The shear fatigue of unidirectional fibre composites

The shear fatigue of unidirectional fibre composites D.C. PHILLIPS and J.M. SCOTT

The shear fatigue of unidirectional composites of carbon, glass and Kevlar 49 fibre, has been studied by low frequency torsion cycling. During either constant shear stress or shear strain amplitude cycling there is initially a slow decrease in shear modulus, strain amplitude increasing and stress amplitude decreasing approximately linearly with log (number of cycles), due to fibre/matrix debonding, until eventually macroscopic cracks initiate and propagate at a clearly definable fatigue life. The rate of change of shear modulus prior to cracking increases, and the fatigue life decreases, with increasing stress or strain amplitude. Fatigue in this mode of testing is considerably more severe than in short beam interlaminar shear fatigue, with fatigue lives of 103 -104 cycles at 50% of ultimate stress or strain. An important objective of the design engineer working with fibre composites is to arrange the lay of fibres so that tensile stresses are maximised in the fibre directions and transverse tensile stresses and shear stresses parallel to the fibres are minimised. Apart from the very simplest applications it is difficult to achieve this ideal and real structures are invariably subjected to stresses acting in directions of weakness. Even in the best designs shear stresses occur parallel to fibres or laminae during bending, at stress concentrations, at joints, and between laminate plies. Under static conditions these stresses can be accommodated in the design because sufficient information already exists about the static shear properties of composites. Under conditions of varying load the situation is quite different and for the accurate design of critical structures there is a need for information about the shear fatigue behaviour of composites. Measurement of the shear properties of fibre composites is not altogether straightforward. Many techniques have been suggested but most, if not all, introduce non-shear stresses which can modify the shear characteristics. 1 Experimentally the easiest and most widely employed method is the short beam interlaminar shear test. While this is economical and simple, and useful for quality control, for more analytical work it suffers from the disadvantages of non-uniform stresses, states of combined stress, and severe stress concentration. A more accurate but more expensive test method for unidirectional composites is the torsion technique, and this has been used to study the shear behaviour of cfrp under rising load, = creep, 3 and fatigue 4,s conditions. When a rod is twisted, shear stresses are induced on planes parallel to the rod axis, the stresses being greatest at the surface and reducing to zero at the centre. For most materials the torque-twist curve is non-linear and the shear stress varies non-linearly from the axis to the surface. Under these conditions the shear stresses can be calculated for circular section rods by a procedure due to Nadai. 6 Ideally the torThe authors are with the Materials Development Division, AERE, Harwell, Didcot, Oxon, UK. This paper was presented at the SEE Fatigue Group conference on 'Fatigue of frp' held on 29 June 1977 at City University, London.

COMPOSITES . OCTOBER 1977

sion test should be carried out on thin-walled tubes, which exhibit a linear behaviour to failure and through which there is negligible shear stress variation, but for ease of fabrication and to reduce costs it is more convenient to use solid rods. Shear strengths obtained from such rods agree well with values obtained from thin-walled tubes, 7 supporting the validity of the Nadai procedure for fibre composites, and the fatigue data described here have been obtained by the low frequency cycling of such solid rods. MA TERIA LS A N D TESTING

Torsion measurements have been carried out on unidirectional fibre composites containing high modulus surface treated carbon fibre (cfrp I), high strength surface treated carbon fibre (cfrp II), glass fibre (grp), and Kevlar 49 (Krp). All were made by a wet lay-up technique in the form of 6 mm square section rods containing 60 volume percent of fibre in an epoxide resin matrix, Ciba-Geigy MY750 cured with methyl nadic anhydride and benzyldimethylamine in the proportions by weight of 100:80:1, heated for 2 hours at 120°C followed by 2 hours at 180°C. The Kevlar fibre was carefully dried out at approximately 110°C to remove absorbed moisture which can reduce adhesion of the matrix and fibres. Some measurements were also carried out on cast resin specimens. Torsion specimens machined from the solid rods were 150 mm long with the centre 100 mm turned down to a 6 mm diameter circular section, the 25 mm long ends being left square to enable them to be gripped in the jaws of the testing machine. During testing, one end was held in a driven chuck and the other end was gripped in a chuck to which was attached a moment arm linked to a tension-compression load cell. 5 Rising torque tests were carried out to measure static shear strengths, and fatigue was carried out at 'x,0.17 Hz under either constant torque (+- T) or twist (+- 0) amplitude conditions at constant speed of angular rotation. During testing torque and twist were monitored continuously. Conventional flexural and short beam interlaminar shear tests were also carried out and data for the composite systems are shown in Table 1.

233

Table 1. Typical mechanical properties of the composites

Flexural data Material

Fibre

Strength MN/m 2

Torsional data

ils* strength MN/m 2

Modulus GN/m 2

Shear strength MN/m 2

Shear modulus GN/m 2

Shear strain (x 10 -3)

cfrp I

Courtaulds Grafil HM-S

18701

611

1801

63

4.3

25

cfrp II

Courtaulds Grafil HT-S

1270

93

106

76

3.7

39

grp

Silenka E glass

1430

82

36

79

3.7

67

Krp

Du Pont Kevlar 49

700

57

56

48

1.9

27

1 Manufacturers' data * Interlaminar shear

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10 3

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Number of cycles

Fig. 2 The variation of torque on reversed cycling cfrp at constant angular amplitude (similar behaviour is observed with other fibre composites), the various curves were obtained by cycling at different percentages of the static failure angle; macroscopic cracking occurs at the first knee (arrowed)

Angle of twist 20 ° II

40 ° II

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I000 I

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Surface shear strain ( x 10 -3)

Fig. 1

Torque-twist

behaviour

of unidirectional

composites

RESULTS

Typical torque-twist curves for cfrp II, grp and Krp are shown in Fig. 1. The curves are non-linear for cfrp and grp and shear strengths, and maximum shear stresses in fatigue, have been calculated by the Nadai procedure. The maximum shear strain at the surface is proportional to the angle of twist, 10 ° of twist being equivalent to a surface shear strain of 5.3 x 10 -3, but the maximum shear stress is not proportional to the torque as it depends on the shape of the torquetwist curve. During fatigue the shape of the curve can vary slightly so that constant torque amplitude conditions are not strictly constant shear stress conditions, but the changes are generally small and may be ignored to a first approximation. s Shear strengths, failure strains and elastic shear moduli calculated from the initial linear stage are also shown in Table 1. On cycling under constant angular amplitude conditions between -+ 0 °, all the composites exhibit behaviour similar

234

to that shown in Fig. 2 for cfrp. Initially torque decreases relatively slowly and linearly with log (No of cycles) until after a lifetime (Nf) characteristic of that amplitude, one or more macroscopic cracks are initiated and propagate along the specimen axis resulting in a rapid decrease in torque. No cracking is observed prior to this. The variation of fatigue life Nf with shear strain amplitude for the different composites is shown in Figs 3-6. Most of the data have been acquired for cfrp and this shows that fatigue life increases logarithmically with decreasing strain amplitude, scatter decreasing as lifetime increases, s Prior to cracking the rate of decrease of torque, or stress, increases with increasing strain amplitude. Previous work s has shown that for cfrp I and cfrp II the slope of this linear region, & T/log N, varies linearly with shear strain amplitude % the data obtained from the different composite systems falling on the same straight line with a correlation coefficient of 0.92. The more recent results for cfrp II, grp and Krp are plotted this way in Fig. 7. The data for cfrp and grp line on a line close to that of the cfrp I and cfrp II investigated earlier, while the Krp data fall on a different line. Analogous behaviour is observed under constant torque amplitude conditions, compliance increasing steadily until macroscopic cracking causes total failure. Fig. 8 shows the behaviour of cfrp, strain amplitude increasing approximately linearly with log (No of cycles) until failure occurs. The

COMPOSITES . OCTOBER 1977

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IO Fig. 3 Fatigue lives of cfrp I in reversed cycling under constant angular amplitude.

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Fotigue life (cycles)

Fig. 5 Fatigue lives of grp in reversed c.4tcling under constant angular amplitude

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Fig. 4 Fatigue lives of cfrp II in reversed c y c l i n g u n d e r c o n s t a n t angular amplitude

variation of fatigue life of cfrp II with shear stress amplitude is shown in Fig. 9. The rate of increase of strain amplitude increases with increasing shear stress.

X

fatigue, the different composite systems behave in a very similar way. Under constant shear strain amplitude conditions torque, and thus shear stress, initially decreases linearly with log (No of cycles). This behaviour is different from that of unreinforced resin s in which the shear modulus of the material remains unchanged on cycling until catastrophic failure occurs, and this and other indirect evidence has suggested that the early increase in compliance of the composite during shear fatigue is due to debonding.S In

Fig. 10 shows the combined fatigue life data obtained from the different composite systems under constant shear strain amplitude. Cycling under purely shear conditions clearly has a very severe effect on unidirectional composites, all failing at approximately half their static strains to failure at approximately 10 3 cycles. Short beam interlaminar shear fatigue experiments do not result in such rapid fatigue failure. Owen and Morris 7 for example, report a shear strength

COMPOSITES

. OCTOBER

1977

i0 3

Fig. 6 Fatigue lives of Krp in reversed cycling under constant angular amplitude

DISCUSSION

The static shear properties of the composite systems are very different. The torque-twist and thus shear stress/shear strain behaviour of Krp is linear to failure while the behaviour of cfrp and grp is distinctly non-linear. The non-linear behaviour of cfrp and grp is due predominantly to viscoelastic deformation of the matrix with possibly a contribution from debonding s but Krp fails in shear before the stresses in the matrix are sufficiently high to induce inelastic matrix deformation.

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~_

04

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0

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3o

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Sheor strata amplitude(x I0 3)

Fig. 7 Rate of decrease of torque during constant strain amplitude cycling

235

reduction of approximately 12% at 103 cycles and only 25% at 106 cycles. Fatigue in torsion results in a more rapid breakdown in the properties of the materials than does short beam interlaminar shear fatigue. The increase in compliance prior to cracking, which has been attributed to debonding, is more rapid at higher stress or strain amplitudes and Fig. 7 shows the behaviour of AT/log N as a function of strain amplitude. The grp and cfrp data fall on one line while those of the Krp fall on another line. Both sets of data suggest that the change in compliance decreases to zero at a shear strain amplitude of between 8 and 12 x 10 -3, implying that debonding does not occur at lower strain. It has been pointed out earlier s that this does not in itself prove that there is a fatigue limit at those amplitudes, since for unreinforced resin AT/log N is zero at all amplitudes, and it is possible that in fibre composites there is a transition in the dominating fatigue mechanism at low strain amplitudes from debonding to the initiation of matrix cracking. It is interesting that the grp and cfrp data are similar while the Krp data is very different. The shear modulus and strength of Krp is much lower than those of the other composite systems, and the effects are probably related.

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I i0 °

I i0 t

I i0 2

I i0 3

I 10 4

Fatigue life (cycles)

Fig. 10 Combined data for resin and composites showing variation of fatigue life with strain amplitude in constant angular amplitude reversed cycling

Cyclic shear stresses clearly have extremely severe effects on unidirectional fibre composites, and fatigue in shear is probably potentially the most dangerous failure mode of high performance composites. Although debonding can be minimised by keeping shear strains low, it is not clear whether there is a fatigue limit below which indefinitely long lives can be achieved. Further work is required to establish this. Care must be taken to accommodate fatigue weaknesses in designing structures, and there is considerable scope for investigating ways of ameliorating shear fatigue by the modification of the matrix and the fibre/matrix interface.

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A CKNOWL EDGEMENTS lO 4

Number of cycles

Fig. 8 The variation of angular amplitude on reversed cycling of cfrp at constant torque amplitude; the mean static failure torque was 4.2 Nm

We are grateful to N. Buckley for carrying out some of the measurements reported here. Part of the work has been funded by the Procurement Executive of the Ministry of Defence.

REFERENCES 5.0 4.5 4.0

1

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}

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2

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L

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10 2

10 3

104

Fatigue life ( c y c l e s )

6 7 8

Fig. 9 Fatigue lives of cfrp II in reversed cycling under constant torque amplitude

236

Purslow, D. 'The shear properties of unidirectional carbon fibre reinforced plastics and their experimental determination', R A E Technical Report 76093 (1976) Hancox, N.L. 'The use of a torsion machine to measure the shear strength and modulus of unidirectional carbon fibre reinforced plastic composites', JMater Sci 7 (1972) p 1030 Hancox, N.L. and Minty, D.C.C. 'The torsional creep of carbon fibre reinforced materials', AERE-R 8499 (July 1976) (to be published in Fibre Science and Technology) Phillips,D.C. and Scott, J.M. 'Matrix toughening and its effect on the behaviour of cfrp, ICCMProceedings o f the 1975 International Conference on Composite Materials, volume 1, p 285 Phillips,D.C. and Scott, J.M. 'The shear fatigue of cfrp under low frequency torsion', AERE-G 645 (July 1976) (to be published in Fibre Science and Technology) Nadai, A. 'Theory o f flow and fracture o f solids" volume 1, (McGraw-Hill, 1970) Chapter 21, see also References 2 and 5. Hancox, N.L. Private communication Owen, MJ. and Morris, S. 'Some interlaminar shear fatigue properties for cfrp, Plastics Institute Conference - Research Projects III, (London, November, 1971) Paper 8

C O M P O S I T E S . O C T O B E R 1977