Correlations for the fracture of composite materials

Scripta

METALLURGICA

Vol. 16, pp. 9 9 - 1 0 3 , 1 9 8 2 Printed in t h e U . S . A .

Pergamon P r e s s Ltd. All rights reserved

CORRELATIONS FOR THE FRACTURE OF COMPOSITE MATERIALS J.K. Wells and P.W.R. Beaumont Department of Engineering University of Cambridge Trumpington Street Cambridge CB2 IPZ

(Received

I.

November

4,

1981)

Introduction

It has long been known that materials with some ductility show two fracture modes, depending on the length of any notch they may contain. When the notch is short, failure occurs by general damage leading to ductile fracture of the remaining section, at a net section stress which is independent of the notch length, a. Longer notches, however, produce crack-tip stresses that are large enough to cause failure at the tip, so that the crack propagates while the deformation in the material remote from it is still elastic, and at an applied stress which depends on the square root of the reciprocal of the crack length, I/~a. We call this the regime of single crack propagation. The overall behaviour is summarised in Fig. I: roughly speaking, the material fails at the lower of the two stresses. Similar regimes may be identified in composite materials. When notches are absent or are short, general damage occurs as dispersed, small cracks in the matrix, as fibre breakage, or as decohesion at the fibre-matrix interface, leading to a degradation and failure of the entire section. But when a long notch is present, it may propagate as a single crack, with little deformation in the material remote from its tip. 2.

Construction of Master Plots

\ b ~o~ w

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The literature (I-16) contains a large a:nount of data ~ "---' ~~ -' - ~ - - - ~ G E N E ~MODE L for fracture strength, o, of fibre-reinforced polymers ~ as a function of crack length, a. These data have been used to construct "master plots" to show the underlying similarities between different materials and lay-ups. To do so, the notched strength data have first been normalised using the unnotched strength quoted by the authors, a, C R A C K L E N G T H and then plotted as a function of crack length. The plots (Figs. 2, 3 and 4) show data for carbon, glass and Kevlar 49 fibres in epoxy or polyester matrices. Only lay-up Fig. i. Schematic showing the sequences which include at least one OO ply are included; variation of fracture strength but these comprise a total of 250 results for 14 diffewith crack length for a ductile rent constructions and three fibre types, and each rematerial. suit is itself the average of several tests. The plots include data from specimens with central circular holes, central slits and inclined slits. The crack length a is taken as half the width of a central hole or slit and equal to half the projected crack length normal to the loading direction for an inclined slit. Specimen widths varied between 12 and 70 nan. The path of the propagating crack varied depending on material type and construction; in general the failure involves splitting parallel to the fibres, and the fracture surface was not always perpendicular to the applied load.

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Variation of normalised strength, cr/O'u, w i t h crack half-length, a, for carbon, glass and Kevlar composite laminates. The references in order are:

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Vol.

16,

No.

I

FRACTURE

OF

COMPOSITE

MATERIALS

i01

The failure stresses quoted in most papers had already been corrected for the finite width of the specimens. Where this had not been done, the standard correction(17) was applied using: Y Ofinite width where

Y = 1.77 + 0.227

(2__aa) _ O.510 w

(2a) 2 + 2.7 (2~a)3 w

w

for a central slit of length 2a, in a specimen of width w. (This correction applies to strictly isotropic materials only, but Nuismer and Whitney(4) note that a rigorous orthotropic correction factor seems to over-compensate. In any event the correction is small for almost all the data.) 3. Figs. 2, 3 ture by general When failure is strength of the

Interpretation

of the Master Plots

and 4 show a pattern of behaviour like that described in the Introduction: fracdamage when cracks are short, and by single crack propagation when they are long. caused by general damage, it occurs when the net section stress exceeds the material, so that: o a --=l--Ou w

Generally w is much larger than a, so that the term a/w can be dropped. terion is plotted as the horizontal line ~/o u = 1 on the figures. When,

instead,

failure is by single crack propagation, o___ =

Ou

This failure cri-

it occurs at the applied stress:

KIC Ou

(where, again, we assume a/w << i). This criterion is plotted for two values of KIC/O u which differ by a factor of 2, on the three figures. The two lines bracket mere than 90 % of all the data, for all lay-ups, fibre types and matrices. The plots show that cracks of length less than about 2 mm fail at stresses between 65 % and 105 % of the nominal unnotched strength. Such cracks are sufficiently short for the net section to fail by general damage. The data for longer cracks are bounded by the two constant KiC/Ou curves. The scatter in the results reflects the inevitable differences in material preparatlon and test methods between authors, for which the normalisation does not allow. Any systematic difference in behaviour between holes, slits and angles slits is small by comparison with the scatter. However, it is noted that 10/+45/90 type laminates have a normalised notched strength which is about 12 % higher than-- O/~451 and other constructions, in the single crack regime. The data from all three master plots are combined in a different way in Fig. 5. plot of the normalised (apparent) fracture toughness from: KIC ou

It shows a

o ~a ou

plotted against crack length, a. When cracks are short (a ~ 1 rmn), the data follows the general damage criterion (plotted as the curve o/o u = I). Just above a = 1 nTn the data deviate from the general damage law, and tend towards the horizontal line expected when failure is by single crack propagation at constant KIC. This plot is a better way o~ estimating the normalised toughness KIC/O u. It is seen that the value KIC/O u = 0.045 m ~ is conservative. 4.

Comparison with Other Theories

Whitney and Nuismar (18) postulated that failure is determined by the stress distributions ahead of the crack tip. They developed two (related) criteria, the first requiring that a critical stress be reached at a point which lay a distance do ahead of the crack (the "point stress" criterion), and the other requiring a critical value of the average stress over a distance extending ao ahead of the crack tip("average stress" criterion). They presented evidence that do

102

FRACTURE

OF

COMPOSITE

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Fig. 5. The variation of normalised fracture toughness, KiC/Ou, for all the data presented in Figs. 2, 3 and 4. The predictions of the P~int Stress and Average Stress criteria are also shown.

and ao are constant for a number of lay-ups, and for a number of combinations of fibre and matrix materials. Their predictions, using their recommended values of do = i.O mm and ao = 3.8 mm are plotted on Fig. 5. Agreement is fair, and could be improved by another choice of do and a o (e.g. do = 0.4 mm and ao = 1.5 n~n for a lower bound). The main feature of these criteria is that, by choosing a fixed critical distance (do or ao), they lead to an apparent fracture toughness which falls when the crack length is shorter than the critical distance. Our interpretation is a different one: that the reduction is due to a change from a single-crack mode of failure to one associated with general damage. 5.

Conclusions

When data for the normalised fracture strength of composites, o/o u (where o is the fracture strength of a sample containing a crack of length a and o u is the unnotched strength) are plotted against crack length, two regimes of behaviour appear. When cracks are short (a < 2 ram), the composite fails by a general-damage mechanism, at a stress which is independent of the initial crack length. But when cracks are longer (a > 2 ram), the composite fails by the propagation of the crack, with little or no general damage, and at a stress which depends on a-~. General damage consists of the accumulation of broken fibres, until the probability of adjacent breaks reaches a critical level, when failure occurs. Single crack failure occurs when the crack length is great enough to focus all damage at the crack tip; then the crack becomes unstable at a stress which can be calculated using the standard methods of fracture mechanics. The data can be plotted to determine the fracture toughness of the composites in this regime. The results show a remarkable consistency: over 90 % of the data for a wide range of composites containing at least one 0 ° ply are bracketted by values of KIC/a u which lie in the range: K

IC _ 0.07 + 0.02 m ½ u

Vol.

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FRACTURE

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Acknowl edsements

The authors would like to thank Professor M.F. Ashby for most helpful discussions and advice in the course of this work. One of us (J.K.W.) wishes to acknowledge the financial support of the Science and Engineering Research Council. 7. I. 2. 3. 4. 5. 6. 7. 8. 9. i0. Ii. 12. 13. 14. 15. 16. 17. 18.

References

Morris, D.H. and Hahn, H.T., ASTM STP 617, p.5, Philadelphia (1977). Morris, D.H. and Hahn, H.T., J. Comp. Mater. ii, 124, (1977). Mar, J.W. and Lin, K.Y., J. Comp. Mater. 13, 278, (1979). Nuismer, R.J. and Whitney, J.M., ASTM STP 593, p.l17, Philadelphia (1975). Whitney, J.M. and Kim, R.Y., "Effect of stacking sequence on the notched strength of laminated composites", ASTM STP 617, p.229, Philadelphia (1977). Whitney, J.M. and Nuismer, R°J., J. Comp. Mater. 8, 253, (1974). Potter, R.T., Proc. Roy. Soc. Lond. A361, 325, (I~78). Cruse, T.A., J. Comp. Mater. 7, 218, (1973). Whitney, J.M. and Kim, R.Y., 7. Comp. Mater. IO, 319, (1976). Bishop, S.M., RAE TR. 77093. Royal Aircraft Establishment, Farnborough, Hants. (1977). Hishop, S.M. and McLaughlin, K.S., RAE TR.79051. Royal Aircraft Establishment, Hants. (1979) Daniel, I.M., AFML-TR-76-244, (1976). Hart, W.G.J., NLR MP79OI6V, National Aerospace Laboratory, NLR, Amsterdam. (1979). McGarry, F.J. and Mandell, J.F., Discussion of the Faraday Division, Chemical Society, University of Nottingham, September (1972). Owen, M.J. and Cann, R.J., J. Mater. Sci. 14, 1982, (1979). Zweben, C., "Fracture of Kevlar, E-glass and graphite composites", presented at ASTM Symposium on Fracture Mechanics in Composites, Gaithersburg, Maryland, (1974). Brown, W.F. and Srawley, J.E., "?lane strain crack toughness testing of high strength metallic materials", ASTM STP 410, ~hiladelphia (1966). Whitney, J.M. and Nuismer, R.J., J. Comp. Mater. 8, 253, (1974).