Composite Materials I

Fibre Reinforced Composite Materials An Introductory Review

BY B. A. PROCTOR Pilkington Research and Development Laboratories, Lathom,

Ormskirk, Lancashire

Received 30th May, 1972

The principles of reinforcement and the properties of fibre reinforced composites are briefly out- lined and then discussed with particular regard to the role which the interface plays in controlling fibre strength and the utilization of fibre properties. The contradictory requirements for interfacial bond strength and the limitations of anisotropy are discussed, and the suggestion made that high performance composites may need to be designed with particular property requirements and com- ponent performance in mind.

1. INTRODUCTION In the design of structures the ratio of material strength (or stiffness) to specific

gravity is often of more importance than the absolute value of strength or stiffness : this is particularly true in the field of aerospace but remains important in transporta- tion and for tall stationary structures such as towers. The specific strengths and stiffnesses of conventional " homogeneous " structural materials lie within a sur- prisingly narrow band (fig. 1) and in order to escape this limitation we have, over the last 10 years or so, turned increasingly to a range of high performance, fibre-reinforced, composite materials.

r - I

specific stiffness (E/s.g.) specific strength (o/s.g.)

FIG. 1 .-Relative specific properties of conventional materials.

For many years, brittle materials such as glasses and ceramics have offered attract- ive specific stiffnesses because of their high intrinsic bond strengths and somewhat open, low density structures. Often they had good high temperature properties too, but had the disadvantages of extreme brittleness and low strengths. Recently the

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64 FIBRE R E I N F O R C E D COMPOSITES

problem of low strength has been largely solved and a number of high strength reinforcing fibres, which offer many-fold increases in specific strength and stiffness over the conventional " homogeneous '' structural materials, have become available (fig. 2). The problem of brittleness has been partially, but none the less usefully, solved by incorporating such fibres as reinforcement in relatively weak matrices to form " Fibre Reinforced Composite Materials '7. This has turned an interesting scientific curiosity into an important branch of materials technology and led to significant improvements in the specific properties of useable solids (fig. 3).

t - L P- glass fibre

boron fibre

carbon fibre

sappnire whiskrr

graphite wl,'sker

specific stiffness (E/s.g.) specific strength (0ls.g.)

FIG. 2.-Relative specific properties of reinforcing fibres with background of conventional metal values.

(* unidirectional)

I - I I I I 1 t I I I L 1 2 3 4 5 4 3 2 1

specific stiffness (E/s.g.) specific strength (a/s.g.)

FIG. 3.-Relative specific properties of unidirectional glass reinforced plastic and carbon fibre reinforced plastic compared with steel, aluminium and titanium (representative alloys).

A true fibre reinforced material may be defined as one in which almost all of the load is carried by the fibres, so that the strength and stiffness are governed by the properties of the fibre. However, the surfaces of the reinforcing fibres and the inter- faces between fibres and matrices play important roles in controlling the properties of the composite. This paper attempts to outline these roles and (hopefully) to set the scene for subsequent papers within the context of a " Discussion Meeting on Surfaces and Solid-Solid Interfaces."

2. THE LAW OF MIXTURES AND THE STRENGTHS OF FIBRES The simplest fibre reinforced system is an array of unidirectional fibres set in a

matrix and stretching continuously through its length ; the whole assembly being stressed along the fibre direction (fig. 4). If A,, Af and A , are the total cross sectional

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B . A . PROCTOR 65

areas of composite, fibre and matrix respectively and E, 0, E (with similar subscripts) are the modulus, stress and strain respectively, then the total load F, borne by the composite will be shared between fibres and matrix according to,

If we make the further assumption that the strain in the fibres is the same as that in the matrix (i.e., Ef = E, = E,) we have

(2.2) This simple equation already indicates certain important requirements which are needed if the composite is to fulfil our definition of true reinforcement, i.e., AfEf must be significantly greater than A,&',, which means that the fibres must be very much stiffer than the matrix and must occupy a reasonable fraction of the composite cross section.

F = AfQf$.AmQm. (2.1)

I; = (AfEf + AmEm)Ec*

F

A f

FIG. 4.--Idealized unidirectional continuous fibre composite.

Since F = a,A, and A,/&, &/Ac represent the volume fractions (Vf and Vm) of fibres and matrix material respectively we can rewrite eqn (2.2) to express the com- posite modulus

Ec = Ef Vf + E m V m which is well known as the " Law of mixtures ". derivations give very similar results and (2.3) is certainly valid within experimental error for a wide range of unidirectional composites (e.g., fig. 5 ref. (3)). Since we have already deduced that the fibre must be significantly stiffer than the matrix, and the fibre content should be fairly high, EfVfgE,V,, and (2.3) illustrates the important con- clusion that composite stiffness is governed by the stiffness and concentration of fibres.

Eqn (2.2) may be rewritten to give the stress in the composite, Q,, in terms of stresses in the fibres and the matrix. Since most load is carried by the fibres we may assume that the composite fails when the fibres fail, hence composite strength 8, is :

(2.3) More rigorous '*

a, = a,v,+a:v, (2.4) where af = fibre strength and 02 = stress in matrix at the failure strain of the fibres. In practice, af Vf % 02 V, so that the strength of the composite (from eqn (2.4)) is seen to depend on the strength of the fibres which is, in its turn, governed by the condition of the fibre surface and hence of the fibre/matrix interface. This is the first way in which surfaces and interfaces are important to composite behaviour.

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66 FIBRE REINFORCED COMPOSITES

Recent papers 4-6 have stressed the importance of the " geometrical " perfection of fibre surfaces. Surface abrasion caused by quite normal handling techniques can easily introduce stress-raising cracks in the surfaces of brittle materials with consequent drastic strength loss. In the glass fibre field a considerable technology has been devoted to the development of surface coatings or " sizes " which lubricate and protect the fibre from the worst of the damage (fig. 6), but this factor should be borne in mind in the handling of all fibres prior to and during their incorporation in composites.

fibre volume fraction/ Vf FIG. 5.-Young's Modulus plotted against fibre volume fraction for carbon fibre-resin composites.

5 = mean value k standard deviation.

I000 2 0'00 3600 4000

breaking s trength/MNm-* FIG. 6.-Tensile strengths of single fibres extracted from a strand and compared with virgin fibre

strengths (E-glass, 2 cm test length).

Most strong solids lose strength as a result of heat treatment ; for glass silica * and sapphire at least, this has been shown to be due to the creation of local flaws at the fibre surface due to interaction between accidental dust contamination and the

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FIG. 7.-(Photograph). Heat treatment flaw on silica rod showing contamination core and surround- ing interacted and cracked region (ref. (9)).

To face page 671

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B . A . PROCTOR 67

fibre material (fig. 7). In composites we deliberately place fibres in intimate contact with the matrix : for metal matrices, in particular, fabrication temperatures are often high and one motive for their use is a need for high temperature composites. Inter- facial reactions occur with drastic effects on composite strength in a number of fibre/ metal systems lo-' (Harris, this Discussion).

Finally, the chemical environment at the fibre-matrix interface during stressing of the composite is important. Brittle solids are frequently subject to a type of stress- corrosion which leads to time-dependant strength effects, or static fatigue, in which the strength falls with longer times of stressing (fig. 8). Silica and glass interact with moisture in this way 4* * ; water diffuses through many resin matrices and may even collect as water at the interface.16* l7 Carbon fibres show this static fatigue behaviour at elevated temperatures in air and again oxygen may diffuse through plastic or metal matrices l8 (also Harris this Discussion w.r.t. nickel) to cause stress-rupture or stress activated corrosion type failure of the fibres. Thus by directly affecting fibre strengths, the condition of the fibre surface and fibre-matrix interface controls the load bearing ability of composites.

I - range of -- failure times

1

I day I yeor I I

10-2 100 10 * 10 (0

time to fracture/min FIG. &--Static fatigue of undamaged silica fibres in air at room temperature.

3. DISCONTINUOUS FIBRES A N D THE SHEAR STRENGTH OF THE INTERFACE

These important conclusions regarding composite behaviour have been derived without specifying in any way the degree or type of bonding at the interface between fibre and matrix. In making the equal strain assumption, however, it had been implicit that fibres and matrix were held together sufficiently for their deformations to be equal. More detailed considerations of load transfer and of the behaviour of composites containing discontinuous fibres impose additional requirements on the interface.

In some instances it is convenient to handle and incorporate reinforcing fibres in relatively short lengths, whilst other reinforcements (e.g., whisker crystals) are only available as short fibres. All brittle fibres contain flaws, and hence weak points, so will break up into discrete lengths under stress even if, as in many carbon and filament wound glass composites, they were originally incorporated as continuous fibres. In all these cases, the matrix must transfer load into the fibre by means of some gripping mechanism at the end region.

Consider a fibre of length I embedded in and bonded to a matrix of much lower modulus (fig. 9), the whole being subject to a tensile strain in the direction of the fibre. It is clear that in the region of the fibre the matrix will be restrained and differential

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68 FIBRE REINFORCED COMPOSITES

displacements near the fibre ends in particular will set up shear stresses in the matrix and at the matrix-fibre interface. This problem has been treated analytically by Cox l9 and others 20* on the assumption that fibre and matrix are elastic and re- main adhering. Cox showed that the tensile stress in the fibre rose rapidly from zero at the end ( x = 0) to a maximum (plateau) in the centre (x = 1/2) (fig. 9) according to

(Of), = EfEm{ l-(c*sh p(;-x))/cosh p i }

where p = (2G,/(Efrf210g,(rl/rf)))~ and E, = matrix strain, rf = fibre radius, rl = interfibre spacing.

Conversely, the shear stress at the interface was shown to be a maximum at the ends of the fibre, falling almost to zero in the centre (fig. 9) according to

Eqn (3.1) and (3.2) and fig. 9 show quite clearly that there is a region at the end of each fibre which is lightly stressed and is thus ineffective in carrying load (the ‘‘ in- effective length ”, Rosen 21) : for this reason the average stress carried by a length I of discontinuous fibre is less than that which would be borne by an equivalent length of continuous fibre ; the shorter the fibre the less effective it is as reinforcement, a fact recognized by Cox.

<Cf f o r frictional or yielding load transfer

FIG. 9.-Diagrammatic illustration of matrix deformation around discontinuous fibre in a low modulus matrix and the rise in fibre stress and interface shear stress along the fibre length.

Eqn (3.1) and (3.2) enable us to calculate the ratio of the maximum interface shear stress at the fibre end to the maximum tensile stress in the centre of the fibre. The values depend on matrix and fibre modulii and on length of fibre and fibre content : but for a long glass fibre in a typical resin matrix at V, = 50 %, the shear stress needed at the ends in order to realize a practical glass strength of -22000 MN/m2 would approach 280 MN/m2. This is clearly greater than the shear strength of any

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B . A . PROCTOR 69

present resin or the bond strength between resin and fibre. The estimates of shear stress are in themselves conservative since stress concentration effects are neglected in the Cox type of shear-lag analysis. More recent treatments based on finite element techniques which take some account of stress concentrations 22-24 indicate that the actual interface shear stresses are at least twice those predicted by Cox. This must imply some form of failure in the matrix at the fibre end which was first recognized by Outwater 25 in 1956 who discussed bond failure at fibre-ends in a glass reinforced plastic material and postulated that load transfer was essentially achieved by a frictional gripping of the fibre due, in turn, to resin shrinkage during curing. Kelly 26

also tackled this problem with reference to the yielding in shear of a metal matrix near the ends of a discontinuous fibre : it is possible that localized yielding may also occur in some resin matrices. Both Outwater's and Kelly's treatments assume essen- tially a constant and limiting value of shear stress, z, around the fibre ends; the tensile stress (0) carried by the fibre then rises linearly from the end according to

where rf = radius of fibres ; the rate of increase in (T being governed by z, the value of yield stress or frictional stress, but inevitably being lower than that in the " unfailed " elastic case (eqn (3.1) and fig. 9). Thus the bond strength and interfacial condition directly affect the " ineffective lengths " at fibre ends, hence the average load borne by discontinuous fibres, and thus both the modulus and strength of the composite in the fibre direction. In practice, the effect of this may be small since fibres are often and wisely used in lengths long compared with those theoretically required ; it may partly account, however, for the relatively low effective reinforcement of thermoplastics by short, chopped, high modulus fibres.

As well as affecting the average utilization of a given fibre strength, the interfacial shear strength may also effect the actual h e 2 of fibre strength utilized in a composite. Flaw-free fibres such as the " virgin " glass fibres tested by Thomas 27 and Cameron 2 8

have consistent strengths which are independent of gauge length, but flawed fibres of boron, carbon, " handled " glass, etc., have variable strengths which, on average, decrease as the tested length increases (or as the probability of including a weak spot increases, fig. 10 and, e.g., ref. (29), (30)). A lower value of interfacial shear strength or shear yield stress effectively spreads out the tensile stress distribution in the fibre as if a longer gauge length were being used, resulting in a lower available strength from flawed fibres.

The strengths of fibres and bundles of fibres have been treated statistically by Daniels 31 and Coleman,32 whereas Rosen in particular has applied these treatments to composite strength predictions.21* 33* 34 The important point here is that in order to make maximum use of fibre strength (and to a lesser extent of modulus) in unidirectional composites reinforced with discontinuous or flawed continuous fibres, the interfacial bond strength and/or shear yield strength should be high. Finally in these types of composites, deterioration in the bond or yield strength as a result of ageing, stress-rupture, stress or temperature cycling, or creep relaxation will lead to a fall in unidirectional composite strength. 34-3 *

mf" do = 27crfz dx. (3.3)

4. CRACK PROPAGATION A N D TOUGHNESS

Problems of low fracture toughness in unidirectional composites are associated with crack propagation perpendicular to the fibres by one, or a combination of more than one, of the mechanisms shown in fig. 11.

In fig. 1 l(a) an advancing matrix crack which may have initiated at a broken or transverse fibre, at a void, pre-existing crack, or surface notch causes direct fracture

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70 F I B R E REINFORCED COMPOSITES

of the reinforcing fibre. Clearly this is a very dangerous situation and such a com- posite will be extremely brittle and notch sensitive. The probability of this behaviour will be increased by high fibre-matrix adhesion, by a stiff and brittle matrix and by

6~

B 5 -

4 -

3 -

2-

FIG.

1 -

I

I000 20bo 3600

strength/MN 10.-Tensile strengths of single E glass fibres extracted from a strand,

B, 2 cm test length.

A

3

A, 10 cm test length;

high rates of loading since in these cases there will be little elastic or plastic relaxation locally and the extra load from the broken matrix will be transferred into a short length of fibre near the crack plane. Even if the matrix bond fails locally, by de- bonding or yield, a high remaining friction or yield stress will help to maintain the probability of fibre fracture as discussed by Cooper and Kelly.39

In practical composite materials, this behaviour is usually avoided, but in carbon fibre reinforced plastics, where the fibre-resin adhesion may be readily increased by surface treatments, the dangers are real as reported by Mallinder 40 and Daniels and H a r a k a ~ . ~ ~ Fig. 12 (ref. (40)) shows a dropin the flexural strength (tensile typefailures) of a carbon/epoxy composite as surface treatment (and interlaminar shear strength) increases.

The more usual and desirable composite situation is indicated in fig. 1 lb where an advancing matrix crack does not immediately break the fibre, which may be left bridging the crack and give a pseudo-ductile behaviour to an all-brittle composite

43 Discontinuous fibres may subsequently pull out of one side of the matrix if the crack advances further, continuous fibres may break at a weak point away from the crack and then pull out. Outwater and Murphy44 discuss this

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B . A . P R O C T O R 71

behaviour in glass reinforced plastics and consider the possibility of fibres debonding at the interface for some distance back from the crack rather than fracturing at the crack plane. They derive a condition for debonding (i.e., desirable behaviour as in fig. l l b ) as

where GI1 = interfacial bond energy, af = fibre strength, a = fibre diameter and Ef = fibre modulus.

G I I = (8:a)/8Ef (4.1)

0, U C

FIG. 11 break.

.-Crack propagation and initiation mechanisms. (a) Advancing matrix crack initiates fibre (c) Fibre break initiates matrix crack. (6) Advancing matrix crack leaves bridging fibre.

(d) Fibre break leaves matrix uncracked.

The same authors then derive an expression for the work to fracture of a com- posite when the crack spreads through an array of bridging fibres and, emphasizing the contribution of the work needed to debond the interfaces for some distance back from the crack surface, they conclude that the work to fracture per unit area of composite (GI) increases as the interfacial bond energy (Gii) and the interfacial frictional shear strength (z) decrease,

where bC = composite strength. G I = (a6:/4E VfT)((8c/Vf) - 2[2E,G, Ja] $} (4.2)

Kelly45 points out that the contribution of work

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72 FIBRE REINFORCED COMPOSITES

of pull out always exceeds that due to debonding. He derives expressions which lead to a work to fracture per unit area of composite of the form

where z = interfacial shear yield strength or frictional shear strength. In contrast to the requirements of the previous section, eqn (4.1), (4.2) and (4.3) indicate that tough unidirectional composites having a high work to fracture normal to the fibre direction must have relatively low interfacial bond strengths.

GI cc VJ&;a/z (4.3)

'"""t N I E

N I

E z

Y (d

FIG. extent of surface treatment+

posite (mean strengths and total spread of results). 12.-Flexural strengths and short beam shear test results for a carbon fibre epoxy-resin com-

The mechanisms shown in fig. l l c and 1 Id are really the inverse of l l a and l lb respectively, 1 Id being generally desirable and 1 lc potentially hazardous. Both types of behaviour have been particularly with carbon-resin systems where the interfacial bond may be varied over a wide range. Mechanism 1 l c is more likely when both bond and fibre strengths are high and when fibre diameters are large ; it is particularly dangerous with brittle matrices when an overlap with the regime of mechanism l l a can lead to entirely brittle behaviour and the complete loss of the point of separating the reinforcement into separate fibrous elements !

5. ANISOTROPY, TRANSVERSE PROPERTIES AND MULTI- DIRECTIONAL REINFORCEMENT

If a simple unidirectional composite is stressed in tension at an angle 0 to the fibres (fig. 13) the applied stress Q may be resolved into a uniaxial component (0,) along the fibres, a transverse component (or) and a shear stress ( T , , , ) . ~ ~ - ~ ~ The values of transverse stress (a,,) and shear stress (z,,) rise rapidly as 8 increases from zero and the

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B . A . PROCTOR 73

strength of the material, at an angle 8 to the fibres (&), may be considered in terms of 3 failure modes ; fibre breakage at very small 8, interfibre shear at intermediate values of 8 and transverse tensile failure at larger 8 (fig. 14, ref. (3)). This simple maximum stress failure criterion does in fact predict composite behaviour quite accurately, and agrees closely with more sophisticated theories.49 9

f i b r e I / d i r e c t i o n .5 - m0 -

FIG. 13.-Resolution of applied stress along and perpendicular to fibre direction in a unidirectional composite ; U, = u cos2 8, uY = u sinz 8, T~~ = u sin 8 cos 8.

In practice, the shear strength (.Zxy) and transverse strength (a,) are interface dominated and are very much less than the axial strength 6,; the composite is thus highly anisotropic, as indicated in fig. 14. Attempts to reduce this anisotropy by increasing the interfacial bond strength are limited by the strength of the matrix itself and by the need for toughness and resistance to crack propogation as discussed in the previous section. Morley 51* 52 (also this Discussion) has suggested a double interface system involving an outer surface which is strongly bonded to the matrix to provide transverse and shear strengths, and an inner surface of controlled and variable shear strength to prevent transverse crack propagation through the core part of the

2 0.05- E Y

0.02 -

I /

/ /.

/ or / interface shear

' matrix shear si necos0

matrix or interlace transverse tensile failure 6 - .zL

sin20 I I I I

30' 6r3' 9 0

angle 8

FIG. 14.-Tensile strength of unidirectional carbon-fibre epoxy-resin composite as a function of angle between fibres and test direction.

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74 FIBRE REINFORCED COMPOSITES

reinforcing fibre. This novel approach separates the competing requirements of high and low interface strength but the shear and transverse strengths of a unidirectional composite are still limited by the matrix properties.

An alternative approach is to arrange for the fibres to lie in more than one direction in order that some fibres will be able to act as " unidirectional " reinforcement against a stress applied in any direction. This also has limitations in that the fibre content and the effective fraction of fibres bearing the load, are both reduced as the degree of " multidirectionality " increases (fig. 15). Further, some fibres will always lie transverse to the applied stress when they will act as rigid inclusions 47* 53* 5 4 rather than reinforcement. They then magnify the stress at the interface and initiate debonding which can spread as a matrix crack. Precisely this failure mechanism has been observed by Owen 5 5 and McGarry 56 in studying the initiation of fatigue failure in multidirectional fibre composites.

6 . CONCLUSIONS Interfacial properties are seen to control, very directly, the strength and toughness

of composites via the initiation and propagation of failure, the efficiency of utilization of fibre strength, and the retention of fibre strength itself: to a smaller extent they affect elastic properties and utilization of fibre modulus. Creep, long term load bearing ability and weathering are also significantly affected. There are competing and contradictory requirements for interfacial properties.

unidirec tiona I

theoretical Vf(max) 91°f0

practical Vf (rnaxl- 80°/0

max i m urn composite properties in the fibre direct ion - 0.8 (0' or Ef)

cross plied

theoretical Vf(max) 79'/0

practical Vf(rnax) 70°/,

maximum corn posite properties in any one fibre direction - 0.35 ( U o r Ef)

ordered 3 - D array

t heo re t ica I

practical Vf(maxl - 40% V' (ma x) 5 0 - 6 0%

maximum composite properties in any one fibre direction "'0.13(0 or E$

FIG. 15.-Fibre packing densities and utilization of fibre properties for unidirectional, cross-plied, and 3-dimensional composites.

Initially, the properties of composites were seen as a relatively simple function of fibre properties and research was concentrated on new and improved fibres for reinforcement. Increasingly, in use, complex and transverse stress systems are encountered which lay emphasis on the important role of both interface and matrix. There will be a tendency and a need to develop more sophisticated composites, optimized for one or more aspects of performance and incorporating such features as controlled and multiple interfaces, flexible and elastic/plastic matrices, selected and mixed fibre lengths and distributions. In the long term however, the cost effectiveness of the property in operation in the component, covering, e.g., fabrication and design as well as material cost, will be important. Means of applying the required sophisti- cation to continuous large scale production will have to be found.

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B. A . PROCTOR 75

I am indebted to many present colleagues at Pilkington Brothers Research and Development, and former colleagues at Rolls Royce Old Hall Laboratories for helpful discussions and information : particularly to Dr. N. G. Nair. I also wish to thank the Directors of Pilkington Brothers and Dr. D. S . Oliver, Director of Group Research and Development for permission to publish this paper.

l R. Hill, J. Mech. Phys. Solids, 1963,11, 357. M. D. Heaton, Brit. J. Appl. Phys. (J. Phys. D.), 1968, 1,1039. F. P. Mallinder, Znst. Rubber Industry Conf. on Advances in Polymer Reinforcement and Blends (Loughborough, September, 1969). B. A. Proctor, Composites, 1971, 2, 85. M. H. de Wad, Relations between the Mechanical Strength of Glass and its Surface State ; (Review of Two Year's Co-operation in Scientific Research on Glass, December, 1971, Organization for Economic Co-operation and Development, DAS/SPR/71.35), p. 128. R. L. Crane and R. E. Tressler, J. Comp. Mat., 1971, 5, 537. W. Brearley and D. G. Holloway, Phys. Chem. Glasses, 1963,4, 69. B. A. Proctor, I. Whitney and J. W. Johnson, Proc. Roy. Soc. A, 1967,297, 534. B. A. Proctor, The Physical Basis of Yield and Fracture (Institute of Physics Conference Series No. 1, 1966, 218.

lo D. Cratchley and A. A. Baker, Compte Rendu Symposium sur le Contact du Verre avec le Metal, 1964, 671 (Union Scientifique Continentale du Verre). H. W. Rauch, Ceramic Fibres and Fibrous Composite Materials (Academic Press, New York, 1968).

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