Compressive failure in two types of carbon fibre-epoxide laminates

Composites Science and Technology 26 (1986) 17-29

Compressive Failure in Two Types of Carbon Fibre-Epoxide Laminates E. Wilkinson,* T. V. Parryt and A. S. Wronski Engineering Materials Research Group. University of Bradford, West Yorkshire BD7 1DP (Great Britain)

SUMMARY The mechanical properties of 0.9 mm thick laminates pressed from balanced five-end sateen and plain-woven carbon fibre cloths, respectively, were determined and in particular the axial compressive behaviour studied for gauge lengths between 5 and 50 ram. The data are presented in terms of bundle strength, i.e. assuming the weft bundles carry no load. Euler buckling analysis was found to be applicable for gauge lengths in excess of ,,~ 15 mm, the 'column' being the specimen in the case of the 'solid' (sateen) laminate and the longitudinal (warp) bundles in the case of the 'perforated" (plain weave) CFRP. For short specimens the (ultimate) compressive bundle strengths were 225 and 980 MPa for the 'perforated' and 'solid" materials, respectively, the latter being close to the tensile strength of 910 MPa. These results were successfully analysed on the matrix-yieMing model of composite compressive failure developed by Piggott and Swift and modified by us for surface bundle detachment, to give values of 216 and910 MPa, respectively. The failure process involved bundle detachment and kinking, similar to the mechanism operating in nominally uniaxially aligned fibrous composites.

INTRODUCTION In order to overcome some of the problems associated with anisotropy of the mechanical properties of unidirectionally aligned fibrous composites, * Present address: BP Research Centre, Chertsey Road, Sunbury, Middlesex, UK. t Present address: Department of Engineering, University of Durham, UK. 17 Composites Science and Technology 0266-3538/86/$03.50 © Elsevier Applied Science Publishers Ltd, England, 1986. Printed in Great Britain

18

E. Wilkinson, T. V. Parry, A. S. Wronski

(a)

(b) Fig. 1. Plan views of weave patterns of interlacings: (a) plain weave: the simplest weave with maximum frequency ofinterlacings of yarns and (b) five-end sateen weave, with equal warp and weft crimp. Note that the diagrams are idealized: the shape of the yarn crosssections tends to be distorted (towards the elliptical in our materials).

cross-ply and angle-ply laminates are often employed. Another approach is the use of woven reinforcement i or three-dimensional 2 composites. In these types of material a particularly important property is the compressive strength, which is expected to be related to the difficulty of kinking. 2 Thus, interestingly, kinking as a mode of structural degradation has been reported as a result of impact damage in a threedimensional carbon fibre/carbon composite. 2 For woven fabric composites another important parameter is the interlaminar fracture energy which does appear to have been considered in this content, 1 unlike the compressive properties. The latter are expected to depend on the curvature of the fibre bundles (tows) making up the woven fabric. A style of weave frequently chosen for woven-cloth-reinforced composites is 'sateen'. Sateen is a weft-faced weave, whereas satin is a warp-faced weave. The attraction of this type of weave in textile terms is that it produces a cloth with a smooth surface free from twill patterns. 3 F r o m the point of view of woven reinforcement for composites, in which the individual warp and weft yarns are replaced by bundles of parallel fibres or rovings, this style of weave has the advantage that a higher proportion of the fibres remain parallel to the cloth axis than would be the case with a plain weave, as illustrated in Fig. 1 which shows diagrammatic

(a)

(b)

Fig. 2. Design paper method of indicating one repeat of (a) plain weave and (b) five-end sateen weave. Each square represents the crossing of individual warp and weft yarns and a shaded square (mark) corresponds to warp yarn passing over the weft yarn (warp up) at the corresponding place in the fabric, whereas a blank indicates weft up.

Compressive failure in carbon fibre fabric-epoxy laminates

19

sections of a plain and a five-end sateen weave. The same weave patterns are illustrated in Fig. 2 in plan view, using the same convention for representing a weave on design paper as is used in the textile industry. Models of compressive strength have initially been developed for perfectly straight, parallel and aligned fibres, but recently Piggott 4,s has re-examined this question, pointing out the necessity of taking into account imperfections in composites, as has always been the case with the development of strength theories for crystalline solids. One such important parameter is fibre straightness and a compressive failure model, based on Swift's 6 analysis, has been postulated by Piggott 4 and used and extended by Wronski and Parry, 7-9 who took the relevant microstructural parameter to be the ply, tow, lamina or bundle rather than the individual fibre. The Piggot analysis considers fibres (or bundles) of circular crosssection and assumes support from both sides. Our experience, however, is that surface bundles 7- 9 detach and delaminate. In this study the fabric contained bundles of approximately elliptical cross-section and accordingly the compression of such a curved bundle will be now considered. Following Piggott 5 we will assume that the bundle axis has a sinusoidal form, noting that by means of Fourier methods any axis trajectory can be reduced to sine waves. Let a and b be the semi-major and semi-minor axes of the fibre bundle, A the amplitude and 2 the wavelength of the sine wave. The axis displacement is then 2nx y = A sin ~ - (1) The small length of bundle, ds, adjoining the antinode at x = 2/4, is sketched as Fig. 3. The bundle radius of curvature, R, is related to y by R

Hyz = -

(2)

If the fibre bundle stress is tyb and try is the stress exerted by the matrix on length ds of the bundle, rcab6 b sin dO = 2a ds ay (3) and since ds

sin dO ~- ~2R

C7b : ~

(4) O'y

(5)

20

E. Wilkinson, T. V. Parry, A. S. Wronski

Fig. 3. Swiftmodel, modified for an elliptical cross-section fibre bundle, of the forces acting on a curved fibrous material strained to a stress ab in a matrix strained to ay. which becomes 2R tr b = -~- try

(6)

for a surface circular bundle of radius r. If failure is controlled by the mechanism of bundle debonding, the composite compressive strength will be attained when try reaches the matrix tensile strength, o"t at the value 2R O'c(my) = O"b = ~ -

O"t

(7)

where R is then the bundle radius of curvature at failure. (Note that Piggott's 4 formula for trc(my) which Parry and Wronski 7'8 have also previously used, gives a result double that of eqn (7), r replacing b for a circular fibre/bundle.)

EXPERIMENTAL PROCEDURE The two types of woven carbon fabric laminate, one 'solid' and one 'perforated', were kindly supplied by Messrs Lucas Aerospace of Burnley, Lancs. The 'solid' 0-9 m m thick laminate was made of three plies of type 914 C-833 five-end sateen-weave prepreg containing 60 ~ Vf of Toray (T) 300 carbon fibres in a Ciba-Geigy type 914 epoxide resin. The 'perforated' laminate, also 0.9 m m thick, which contained the same type of fibres, was loosely woven in a plain-weave configuration. To ensure the correct spacing of'holes' (intended to improve acoustic properties in a potential application) brass wires were introduced into the composite. Both the

Compressive failure in carbon fibre fabric-epoxy laminates

21

11ram t Fig. 4. Optical micrograph of the'solid' five-end sateen-weave laminate section showing the three plies, the approximately elliptical cross-section of the bundles, their curvature and the resin-rich areas.

composites were balanced, i.e. had the same fibre volume and geometry in orthogonal directions. Representative samples of each laminate were mounted in polyester resin and sectioned and polished perpendicular to the 'warp' direction. The volume fraction of composite aligned parallel to the loading direction as a proportion of the laminate cross-section was estimated, for the case of the 'solid' laminate from Fig. 4, to be 47 %. For the 'perforated' material, the laminate cross-section shown in Fig. 5 was used to determine the average major and minor axes, 2a and 2b, of the elliptical bundle sections. Composite properties could therefore be presented in terms of stress per unit cross-sectional area of composite containing fibres aligned parallel to the straining axis for the case of the 'solid' laminate and as stress per fibre bundle for the perforated material. In both cases it is assumed that the weft fibre bundles do not contribute to the load-carrying capacity of the laminate. Direct compression testing was carried out on 18 mm wide strips of composite machined from each laminate. The ends of each strip were supported transversely by split steel grips. Each grip contained an accurately machined channel into which the test strip was located. The grip halves were clamped together with two high tensile steel screws. The faces of the grip halves were covered with two layers of adhesive tape

Fig. 5. Optical micrograph of the'perforated' plain-weave laminate section showing the brass wires (white), approximately elliptical cross-section of the bundles and their curvature.

22

E. Wilkinson, T. V. Parry, A. S. Wronski

which served to prevent slippage and damage to the specimen corners. The grips were therefore re-usable and specimens of various gauge lengths (measured between the lower face of the upper grip and the upper face of the lower grip) were prepared with the aid of an alignment jig. Poorly aligned specimens could be readily identified from the type of load
(a) Microstructure The cross-sectional area of the fibre bundles in the balanced 'perforated' laminate was determined by photographing six bundles and tracing the resultant micrographs on to graph paper. The value obtained in this manner was 0.876 + 0.042mm 2. As there were discontinuities in the laminate, subsequent calculations refer to bundle loading, i.e. to the warp area of C F R P carrying the load. The microstructure of the balanced 'solid' laminate was similarly investigated by photographing transverse sections (e.g. Fig. 4). The approximately equal fibre loading in the orthogonal directions, the three plies, the bundle curvatures, and resin-rich areas ( ,-~6 ~o) are to be noted in this Figure. As the number of warp and weft bundles is equal and the

Compressive failure in carbon fibre fabric-epoxy laminates

23

latter do not contribute significantly to the axial load-carrying capacity, the mechanical properties data will be presented in terms of actual crosssectional area loading and also in terms of all the stresses being carried by the warp bundles of the plies, which amounted to 47 % of the total crosssectional area. Figure 4 also allows the measurement of the bundle radii of curvature. The maximum curvature in each bundle was staggered from ply to ply and approximated to 0-25 m m - 1 (Fig. 4). The bundle semiminor axis (see Fig. 4), b, was ~ 0.08 mm. Similar measurements (Fig. 5) gave a value for b in the 'perforated' material of 0.225 mm. Simple geometry 1° was employed to calculate the pre-existing bundle radius of curvature, R. The length of 40 bundle units was measured to be l 1 6 . 6 m m and the total lamina thickness was 0.90mm, giving the centre line of a single bundle an amplitude of 0-45 mm. Half this amplitude, 0.225 mm, was the height of the segment of length 2.92mm, i.e. by Pythagoras's theorem, R was evaluated at 4.85 mm.

(b) Mechanical properties The tensile strength of the 'solid' specimens was 430 + 40 MPa which translates to a bundle strength of 910 _+ 90 MPa, compared with the bundle strength of 650 _+40 M Pa in the 'perforated' laminate. From bend testing the Young's modulus of the composite was found to be 60 _+ 3 GPa. The bundle testing strength of the 'perforated' material was 650 _+ 40 M P a and the modulus was 110 _+ 4 G P a . The majority of the tests were performed in axial compression and the data are presented in Figs 6 and 7. It is seen that as the gauge length decreased from ,-~45 m m to 5 m m the bundle strength rose from ~ 110 to 980 MPa for the 'solid' laminate and from ~ 2 5 to ~225 MPa for the 'perforated'. 'Solid' samples with gauge length exceeding --~20 m m failed by Euler buckling (of the specimen), commencing on the compressive surface and subsequently on the tensile. In the transition region of 15-20mm gauge-length compression failure was associated with interlaminar (shear) cracking. The short samples failed by kinking and delamination (e.g. Fig. 8). In no case, with this or 'perforated' material, did the grips appear to cause the initiation of failure. In the 'perforated' material a transition in failure mode again occurred at a gauge length of ~ 12 ram, with longer samples failing between the two central weft bundles by Euler buckling in the middle of the gauge length.

E. Wilkinson, T. V. Parry, A. S. Wronski

24

20

40

60

i

i

I

Slenderness Ratio 80 100 120 140 i

i

160

i

180

I

i

1400 6OO ~'zE1200 (a) ,

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-'~

~ 80O "

"-- ...

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._=

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... (c)

=

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600 -

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200

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0

I

I

I

5

10

15

1

I

I

1

0

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0

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I

I

20 25 30 35 40 45 Gauge Length in mm Fig. 6. Compression strengths (expressed as load per unit specimen area and per warp bundle) of the 'solid' laminate for various gauge lengths (expressed also as the ratio of gauge length to radius of gyration). Plotted also are the Euler curve, (b), its tangent-modulus modification with E t = 0.25E c, (c), and the Parry-Wronski bundle compressive strength, (a).

20 i

~ 24C

40 ~

60 ~r

Slenderness Ratio 80i 100 120 i i

140 i

160 n

180 n

I

I

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-

(a) --'---

1

{~ 16C

" ~ \ \ \

120[

0

f

I

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5

10

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- I- -

20 25 30 35 40 45 Gauge Length in mm Fig. 7. Compression strengths, expressed as load per unit warp bundle area, of the 'perforated' laminate for various gauge lengths (expressed also as a slenderness ratio). Plotted also are the Euler curve (for individual bundles), (b), and the Parry-Wronski compressive bundle strength, (a).

Compressive failure in carbon fibre fabric-epoxy laminates

25

Fig. 8. Longitudinal section of the failed region of a long 'solid' specimen. Note in (a) the splitting and compressivefailure of the central ply, shown at higher magnification in (b) to be kink-initiated.

Fig. 9. Compressive failure in short 'perforated' specimen showing in (a) the breaking away of the curved warp bundle from the weft bundle and in (b) kinking of the central bundle which resulted in failure. The compressive failure mode of the short samples (e.g. Fig. 9) was associated with kinking and bundle delamination. Microscopic examination indicated that failure was initiated by the breaking away o f the (already) curved longitudinal fibre bundles from the weft bundles (e.g. Fig. 9(a)). This detachment led to kinking of the longitudinal (warp) bundles (e.g. Fig. 9(b)).

26

E. Wilkinson, T. V. Parry, A. S. Wronski

The transverse tensile strength of the 'perforated' materials was evaluated at 15.6 + 2.9 MPa, whereas that of the 'solid' C F R P was no less than 27 MPa.

DISCUSSION The relevant Euler buckling formula for our loading geometry is:

4n2E O-c =

(8)

where a c is the compressive strength, E the composite modulus, l the gauge length and K the radius of gyration. F r o m flexural tests E was estimated to be 60 G P a for the 'solid' material (128 G P a bundle modulus) and 110 G P a was the value for bundle modulus in the 'perforated' CFRP. The ratio of the second m o m e n t o f area to the cross-sectional area, K 2, was calculated for the specimen dimensions in the case of the 'solid' C FR P and for an elliptical bundle, a = 1.05 m m and b = 0.225 ram, for the 'perforated' material. The resultant Euler curves are plotted in Figs 6 and 7. It is seen that down to a cut-off at a slenderness ratio (gauge length/K) of ~ 60 the fit is good for the 'perforated' material, but that deviations exist for the 'solid' C F R P . This may be due to insufficient account being taken of the microstructure and/or non-linear effects. A reduced-modulus 12 theory curve is therefore plotted from 0.5 O'max for the reduced modulus value of 0.25E (Fig. 6(c)). The composite compressive strengths (small gauge lengths) were calculated using the Wronski and Parry 7-9 modification of the Swift-Piggott 4-6 analysis for surface fibre bundles with existing curvature. Recalling eqn (7), 2R

O-c(my)- 7tb O't

and taking, for the 'perforated' laminate, R = 4.9 mm O"m = 15.6 M P a

b = 0.225 mm

(7)

Compressive failure in carbon fibre fabric-epoxy laminates

27

ire evaluates at 216 MPa, in agreement with the observed values. For the 'solid' C F R P the relevant parameters were R = 4mm O"m =

27 MPa

b = 0.08 mm but the critical situation arises in the region where adjoining bundles have opposite curvature. As 1/Reff= 1/R 1 + 1/R 2, l/Refr being the total curvature and R1 and R 2 the radii of curvature of the adjoining bundles, the value of R employed should be 2 mm. Accordingly trc evaluates at 430 MPa, again in agreement with the data. The excellence of this agreement may be fortuitous, but we would suggest that its existence is not. The importance of curvature of fibre bundles and their action in unison and the role of the matrix have been demonstrated by Piggott 4 and Parry and Wronski 7-9 in nominally uniaxially aligned glass and carbon fibre composites. Material characteristics such as bundle size and curvature are designed in woven fabric composites and it is encouraging that our simple analysis appears applicable to quite complex materials. The analysis indicates the role of cloth geometry in determining compressive strength and permits a comparison of the relative efficiency of the two types of weave. Resolving the properties to (ultimate) bundle compressive strengths, 980 MPa for the five-end sateen 'solid' should be compared with 225 MPa for the plainweave 'perforated' CFRP. This difference we have associated with the stronger matrix (27 compared to 16 MPa) and, particularly, the smaller curvature and ply thickness (b) in the sateen-weave material. Interestingly, the actual bundle curvatures are not very different (0.20 compared to 0-25 mm-1), but, whereas in the plain-weave there is no 'opposite' curvature for the inter-bundle matrix to support, in the sateen weave there is, to such an extent that the curvature is doubled to 0.5 mm - 1 (see Fig. 4). The applicability of the Euler buckling analysis to the 'solid' laminate specimen and to the entire bundle length for the 'perforated' CFRP is also interesting and clearly shows why different specimen geometries should yield different values for the 'compressive strength'. The fit for the 'solid' laminate was imperfect, even at large gauge lengths and if agreement between data and theory was secured for these, it would persist also for intermediate slenderness ratios.

28

E. Wilkinson, T. V. Parry, A. S. Wronski

Attention should also be drawn to the similarity between the tensile and compressive bundle strengths of the 'solid' CFRP: 910 and 980 MPa, indicating to us, again, the importance of the resin and interfacial strengths 9 which can influence both the tensile and compressive strengths of composites. In the sandwich beam with Nomex core the compressioninduced failure corresponded to a skin flexural value (resolved on to axial bundles) of ~ 670 MPa. There is no correspondence between tensile and compressive strengths of the 'perforated' laminate: 650 compared to 225 MPa. This is but one indication that our simple approach, though encouraging, needs development and the study of woven fabrics of varied geometries.

ACKNOWLEDGEMENTS The authors are grateful to Mr B. Hicks and Mr C. Burrows of Lucas Aerospace for the gift of the materials and useful discussions during the course of this investigation.

REFERENCES 1. W. D. Bascom, J. L. Bitner, R. J. Moulton and A. R. Siebert, The interlaminar fracture of organic matrix, woven reinforcement composites, Composites, |1 (1980) pp.9 18. 2. A. G. Evans and W. F. Alder, Kinking as a mode of structural degradation in carbon fibre composites, Acta Metall., 26 (1978) pp. 725-38. 3. A. T. C. Robinson and R. Marks, Woven Cloth Construction, The Textile Institute and Butterworths, Manchester, 1967, pp. 36 and 132. 4. M. R. Piggott, A theoretical framework for the compressive properties of aligned fibre composites, J. Mater. Sci., 16 (1981) pp. 2837 45. 5. M. R. Piggott, Compressive properties of resins and composites, in: Developments in Reinforced Plastics--4 (ed. G. Pritchard), Elsevier Applied Science, London, 1984, pp. 131-63. 6. D. G. Swift, Elastic moduli of fibrous composites containing misaligned fibres, J. Phys. D.: Appl. Phys., 8 (1975) pp. 223-40. 7. T. V. Parry and A. S. Wronski, Kinking and compressive failure in uniaxially aligned carbon fibre composite tested under superposed hydrostatic pressure, J. Mater. Sci., 17 (1982) pp. 893-900. 8. A. S. Wronski and T. V. Parry, Compressive failure and kinking in uniaxially aligned glass-resin composite under superposed hydrostatic pressure, J. Mater. Sci., 17 (1981) pp. 3656-62.

Compressivefailure in carbonfibre fabric-epoxy laminates

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9. A. S. Wronski and T. V. Parry, Testing under complex loading to aid analysis of failure in fibrous composites, in: Proc. First Int. Conf. Post Failure Analysis Techniques for Fiber Reinforced Composites, Dayton, Ohio, 1985. 10. E. Wilkinson, Final Year Materials Project Report, University of Bradford, 1985. 11. T. V. Parry and A. S. Wronski, Selective reinforcement of an aluminium alloy by adhesive bonding with uniaxially aligned carbon fibre/epoxy composites, Composites, 12 (1981)pp. 249-56. 12. J. M. Gere and S. P. Timoshenko, Mechanics of Materials, 2nd edn, Wadsworth International, Boston, 1985, p. 580.