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The effect of specimen size on the bending strength of unidirectional carbon fibre-epoxy
Composite Structures 1$ (1991) 47 -63
The Effect of Specimen Size on the Bending Strength of Unidirectional Carbon Fibre-Epoxy Michael R. Wisnom Department of Aerospace Engineering,Universityof Bristol, Bristol BS8 1TR, UK ABSTRACT Four-point bending and pinned-end buckling tests were carried out on scaled specimens of 25, 50 and 100 plies. Both types of test gave similar results and showed a significant decrease in strength with increasing specimen size. The smaller specimens tended to fail progressively in tension. The tensile strain to failure decreased by about 8% for each doubling of specimen size. This corresponds to a Weibull modulus of about 25. However the amount of scatter in the results was much smaller than that expected based on Weibull strength theory. The larger specimens tended to fail catastrophically in compression. This suggests a reduction in compressive strength with specimen size which may be even larger than the reduction in tensile strength.
1 INTRODUCTION It is well known that there is a tendency for the strength of fibrereinforced composites to decrease with increasing specimen size. This has major implications for the design of large composite structures. If design allowables are based on small coupon tests, as is usually done, then the strength of the full-scale structure may be significantly overestimated if the size effect is not taken into account. This problem is often ignored in design. It has been possible to do this because of the inherent conservatism of most composite design, with large reduction factors usually being applied to design allowables. Structures in safetycritical applications are invariably tested at full size anyway. Also even in large structures, the strength may be controlled by a local feature which causes a high stress in a relatively small volume of material. However, as it is attempted to develop more efficient composite structures and to predict their strength without the need for costly and time-consuming 47 Composite Structures 0263-8223/91/S03.50 © 1991 Elsevier Science Publishers Ltd, England. Printed in Great Britain
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M. R. Wisnom
tests, it becomes more important to understand the effect of specimen size on strength. Despite the importance of this subject there has been relatively little work done to quantify the effect. It is well documented that the strength of the basic glass and carbon fibres used in most composites decreases with increasing gauge length tested.l' 2 This is because the strength is controlled by the presence of flaws which are statistically distributed. Weibull strength theory may be applied to brittle materials such as these? It can be shown 4 that for geometrically identical specimens subject to identical stress distributions, the relationship between their strengths is given by:
(1) where $1 and S 2 a r e the mean strengths of the two specimens which may be expressed in terms of either stress or strain to failure, V1 and V2 are the volumes and m is the Weibull modulus, which is a measure of the variability of the material. A low Weibull modulus implies a high degree of material variability which will lead to a large amount of scatter in strengths of individual specimens and a large size effect. The modulus m can be related approximately to the coefficient of variation (c.v.) of specimen strengths through the expression: 4 m = l-2/c.v.
(2)
Weibull strength theory has been shown to apply satisfactorily to individual carbon fibres, 2 which are inherently brittle. However its application to carbon-fibre composites is less clear. Although they have some of the characteristics of brittle materials, they are able to withstand some damage without failing. Bullock found that Weibull theory satisfactorily predicts the higher tensile strength of impregnated tows compared with tensile coupons. 5 However Bader and Priest found that although the strength of impregnated tows of different lengths decreased with increasing length, they did not behave as ideal Weibull solids. 2 The size effect in full-size composite components and structures has received less attention. Kies demonstrated that the strength of glass-fibre pressure vessels decreases with increasing size up to a vessel with a mass of about 200 kg of glass. 6 However a consistent Weibull modulus covering all the results was not found. Hitchon and Phillips found a large difference in strength between relatively small carbon fibre-epoxy tensile specimens and much larger hoop burst specimens, but no significant difference between hoop burst specimens of different sizes?
Effect of specimen size on bending strength of carbon fibre-epoxy
49
Kretsis et al. presented data for the flexural strength of glass fibre-epoxy, carbon fibre-epoxy and hybrid specimens which shows a definite decrease in strength with increasing size. 7 However the specimens were relatively small, 1 mm and 2 mm thick, and it has been argued on theoretical grounds that the variability and hence the magnitude of the size effect decreases with increasing specimen size. 8 Little work appears to have been done on the effect of specimen size on compressive strength. The objective of this work was to provide further experimental data to estimate the magnitude of the size effect in carbon-fibre composites. In particular the trend of decreasing strength with increasing size found in small coupons was investigated to see whether it continues as the size of specimens is increased towards the size of real structural components. Bending tests were carried out on three sets of geometrically scaled unidirectional carbon fibre-epoxy specimens of 25, 50 and 100 plies thick. Although most composite structures are made of laminates with plies of different orientations, it is of fundamental importance to understand the behaviour of the basic unidirectional material from which the laminates are made. Also unidirectional material is used in certain important applications such as helicopter rotor blades. Bending tests are simple and can give very repeatable results which is important when trying to detect relatively small differences in strength. In addition bending is of interest as a major form of loading for helicopter rotor components. Surface strains at failure were used rather than stresses as a measure of strength because more consistent values can be obtained. It is difficult to calculate stresses accurately in bending tests. If simple bending theory is used, large errors can arise due to the effects of material non-linearity and large deflections.9 Also there are inevitably small variations in thickness and volume fraction of composite panels which can cause problems. Variations in thickness lead to errors in calculating stresses, whilst variations in volume fraction cause differences in tensile strength. Strains however can be measured simply and accurately with strain gauges, and do not need to be corrected for small changes in thickness or volume fraction. Initially four-point bending tests were carried out, with the specimens and rigs scaled as closely as possible. Using the same test methods for specimens of different size was important in trying to eliminate variability due to differences in the test procedures. The smaller two specimen sizes behaved satisfactorily with failure occurring in the middle, but the larger ones failed at the point of load application. In order to try to get round this a second series of tests was performed on
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M. R. Wisnom
the smallest and largest specimens. Pinned-end buckling tests were carried out, which again produced failures in bending, but with no stress concentrations in the area where failure occurred.
2 EXPERIMENTAL PROCEDURE
2.1 Four-point bending tests Three series of tests were carried out, with all linear dimensions scaled up by a factor of two between each series. A stiff steel fixture was used with fixed loading and support noses. In order to try to avoid failures at the point of loading whilst keeping the specimen reasonably short, the distance between the central loading noses was fixed at one-sixth of the distance between the outer support noses. The dimensions for the smallest specimens are shown in Fig. 1. Small pads of 1 mm-thick fabricreinforced rubber were greased and placed underneath the loading noses in order to distribute loads into the specimens and avoid local failures. Thicker sheets of the same rubber were not available and so two or four thicknesses of rubber were used for the larger specimens. The width of the support and loading noses was kept constant as it was not thought that this would have any influence on the results. All specimens were cut with a diamond wheel from plates of unidirectional 913/XAS carbon fibre-epoxy of 60% nominal volume fraction supplied by Westland Helicopters. 25, 50 and 100 plies were used, giving nominal thicknesses of 3.175, 6.35 and 12.7 mm. Care was taken during
~ 3.175
t
r5
zO 10 | !
50 102 t27
Fig. 1. Dimensions for four-point bending tests on small specimens (mm).
Effect of specimen size on bending strength of carbon fibre-epoxy
51
manufacture to try to achieve consistent thicknesses. Non-porous release layers were used to produce a smooth surface and avoid problems due to different amounts of resin being removed during curing. However there was still some variation in thickness with a maximum deviation of +0-1 m m from the nominal value of 3.175 mm for the 25-ply specimens. There was less thickness variation with the 50-ply specimens, the maximum variation being + 0.05 m m from the nominal thickness of 6"35 mm. The 100-ply specimens were all found to be significantly thicker than the nominal 12.7 mm. Mean thickness was 13.28 m m with a variation of about + 0.1 mm. This was because these plates were manufactured in an autoclave, whereas the thinner ones were pressed between rigid plates. The same cure cycles were used, except that the 100-ply panel was preheated to avoid problems due to exotherms. Strain gauges with 2-mm gauge length were attached to the centre of each specimen on the tension side. They were then loaded in an Avery Denison test machine under load control. Load was applied very slowly, each test taking approximately 10 min. The strain was monitored and the maximum value at failure recorded.
2.2 Buckling tests Two series of tests were carried out, corresponding to the smallest and largest specimens tested in four-point bending. Specimens were compressed between two fixtures with semicircular rollers to permit rotation of the ends. To allow smooth rotation the rollers were made with a slightly smaller radius than the seats in which they fitted and PTFE tape was laid between the two surfaces. The specimens were located in slots in the rollers which were designed to be a tight fit. To facilitate bending of the specimens the slots were positioned eccentrically such that in the unloaded position one surface of the specimen lay along the centre line of the rig. The specimens were the same dimensions and from the same plates as for the four-point bending tests. Strain gauges were attached at the centre of both sides of the specimens. Dimensions for the rig with the smaller specimens are shown in Fig. 2. For the tests on the larger specimens all dimensions on the test pieces and rig were scaled up by a factor of four except for the width of the rollers and seats, which for practical reasons were doubled. This was not thought likely to have any significant effect, although it would increase the contact pressure between the rollers and seats and might make sticking more likely. A problem was encountered with the large specimens because it was found that they would not fit in the test machine. It was therefore necessary to cut 25 m m from them.
M. R. Wisnom
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3.!75
Fig. 2.
~-7
Dimensions for buckling tests on small specimens (mm).
This reduced their length from 508 to 483 m m and meant they were not exactly scaled. This was unfortunate, but it was thought that with careful interpretation the tests could still yield useful results. Tests were carried out in an Avery Denison machine under load control. Early tests showed a tendency for the specimens to delaminate from the ends if loaded too quickly and so the tests were performed very slowly, taking about 10 min for the smaller ones and 30 min for the larger specimens. Loads and strains as a function of time were recorded by a computer data-logging system.
3 RESULTS
3.1 Four-point bending tests
3.1.1 25-ply specimens Ten specimens were tested. In most cases fibre breaks could be heard well before final failure. Sometimes no damage could be seen at this
Effect of specimen size on bending strength of carbon fibre-epoxy
53
stage, but frequently small bundles of fibres were seen to split off from the specimens, usually starting at the edges. As the load was increased, more bundles failed until finally the whole specimen failed as a collection of split bundles with a brush like appearance. There was quite a significant variation in the way the failures initiated. On one test there was no apparent fibre breakage at all until a large number of fibres broke together, whilst on other tests failure of the surface fibres occurred gradually over a range of strains. However, once a large number of surface fibres were broken the failure propagated stably through the thickness, with more and more bundles of fibres failing, and the load steadily falling off. It proved impossible to actually break the specimens. They continued failing until the intact section was very thin and flexible and deflections were so large that the specimen touched the bottom of the rig. Figure 3 shows one of the specimens in the rig at quite an advanced stage in the failure. The failure consists of a whole mass of bundles which have each failed in tension and split off from the rest of the specimen. The splitting has continued almost as far as the outer support noses. The bundles are generally one ply thick, and around 1 m m wide at the ends. Most of the bundles have failed along lines at a small angle to the fibre direction to produce two sharp spears. It is the mass of these overlapping
Fig. 3.
25-Plyfour-point bending specimenunder load.
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M. R. Wisnom
spears which gives the specimen its brush-like appearance. In most cases no evidence of any damage could be seen on the compression surface. However some specimens did show initiation of failure on the compression side with very similar appearance to the tension failures. Small bundles of fibres split off from the edge of the specimen to form sharp spikes. Three of the specimens failed in a different way. Initially some bundles failed in tension, but then there was a sudden catastrophic failure. In two cases this occurred at one of the loading noses, but in the third case it failed close to the centre of the specimen. Failure appeared to have initiated on the compression side and propagated across most of the depth of the specimen as a single fracture surface. The compressive fracture surfaces had a smooth, matt appearance. Final failure at the other surface of the specimen still occurred in tension, but without the extensive splitting seen on other tests. Some splitting however initiated from the compressive failure region, both across the width and through the thickness of the specimen. Table 1 shows the strains at which fibre breaks were heard, when fibre bundles first split off and the maximum strain. This is in fact the strain at which the gauge broke, but since this normally occurred when a large
TABLE 1
Results for Four-Point BendingTests with 25-Ply Specimens Specimen no.
2 3 4 5 6 8 9 10 19 20
Strains on tension side (microstrain) First audible fibre break
First visible fibre bundle split off
Maximum
14 820 14 360 14 040 14 900 14 560 9 500 -18 500 17 350 16 340
14 920 14 930 15 810 16 120 15 810 14 310 < 16 650 18 500 17 350 16 570
19 360 17 140 19 360 17 570 18 150 18 620 18 980 18 500 17 690 18 080
Mean strain (brush failures only)
18 480
Coefficientof variation
3.07%
Mean strain (compressionfailures only)
18 020
Failure mode
Compression Compression Brush Compression Brush Brush Brush Brush Brush Brush
Effect of specimen size on bending strength of carbon fibre-epoxy
55
number of fibres had failed, it is considered to be a reasonable estimate of the ultimate failure strain. Although there are fairly large variations in the strains at which fibre breaks were heard or seen, the results for final failure of the specimens failing in a brush mode are quite consistent, with a mean maximum strain of 1 8 4 8 0 microstrain and a coefficient of variation of 3.07%.
3.1.2 50-ply specimens Eleven specimens were tested and they behaved very similarly to the previous set. Fibre breaks were heard and seen well before ultimate failure in most cases, as before, and in most cases final failure occurred in a brush-like mode. The individual failed bundles were of similar size to those in the previous tests, with a thickness normally equal to one ply. The bundles split into overlapping spears at a similar angle to the fibre direction as before, but with bundles around 2 mm wide at their ends. Several specimens had fibre bundles split off on the compression side as well. Two specimens failed at the loading noses with a compressive failure very similar to that seen on some of the smaller specimens. A third specimen started to fail in tension and then failed suddenly at the loading nose. Table 2 summarises the results. Since the results were so similar to the previous set, only maximum strains are presented. The mean value of TABLE 2 Results for Four-Point Bending Tests with 50-Ply Specimens
Specimen no.
Maximum tensile strain (microstrain)
Failure mode
2 3 5 6 7 8 9 10 11 12 13
17 110 15 980 17 100 16 810 17 550 16 970 15 660 16 550 16 660 17 200 17 310
Brush Compression Brush Brush then compression Brush Brush Compression Brush Brush Brush Brush
Mean st rain
17 030
(Brush failures only)
Coefficient of variation
1'87%
Mean strain
16 150
(Compression failures only)
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M. R. Wisnom
maximum strain is 17 030 microstrain. Results are very consistent, with a coefficient of variation of only 1.87%.
3.1.3 lO0-plyspecimens Five of the specimens failed in compression at the loading nose. After three such failures some different materials were tried under the loading noses to try to redistribute the loads better. High-strength polyurethane rubber and PTFE were used, but did not appear to make any difference. Only one specimen failed in tension in a brush mode, and this finally failed in compression as well. The appearance of the failures was similar to the previous specimens. During the last test a loud noise was heard at a very low strain and the test was stopped. A crack a few minimetres long was visible running across the specimen underneath one of the loading noses. Some delamination occurred on the compression side between the loading noses on two of the specimens. Strips of around 1 mm wide which appeared to be 1-ply thick split away. However, they did not break, but buckled to form loops with quite a large separation from the rest of the specimen. Maximum recorded strains are presented in Table 3.
3.2 Buckling tests
3.2.1 25-plyspecimens Six specimens were tested. Initially they bent gradually with the ends rotating smoothly as the load was increased. As the buckling load was approached, deflections increased rapidly whilst the load steadied to an approximately constant value. Five of the specimens failed in a brushTABLE 3 Results for Four-Point Bending Tests with 100-Ply Specimens Specimen no.
Maximum tensile strain (microstrain)
Failure mode
1 2 3 4 5 6
13 680 15 820 12 500 12 000 13 470 7 800
Compression Brush, then compression Compression Compression Compression Cracked only
Mean strain (excluding no. 6)
13 490
Coefficient of variation
10.9%
Effect of specimen size on bending strength of carbon fibre-epoxy
57
type failure very similar to that seen in the four-point bending tests. Bundles of fibres split off along almost the whole length of the specimens. Some fibres split off on the compression sides. One specimen failed suddenly in compression, but only after the brush failure was well advanced. One specimen delaminated along its whole length before reaching the maximum strain and so this result was discarded. Table 4 shows the maximum recorded tensile strains. The mean value is 19 120 microstrain, with a very low coefficient of variation of 0-64%. Strains from both the tension and compression surface were logged onto the computer. The compression gauges continued to record after the tension gauges had failed. In some cases the maximum tensile strain corresponded to the point when there was a large drop in the compressive strain. Where this was the maximum compressive strain recorded the tensile strain corresponds to the true maximum. However in other tests higher values of compressive strain were subsequently attained, 500 microstrain higher in one case. The maximum tensile strain may therefore have been underestimated for these specimens. In other cases there was a very rapid rise in tensile strain after the first large drop in compressive strain by up to 500 microstrain in one case. This was probably caused by the tensile gauge continuing to read after failure had initiated, and so these results may be overestimates of the true maximum tensile strains. In a series of tests these effects will tend to cancel out and it is believed that the mean of the maximum recorded tensile strains is a reasonable estimate of the true maximum. There is an error band on individual results of up to approximately + 500 microstrain, and so the very low coefficient of variation recorded in this series of tests is probably fortuitous.
TABLE4 Results~rBuc~ingTestswith25-PlySpecimens
Specimen no.
Maximum tensile strain (microstrain)
Failure mode
1 2 3 4 5
19320 19090 19000 19 050 19 120
Brush Brush Brush, then compression Brush Brush
Mean
19 120
Coefficientofvariation
0.64%
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M. R. Wisnom
3.2.2 lO0-plyspecimens Six specimens were tested and they again behaved very similarly to the four-point bending tests. One specimen started to fail in tension in a brush-type mode but finally failed suddenly in compression. A second specimen also started to fail in tension, but before many fibre bundles had split off it failed in compression. The remaining specimens all failed suddenly in compression, with some bundles of fibres delaminating on the compression side to form unbroken loops. The catastrophic compression failures occurred approximately in the centre of the specimens, and had similar appearance to the four-point bending failures. Table 5 shows the maximum tensile strains obtained.
4 DISCUSSION The 25-ply and 50-ply thick four-point bending specimens mostly failed in tension despite the fact that the tensile strength of unidirectional X.AS/ 913 is generally believed to be almost twice the compressive strength. This may be due to the material having a higher compressive strength than that normally attributed to it. For example it has been shown that in the commonly used indirect compression tests the presence of large shear stresses can be expected to reduce significantly the measured compressive strength. 1° Non-linear material response may also be a factor. The compressive modulus of carbon fibre-epoxy decreases with strain whilst the tensile modulus increases. This can result in much lower
TABLE 5
Results for Buckling Tests with 100-Ply Specimens Specimen no.
Maximum tensile strain (microstrain)
Failure mode
2
15 550
3 4 5 6 7
15090 16 510 11 020 11320 11480
Few bundles in tension, then compression Compression Brush, then compression Compression Compression Compression
Mean strain
13500
Coefficient ofvariation
18"4%
Effect of specimen size on bending strength of carbon fibre-epoxy
59
stresses on the compression side of the specimen than on the tension side during pure bending. 9 Table 6 shows the relative magnitude of the tensile strains at failure for the three sets of tests including only the tensile failures. It should be noted that there is no overlap between the ranges of tensile strains for the three specimen sizes. The first two series of tests provide a good set of results to assess the effect of specimen size on bending strength controlled by tensile failure. The failure modes are very similar. The results are very consistent, as shown by the low coefficients of variation, and the number of tests provides a reasonable sample size. However the third set produced only one tensile failure and so this result must be treated with caution. The ratio of mean strains for the 25- and 50-ply cases is 1.085, a statistically significant difference. Based on Weibull strength theory using eqn (1) and the volume ratio of 8 between the two specimens gives a Weibull exponent of 25-4. This is typical of values quoted elsewhere for carbon fibre-epoxy, t~ The ratio between the mean strain for the 50-ply case and the single 100-ply result is 1-076. Since the volume ratio based on nominal thickness is also 8 for this case, the expected ratio of strains to failure is the same as the previous case, i.e. 1.085. Although the ratio of 1.076 is based on only one failure it is very close to the previous result of 1.085 and so does provide further support for the magnitude of the size effect. There is no indication of a reduction in the size effect with increasing specimen size. However if the material has a Weibull modulus of 25.4, significant scatter would be expected in the measured strains to failure. Based on the approximate eqn (2), a coefficient of variation due to material variability alone of about 4.7% would be expected. The actual coefficients of variation are considerably smaller. This inconsistency with Weibull strength theory has been further investigated and is reported on separately) 2
TABLE 6 Size Effect on Tensile Failure in Four-Point Bending Tests
Specimen thickness 25 plies 50 plies 100 plies
Mean tensile s t r a i n (microstrain) 18 480 17 030 15 820
Coefficient of variation
Number of specimens
3-07% 1.87% --
7 9 1
M. R. Wisnom
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The predominantly compressive failure modes of the 100-ply specimens were initially unexpected. There was some concern that this might be due to a difference in the material. The only significant difference in the manufacturing process was the use of an autoclave to cure the thick specimens whilst the others were pressed between plates. However C-scan and X-ray testing of the thick plate had indicated satisfactory quality and a polished section had not shown any significant voidage. The thicker plate may have had a slightly lower volume fraction in view of its greater nominal thickness, but this is not thought likely to be a major factor. Table 7 shows the strains to failure of the specimens of each size which failed in compression. The values are actually tensile strains as the compressive strains were not measured. The trend of decreasing strain to failure with increasing size can also be seen between the 25- and 50-ply specimens. Since the processing of these specimens was identical, it suggests that this is a real material effect rather than an effect due to differences in the manufacturing process. The compressive failures were catastrophic events typical of a brittle material. Weibull strength theory might therefore be expected to apply to these failures. The compressive strains at failure can be taken as approximately proportional to the measured tensile strains. The coefficient of variation for the five 100-ply thick four-point bending compressive failures is 10"9%. Using eqn (2) this corresponds approximately to a Weibull modulus m of 11. The expected ratio of failure strains for a volume ratio of 8 and m = 11 from eqn (1) is 1.21. The mean failure strain for the 100-ply specimens is 13490 microstrain, and so the expected strains for 50- and 25-ply specimens would be 16 320 and 19750 microstrain. These values are of the same order as measured failure strains for the specimens failing in compression. The average strains for the 50- and 25-ply specimens were 16 150 and 18 020 microstrain, respectively. These calculations are only approximate. The Weibull modulus was based on the coefficient of variation of the 1()0-ply
TABLE 7
Size Effect on Compressive Failure in Four-Point Bending
Specimen thickness
Mean tensile strain (microstrain)
Number of specimens
25 plies 50 plies 100 plies
18 020 16 150 13 490
3 3 5
Effect of specimen size on bending strength of carbon fibre-epoxy
61
specimens. The values for the 25- and 50-ply specimen compressive failures were lower, although there were only three failures in each case. On the other hand, the 100-ply buckling tests showed a higher coefficient of variation. Nevertheless the results do show an interesting trend. Despite the uncertainties and the relatively small amount of data, it would appear that there is a size effect operating on compressive strength, but with a smaller Weibull modulus than for tensile strength. As the specimen size increases, both the compressive and tensile strains to failure decrease, but the latter more slowly than the former. Therefore for small specimens tensile failure is more likely to be critical, whereas for larger specimens compressive failure may predominate. It also appears that for compressive failure the magnitude of the size effect may be consistent with the scatter in the experimental results due to material variability whereas for tensile failure it is definitely not. This is reasonable since compressive failure is a sudden catastrophic event which might be expected to conform to Weibull strength theory. Tensile failure on the other hand is a non-catastrophic event, with the failure propagating gradually through the specimen. It is perhaps not surprising that this does not conform to a theory intended for brittle materials. The results of the buckling tests broadly confirm the four-point bending results. Due to the necessity of slightly shortening the larger specimens to get them in the rig the ratio of lengths was 3-8 rather than 4 and so the specimens were not exactly scaled. However, since the results are in fact very similar to the bending results, they do provide further support to the conclusions already drawn. Unfortunately only one 100-ply specimen failed in tension. The ratio of this strain to the mean of the smaller specimens is 1"158. Based on the actual length and width ratios and the nominal thickness ratio and using eqn (1) gives a Weibull exponent of 28.0. This is close to the value of 25.4 calculated from the more complete set of four-point bending tests. It was expected that the buckling tests should be less susceptible to compressive failures because of the absence of the stress concentrations at the loading noses present in the bending tests. Whilst this was true for the smaller specimens, it was not the case for the larger specimens which all failed in compression. The mean tensile strain for the 100-ply compressive failures was 13 500 microstrain, very close to the value of 13 490 for the four-point bending tests. This suggests that it is primarily the stresses due to overall bending that are responsible for the compressive failure rather than the local stresses at the loading noses. Another interesting observation in these tests was the non-catastrophic splitting off of fibre bundles from the compression surface of both four-point bending and buckling specimens. This occurred at much
62
M. R. Wisnom
lower strains in the largest specimens than in the others. It may be because the higher ratio of length or radius of curvature to ply thickness made it easier for a section of one ply to delaminate and buckle. At these lower strains fibre breakage did not occur and so the loops remained unbroken. With the smaller specimens delamination occurred at higher strains where it was accompanied by fibre failures leading to splitting off of individual spears.
5 CONCLUSIONS There is a significant size effect in the bending strength of unidirectional XAS/913 carbon fibre-epoxy. Tests were carried out on geometrically scaled specimens of 25, 50 and 100 plies. The 25- and 50-ply specimens failed mainly in tension despite the material supposedly having a much higher tensile strength than compressive strength. The failure was a gradual splitting-off of individual bundles of fibres, leading to a brushlike appearance for the failed specimens. The tensile strain to failure decreased by about 8% for each doubling of linear specimen dimensions. This corresponds to a Weibull modulus of about 25. However the coefficients of variation were consistently found to be much lower than those expected based on Weibull strength theory. Similar behaviour was found in both four-point bending and buckling tests. The 100-ply specimens failed mainly in compression. The failures were sudden catastrophic events starting at the loading noses in the fourpoint bending specimens or near the centre of the buckling specimens. A few of the smaller specimens also failed in compression, although at much higher strains. This suggests a size effect with a significant decrease in compressive strength as the specimen becomes larger. The magnitude of this effect may be even greater than the size effect in tensile strength. The decrease in strength with increasing size appears to continue undiminished even at the moderately sized specimens tested in this study. This confirms the need for caution in applying design allowables derived from small scale tests to large carbon-fibre structures.
ACKNOWLEDGEMENT The author would like to thank the UK Science and Engineering Research Council and Westland Helicopters for supporting this work, and Michael Jones and Barry Lewis for assistance with the experimental work. The buckling rig was developed by Barry Lewis and Vincent Shin.
Effect of specimen size on bendingstrength of carbonfibre-epoxy
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REFERENCES 1. Metcalfe, A. G. & Schmitz, G. K., Effect of length on the strength of glass fibres. American Society for Testing Materials, Preprint 87, 1964. 2. Bader, M. G. & Priest, A. M., Statistical aspects of fibre and bundle strength in hybrid composites. Proceedings of the 4th International Conference on Composite Materials, (ICCM-IV) Tokyo, 1982, pp. 1129-36. 3. Weibull, W., A statistical distribution function of wide applicability. J. Applied Mechanics, 18 ( 1951 ) 293. 4. Hitchon, J. W. & Phillips, D. C., The effect of specimen size on the strength of cfrp. Composites, 9 (1978) 119-24. 5. Bullock, R. E., Strength ratios of composite materials in flexure and in tension. J. Composite Materials, 8 (1974) 200-6. 6. Kies, J. A., The strength of glass fibers and failure of filament wound pressure vessels. NRL Report No. 6034, US Naval Research Laboratory, Washington, 1964. 7. Kretsis, G., Matthews, F. L., Morton, J. & Davies, G. A. O., Flexural behaviour of unidirectional glass-carbon hybrid laminates, Proceedings of the InternatiOnal Symposium on Composites, Patras, Greece, 1986, pp. 421-32. 8. Batdorf, S. B. & Ghaffarian, R., Size effect and strength variability of unidirectional composites. Int. J. Fracture, 26 (1984) 113-22. 9. Wisnom, M. R., Limitations of linear elastic bending theory applied to four point bending of unidirectional carbon fibre/epoxy. Proceedings of the AIAA Structures, Structural Dynamics and Materials Conference, Long Beach, 1990, pp. 740-7. 10. Wisnom, M. R., The effect of shear stresses in indirect compression tests of unidirectional carbon fibre/epoxy. AIAA J., (to be published). 11. Whitney, J. M., Daniel, I. M. & Pipes, R. B., Experimental Mechanics of Fiber Reinforced Composite Materials, revised edn. SEM, 1984, p. 171. 12. Wisnom, M. R., The relationship between strength variability and size effect in unidirectional carbon fibre-epoxy. Composites, to be published.
The Effect of Specimen Size on the Bending Strength of Unidirectional Carbon Fibre-Epoxy Michael R. Wisnom Department of Aerospace Engineering,Universityof Bristol, Bristol BS8 1TR, UK ABSTRACT Four-point bending and pinned-end buckling tests were carried out on scaled specimens of 25, 50 and 100 plies. Both types of test gave similar results and showed a significant decrease in strength with increasing specimen size. The smaller specimens tended to fail progressively in tension. The tensile strain to failure decreased by about 8% for each doubling of specimen size. This corresponds to a Weibull modulus of about 25. However the amount of scatter in the results was much smaller than that expected based on Weibull strength theory. The larger specimens tended to fail catastrophically in compression. This suggests a reduction in compressive strength with specimen size which may be even larger than the reduction in tensile strength.
1 INTRODUCTION It is well known that there is a tendency for the strength of fibrereinforced composites to decrease with increasing specimen size. This has major implications for the design of large composite structures. If design allowables are based on small coupon tests, as is usually done, then the strength of the full-scale structure may be significantly overestimated if the size effect is not taken into account. This problem is often ignored in design. It has been possible to do this because of the inherent conservatism of most composite design, with large reduction factors usually being applied to design allowables. Structures in safetycritical applications are invariably tested at full size anyway. Also even in large structures, the strength may be controlled by a local feature which causes a high stress in a relatively small volume of material. However, as it is attempted to develop more efficient composite structures and to predict their strength without the need for costly and time-consuming 47 Composite Structures 0263-8223/91/S03.50 © 1991 Elsevier Science Publishers Ltd, England. Printed in Great Britain
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tests, it becomes more important to understand the effect of specimen size on strength. Despite the importance of this subject there has been relatively little work done to quantify the effect. It is well documented that the strength of the basic glass and carbon fibres used in most composites decreases with increasing gauge length tested.l' 2 This is because the strength is controlled by the presence of flaws which are statistically distributed. Weibull strength theory may be applied to brittle materials such as these? It can be shown 4 that for geometrically identical specimens subject to identical stress distributions, the relationship between their strengths is given by:
(1) where $1 and S 2 a r e the mean strengths of the two specimens which may be expressed in terms of either stress or strain to failure, V1 and V2 are the volumes and m is the Weibull modulus, which is a measure of the variability of the material. A low Weibull modulus implies a high degree of material variability which will lead to a large amount of scatter in strengths of individual specimens and a large size effect. The modulus m can be related approximately to the coefficient of variation (c.v.) of specimen strengths through the expression: 4 m = l-2/c.v.
(2)
Weibull strength theory has been shown to apply satisfactorily to individual carbon fibres, 2 which are inherently brittle. However its application to carbon-fibre composites is less clear. Although they have some of the characteristics of brittle materials, they are able to withstand some damage without failing. Bullock found that Weibull theory satisfactorily predicts the higher tensile strength of impregnated tows compared with tensile coupons. 5 However Bader and Priest found that although the strength of impregnated tows of different lengths decreased with increasing length, they did not behave as ideal Weibull solids. 2 The size effect in full-size composite components and structures has received less attention. Kies demonstrated that the strength of glass-fibre pressure vessels decreases with increasing size up to a vessel with a mass of about 200 kg of glass. 6 However a consistent Weibull modulus covering all the results was not found. Hitchon and Phillips found a large difference in strength between relatively small carbon fibre-epoxy tensile specimens and much larger hoop burst specimens, but no significant difference between hoop burst specimens of different sizes?
Effect of specimen size on bending strength of carbon fibre-epoxy
49
Kretsis et al. presented data for the flexural strength of glass fibre-epoxy, carbon fibre-epoxy and hybrid specimens which shows a definite decrease in strength with increasing size. 7 However the specimens were relatively small, 1 mm and 2 mm thick, and it has been argued on theoretical grounds that the variability and hence the magnitude of the size effect decreases with increasing specimen size. 8 Little work appears to have been done on the effect of specimen size on compressive strength. The objective of this work was to provide further experimental data to estimate the magnitude of the size effect in carbon-fibre composites. In particular the trend of decreasing strength with increasing size found in small coupons was investigated to see whether it continues as the size of specimens is increased towards the size of real structural components. Bending tests were carried out on three sets of geometrically scaled unidirectional carbon fibre-epoxy specimens of 25, 50 and 100 plies thick. Although most composite structures are made of laminates with plies of different orientations, it is of fundamental importance to understand the behaviour of the basic unidirectional material from which the laminates are made. Also unidirectional material is used in certain important applications such as helicopter rotor blades. Bending tests are simple and can give very repeatable results which is important when trying to detect relatively small differences in strength. In addition bending is of interest as a major form of loading for helicopter rotor components. Surface strains at failure were used rather than stresses as a measure of strength because more consistent values can be obtained. It is difficult to calculate stresses accurately in bending tests. If simple bending theory is used, large errors can arise due to the effects of material non-linearity and large deflections.9 Also there are inevitably small variations in thickness and volume fraction of composite panels which can cause problems. Variations in thickness lead to errors in calculating stresses, whilst variations in volume fraction cause differences in tensile strength. Strains however can be measured simply and accurately with strain gauges, and do not need to be corrected for small changes in thickness or volume fraction. Initially four-point bending tests were carried out, with the specimens and rigs scaled as closely as possible. Using the same test methods for specimens of different size was important in trying to eliminate variability due to differences in the test procedures. The smaller two specimen sizes behaved satisfactorily with failure occurring in the middle, but the larger ones failed at the point of load application. In order to try to get round this a second series of tests was performed on
50
M. R. Wisnom
the smallest and largest specimens. Pinned-end buckling tests were carried out, which again produced failures in bending, but with no stress concentrations in the area where failure occurred.
2 EXPERIMENTAL PROCEDURE
2.1 Four-point bending tests Three series of tests were carried out, with all linear dimensions scaled up by a factor of two between each series. A stiff steel fixture was used with fixed loading and support noses. In order to try to avoid failures at the point of loading whilst keeping the specimen reasonably short, the distance between the central loading noses was fixed at one-sixth of the distance between the outer support noses. The dimensions for the smallest specimens are shown in Fig. 1. Small pads of 1 mm-thick fabricreinforced rubber were greased and placed underneath the loading noses in order to distribute loads into the specimens and avoid local failures. Thicker sheets of the same rubber were not available and so two or four thicknesses of rubber were used for the larger specimens. The width of the support and loading noses was kept constant as it was not thought that this would have any influence on the results. All specimens were cut with a diamond wheel from plates of unidirectional 913/XAS carbon fibre-epoxy of 60% nominal volume fraction supplied by Westland Helicopters. 25, 50 and 100 plies were used, giving nominal thicknesses of 3.175, 6.35 and 12.7 mm. Care was taken during
~ 3.175
t
r5
zO 10 | !
50 102 t27
Fig. 1. Dimensions for four-point bending tests on small specimens (mm).
Effect of specimen size on bending strength of carbon fibre-epoxy
51
manufacture to try to achieve consistent thicknesses. Non-porous release layers were used to produce a smooth surface and avoid problems due to different amounts of resin being removed during curing. However there was still some variation in thickness with a maximum deviation of +0-1 m m from the nominal value of 3.175 mm for the 25-ply specimens. There was less thickness variation with the 50-ply specimens, the maximum variation being + 0.05 m m from the nominal thickness of 6"35 mm. The 100-ply specimens were all found to be significantly thicker than the nominal 12.7 mm. Mean thickness was 13.28 m m with a variation of about + 0.1 mm. This was because these plates were manufactured in an autoclave, whereas the thinner ones were pressed between rigid plates. The same cure cycles were used, except that the 100-ply panel was preheated to avoid problems due to exotherms. Strain gauges with 2-mm gauge length were attached to the centre of each specimen on the tension side. They were then loaded in an Avery Denison test machine under load control. Load was applied very slowly, each test taking approximately 10 min. The strain was monitored and the maximum value at failure recorded.
2.2 Buckling tests Two series of tests were carried out, corresponding to the smallest and largest specimens tested in four-point bending. Specimens were compressed between two fixtures with semicircular rollers to permit rotation of the ends. To allow smooth rotation the rollers were made with a slightly smaller radius than the seats in which they fitted and PTFE tape was laid between the two surfaces. The specimens were located in slots in the rollers which were designed to be a tight fit. To facilitate bending of the specimens the slots were positioned eccentrically such that in the unloaded position one surface of the specimen lay along the centre line of the rig. The specimens were the same dimensions and from the same plates as for the four-point bending tests. Strain gauges were attached at the centre of both sides of the specimens. Dimensions for the rig with the smaller specimens are shown in Fig. 2. For the tests on the larger specimens all dimensions on the test pieces and rig were scaled up by a factor of four except for the width of the rollers and seats, which for practical reasons were doubled. This was not thought likely to have any significant effect, although it would increase the contact pressure between the rollers and seats and might make sticking more likely. A problem was encountered with the large specimens because it was found that they would not fit in the test machine. It was therefore necessary to cut 25 m m from them.
M. R. Wisnom
52
3.!75
Fig. 2.
~-7
Dimensions for buckling tests on small specimens (mm).
This reduced their length from 508 to 483 m m and meant they were not exactly scaled. This was unfortunate, but it was thought that with careful interpretation the tests could still yield useful results. Tests were carried out in an Avery Denison machine under load control. Early tests showed a tendency for the specimens to delaminate from the ends if loaded too quickly and so the tests were performed very slowly, taking about 10 min for the smaller ones and 30 min for the larger specimens. Loads and strains as a function of time were recorded by a computer data-logging system.
3 RESULTS
3.1 Four-point bending tests
3.1.1 25-ply specimens Ten specimens were tested. In most cases fibre breaks could be heard well before final failure. Sometimes no damage could be seen at this
Effect of specimen size on bending strength of carbon fibre-epoxy
53
stage, but frequently small bundles of fibres were seen to split off from the specimens, usually starting at the edges. As the load was increased, more bundles failed until finally the whole specimen failed as a collection of split bundles with a brush like appearance. There was quite a significant variation in the way the failures initiated. On one test there was no apparent fibre breakage at all until a large number of fibres broke together, whilst on other tests failure of the surface fibres occurred gradually over a range of strains. However, once a large number of surface fibres were broken the failure propagated stably through the thickness, with more and more bundles of fibres failing, and the load steadily falling off. It proved impossible to actually break the specimens. They continued failing until the intact section was very thin and flexible and deflections were so large that the specimen touched the bottom of the rig. Figure 3 shows one of the specimens in the rig at quite an advanced stage in the failure. The failure consists of a whole mass of bundles which have each failed in tension and split off from the rest of the specimen. The splitting has continued almost as far as the outer support noses. The bundles are generally one ply thick, and around 1 m m wide at the ends. Most of the bundles have failed along lines at a small angle to the fibre direction to produce two sharp spears. It is the mass of these overlapping
Fig. 3.
25-Plyfour-point bending specimenunder load.
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M. R. Wisnom
spears which gives the specimen its brush-like appearance. In most cases no evidence of any damage could be seen on the compression surface. However some specimens did show initiation of failure on the compression side with very similar appearance to the tension failures. Small bundles of fibres split off from the edge of the specimen to form sharp spikes. Three of the specimens failed in a different way. Initially some bundles failed in tension, but then there was a sudden catastrophic failure. In two cases this occurred at one of the loading noses, but in the third case it failed close to the centre of the specimen. Failure appeared to have initiated on the compression side and propagated across most of the depth of the specimen as a single fracture surface. The compressive fracture surfaces had a smooth, matt appearance. Final failure at the other surface of the specimen still occurred in tension, but without the extensive splitting seen on other tests. Some splitting however initiated from the compressive failure region, both across the width and through the thickness of the specimen. Table 1 shows the strains at which fibre breaks were heard, when fibre bundles first split off and the maximum strain. This is in fact the strain at which the gauge broke, but since this normally occurred when a large
TABLE 1
Results for Four-Point BendingTests with 25-Ply Specimens Specimen no.
2 3 4 5 6 8 9 10 19 20
Strains on tension side (microstrain) First audible fibre break
First visible fibre bundle split off
Maximum
14 820 14 360 14 040 14 900 14 560 9 500 -18 500 17 350 16 340
14 920 14 930 15 810 16 120 15 810 14 310 < 16 650 18 500 17 350 16 570
19 360 17 140 19 360 17 570 18 150 18 620 18 980 18 500 17 690 18 080
Mean strain (brush failures only)
18 480
Coefficientof variation
3.07%
Mean strain (compressionfailures only)
18 020
Failure mode
Compression Compression Brush Compression Brush Brush Brush Brush Brush Brush
Effect of specimen size on bending strength of carbon fibre-epoxy
55
number of fibres had failed, it is considered to be a reasonable estimate of the ultimate failure strain. Although there are fairly large variations in the strains at which fibre breaks were heard or seen, the results for final failure of the specimens failing in a brush mode are quite consistent, with a mean maximum strain of 1 8 4 8 0 microstrain and a coefficient of variation of 3.07%.
3.1.2 50-ply specimens Eleven specimens were tested and they behaved very similarly to the previous set. Fibre breaks were heard and seen well before ultimate failure in most cases, as before, and in most cases final failure occurred in a brush-like mode. The individual failed bundles were of similar size to those in the previous tests, with a thickness normally equal to one ply. The bundles split into overlapping spears at a similar angle to the fibre direction as before, but with bundles around 2 mm wide at their ends. Several specimens had fibre bundles split off on the compression side as well. Two specimens failed at the loading noses with a compressive failure very similar to that seen on some of the smaller specimens. A third specimen started to fail in tension and then failed suddenly at the loading nose. Table 2 summarises the results. Since the results were so similar to the previous set, only maximum strains are presented. The mean value of TABLE 2 Results for Four-Point Bending Tests with 50-Ply Specimens
Specimen no.
Maximum tensile strain (microstrain)
Failure mode
2 3 5 6 7 8 9 10 11 12 13
17 110 15 980 17 100 16 810 17 550 16 970 15 660 16 550 16 660 17 200 17 310
Brush Compression Brush Brush then compression Brush Brush Compression Brush Brush Brush Brush
Mean st rain
17 030
(Brush failures only)
Coefficient of variation
1'87%
Mean strain
16 150
(Compression failures only)
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M. R. Wisnom
maximum strain is 17 030 microstrain. Results are very consistent, with a coefficient of variation of only 1.87%.
3.1.3 lO0-plyspecimens Five of the specimens failed in compression at the loading nose. After three such failures some different materials were tried under the loading noses to try to redistribute the loads better. High-strength polyurethane rubber and PTFE were used, but did not appear to make any difference. Only one specimen failed in tension in a brush mode, and this finally failed in compression as well. The appearance of the failures was similar to the previous specimens. During the last test a loud noise was heard at a very low strain and the test was stopped. A crack a few minimetres long was visible running across the specimen underneath one of the loading noses. Some delamination occurred on the compression side between the loading noses on two of the specimens. Strips of around 1 mm wide which appeared to be 1-ply thick split away. However, they did not break, but buckled to form loops with quite a large separation from the rest of the specimen. Maximum recorded strains are presented in Table 3.
3.2 Buckling tests
3.2.1 25-plyspecimens Six specimens were tested. Initially they bent gradually with the ends rotating smoothly as the load was increased. As the buckling load was approached, deflections increased rapidly whilst the load steadied to an approximately constant value. Five of the specimens failed in a brushTABLE 3 Results for Four-Point Bending Tests with 100-Ply Specimens Specimen no.
Maximum tensile strain (microstrain)
Failure mode
1 2 3 4 5 6
13 680 15 820 12 500 12 000 13 470 7 800
Compression Brush, then compression Compression Compression Compression Cracked only
Mean strain (excluding no. 6)
13 490
Coefficient of variation
10.9%
Effect of specimen size on bending strength of carbon fibre-epoxy
57
type failure very similar to that seen in the four-point bending tests. Bundles of fibres split off along almost the whole length of the specimens. Some fibres split off on the compression sides. One specimen failed suddenly in compression, but only after the brush failure was well advanced. One specimen delaminated along its whole length before reaching the maximum strain and so this result was discarded. Table 4 shows the maximum recorded tensile strains. The mean value is 19 120 microstrain, with a very low coefficient of variation of 0-64%. Strains from both the tension and compression surface were logged onto the computer. The compression gauges continued to record after the tension gauges had failed. In some cases the maximum tensile strain corresponded to the point when there was a large drop in the compressive strain. Where this was the maximum compressive strain recorded the tensile strain corresponds to the true maximum. However in other tests higher values of compressive strain were subsequently attained, 500 microstrain higher in one case. The maximum tensile strain may therefore have been underestimated for these specimens. In other cases there was a very rapid rise in tensile strain after the first large drop in compressive strain by up to 500 microstrain in one case. This was probably caused by the tensile gauge continuing to read after failure had initiated, and so these results may be overestimates of the true maximum tensile strains. In a series of tests these effects will tend to cancel out and it is believed that the mean of the maximum recorded tensile strains is a reasonable estimate of the true maximum. There is an error band on individual results of up to approximately + 500 microstrain, and so the very low coefficient of variation recorded in this series of tests is probably fortuitous.
TABLE4 Results~rBuc~ingTestswith25-PlySpecimens
Specimen no.
Maximum tensile strain (microstrain)
Failure mode
1 2 3 4 5
19320 19090 19000 19 050 19 120
Brush Brush Brush, then compression Brush Brush
Mean
19 120
Coefficientofvariation
0.64%
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M. R. Wisnom
3.2.2 lO0-plyspecimens Six specimens were tested and they again behaved very similarly to the four-point bending tests. One specimen started to fail in tension in a brush-type mode but finally failed suddenly in compression. A second specimen also started to fail in tension, but before many fibre bundles had split off it failed in compression. The remaining specimens all failed suddenly in compression, with some bundles of fibres delaminating on the compression side to form unbroken loops. The catastrophic compression failures occurred approximately in the centre of the specimens, and had similar appearance to the four-point bending failures. Table 5 shows the maximum tensile strains obtained.
4 DISCUSSION The 25-ply and 50-ply thick four-point bending specimens mostly failed in tension despite the fact that the tensile strength of unidirectional X.AS/ 913 is generally believed to be almost twice the compressive strength. This may be due to the material having a higher compressive strength than that normally attributed to it. For example it has been shown that in the commonly used indirect compression tests the presence of large shear stresses can be expected to reduce significantly the measured compressive strength. 1° Non-linear material response may also be a factor. The compressive modulus of carbon fibre-epoxy decreases with strain whilst the tensile modulus increases. This can result in much lower
TABLE 5
Results for Buckling Tests with 100-Ply Specimens Specimen no.
Maximum tensile strain (microstrain)
Failure mode
2
15 550
3 4 5 6 7
15090 16 510 11 020 11320 11480
Few bundles in tension, then compression Compression Brush, then compression Compression Compression Compression
Mean strain
13500
Coefficient ofvariation
18"4%
Effect of specimen size on bending strength of carbon fibre-epoxy
59
stresses on the compression side of the specimen than on the tension side during pure bending. 9 Table 6 shows the relative magnitude of the tensile strains at failure for the three sets of tests including only the tensile failures. It should be noted that there is no overlap between the ranges of tensile strains for the three specimen sizes. The first two series of tests provide a good set of results to assess the effect of specimen size on bending strength controlled by tensile failure. The failure modes are very similar. The results are very consistent, as shown by the low coefficients of variation, and the number of tests provides a reasonable sample size. However the third set produced only one tensile failure and so this result must be treated with caution. The ratio of mean strains for the 25- and 50-ply cases is 1.085, a statistically significant difference. Based on Weibull strength theory using eqn (1) and the volume ratio of 8 between the two specimens gives a Weibull exponent of 25-4. This is typical of values quoted elsewhere for carbon fibre-epoxy, t~ The ratio between the mean strain for the 50-ply case and the single 100-ply result is 1-076. Since the volume ratio based on nominal thickness is also 8 for this case, the expected ratio of strains to failure is the same as the previous case, i.e. 1.085. Although the ratio of 1.076 is based on only one failure it is very close to the previous result of 1.085 and so does provide further support for the magnitude of the size effect. There is no indication of a reduction in the size effect with increasing specimen size. However if the material has a Weibull modulus of 25.4, significant scatter would be expected in the measured strains to failure. Based on the approximate eqn (2), a coefficient of variation due to material variability alone of about 4.7% would be expected. The actual coefficients of variation are considerably smaller. This inconsistency with Weibull strength theory has been further investigated and is reported on separately) 2
TABLE 6 Size Effect on Tensile Failure in Four-Point Bending Tests
Specimen thickness 25 plies 50 plies 100 plies
Mean tensile s t r a i n (microstrain) 18 480 17 030 15 820
Coefficient of variation
Number of specimens
3-07% 1.87% --
7 9 1
M. R. Wisnom
60
The predominantly compressive failure modes of the 100-ply specimens were initially unexpected. There was some concern that this might be due to a difference in the material. The only significant difference in the manufacturing process was the use of an autoclave to cure the thick specimens whilst the others were pressed between plates. However C-scan and X-ray testing of the thick plate had indicated satisfactory quality and a polished section had not shown any significant voidage. The thicker plate may have had a slightly lower volume fraction in view of its greater nominal thickness, but this is not thought likely to be a major factor. Table 7 shows the strains to failure of the specimens of each size which failed in compression. The values are actually tensile strains as the compressive strains were not measured. The trend of decreasing strain to failure with increasing size can also be seen between the 25- and 50-ply specimens. Since the processing of these specimens was identical, it suggests that this is a real material effect rather than an effect due to differences in the manufacturing process. The compressive failures were catastrophic events typical of a brittle material. Weibull strength theory might therefore be expected to apply to these failures. The compressive strains at failure can be taken as approximately proportional to the measured tensile strains. The coefficient of variation for the five 100-ply thick four-point bending compressive failures is 10"9%. Using eqn (2) this corresponds approximately to a Weibull modulus m of 11. The expected ratio of failure strains for a volume ratio of 8 and m = 11 from eqn (1) is 1.21. The mean failure strain for the 100-ply specimens is 13490 microstrain, and so the expected strains for 50- and 25-ply specimens would be 16 320 and 19750 microstrain. These values are of the same order as measured failure strains for the specimens failing in compression. The average strains for the 50- and 25-ply specimens were 16 150 and 18 020 microstrain, respectively. These calculations are only approximate. The Weibull modulus was based on the coefficient of variation of the 1()0-ply
TABLE 7
Size Effect on Compressive Failure in Four-Point Bending
Specimen thickness
Mean tensile strain (microstrain)
Number of specimens
25 plies 50 plies 100 plies
18 020 16 150 13 490
3 3 5
Effect of specimen size on bending strength of carbon fibre-epoxy
61
specimens. The values for the 25- and 50-ply specimen compressive failures were lower, although there were only three failures in each case. On the other hand, the 100-ply buckling tests showed a higher coefficient of variation. Nevertheless the results do show an interesting trend. Despite the uncertainties and the relatively small amount of data, it would appear that there is a size effect operating on compressive strength, but with a smaller Weibull modulus than for tensile strength. As the specimen size increases, both the compressive and tensile strains to failure decrease, but the latter more slowly than the former. Therefore for small specimens tensile failure is more likely to be critical, whereas for larger specimens compressive failure may predominate. It also appears that for compressive failure the magnitude of the size effect may be consistent with the scatter in the experimental results due to material variability whereas for tensile failure it is definitely not. This is reasonable since compressive failure is a sudden catastrophic event which might be expected to conform to Weibull strength theory. Tensile failure on the other hand is a non-catastrophic event, with the failure propagating gradually through the specimen. It is perhaps not surprising that this does not conform to a theory intended for brittle materials. The results of the buckling tests broadly confirm the four-point bending results. Due to the necessity of slightly shortening the larger specimens to get them in the rig the ratio of lengths was 3-8 rather than 4 and so the specimens were not exactly scaled. However, since the results are in fact very similar to the bending results, they do provide further support to the conclusions already drawn. Unfortunately only one 100-ply specimen failed in tension. The ratio of this strain to the mean of the smaller specimens is 1"158. Based on the actual length and width ratios and the nominal thickness ratio and using eqn (1) gives a Weibull exponent of 28.0. This is close to the value of 25.4 calculated from the more complete set of four-point bending tests. It was expected that the buckling tests should be less susceptible to compressive failures because of the absence of the stress concentrations at the loading noses present in the bending tests. Whilst this was true for the smaller specimens, it was not the case for the larger specimens which all failed in compression. The mean tensile strain for the 100-ply compressive failures was 13 500 microstrain, very close to the value of 13 490 for the four-point bending tests. This suggests that it is primarily the stresses due to overall bending that are responsible for the compressive failure rather than the local stresses at the loading noses. Another interesting observation in these tests was the non-catastrophic splitting off of fibre bundles from the compression surface of both four-point bending and buckling specimens. This occurred at much
62
M. R. Wisnom
lower strains in the largest specimens than in the others. It may be because the higher ratio of length or radius of curvature to ply thickness made it easier for a section of one ply to delaminate and buckle. At these lower strains fibre breakage did not occur and so the loops remained unbroken. With the smaller specimens delamination occurred at higher strains where it was accompanied by fibre failures leading to splitting off of individual spears.
5 CONCLUSIONS There is a significant size effect in the bending strength of unidirectional XAS/913 carbon fibre-epoxy. Tests were carried out on geometrically scaled specimens of 25, 50 and 100 plies. The 25- and 50-ply specimens failed mainly in tension despite the material supposedly having a much higher tensile strength than compressive strength. The failure was a gradual splitting-off of individual bundles of fibres, leading to a brushlike appearance for the failed specimens. The tensile strain to failure decreased by about 8% for each doubling of linear specimen dimensions. This corresponds to a Weibull modulus of about 25. However the coefficients of variation were consistently found to be much lower than those expected based on Weibull strength theory. Similar behaviour was found in both four-point bending and buckling tests. The 100-ply specimens failed mainly in compression. The failures were sudden catastrophic events starting at the loading noses in the fourpoint bending specimens or near the centre of the buckling specimens. A few of the smaller specimens also failed in compression, although at much higher strains. This suggests a size effect with a significant decrease in compressive strength as the specimen becomes larger. The magnitude of this effect may be even greater than the size effect in tensile strength. The decrease in strength with increasing size appears to continue undiminished even at the moderately sized specimens tested in this study. This confirms the need for caution in applying design allowables derived from small scale tests to large carbon-fibre structures.
ACKNOWLEDGEMENT The author would like to thank the UK Science and Engineering Research Council and Westland Helicopters for supporting this work, and Michael Jones and Barry Lewis for assistance with the experimental work. The buckling rig was developed by Barry Lewis and Vincent Shin.
Effect of specimen size on bendingstrength of carbonfibre-epoxy
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REFERENCES 1. Metcalfe, A. G. & Schmitz, G. K., Effect of length on the strength of glass fibres. American Society for Testing Materials, Preprint 87, 1964. 2. Bader, M. G. & Priest, A. M., Statistical aspects of fibre and bundle strength in hybrid composites. Proceedings of the 4th International Conference on Composite Materials, (ICCM-IV) Tokyo, 1982, pp. 1129-36. 3. Weibull, W., A statistical distribution function of wide applicability. J. Applied Mechanics, 18 ( 1951 ) 293. 4. Hitchon, J. W. & Phillips, D. C., The effect of specimen size on the strength of cfrp. Composites, 9 (1978) 119-24. 5. Bullock, R. E., Strength ratios of composite materials in flexure and in tension. J. Composite Materials, 8 (1974) 200-6. 6. Kies, J. A., The strength of glass fibers and failure of filament wound pressure vessels. NRL Report No. 6034, US Naval Research Laboratory, Washington, 1964. 7. Kretsis, G., Matthews, F. L., Morton, J. & Davies, G. A. O., Flexural behaviour of unidirectional glass-carbon hybrid laminates, Proceedings of the InternatiOnal Symposium on Composites, Patras, Greece, 1986, pp. 421-32. 8. Batdorf, S. B. & Ghaffarian, R., Size effect and strength variability of unidirectional composites. Int. J. Fracture, 26 (1984) 113-22. 9. Wisnom, M. R., Limitations of linear elastic bending theory applied to four point bending of unidirectional carbon fibre/epoxy. Proceedings of the AIAA Structures, Structural Dynamics and Materials Conference, Long Beach, 1990, pp. 740-7. 10. Wisnom, M. R., The effect of shear stresses in indirect compression tests of unidirectional carbon fibre/epoxy. AIAA J., (to be published). 11. Whitney, J. M., Daniel, I. M. & Pipes, R. B., Experimental Mechanics of Fiber Reinforced Composite Materials, revised edn. SEM, 1984, p. 171. 12. Wisnom, M. R., The relationship between strength variability and size effect in unidirectional carbon fibre-epoxy. Composites, to be published.