile stresses being higher at the edges than at the centre. For the specimens with _+45” plies, greater non-uniformity would be expected, with a difference of up to 20%. The variation of both longitudinal and transverse stresses across the width of the specimen makes interpretation of the results more difficult. The higher fibre direction stresses may cause failure to initiate near the edges before at the centre. However, the gauges do accurately measure the strains at failure at the point on the specimen where they are attached. A comparison can therefore still be made between the different results, although possible effects due to different stress gradients cannot be excluded. Figure 2 shows that the fibre direction strains at failure are reasonably constant. A least squares fit based on the mean strains for each of the three cases is also shown. The range of transverse strains covered in quite high. There is some indication of a reduction in strain with increasing transverse compressive strain, but the effect is small. There is certainly no evidence to support a 45” cut off of the type implied by Hart Smith’s criterion.
Fig. 4.
Comparison
of failure criteria, verse response.
nonlinear
trans-
Results in terms of stresses at failure from the linear and non-linear analyses are shown in Figs 3 and 4. Least squares fit straight lines are also shown, and fit the data quite well. The maximum stress and Tsai-Hill failure envelopes are also plotted based on the transverse compressive strength of the material of 199 MPa and the point where the least squares fits cross the fibre direction stress axis. This point is virtually the same for both the linear and non-linear analyses. Figure 3 shows that the data lies between the two envelopes, but much closer to the maximum stress criterion. The same is true in Fig. 4 with the transverse stresses from the non-linear analysis, although the Tsai-Hill fit is improved. Whilst the parameters could be adjusted to make the Tsai-Hill criterion fit the data better, the implied large drop in fibre direction strength under high transverse compressive stresses is not supported by the experimental results. However, the Tsai-Hill criterion does have the advantage that it is conservative. The maximum strain criterion also fits the data reasonably well as can be seen in Fig. 2, although an experimental value for transverse compressive failure strain was not available for comparison. The appearance of the failed specimens was very similar in all the tests, with no change in
626
M. R. Whom
the failure mechanism at high transverse stresses. This is consistent with failure being controlled by the maximum fibre direction stress and supports the conclusion that interaction with transverse compressive stresses is not very significant. These results were based on bending tests. Different magnitudes of tensile failure strains would be expected under pure tension loading, but the trend for the effect of transverse compression should be similar. The results of this study are consistent with those of Sun & Quinn’ based on in-plane tests on off-axis laminates with adhesive films between the plies. They reported that the maximum stress and strain criteria gave a better fit than Tsai-Hill, although the former were slightly unconservative. The maximum stress criterion is therefore recommended for design purposes. It is simple to use, and the slight lack of conservatism can be rectified by using a reduced value of tensile strength.
6 CONCLUSIONS Flexural specimens with 0” surface plies failed in a similar manner irrespective of whether the subsequent plies were all o”, all +45” or some 0” followed by +45” interior plies. In all cases failure was by fibre direction tension, with similar appearance. Fibre direction tensile strains at failure showed only a small decrease in the presence of large transverse compressive strains and stresses from the k45” plies. There was no indication of a 45” cut off between fibre direction strain and transverse strain as implied by the Hart-Smith criterion in the tension-compression quadrant. It is concluded that transverse compressive stresses have a relatively small effect on fibre direction tensile strength. The Tsai-Hill criterion is conservative, but implies a large drop in strength under high
transverse compressive stresses which was not apparent in the tests. The maximum stress criterion provides a better fit to the experimental results, and is recommended for design purposes.
ACKNOWLEDGEMENTS This paper is based on work carried out by Andrew Daley and David Herranz-Elliott. The study was initiated following discussions with Dr C. Allen of Rolls Royce, and Mr C. West of Westland Helicopters, whose contribution is acknowledged.
REFERENCES 1. Hart Smith, L. J., A strain-based maximum-shear-stress failure criterion for fibrous composites. AIM paper 90-095&CP, presented at the AIAA Structures, Structural Dynamics and Materials Conf., Long Beach, 1990. 2. Swanson, S. R. & Nelson, M., Failure properties of carbon/epoxy laminates under tension-compression biaxial stress. In Proc. Japan-US. CCM-III, Tokyo, 1986, pp. 279-86. 3. Swanson, S. R. & Qian, Y., Multiaxial characterisation of T800/3900-2 carbon/epoxy composites. Comp. Sci. & Tech ., 43 (1992) 197-203. 4. Swanson, S. R., Strength design criteria for carbon/ epoxy pressure vessels. J. Spacecraf, 27 (1990) 522-6. 5. Wisnom, M. R., The relationship between flexural and tensile strength of unidirectional carbon fibre-epoxy. J. Comp. Mat., 26 (1992) 1173-80. 6. Whitney, J. M. & Knight, M., The relationship between tensile strength and flexure strength in fiber-reinforced composites. Experimental Mechanics, XXXVII pt 1, (1980) 211-16. 7. Wisnom, M. R., The effect of specimen size on the tlexnral strength of unidirectional carbon fibre-epoxy. Comp. Shuct., 18 (1991) 47-63. 8. Wisnom, M. R., The effect of fibre rotation in +45 tension tests on measured shear properties. Comp., 26 (1995) 25-32. 9. Sun, C. T. & Quinn, B. J., Evaluation of failure criteria using off-axis laminate specimens. In Proc. Am. Sot. C$_r_z5Tech. Conf., University of Delaware, 1994, pp.
The effect of transverse compressive stresses on tensile failure of glass fibre-epoxy Michael R. Wisnom Department of Aerospace Engineering Universityof Bristol, Brktol BS8 1 TR, UK
Four point bending tests were carried out on 32-ply glass fibre-epoxy specimens with 0” plies on the surface. Different combinations of 0” and +45” interior plies allowed the transverse stresses at the surface to be varied. All specimens failed by fibre tension, and the strength was relatively insensitive to transverse compressive strengths. The maximum stress failure criterion was found to provide a reasonable fit to the experimental data, and is recommended for design purposes.
own failure envelope in the area of the 45” cut-off.’ There is a need for further experimental evidence to help to resolve this controversy. The objective of the present study was to carry out a series of carefully controlled tests to assess the degree to which transverse compressive stresses influence the fibre direction tensile strength, and provide data for comparing the various failure criteria.
1 INTRODUCTION Knowledge of the strength of fibre reinforced composites under combined states of stress is important for the reliable design of composite structures. Many failure criteria have been proposed over the years. The most commonly used are the simple maximum stress or strain criteria, and interactive ones such as the Tsai-Hill and Tsai-Wu criteria. Despite the importance of the topic, there is still considerable disagreement about which criteria are best. The problems of carrying out satisfactory tests and the consequent paucity of good experimental data has made it difficult to resolve this issue. One particularly problematic area is in the tension-compression quadrant, concerning the effect of transverse compression stresses on fibre direction tensile strength. Hart Smith has proposed a strain based maximum shear stress failure criterion which implies a 45” cut off between longitudinal tensile strain and transverse compressive strain.’ Tests by Swanson and coworkers on laminated cylinders under internal pressure and axial compression have suggested that the maximum strain and maximum stress criteria give satisfactory results in the tension-compression quadrant.2-4 However, the results show considerable scatter, and Hart Smith states that the data in Ref. 2 gives good agreement with his
2 DESIGN OF TESTS Design of a good specimen to investigate the effect of transverse compressive stresses is a challenging task. Ideally there should be a uniform stress field with no stress concentrations and no components of stress present other than tension and transverse compression. As many factors as possible should be kept constant between different specimens to avoid other possible influences on the results apart from the transverse stresses. It was decided to use four point bending tests since these enable tensile failure to be obtained in an area with uniform loading and no significant stress concentrations. Direct tension tests are much more difficult because failure often occurs near the grips where there are stress concentrations and in-plane and interla621
M. R. Whom
622
minar shear and normal stresses arise. Previous work had shown that very good repeatability could be achieved with flexural tests, which is important in investigating effects which may not be all that large. Tensile failure under bending may give a higher strength than under pure tension due to the effect of the stress gradient,576 but on a comparative basis this is still valid provided the stress gradient remains the same. 0” plies were always placed on the surface where the maximum stress arises and where failure was expected to occur. In order to generate transverse compressive stresses, + 45” plies were introduced into the layup. By altering the ratio of +45” to 0” plies the amount of transverse stress could be varied. Another important factor was the avoidance of premature failure due to delamination at the free edge. Laminates with +45” plies have the advantage of not being particularly susceptible to this type of damage. Three different types of specimen were selected, all with the same total number of plies. This is important in order to keep the stress gradient the same for the same surface stress. The layups adopted were 032, [04/( +45/-45)6]s and [O/(+45/-45),/+45],. Laminated plate analysis was carried out using the properties for 60% volume fraction E glass/913 epoxy given in Table 1 and with a ply thickness of 0.127 mm. Pure bending was applied with moments to give a fibre direction stress of 1500 MPa in the surface ply, close to the expected tensile failure stress for the material. Results are given in Table 2 for the stresses at the centre of the surface 0” ply and at the centre of the outermost 45” ply. Stresses are in Table 1. Material properties for glass fibre-epoxy
Fibre direction modulus, E 1 Transverse modulus, Ez Poisson’s ratio, v12 Shear modulus, G12
43.9 GPa 15.4 GPa 0.29 4.34 GPa
the ply coordinate system, with g1 being the fibre direction stress, c2 the transverse stress and r12 the in-plane shear stress. It can be seen that the [O/(+45/-45)7/+45], layup generates a very substantial transverse compressive stress in the surface 0” ply, with the [04/( + 45/ -45)& layup producing an intermediate value. Fibre direction stresses in the outermost 45” plies are relatively low. There are high shear and transverse tensile stresses which could present a risk of transverse cracking in the 45” plies, but this is minimised by having only single adjacent plies with the same orientation. The layups with +45” plies are not balanced under bending due to the different positions of the + 45” and -45” relative to the neutral axis, and due to the extra +45” plies in the [O/(+45/-45),/+45], layup. This gives rise to a small amount of torsion which produces some shear stresses in the surface plies. However as can be seen in Table 2, the magnitudes of these stresses are very small, and they are not likely to have any significant influence on failure. It is important to keep the stressed volume the same between different specimens since there can be significant size effects on tensile strength in bending.7 This was achieved by using the same dimensions for all specimens. There could also be an effect due to the different number of 0” plies in each specimen. This would not be expected to be a large effect since failure should be mainly controlled by the surface ply where the stress is highest, and this is a 0” ply for all specimens. Calculations based on Weibull statistical strength theory confirmed this effect to be negligible. The centre span was selected to have a reasonably large volume subject to the maximum stress without the deflections becoming excessive. The outer span was sized to avoid the possibility of shear failure. The choice of width was a difficult compromise. A wide specimen is required to ensure
Table 2. Laminated plate theory stresses at centre of outer plies (MPa)
Outer 0” ply LayuP
0 [(c/C+45/-45)&
[O/(+45/-45)7/+45],
61
1500 1500 1500
02
-86q6 - 151.3
Outer 45” ply z12
01
-:.o -3.5
3G2 344.3
62
167 152.0
712
161.9 - 222.9
Tensilefailure of glass Jibre-epoxy
that the free edge region does not unduly affect the results. On the other hand a narrow specimen is necessary in order to reduce effects due to restriction of anticlastic curvature. A width of 20 mm was chosen, which was considered satisfactory in terms of minimising free edge effects. However, there were anticlastic curvature effects present, which will be discussed later. The radius of the loading and support noses was chosen to avoid local failure at the contact points. Figure 1 shows the final configuration chosen.
3 EXPERIMENTAL RESULTS
PROCEDURE
AND
Three panels were laid up from Ciba E glass/ 913 prepreg. All the prepreg was from the same batch, and the panels were cured according to the manufacturer‘s instructions using the same cure cycles. Specimens were cut out with a diaCombined longitudinal and mond saw. transverse strain gauges were attached to the centre of each surface of each specimen. Six specimens of each type were tested in a servo-hydraulic test machine. Fixed loading and support noses were used, with thin greased rubber pads placed between them and the specimens to redistribute loads at the contact points. Tests were carried out under displacement control at a nominal rate of 5 mm/min. Values of load, cross-head displacement and strain gauge readings were logged on a computer. All specimens failed in tension, with very similar appearance. Initially a few small bundles of fibres broke and split off from the tensile surface, followed by more extensive fibre fracture accompanied by splitting and delamination. Crosshead displacements at initiation of failure were about 26, 24 and 21 mm for the Oj2,
Fig. 1.
Test
623
and [O/( +45/-45)7/+45], [04/( +45/-45)& specimens respectively. Complete fracture did not occur, but failure propagated through the thickness with increasing deflection until the test was stopped because the displacements were excessive. Fibre fracture initiated near the centre of the span, with no apparent tendency for it to start closer to the loading noses. There were no indications of edge delamination preceding fibre failure for any of the specimens. For the 032 and [04/( + 45/- 45),], specimens no damage occurred on the compression side except for a few small splits apparently initiating from cut fibres at the edge. However, most of the [O/( + 45/ - 45)7/ + 451, specimens showed a small amount of splitting, delamination and fibre failure on the compression surface. The damage occurred in the centre span, away from the edges, presumably as a result of the high transverse tensile stresses induced in the 0” plies by the underlying +45” plies. On one specimen the damage was more extensive, and the overall appearance was very similar to that on the tension side. In all cases failure was predominantly on the tension surface, and the presence of some damage on the compression surface should not have had a significant influence on the tensile failure. Failure was taken as the strain at which the longitudinal strain gauge on the tension side broke. This normally occurred when a large area of fibres on the surface fractured, and therefore is a reasonably accurate measure of the tensile strain at failure. For three of the OS2 specimens this happened at or very close to the maximum load. However for the other three, and for all of the specimens with +45” plies the load reached a peak, started to drop and then gauge failure occurred. This suggests that tensile failure may have initiated away from the central area where the gauge was attached. In a few cases the strain gauge reading accelerated just before it stopped working. The last reading
dimensions (mm, not to scale).
M. R. Wisnom
624
Table 3. Strain gauge readings on tensile surface at failure (microstrain) 0 32
Tensile 34570 38 460 37 300 38 830 37 900 40 360 37 900 5.1
Mean C.V. (%)
[W(
+
49 - 45)&
LO/(+45/-45),/+45],
Transverse - 8790 - 8240 - 8240* -9210 - 8480 - 9660”
Tensile 35 170 37 260 33 880 36 100 34 860 35 450
Transverse - 17 360 - 19 160 - 16570 -18510 - 18700 - 17 770
Tensile 34 670 38 180 32350 36050 33 560 37 630
Transverse - 24 540* -24220* - 21890 -23560 - 22 860 -25 740*
- 8770 6.5
35 450 3.2
- 18010 5.3
35 410 6.5
- 23 800 5.7
* Estimated. Transverse strain (microstrain) 0
-1oaxl
-20000
0
10,000
moo0
3%~
4woo
Fibre direction strain (microstrain) Fig. 2.
Measured
strains at failure.
corresponding to steady increase in the strain was taken. Table 3 summarises the results, and they are plotted in Fig. 2. In most cases transverse strains were taken at the same instant as the longitudinal strains. Some transverse gauges broke slightly earlier than the longitudinal ones, and it was necessary to estimate the final strain. This was done by linear extrapolation based on the last transverse gauge reading. Checks on specimens where no premature gauge failure occurred showed that for the unidirectional specimens it was best to base the extrapolation on the transverse gauge on the compression surface. For the specimens with _+45” plies use of the longitudinal tensile strain readings was found to be more accurate.
4 INTERPRETATION OF RESULTS IN TERMS OF STRESSES The experimental results can be converted into stresses using the stress-strain equations.
Results based on the mean strains from Table 3 and the linear elastic properties from Table 1 are shown in Table 4, and plotted in Fig. 3. The calculated transverse compressive stresses are very high, in the most severe case even greater than the measured transverse compressive strength of the material of 199 MPa. This is explained by the significant non-linearity of the transverse stress-strain response, which should be taken into account. Based on data from Ref. 8, the following relations for the transverse compression secant modulus E2 (MPa) in terms of the stress c2 (MPa) were used: E,=17000+68(50+02)
02< -50
E,=l7000
022 -50
(1)
The response in the fibre direction is dominated by the fibres, and linear elasticity is a good assumption. Mean stresses calculated using (1) and the other properties from Table 1 are also shown in Table 4. These results for stresses at failure based on the non-linear calculations are plotted in Fig. 4.
5 DISCUSSION The results for the unidirectional specimens show that there are transverse tensile as well as longitudinal tensile stresses present at the centre of the tensile surface. The reason for this is restriction of anticlastic curvature due to the large deflections and the relatively wide specimen. The transverse stresses must go to zero at the edges, but vary across the width with a maximum at the centre where the strain gauges were located. The anticlastic curvature also causes a variation of fibre direction stress across the width due to the differences in distance
Tensilefailure of glass fibre-epoxy
625
Table 4. Average stresses at failure (MPa) Transverse
response
0 32
Linear
1674 35.2 1675 39.0
61 62
Non-linear
[W(
01 62
+
45/ - 45),],
[W( + 45/- 45)d + 451S
1521 - 122.7 1526 - 10.5 1
1492 - 214.7 1512 - 145.3
Transverse stress (MPa) 50
Transverse stress (MPa) 50
Tsai_Hill
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,,.....
.
).....
,,,,.... .,”
MEW stress
/
...’
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,,,,....
....
”
-200 t .~r._:-';'~~_-..______.____________-______.__ 1 ___I j
I
Best fit to data -
Best fit to data -
-250 0
-250 2nOO FTre
Fig. 3.
Comparison
direct~Ktress
0
2,~
&E)
of failure criteria, response.
linear
transverse
from the neutral axis at the centre and edge of the specimen. Large deflection finite element analysis indicated that the magnitude of this variation at failure would be about lo%, with the fibre direction tensile stresses being higher at the edges than at the centre. For the specimens with _+45” plies, greater non-uniformity would be expected, with a difference of up to 20%. The variation of both longitudinal and transverse stresses across the width of the specimen makes interpretation of the results more difficult. The higher fibre direction stresses may cause failure to initiate near the edges before at the centre. However, the gauges do accurately measure the strains at failure at the point on the specimen where they are attached. A comparison can therefore still be made between the different results, although possible effects due to different stress gradients cannot be excluded. Figure 2 shows that the fibre direction strains at failure are reasonably constant. A least squares fit based on the mean strains for each of the three cases is also shown. The range of transverse strains covered in quite high. There is some indication of a reduction in strain with increasing transverse compressive strain, but the effect is small. There is certainly no evidence to support a 45” cut off of the type implied by Hart Smith’s criterion.
Fig. 4.
Comparison
of failure criteria, verse response.
nonlinear
trans-
Results in terms of stresses at failure from the linear and non-linear analyses are shown in Figs 3 and 4. Least squares fit straight lines are also shown, and fit the data quite well. The maximum stress and Tsai-Hill failure envelopes are also plotted based on the transverse compressive strength of the material of 199 MPa and the point where the least squares fits cross the fibre direction stress axis. This point is virtually the same for both the linear and non-linear analyses. Figure 3 shows that the data lies between the two envelopes, but much closer to the maximum stress criterion. The same is true in Fig. 4 with the transverse stresses from the non-linear analysis, although the Tsai-Hill fit is improved. Whilst the parameters could be adjusted to make the Tsai-Hill criterion fit the data better, the implied large drop in fibre direction strength under high transverse compressive stresses is not supported by the experimental results. However, the Tsai-Hill criterion does have the advantage that it is conservative. The maximum strain criterion also fits the data reasonably well as can be seen in Fig. 2, although an experimental value for transverse compressive failure strain was not available for comparison. The appearance of the failed specimens was very similar in all the tests, with no change in
626
M. R. Whom
the failure mechanism at high transverse stresses. This is consistent with failure being controlled by the maximum fibre direction stress and supports the conclusion that interaction with transverse compressive stresses is not very significant. These results were based on bending tests. Different magnitudes of tensile failure strains would be expected under pure tension loading, but the trend for the effect of transverse compression should be similar. The results of this study are consistent with those of Sun & Quinn’ based on in-plane tests on off-axis laminates with adhesive films between the plies. They reported that the maximum stress and strain criteria gave a better fit than Tsai-Hill, although the former were slightly unconservative. The maximum stress criterion is therefore recommended for design purposes. It is simple to use, and the slight lack of conservatism can be rectified by using a reduced value of tensile strength.
6 CONCLUSIONS Flexural specimens with 0” surface plies failed in a similar manner irrespective of whether the subsequent plies were all o”, all +45” or some 0” followed by +45” interior plies. In all cases failure was by fibre direction tension, with similar appearance. Fibre direction tensile strains at failure showed only a small decrease in the presence of large transverse compressive strains and stresses from the k45” plies. There was no indication of a 45” cut off between fibre direction strain and transverse strain as implied by the Hart-Smith criterion in the tension-compression quadrant. It is concluded that transverse compressive stresses have a relatively small effect on fibre direction tensile strength. The Tsai-Hill criterion is conservative, but implies a large drop in strength under high
transverse compressive stresses which was not apparent in the tests. The maximum stress criterion provides a better fit to the experimental results, and is recommended for design purposes.
ACKNOWLEDGEMENTS This paper is based on work carried out by Andrew Daley and David Herranz-Elliott. The study was initiated following discussions with Dr C. Allen of Rolls Royce, and Mr C. West of Westland Helicopters, whose contribution is acknowledged.
REFERENCES 1. Hart Smith, L. J., A strain-based maximum-shear-stress failure criterion for fibrous composites. AIM paper 90-095&CP, presented at the AIAA Structures, Structural Dynamics and Materials Conf., Long Beach, 1990. 2. Swanson, S. R. & Nelson, M., Failure properties of carbon/epoxy laminates under tension-compression biaxial stress. In Proc. Japan-US. CCM-III, Tokyo, 1986, pp. 279-86. 3. Swanson, S. R. & Qian, Y., Multiaxial characterisation of T800/3900-2 carbon/epoxy composites. Comp. Sci. & Tech ., 43 (1992) 197-203. 4. Swanson, S. R., Strength design criteria for carbon/ epoxy pressure vessels. J. Spacecraf, 27 (1990) 522-6. 5. Wisnom, M. R., The relationship between flexural and tensile strength of unidirectional carbon fibre-epoxy. J. Comp. Mat., 26 (1992) 1173-80. 6. Whitney, J. M. & Knight, M., The relationship between tensile strength and flexure strength in fiber-reinforced composites. Experimental Mechanics, XXXVII pt 1, (1980) 211-16. 7. Wisnom, M. R., The effect of specimen size on the tlexnral strength of unidirectional carbon fibre-epoxy. Comp. Shuct., 18 (1991) 47-63. 8. Wisnom, M. R., The effect of fibre rotation in +45 tension tests on measured shear properties. Comp., 26 (1995) 25-32. 9. Sun, C. T. & Quinn, B. J., Evaluation of failure criteria using off-axis laminate specimens. In Proc. Am. Sot. C$_r_z5Tech. Conf., University of Delaware, 1994, pp.