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Reduction in compressive strain to failure with increasing specimen size in pin-ended buckling tests
ELSEVIER
PII:
SO266-3538(97)00057-Z
Composites Science and Technology 57 (1997) 1303-1308 &?J1997 Elsevier Science Liited Printed in Northern Ireland. All rights reserved 0266-3538197/$17.00
REDUCTION IN COMPRESSIVE STRAIN TO FAILURE WITH INCREASING SPECIMEN SIZE IN PIN-ENDED BUCKLING TESTS M. R. Whom,
J. W. Atkinson & M. I. Jones
Department of Aerospace Engineering, Universityof Bristol, UniversityWalk, Bristol BS8 1 TR, UK (Received 1 November 1996; revised 7 February 1997; accepted 10 February 1997)
Abstract
ratio of tensile to compressive strength compared with high-strength carbon-fibre materials. In this study a series of flexural tests was carried out on unidirectional T800/924 to investigate size effects. A pin-ended buckling rig was used in order to produce flexural failure whilst avoiding the influence of local stress concentrations at the loading points Geometrically scaled tests were undertaken, and also tests where the thickness was maintained constant and the width and length of the specimens were varied in order to determine the relative importance of the different dimensions.
Flexural tests were performed on unidirectional TgOO/924 carbon-fibre/epoxy composites in a pin-ended buckling rig producing consistent compressive failures. Three sets of tests were carried out with all dimensions geometrically scaled. The results showed a strong decrease in strain at failure with increasing specimen size. Three further sets of tests were conducted where the thickness was kept constant and the length and width of the specimens varied. These showed similar strains at failure, suggesting that the size effect observed with the scaled specimens is predominantly due to the reduction in strain gradient with increasing specimen thickness. 0 1997 Elsevier Science Limited Keywords: A. polymer-matrix
2 EXPERIMENTAL 2.1 Pin-ended buckling rig The rig developed in a previous study2 was used, consisting of two fixtures with semicircular rollers to permit rotation of the ends of the specimen. To allow smooth rotation the rollers were made with a slightly smaller radius than the seats in which they fitted, and polytetrafluoroethylene tape was laid between the two surfaces. The specimens were located in slots in the rollers, with packing to ensure that they were a tight fit. To facilitate bending, the slots were positioned eccentrically so that in the unloaded position one surface of the specimen lay along the centreline of the rig. The rig and dimensions are shown in Fig. 1, with the specimen in the loaded position. Two further rigs were made, with the roller radii reduced by a factor of two and increased by a factor of four, to allow scaled testing of different sized specimens. The width of the roller was kept at 40 mm for the smaller rig, but increased to 50 mm for the larger one. The stresses in the specimen are not affected by this dimension provided it is greater than the specimen width.
composites; B. strength;
size effects 1 INTRODUCTION Size effects in composites are observed experimentally, with strength decreasing with increasing specimen dimensions Such effects are fundamental in understanding failure mechanisms, and are also of practical importance in predicting failure and determining allowable stresses. There have been many reports of size effects in different failure modes, for example in tension,’ bending,* transverse tension3 and interlaminar shear and tension.4 Reducing compressive strengths with increasing volume have also been reported,’ but the difficulties in obtaining reliable test results makes investigation of size effects in compression much harder. Flexural testing avoids some of the problems associated with gripping the specimens. In a previous study on flexural strength of scaled, unidirectional, high-strength carbon-fibre/epoxy composites most specimens failed in tension.* However, some did fail in compression, and for these specimens there was a significant decrease in strength with increasing size. It has been found that T8001924 intermediatemodulus carbon-fibrelepoxy fails consistently in compression under flexural loading owing to the higher
2.2 Scaled buckling tests Three sets of scaled tests were carried out in the pinended buckling rig to investigate the effect of specimen size on strength whilst maintaining the same stress distribution. 1303
M. R. Wisnom et al.
Fig. 1. Medium sized pin-ended
(dimensions
buckling rig and specimen
It was observed that there was some slight fibre waviness in the upper layers of the plate. This appeared as areas of about 1 cm diameter which reflected light differently from the rest of the laminate when held at an angle to the light. No such waviness was visible on the bottom surface, suggesting that it might have been associated with the lack of a caul plate on top. Attempts were made to quantify the waviness, but this proved difficult and it was unfortunately not possible to obtain any satisfactory measurements in the time available. The large specimens were almost as thick as the original plate, and they were always tested with the straightest fibres on the compression face. Specimens of the medium size were cut from close to both the top and bottom surfaces of the plate. The small specimens were from the lower part of the plate where the fibres were straighter.
in mm).
A 66-ply plate of unidirectional Ciba T800/924 unidirectional carbon-fibre/epoxy composite was laid up on a thick aluminium base plate and cured with no caul plate on the upper surface. Specimens nominally 50 mm long, 10 mm wide and 2 mm thick were cut from the plate with a water-cooled diamond saw. They were then wet ground on progressively finer grades of emery paper. Scaled specimens were also cut from the plate with all linear dimensions one-half or four times those of the standard ones. Taking all specimens from the same plate eliminated possible effects arising from differences in the manufacturing process for thick and thin plates. The actual mean dimensions of the finished specimens are shown in the top half of Table 1. Strain gauges of 1 mm gauge length were bonded to the centre of each face of the specimens with cyanoacrylate adhesive after local abrasion and degreasing. Specimens of all three sizes were tested in the corresponding scale buckling rig at a rate producing failure in about 90 s. Load, displacement and strain readings were logged on a data acquisition
2.3 Buckling tests with different lengths and widths To investigate the effect of different specimen dimensions where the thickness was held constant, three further sets of tests were carried out. A 16-ply plate of TWO/924 nominally 2 mm thick was supplied by DRA Farnborough. Specimens with dimensions 30 mm x 10 mm, 150 mm X 10 mm and 150 mm X 40 mm were cut out with a diamond saw. The first two sets allowed the effect of length to be assessed at constant width, whilst the latter two enabled the effect of width at constant length to be investigated. The surfaces were not machined. Actual mean specimen thicknesses are shown in the lower half of Table 1. Strain gauges of 1 mm length were bonded at the centre on both sides of each specimen after local abrasion of the surface to remove the fabric texture from the release cloth. Specimens were tested in the middle-sized buckling rig under displacement control at a slow loading rate, causing failure within about 12 to 20 min. Since the specimens were cut from a thinner plate than for the scaled buckling tests, and were tested at a slower loading rate, some caution is necessary in comparing the results of the two series of tests.
system.
3 RESULTS AND DISCUSSION Table 1. Dimensions
Nominal dimensions
200~40x8 50 x 10 x 2 25X5X1 150 x 40 x 2 150 x 10 x 2 30X10X2
(mm)
of specimens tested
Actual dimensions
3.1 Scaled buckling tests (mm)
Length
Width
Thickness
198.2 50.0 25.0
38.31 10.09 4.89
7.57 1.84 0.93
150-o
40.0
2.21
150.0 30.0
10.0 10.0
2.17 2.23
Figure 2 shows a typical load/strain response for one of the large specimens. Bending started immediately due to the eccentric loading, and then gradually increased. The load approached closer to an asymptote for the smaller specimens, and even decreased slightly before failure for some of the smallest ones. In all cases failure occurred suddenly with no indications of damage initiation. The specimens broke into two pieces, with the fracture close to the midpoint along the length. The fracture surfaces were inclined at
Compressive strain to failure and specimen size
1305
Load (kN)
-2
-1.5
-1
4.5
0
1
0.5
1.5
2
Surface strains (%)
Fig. 2. Typical response for a 200 mm X 40 mm X an angle of approximately 75” to the fibre direction, and had the smooth appearance typical of compressive failures. There was also some delamination and splitting along the length, and fibre tensile failure close to the tension surface. The failures of the different sized specimens all looked very similar. Table 2 shows the compressive and tensile strains at failure, along with their coefficient of variation (CV). The results for the middle-sized specimens are all from those cut from the bottom of the plate. The three sets of results are therefore consistent, with the straightest fibres on the compressive surface in all cases. A strong size effect is evident, with a 32% reduction in the mean compressive strains at failure from 2.16% for the smallest to 1.47% for the largest specimens. The trend from these results is quite similar to that found previously from scaled four-point bending tests of unidirectional XAS/913 carbon-fibre/epoxy.’ For those specimens failing in compression, a 25% reduction in strain was obtained for an increase in linear dimensions of a factor of 4. This compares with a 17% reduction between the medium and large specimens in the present tests, which were also scaled by a factor of 4. One explanation for the size effect is that failure initiates from a critical defect, and the larger the stressed volume, the worse the defect that is likely to
8
mm specimen.
be present. Since failure occurs suddenly in a brittle manner, this is a plausible explanation, with a critical area of fibre misalignment being the most likely defect. In this case Weibull statistical strength theory should apply, and there should be a relationship between the strains at failure, cl and Em,of different sized specimens and the stressed volumes V, and V2 of the form:’ El/E2 = (V,/V,)“”
(1)
where m is the Weibull modulus. Figure 3 shows the results plotted against total specimen volume on a log-log plot. The error bars correspond to one standard deviation on each side of the mean. A good straight line is obtained, suggesting that the Weibull model may be satisfactorily fitted to the data. The Weibull modulus based on least-squares fitting of the data is 16.8. Modelling studies have shown that where fibre waviness varies over a small area, failure is controlled more by the average misalignment than by the worst misalignment.6 It is only where waviness varies gradually over distances of millimetres that the maximum misalignment is critical. There are problems reconciling this with the Weibull explanation of the size effect, since it is questionable whether the average fibre misalignment over a certain volume varies
Table 2. Results of saded buckling tests
Specimen size (mm)
200X40X8 50X10X2 25X5X1
Mean strains at failure (%) Compressive (CV)
Tensile (CV)
1469 (1.9) 1.768 (5.6) 2.160 (5.7)
1.126 (6.1) 1.346 (3.2) 1.673 (2.7)
Mean failure load (kN) (CV)
Number of specimens
49.23 (1.9) 2.99 (8.4) 0.923 (8.1)
4 9 7
1306
M. R. Wisnom et al.
Compressive strain at failure (%) 2.4 2.2 2
1.6
loo
200
5ca
1,ooo
2,cml
5,000
10,ooo
20,ooo
50,coo
lca,ofJJ
Specimen volume (mm3) Fig. 3. Weibull plot for scaled buckling tests. sufficiently with size reduction in strength.
to
produce
the
most waviness positioned on either the tensile or compressive surface of the specimen. There is no significant difference between the mean results for the specimens with waviness and the previous results for the nominally straight material from the bottom of the plate. The subset of specimens with fibre waviness on the compression surface showed very similar strains to those for the straight material, and the ones with waviness on the tension surface actually gave marginally higher strains. It is concluded that the level and type of waviness observed does not have a significant effect on the compressive strain at failure of the material. The insensitivity to waviness may have been because it was limited to a small region close to the surface. Based on Weibull theory with failure controlled by the worst waviness, a difference in strength would have been expected. On the other hand, if failure is controlled by some measure of the ayerage intrinsic misalignment together with the stress gradient, then higher waviness occurring locally would not be expected to be so important. The results are therefore more consistent with the stress gradient explanation for the size effect.
observed
An alternative explanation is that the size effect is a consequence of the variation in stress gradient, and is therefore a function of specimen thickness rather than volume. This is supported by modelling results which show a strong effect of stress gradient on failure for flexural specimens with the same fibre waviness, but with different thicknesses.7 Where there is a large stress gradient, the fibres receive greater support from adjacent less highly loaded material than when the stress field is more uniform, and the compressive stress before instability occurs is therefore higher. Similar trends have been predicted in several other studies.%‘” It is not possible to prove one or other of these two explanations on the basis of the scaled tests alone, since the stressed volume and stress gradient change simultaneously. However, the other results for different sized specimens with the thickness maintained constant will allow further consideration of the relative importance of these two effects.
3.2 Buckling tests with waviness Table 3 shows the results for the middle-sized specimens cut from the top of the plate rather than from near the bottom. Two orientations were tested, with the surface from the top of the plate with the
3.3 Buckling tests with different widths The 150 mm long specimens behaved similarly to the previous ones, although they showed a more classical
Table 3. Effect of Bbre waviness on 50 mm X 10 mm X 2 mm specimens Mean strains at failure (%) Compressive (CV) Waviness on compression surface Waviness on tension surface Mean, with waviness Nominally straight material
1.742 (4.8) 1.833 (6.2) 1.783 (5.9) 1.768 (5.6)
Mean failure load (kN) (CV)
___Number of specimens
Tensile (CV) 1.298 1.452 I ,368 1.346
(11.8) (5.5) (10.5) (3.2)
3.26 3.07 3.17 2.99
(7.5) (6.6) (7.5) (8.4)
6 5 11 7
1307
Compressive strain to failure and specimen size Table 4. Results for constant thickness buckling tests
Specimen size (mm)
Means strains at failure (%) Compressive (CV)
150 x 40 x 2 150 x 10 x 2 30 x 10 x 2
1.824 (8.2) 1.891 (5.2) 1.888 (9.6)
Mean failure load (kN) (CV)
Number of specimens
Tensile (CV) 1.545 (7.7) 1.575 (5.6) 1.057 (11.3)
buckling response, reaching an approximately constant load well before failure. All specimens failed suddenly, with similar appearance to those from the scaled tests. One concern with these tests was that the stress distributions might be different owing to changes in the amount of anticlastic bending with specimen width. However, preliminary non-linear finite-element analysis with large deflections suggested that even for the 40 mm wide specimens, there would be very little variation of strain in the fibre direction across the width. Table 4 shows the mean strains at failure. The 40 mm wide specimens gave 3.4% lower strain than the 10 mm ones. There is significant scatter in the results, and despite the reasonably large number of specimens, the data are unfortunately not conclusive as to whether there is a width effect or not. It is therefore not possible to prove from these results if the previously observed size effect is due to the effect of the stressed volume or the stress gradient through the thickness. However, the results do give greater support to the stress gradient hypothesis. On the basis of Weibull theory with a modulus of 16.8, a reduction in strength of 7.9% would be expected from eqn (1)for a factor of four increase in specimen volume. The actual reduction is only 3*4%, i.e. 4.5% less than indicated by Weibull theory. Although there is a fair amount of scatter in the results, with 15 specimens in each batch the difference of 4.5% is statistically significant (t test at 5% significance level). It is therefore possible to reject the hypothesis that the size effect is solely caused by a stressed volume effect with a Weibull modulus of 16.8. On the other hand, the measured difference in strength of 3.4% is not statistically significant, and with the degree of scatter in the results could just be a chance occurrence. The hypothesis that the size effect is due solely to the stress gradient and that there is no effect of stressed volume therefore cannot be rejected. It should also be noted that the difference in tensile strains at failure is only 1.9%. The tensile and compressive strains should in principle be correlated, and so similar differences would be expected between the two sets of results for gauges on both surfaces. Given that there will be some error in the strain measurements, the fact that the difference in tensile
2.505 (5.0) 0.618 (14.7) 9.419 (5.2)
15 15 15
strains is smaller than the recorded difference in compressive strains implies that, if anything, the true difference may be smaller than 3.4%. This further weakens the support for a size effect based on volume. 3.4 Buckling tests with different lengths The shorter specimens behaved very similarly to all the previous ones. As can be seen in Table 4, the compressive strains at failure are the same as those for the longer specimens. The load/strain response was not very smooth, apparently due to the characteristics of the servo-hydraulic test machine with a stiff specimen. This is not believed to have been significant, but an influence on the behaviour of the specimens cannot be ruled out. Changing the length of the specimens causes a change in stressed volume, and also a change in the ratio of compressive to bending stress owing to the different buckling load. The larger volume of the longer specimens would tend to reduce their strength, whereas the lower direct compressive stress would tend to raise it because of the small increase in stress gradient through the thickness. The fact that there is no change in strain to failure with a factor of five change in nominal stressed volume again suggests that the change in volume is not primarily responsible for the size effect. However, the possibility that the volume effect and the stress ratio effect cancel each other out cannot be excluded on the basis of these results alone. 3.5 Compressive
failure strain as a function of strain
gradient
All the previous results are plotted in Fig. 4 in terms of the strain gradient, defined as the difference in strains at failure between the compressive and tensile surfaces divided by the specimen thickness. A least-squares straight line has been put through the scaled specimen results, and the fit is very good. The extrapolated value of compressive strain at failure under pure compression of 1.43% appears to be reasonable. The graph also shows that the difference in strain gradient between the different length specimens is small compared with those for the scaled specimens. A significant effect of length on strength would therefore not be expected. The three sets of results from the second series of tests are slightly above the
1308
M. R. Wisnom et al. Compressive strain at failure (%) 2.4 ,
1.6
0
4
1
5
Straig gradient (%ymm) Fig.4. Strain gradient effect.
line, which could be because the specimens were cut from a thin plate where the fibre alignment may have been better. To investigate further the effect of strain gradient, a new constrained buckling rig was subsequently developed which allowed the ratio between compression and bending to be varied independently from the specimen length. Results from this are reported elsewhere,” and give further support for the size effects observed here being predominantly due to the strain gradient.
4 CONCLUSIONS failure of unidirectional carbon-fibre/epoxy under flexural loading, with scaled buckling tests showing a 32% reduction in strain at failure for a factor of eight increase in specimen dimensions. Changing the length by a factor of five had no effect on the failure strain, and increasing the width by a factor of four caused only a small reduction. The effect of visible waviness on the surfaces of the specimens was not significant. The results suggest that the size effect is predominantly a consequence of the reduction in strain gradient with increasing specimen thickness rather than due to the increase in stressed volume. There
is a strong size effect in compressive
ACKNOWLEDGEMENTS This work was funded by EPSRUMOD under contract no. GR/H75017 in collaboration with Westland Helicopters and DRA Farnborough.
REFERENCES 1. Hitchon, J. W. and Phillips, D. C., The effect of specimen size on the strength of CFRP Composites 1978, 9, 119-124. 2. Wisnom, M. R., The effect of specimen size on flexural
strength of unidirectional carbon fibre-epoxy. Compos. Struct. 1991,18,47-63. 3. O’Brien, T. K. and Salpekar, S. A., Scale effects on the transverse tensile strength of graphite epoxy composites. In Composite Materials: Testing and Design Vol. 11, ASTM STP 1206. American Society for testing and Materials, Philadelphia, PA, 1993, pp. 23-52. 4. Wisnom, M. R. and Jones, M. I., Size effects in interlaminar tensile and shear strength of unidirectional glass fibre-epoxy. .I. ReinjY Plast. Compos. 1996, l&2-15. matrix5. Reeder, J. R., Stitching vs a toughened compressive strength effects. J. Compos. Mater. 1995, 29, 2464-2487.
6. Wisnom, M. R., Analysis of shear instability compression due to fibre waviness. J. Reinj
under Plast.
Compos. 1993,x& 1171-1189.
7. Wisnom, M. R., The effect of fibre waviness on the relationship between compressive and flexural strengths of unidirectional composites. .I. Compos. Mater. 1994, 28, 66-76.
8. Gardin, C., Grandidier, J. C. and Potier-Ferry, M., Compressive behaviour of composite materials: a theoretical and experimental study. In Proc. ICCM9, Madrid, July 1993. Woodhead Publishing Ltd, Cambridge, UK, Vol. III. pp. 301-307. 9. Swanson, S. R., Constraint effects in compression failure of fiber composites. In Proc. ICCMIO, Whistler, Canada, August 1995. Woodhead Publishing Ltd, Cambridge, UK, Vol. I. pp. 739-746. 10.Drapier, S., Grandidier, J. C. and Potier-Ferry, M., Towards a model of the compression strength for longfibre composites. Submitted to Eur. J. Mech. 11. Wisnom, M. R. and Atkinson, J. A., Constrained buckling tests show increasing compressive strain to failure with increasing strain gradient. Composites, in press.
PII:
SO266-3538(97)00057-Z
Composites Science and Technology 57 (1997) 1303-1308 &?J1997 Elsevier Science Liited Printed in Northern Ireland. All rights reserved 0266-3538197/$17.00
REDUCTION IN COMPRESSIVE STRAIN TO FAILURE WITH INCREASING SPECIMEN SIZE IN PIN-ENDED BUCKLING TESTS M. R. Whom,
J. W. Atkinson & M. I. Jones
Department of Aerospace Engineering, Universityof Bristol, UniversityWalk, Bristol BS8 1 TR, UK (Received 1 November 1996; revised 7 February 1997; accepted 10 February 1997)
Abstract
ratio of tensile to compressive strength compared with high-strength carbon-fibre materials. In this study a series of flexural tests was carried out on unidirectional T800/924 to investigate size effects. A pin-ended buckling rig was used in order to produce flexural failure whilst avoiding the influence of local stress concentrations at the loading points Geometrically scaled tests were undertaken, and also tests where the thickness was maintained constant and the width and length of the specimens were varied in order to determine the relative importance of the different dimensions.
Flexural tests were performed on unidirectional TgOO/924 carbon-fibre/epoxy composites in a pin-ended buckling rig producing consistent compressive failures. Three sets of tests were carried out with all dimensions geometrically scaled. The results showed a strong decrease in strain at failure with increasing specimen size. Three further sets of tests were conducted where the thickness was kept constant and the length and width of the specimens varied. These showed similar strains at failure, suggesting that the size effect observed with the scaled specimens is predominantly due to the reduction in strain gradient with increasing specimen thickness. 0 1997 Elsevier Science Limited Keywords: A. polymer-matrix
2 EXPERIMENTAL 2.1 Pin-ended buckling rig The rig developed in a previous study2 was used, consisting of two fixtures with semicircular rollers to permit rotation of the ends of the specimen. To allow smooth rotation the rollers were made with a slightly smaller radius than the seats in which they fitted, and polytetrafluoroethylene tape was laid between the two surfaces. The specimens were located in slots in the rollers, with packing to ensure that they were a tight fit. To facilitate bending, the slots were positioned eccentrically so that in the unloaded position one surface of the specimen lay along the centreline of the rig. The rig and dimensions are shown in Fig. 1, with the specimen in the loaded position. Two further rigs were made, with the roller radii reduced by a factor of two and increased by a factor of four, to allow scaled testing of different sized specimens. The width of the roller was kept at 40 mm for the smaller rig, but increased to 50 mm for the larger one. The stresses in the specimen are not affected by this dimension provided it is greater than the specimen width.
composites; B. strength;
size effects 1 INTRODUCTION Size effects in composites are observed experimentally, with strength decreasing with increasing specimen dimensions Such effects are fundamental in understanding failure mechanisms, and are also of practical importance in predicting failure and determining allowable stresses. There have been many reports of size effects in different failure modes, for example in tension,’ bending,* transverse tension3 and interlaminar shear and tension.4 Reducing compressive strengths with increasing volume have also been reported,’ but the difficulties in obtaining reliable test results makes investigation of size effects in compression much harder. Flexural testing avoids some of the problems associated with gripping the specimens. In a previous study on flexural strength of scaled, unidirectional, high-strength carbon-fibre/epoxy composites most specimens failed in tension.* However, some did fail in compression, and for these specimens there was a significant decrease in strength with increasing size. It has been found that T8001924 intermediatemodulus carbon-fibrelepoxy fails consistently in compression under flexural loading owing to the higher
2.2 Scaled buckling tests Three sets of scaled tests were carried out in the pinended buckling rig to investigate the effect of specimen size on strength whilst maintaining the same stress distribution. 1303
M. R. Wisnom et al.
Fig. 1. Medium sized pin-ended
(dimensions
buckling rig and specimen
It was observed that there was some slight fibre waviness in the upper layers of the plate. This appeared as areas of about 1 cm diameter which reflected light differently from the rest of the laminate when held at an angle to the light. No such waviness was visible on the bottom surface, suggesting that it might have been associated with the lack of a caul plate on top. Attempts were made to quantify the waviness, but this proved difficult and it was unfortunately not possible to obtain any satisfactory measurements in the time available. The large specimens were almost as thick as the original plate, and they were always tested with the straightest fibres on the compression face. Specimens of the medium size were cut from close to both the top and bottom surfaces of the plate. The small specimens were from the lower part of the plate where the fibres were straighter.
in mm).
A 66-ply plate of unidirectional Ciba T800/924 unidirectional carbon-fibre/epoxy composite was laid up on a thick aluminium base plate and cured with no caul plate on the upper surface. Specimens nominally 50 mm long, 10 mm wide and 2 mm thick were cut from the plate with a water-cooled diamond saw. They were then wet ground on progressively finer grades of emery paper. Scaled specimens were also cut from the plate with all linear dimensions one-half or four times those of the standard ones. Taking all specimens from the same plate eliminated possible effects arising from differences in the manufacturing process for thick and thin plates. The actual mean dimensions of the finished specimens are shown in the top half of Table 1. Strain gauges of 1 mm gauge length were bonded to the centre of each face of the specimens with cyanoacrylate adhesive after local abrasion and degreasing. Specimens of all three sizes were tested in the corresponding scale buckling rig at a rate producing failure in about 90 s. Load, displacement and strain readings were logged on a data acquisition
2.3 Buckling tests with different lengths and widths To investigate the effect of different specimen dimensions where the thickness was held constant, three further sets of tests were carried out. A 16-ply plate of TWO/924 nominally 2 mm thick was supplied by DRA Farnborough. Specimens with dimensions 30 mm x 10 mm, 150 mm X 10 mm and 150 mm X 40 mm were cut out with a diamond saw. The first two sets allowed the effect of length to be assessed at constant width, whilst the latter two enabled the effect of width at constant length to be investigated. The surfaces were not machined. Actual mean specimen thicknesses are shown in the lower half of Table 1. Strain gauges of 1 mm length were bonded at the centre on both sides of each specimen after local abrasion of the surface to remove the fabric texture from the release cloth. Specimens were tested in the middle-sized buckling rig under displacement control at a slow loading rate, causing failure within about 12 to 20 min. Since the specimens were cut from a thinner plate than for the scaled buckling tests, and were tested at a slower loading rate, some caution is necessary in comparing the results of the two series of tests.
system.
3 RESULTS AND DISCUSSION Table 1. Dimensions
Nominal dimensions
200~40x8 50 x 10 x 2 25X5X1 150 x 40 x 2 150 x 10 x 2 30X10X2
(mm)
of specimens tested
Actual dimensions
3.1 Scaled buckling tests (mm)
Length
Width
Thickness
198.2 50.0 25.0
38.31 10.09 4.89
7.57 1.84 0.93
150-o
40.0
2.21
150.0 30.0
10.0 10.0
2.17 2.23
Figure 2 shows a typical load/strain response for one of the large specimens. Bending started immediately due to the eccentric loading, and then gradually increased. The load approached closer to an asymptote for the smaller specimens, and even decreased slightly before failure for some of the smallest ones. In all cases failure occurred suddenly with no indications of damage initiation. The specimens broke into two pieces, with the fracture close to the midpoint along the length. The fracture surfaces were inclined at
Compressive strain to failure and specimen size
1305
Load (kN)
-2
-1.5
-1
4.5
0
1
0.5
1.5
2
Surface strains (%)
Fig. 2. Typical response for a 200 mm X 40 mm X an angle of approximately 75” to the fibre direction, and had the smooth appearance typical of compressive failures. There was also some delamination and splitting along the length, and fibre tensile failure close to the tension surface. The failures of the different sized specimens all looked very similar. Table 2 shows the compressive and tensile strains at failure, along with their coefficient of variation (CV). The results for the middle-sized specimens are all from those cut from the bottom of the plate. The three sets of results are therefore consistent, with the straightest fibres on the compressive surface in all cases. A strong size effect is evident, with a 32% reduction in the mean compressive strains at failure from 2.16% for the smallest to 1.47% for the largest specimens. The trend from these results is quite similar to that found previously from scaled four-point bending tests of unidirectional XAS/913 carbon-fibre/epoxy.’ For those specimens failing in compression, a 25% reduction in strain was obtained for an increase in linear dimensions of a factor of 4. This compares with a 17% reduction between the medium and large specimens in the present tests, which were also scaled by a factor of 4. One explanation for the size effect is that failure initiates from a critical defect, and the larger the stressed volume, the worse the defect that is likely to
8
mm specimen.
be present. Since failure occurs suddenly in a brittle manner, this is a plausible explanation, with a critical area of fibre misalignment being the most likely defect. In this case Weibull statistical strength theory should apply, and there should be a relationship between the strains at failure, cl and Em,of different sized specimens and the stressed volumes V, and V2 of the form:’ El/E2 = (V,/V,)“”
(1)
where m is the Weibull modulus. Figure 3 shows the results plotted against total specimen volume on a log-log plot. The error bars correspond to one standard deviation on each side of the mean. A good straight line is obtained, suggesting that the Weibull model may be satisfactorily fitted to the data. The Weibull modulus based on least-squares fitting of the data is 16.8. Modelling studies have shown that where fibre waviness varies over a small area, failure is controlled more by the average misalignment than by the worst misalignment.6 It is only where waviness varies gradually over distances of millimetres that the maximum misalignment is critical. There are problems reconciling this with the Weibull explanation of the size effect, since it is questionable whether the average fibre misalignment over a certain volume varies
Table 2. Results of saded buckling tests
Specimen size (mm)
200X40X8 50X10X2 25X5X1
Mean strains at failure (%) Compressive (CV)
Tensile (CV)
1469 (1.9) 1.768 (5.6) 2.160 (5.7)
1.126 (6.1) 1.346 (3.2) 1.673 (2.7)
Mean failure load (kN) (CV)
Number of specimens
49.23 (1.9) 2.99 (8.4) 0.923 (8.1)
4 9 7
1306
M. R. Wisnom et al.
Compressive strain at failure (%) 2.4 2.2 2
1.6
loo
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Specimen volume (mm3) Fig. 3. Weibull plot for scaled buckling tests. sufficiently with size reduction in strength.
to
produce
the
most waviness positioned on either the tensile or compressive surface of the specimen. There is no significant difference between the mean results for the specimens with waviness and the previous results for the nominally straight material from the bottom of the plate. The subset of specimens with fibre waviness on the compression surface showed very similar strains to those for the straight material, and the ones with waviness on the tension surface actually gave marginally higher strains. It is concluded that the level and type of waviness observed does not have a significant effect on the compressive strain at failure of the material. The insensitivity to waviness may have been because it was limited to a small region close to the surface. Based on Weibull theory with failure controlled by the worst waviness, a difference in strength would have been expected. On the other hand, if failure is controlled by some measure of the ayerage intrinsic misalignment together with the stress gradient, then higher waviness occurring locally would not be expected to be so important. The results are therefore more consistent with the stress gradient explanation for the size effect.
observed
An alternative explanation is that the size effect is a consequence of the variation in stress gradient, and is therefore a function of specimen thickness rather than volume. This is supported by modelling results which show a strong effect of stress gradient on failure for flexural specimens with the same fibre waviness, but with different thicknesses.7 Where there is a large stress gradient, the fibres receive greater support from adjacent less highly loaded material than when the stress field is more uniform, and the compressive stress before instability occurs is therefore higher. Similar trends have been predicted in several other studies.%‘” It is not possible to prove one or other of these two explanations on the basis of the scaled tests alone, since the stressed volume and stress gradient change simultaneously. However, the other results for different sized specimens with the thickness maintained constant will allow further consideration of the relative importance of these two effects.
3.2 Buckling tests with waviness Table 3 shows the results for the middle-sized specimens cut from the top of the plate rather than from near the bottom. Two orientations were tested, with the surface from the top of the plate with the
3.3 Buckling tests with different widths The 150 mm long specimens behaved similarly to the previous ones, although they showed a more classical
Table 3. Effect of Bbre waviness on 50 mm X 10 mm X 2 mm specimens Mean strains at failure (%) Compressive (CV) Waviness on compression surface Waviness on tension surface Mean, with waviness Nominally straight material
1.742 (4.8) 1.833 (6.2) 1.783 (5.9) 1.768 (5.6)
Mean failure load (kN) (CV)
___Number of specimens
Tensile (CV) 1.298 1.452 I ,368 1.346
(11.8) (5.5) (10.5) (3.2)
3.26 3.07 3.17 2.99
(7.5) (6.6) (7.5) (8.4)
6 5 11 7
1307
Compressive strain to failure and specimen size Table 4. Results for constant thickness buckling tests
Specimen size (mm)
Means strains at failure (%) Compressive (CV)
150 x 40 x 2 150 x 10 x 2 30 x 10 x 2
1.824 (8.2) 1.891 (5.2) 1.888 (9.6)
Mean failure load (kN) (CV)
Number of specimens
Tensile (CV) 1.545 (7.7) 1.575 (5.6) 1.057 (11.3)
buckling response, reaching an approximately constant load well before failure. All specimens failed suddenly, with similar appearance to those from the scaled tests. One concern with these tests was that the stress distributions might be different owing to changes in the amount of anticlastic bending with specimen width. However, preliminary non-linear finite-element analysis with large deflections suggested that even for the 40 mm wide specimens, there would be very little variation of strain in the fibre direction across the width. Table 4 shows the mean strains at failure. The 40 mm wide specimens gave 3.4% lower strain than the 10 mm ones. There is significant scatter in the results, and despite the reasonably large number of specimens, the data are unfortunately not conclusive as to whether there is a width effect or not. It is therefore not possible to prove from these results if the previously observed size effect is due to the effect of the stressed volume or the stress gradient through the thickness. However, the results do give greater support to the stress gradient hypothesis. On the basis of Weibull theory with a modulus of 16.8, a reduction in strength of 7.9% would be expected from eqn (1)for a factor of four increase in specimen volume. The actual reduction is only 3*4%, i.e. 4.5% less than indicated by Weibull theory. Although there is a fair amount of scatter in the results, with 15 specimens in each batch the difference of 4.5% is statistically significant (t test at 5% significance level). It is therefore possible to reject the hypothesis that the size effect is solely caused by a stressed volume effect with a Weibull modulus of 16.8. On the other hand, the measured difference in strength of 3.4% is not statistically significant, and with the degree of scatter in the results could just be a chance occurrence. The hypothesis that the size effect is due solely to the stress gradient and that there is no effect of stressed volume therefore cannot be rejected. It should also be noted that the difference in tensile strains at failure is only 1.9%. The tensile and compressive strains should in principle be correlated, and so similar differences would be expected between the two sets of results for gauges on both surfaces. Given that there will be some error in the strain measurements, the fact that the difference in tensile
2.505 (5.0) 0.618 (14.7) 9.419 (5.2)
15 15 15
strains is smaller than the recorded difference in compressive strains implies that, if anything, the true difference may be smaller than 3.4%. This further weakens the support for a size effect based on volume. 3.4 Buckling tests with different lengths The shorter specimens behaved very similarly to all the previous ones. As can be seen in Table 4, the compressive strains at failure are the same as those for the longer specimens. The load/strain response was not very smooth, apparently due to the characteristics of the servo-hydraulic test machine with a stiff specimen. This is not believed to have been significant, but an influence on the behaviour of the specimens cannot be ruled out. Changing the length of the specimens causes a change in stressed volume, and also a change in the ratio of compressive to bending stress owing to the different buckling load. The larger volume of the longer specimens would tend to reduce their strength, whereas the lower direct compressive stress would tend to raise it because of the small increase in stress gradient through the thickness. The fact that there is no change in strain to failure with a factor of five change in nominal stressed volume again suggests that the change in volume is not primarily responsible for the size effect. However, the possibility that the volume effect and the stress ratio effect cancel each other out cannot be excluded on the basis of these results alone. 3.5 Compressive
failure strain as a function of strain
gradient
All the previous results are plotted in Fig. 4 in terms of the strain gradient, defined as the difference in strains at failure between the compressive and tensile surfaces divided by the specimen thickness. A least-squares straight line has been put through the scaled specimen results, and the fit is very good. The extrapolated value of compressive strain at failure under pure compression of 1.43% appears to be reasonable. The graph also shows that the difference in strain gradient between the different length specimens is small compared with those for the scaled specimens. A significant effect of length on strength would therefore not be expected. The three sets of results from the second series of tests are slightly above the
1308
M. R. Wisnom et al. Compressive strain at failure (%) 2.4 ,
1.6
0
4
1
5
Straig gradient (%ymm) Fig.4. Strain gradient effect.
line, which could be because the specimens were cut from a thin plate where the fibre alignment may have been better. To investigate further the effect of strain gradient, a new constrained buckling rig was subsequently developed which allowed the ratio between compression and bending to be varied independently from the specimen length. Results from this are reported elsewhere,” and give further support for the size effects observed here being predominantly due to the strain gradient.
4 CONCLUSIONS failure of unidirectional carbon-fibre/epoxy under flexural loading, with scaled buckling tests showing a 32% reduction in strain at failure for a factor of eight increase in specimen dimensions. Changing the length by a factor of five had no effect on the failure strain, and increasing the width by a factor of four caused only a small reduction. The effect of visible waviness on the surfaces of the specimens was not significant. The results suggest that the size effect is predominantly a consequence of the reduction in strain gradient with increasing specimen thickness rather than due to the increase in stressed volume. There
is a strong size effect in compressive
ACKNOWLEDGEMENTS This work was funded by EPSRUMOD under contract no. GR/H75017 in collaboration with Westland Helicopters and DRA Farnborough.
REFERENCES 1. Hitchon, J. W. and Phillips, D. C., The effect of specimen size on the strength of CFRP Composites 1978, 9, 119-124. 2. Wisnom, M. R., The effect of specimen size on flexural
strength of unidirectional carbon fibre-epoxy. Compos. Struct. 1991,18,47-63. 3. O’Brien, T. K. and Salpekar, S. A., Scale effects on the transverse tensile strength of graphite epoxy composites. In Composite Materials: Testing and Design Vol. 11, ASTM STP 1206. American Society for testing and Materials, Philadelphia, PA, 1993, pp. 23-52. 4. Wisnom, M. R. and Jones, M. I., Size effects in interlaminar tensile and shear strength of unidirectional glass fibre-epoxy. .I. ReinjY Plast. Compos. 1996, l&2-15. matrix5. Reeder, J. R., Stitching vs a toughened compressive strength effects. J. Compos. Mater. 1995, 29, 2464-2487.
6. Wisnom, M. R., Analysis of shear instability compression due to fibre waviness. J. Reinj
under Plast.
Compos. 1993,x& 1171-1189.
7. Wisnom, M. R., The effect of fibre waviness on the relationship between compressive and flexural strengths of unidirectional composites. .I. Compos. Mater. 1994, 28, 66-76.
8. Gardin, C., Grandidier, J. C. and Potier-Ferry, M., Compressive behaviour of composite materials: a theoretical and experimental study. In Proc. ICCM9, Madrid, July 1993. Woodhead Publishing Ltd, Cambridge, UK, Vol. III. pp. 301-307. 9. Swanson, S. R., Constraint effects in compression failure of fiber composites. In Proc. ICCMIO, Whistler, Canada, August 1995. Woodhead Publishing Ltd, Cambridge, UK, Vol. I. pp. 739-746. 10.Drapier, S., Grandidier, J. C. and Potier-Ferry, M., Towards a model of the compression strength for longfibre composites. Submitted to Eur. J. Mech. 11. Wisnom, M. R. and Atkinson, J. A., Constrained buckling tests show increasing compressive strain to failure with increasing strain gradient. Composites, in press.