Tensile failure of pultruded glass-polyester composites under superimposed hydrostatic pressure

Composites Science and Technology 41 (1991) 395-409

Tensile Failure of Pultruded Glass-Polyester Composites Under Superimposed Hydrostatic Pressure R. H. Sigley, A. S, W r o n s k i & T. V. P a r r y * Engineering Materials Research Group. University of Bradford, West Yorkshire BD7 IDP, UK (Received 21 September 1989; revised version received I0 July 1990; accepted 27 July 1990)

ABSTRACT The tensile properties of five types of pultrt~ded 0"52 Vf glass fibre-polyester rods were #westigated by extending waisted round specimens at atmospheric and superimposed hydrostatic pressures, - H. to 300 MPa. The maximum principal stress at fracture, - 7 0 0 MPa, decreased, with the superimposition of - H , approximately by its magnitude. As - H increased the failure surfaces became flatter, the amount of fibre pull-out decreased and transt'erse cracks became shorter or were eliminated. Glass fibres in the failure surfaces were resin free, and failure of the glass fibre bundles appeared to control the fracture process in the entire pressure range for all materials. The decrease in maximum principal tensile stress with increasing - H indicates that the glass .fibre failure process is not controlled by a critical tensile stress. Failure criteria are discussed, and in the tension-compression-compression octant of stress space the relevant criteria appear to be strain energy and deviatoric tensile stress, strain and strain energy for these GRPs and glass itself.

INTRODUCTION Statistical models of tensile fracture I -'~ of unidirectionally aligned fibrous composites predict failure at a single cross-section and relate strength to the fibre fracture strength. Tensile specimens, however, usually fracture on *Present address: School of Engineering and Applied Science, University of Durham, Durham DHI 3LE, UK. 395 Composites Science and Technology 0266-3538/91/$03.50 © 1991 Elsevier Science Publishers Ltd, England. Printed in Great Britain

396

R. H. Sigley, A. S. Wronski, T. V. Parry

several levels, with cracks parallel to the fibres, and the failure surfaces have many fibres that have pulled out of the composite. These cracks and the fibre pull-out are usually explained in terms of shear cracking after fibre failure, 5 or as the final shear failure that links neighbouring groups of fractured fibres. 6 Cracks parallel to the fibres have been found in unidirectional composites loaded in tension along the fibres, but unloaded before fibre fracture, v When the specimen geometry was changed to reduce stress concentrators, such cracks were still discovered in unfractured specimens, v It has been suggested that the initiation of these cracks is caused by the straightening of curved fibres within the composite as a tensile load is applied. 7-9 This demonstrates that composite imperfections can have a considerable effect on composite mechanical properties. It has also been proposed that groups of fibres within the composite could be considered to act in unison. ~°'1~ As a consequence of such interaction, groups of fibres or 'bundles' were regarded as a microstructural unit v in analyses of composite compressive and tensile strengths. Parry and Wronski 7- 9 proposed a threestage process to interpret data on the mechanical properties of carbon- and glass-fibre-reinforced epoxides, in which tensile properties were influenced by matrix yield strength, interface strength, fibre curvature and the interaction of groups of fibres within the composite. This paper reports on the tensile failure mechanisms of glass-reinforced polyester composites and, by applying hydrostatic pressure as an additional experimental variable, attempts to identify the extensile failure criterion of glass (fibres) under complex loading.

EXPERIMENTAL PROCEDURE Five glass-reinforced polyester composites, supplied as pultruded rod by either Pultrex Ltd or RBJ Reinforced Plastics, were used in the investigation. They all contained unidirectionally aligned E-glass rovings, with a volume fraction of about 52%. Details of the materials and their strengths at atmospheric pressure are recorded in Table I. Glasses A, B, C, D and E were 28 x 2400 tex Equerove, 28 x 2400 tex Equerove 23/47, 28 × 2400 rex R0 99, 18 x 2400 tex ECR 1688 and 9 × 4800 rex E C R 1688; matrices 1 and 2 were Stypol 40-1077 with 25% talc as filler and 'Beetle' 811 with 10% calcium carbonate, respectively. Mechanical testing was carried out on a Hedeby universal testing machine, fitted with a 300-MPa Coleraine pressure cell. Details of the experimental technique have been given elsewhere. 8"9 The specimen was placed in the tensile loading jig within the pressure cell, which was filled with the pressurizing fluid. The cell was then pressurized to the required

Tensile failure o f pultruded composites

397

TABLE 1

Materials Tested, Together with their/Principal) Tensile Stresses at the Limit of Proportionality, aE(A), and Fracture, av(A), and their Pressure ( - H i Dependences, m, in oF = ~rv(A ) + mH, if a linear dependence is assumed

Material 1

2

3

4

5

Composition

Glass A Matrix 1

Glass B Matrix 1

Glass C Matrix 1

Glass D Matrix 2

Glass E Matrix 2

aE(A) (MPa) oF(A) (MPa)

580+20 700 ___30

560+ 15 650 + 85

520+ I0 660 ___59

490+ 10 730 + 39

520+ 10 760 + 95

0'75

0"63

0'65

1"17

1"06

m

hydrostatic pressure, - H , and tested by the external application of tensile stress, a A, resulting in principal stresses on the specimen of a t = a a + H and a 2 = a 3 = H. So that tensile tests could be carried out in the limited space o f the pressure cell, tensile specimens were double waisted (Fig. 1) with no region of constant cross-section in the gauge length. The diameter was reduced to a b o u t 1 mm at the centre. Shoulders were made sufficiently long to ensure failure within the gauge length, rather than by shoulders being pulled-off, v-9 Specimens were extended at 0 " l m m m i n - t in 'Plexol', a synthetic diester. In the course of this research programme, ~z it became apparent that environmental interracial attack took place by the action of this pressurizing fluid on some of these glass-polyester composites, thus affecting their mechanical properties. Some specimens were therefore coated with a silicone rubber solution to protect them from pressurizing fluid interaction. This rubber solution was painted onto the specimen gauge lengths and allowed to cure for 12 h. Tests, including tensile testing o f coated materials, showed, however, that materials 1 and 2 (Table 1) did not undergo interaction with the pressurizing ftuid.~2 F o r composites 3, 4 and 5 tested in tension, only the stress at the onset of non-linear stress-strain behaviour was significantly affected; x2 no effect on the fracture strength was detected. Accordingly, strength, a v, data on all five materials will be considered. 1.0 5.5

20.0

Fig. 1.

20.0

Tensile specimen design and dimensions (in mm).

398

R. H. Sigley, A. S. Wronski, T. V. Parr)' 8001

I[2

6O(

o.

No

,;0

260

360

Superposed Hydrostatic Pressure -H, in NPo

Fig. 2.

Maximum principal stresses at the limit ofproportionality (C)) and at failure (O) for material 1 tensile specimens tested under superimposed hydrostatic pressure.

Applied tensile stresses, o% and the hydrostatic pressure, H, were recorded. Failure surfaces were examined in an ISI scanning electron microscope. Some fractured specimens and some samples which were unloaded before fracture were sectioned parallel to the fibres for examination by reflected light microscopy. For comparison, similar sections of untested material were also prepared for microstructural examination. Fracture strengths of glasses C, D and E (A and B not being available) were determined, as were tensile and compressive properties of resins 1 and 2. t2

RESULTS The atmospheric tensile strengths of the materials 1-5 were 700, 650, 660, 730 and 760 MPa respectively (Table 1). For composites 1 and 2 (which did not interact with the pressurizing fluid) deviations from linearity on the load-time curves before failure were detected at aE of 580 and 560 MPa ( ~ 8 0 % of the fracture strength, aF). Whereas the fracture strength decreased with increasing pressure, aE (principal stress) increased to ~ 630 MPa (Figs 2 and 3) such that only linear behaviour until failure was observed at pressures exceeding 150 MPa. Application of coatings or sheaths to prevent interaction of pressurizing fluid with the composites had no detectable effects on materials 1 and 2 and no significant effects on atmospheric a E and on a F, and thus the pressure dependence of fracture strength, of materials 3, 4 and 5. The major influence

Tensile failure of pultruded composites ~00,

399

,

s-

& 2oo

I

I

Superposed Hydrostotic Pressure,-H,inHPc~

Fig. 3.

Maximum principal stresses at the limit of proportionality (O) and at failure (O) for material 2 tensile specimens tested under superimposed hydrostatic pressure.

of coatings on these materials was to increase a E at elevated pressures, ~2 such that the tensile behaviour of coated 3, 4 and 5 materials closely resembled that of composites 1 and 2 (coated and uncoated). Thus the main effect of fluid interaction for materials 3, 4 and 5, at all pressures, was to decrease the principal stress at the deviation from linearity to about 75% of the value of atmospheric strength; this critical stress then remained approximately constant with increasing hydrostatic pressure. ~2 For all composites tested, the m a x i m u m principal tensile stress, al, at fracture, a v , decreased with increasing superimposed pressure: if linear relations are assumed for all materials tested, the slopes are found to be 0.75H, 0"63H, 0-65H, 1.17H and 1.06H for composites 1, 2, 3, 4 and 5,12 respectively. Failure surfaces of specimens tested at atmospheric pressure were very irregular and the fracture paths were not associated with any one cross-section. There was a large a m o u n t of fibre pull-out, although groups of fibres were apparently still bonded together and there were very fe~v pulledout single fibres (Fig. 4(a) and (b)). Cracks in the sample shoulders parallel to the fibre direction were visible, and fibre surfaces were free of resin (Fig. 4(c)). As the superimposed pressure was increased, the failure surfaces became flatter, the a m o u n t of fibre pull-out decreased and the shoulder cracks became shorter. No shoulder cracks were visible in samples of composites 1 or 2 tested at pressures greater than 150 MPa (Fig. 5). Fibre surfaces were free from resin at all pressures. Parallel longitudinal cracks were found in samples loaded beyond the linear deviation point, but unloaded before fracture (Fig. 6). Longitudinal sections of both untested and tested

(a)

(b)

OID,

Q P

•

•"

,)

"

|ram

~

: ;

@

tcl Fig. 4. Fracture surfaces of material 1 specimens tested at atmospheric pressure. The following should be noted: t l) specimen fractured at ,,arious cross-sections, with groups of fibres remaining bonded together ((a) and (b)l: {2) longitudinal cracks ran into the specimen shoulders fla) and (b)l; and {3) fibre surfaces were resin free (c).

Fig. 5.

Fracture surface of material l specimen tested under pressure of 250 MPa. showing absence of longitudinal cracks and generally a flat failure surface.

Tensile failure of pultruded composites

Fig. 6.

40 l

Longitudinal cracks in material I specimen loaded beyond the linear deviation point, but unloaded before fracture.

composites showed considerable amounts of fibre curvature and misalignment (Fig. 7). Radii of curvature before straining were estimated to range from 2 to 10mm. Fibres were tested only at atmospheric pressure, but resins were also tested under superimposed pressures, t'~ The mean strengths of glasses C, D and E were 1"68 +_ 0"50, 1"65 + 0"35 and 1"31 +_ 0-20 GPa. Tests were carried out on at least 25 fibres of each type and Weibull analysis gave m values o f 4.0 +_ 0-5, 4-7 +_ 1'0 and 6.7 + 1-0, for C, D and E. Compressive yield strengths of resins 1 and 2 were 120 + 1 and 77 _+ 2 MPa; tensile (fracture) strengths were 54 + 4 and 31 + 5 MPa. Resin 2 showed a clear deviation from linear behaviour at 23 + 4 MPa (at atmospheric pressure).

DISCUSSION The general features of the glass-polyester composite data are qualitatively similar to those for carbon- and glass-reinforced epoxides tested under similar conditions. 8'9 The fracture of these materials was discussed in terms

Fig. 7.

Pulled-out region of tensile specimen of material 4, showing curvature of the bonded fibres after testing under pressure of 50 MPa.

402

R. H. S~gley, A. S. ~Vronski, 7-. I. Parry

of a three-stage failure process; first, debonding of surface bundles, associated with the straightening of curved fibre bundles at the gauge diameter surfaces against the transverse support of the matrix; second, the gro~vth of these inter-bundle cracks parallel to the fibre direction, eventually leading to detachment of the surface bundles, such that they are unable to support the tensile load: and third, catastrophic failure when a critical stress is transferred to the remaining fibre bundles. The onset ofdebonding may be identified with the deviation from linearity observed on the load-time curve, as longitudinal cracks were observed in samples unloaded after the deviation but before fracture (Fig. 6). Two possible mechanisms involved in debonding are matrix failure and interlace failure. In carbon-fibre-reinforced epoxide, 8 the critical stress for delamination was associated with matrix yielding. However, in glass-epoxide 9 and the glass-polyesters, micrographic evidence showed that failure was interracial, as fibre surfaces were free from resin (Fig. 4(c)). The relevant interfaces were between fibre bundles, rather than individual fibre-matrix interfaces, as in these glass-polyesters (and in the glass-epoxide 9) groups of fibres ('bundles') remained intact (Fig. 4(a)). The second stage of the failure process in the Parry and Wronski model is the propagation of the debonding cracks, s9 This type of crack growth has been considered by Kendall, t3 who proposed that, for cracks to grow parallel to the applied load, some initiating detect is necessary. Once a defect exists, propagation will take place if energy conditions are satisfied. He derived a criterion for propagation, which involved specimen dimensions and the fracture surface energy of the interface. In our materials the defect is caused by bundle straightening, which initiates interface failure. The necessity' of an initiating detect can also account for observations in woven materials, when a threshold stress for delamination was observed. ~'~ Similarly', in our experiments on glass-polyesters, a threshold stress was required to initiate the first debond. As the load continues to rise in the tensile specimens, the bundles straighten and the longitudinal cracks lengthen. When sufficient load is applied, the detached bundle fractures (and the applied load may' drop) with the load being transferred to the remaining bundles. If they can support this load, the non-linear behaviour continues, with the load continuing to rise as these bundles straighten and support more load. The process is repeated until the remaining unfractured bundles cannot support the load and the specimen breaks. With increasing pressure, the initiation and growth of longitudinal cracks is made more difficult as a result of the transverse component of the superimposed pressure. A curved bundle may not be fully' straightened and therefore may be unable to support as high a load under a superimposed pressure as at atmospheric pressure. This would cause the specimen to

Tensile failure of pultruded composites

403

fracture at a lower stress, if tensile stress was the critical parameter controlling fracture of the glass. Load redistribution is also inhibited by pressure because of the increased difficulty of bundle detachment. Thus the first fibre fractures may propagate throughout the cross-section, resulting in a flat fracture, as observed (Fig. 5). The (maximum) principal stress at fracture of the composite can therefore decrease with increasing pressure. The fractional decreases, per 100 MPa superimposed pressure, in the maximum principal stresses for these glass-reinforced polyesters are similar, about 0.17, and they are also close to the values observed for carbon-fibre- and glass-fibre-reinforced epoxides. It should be added, however, that in the carbon-epoxide there was a 'cut-off" at ~150MPa, above which the principal stress at failure remained constant as debonding was suppressed above this pressure. 8 The failure process, when debonding and delamination are suppressed, may be interpreted in terms of statistical theories of tensile strength. No such transition was observed for the glass--epoxide, as debonding persisted up to 300MPa superimposed pressure. 9 Although failure was preceded by delamination, the critical failure stage at all pressures was fibre fracture. In these glass-reinforced polyesters, however, the maximum principal tensile stress decreased throughout the pressure range used for the tests. This was so even when all non-linear behaviour was suppressed, above a pressure of 150 MPa, when the composite (on the Parry-Wronski model) would be expected to fail at a constant principal stress. Initial analyses assumed a linear dependence of a I on H. Linear regressions carried out on the current data for all five materials show a range of slopes near - 1 , i.e. between -0-65 and -1.2, although there was a wide range in mean strengths, particularly at higher superimposed pressures. This decrease in maximum principal tensile stress with increasing pressure clearly indicates that the process of fracture of fibres, which controls extensile failure in these composites, is not itself controlled by a critical tensile stress, requiring a pressure-independent principal stress at fracture. Though the composite is highly anisotropic in its elastic properties, glass is not, and as its fracture has been identified as the critical stage of failure of the composite, it is thought relevant to consider isotropic failure theories of brittle materials, and their pressure dependences, in the subsequent discussion. An instructive method is to consider the failure surface in stress space; our az = a3 experimental condition identifies a plane, and failure loci on it can be plotted with a 1 and x/2a 2 as the axes. To present several sets of results it is convenient not to plot the absolute values but to normalize with respect to the atmospheric tensile strength, av(A). For the sake of completeness, all the 'simple' criteria--principal and deviatoric tensile and shear stresses, principal and deviatoric tensile strains

404

R. H. Sigley, A. S. WronskL T. V. Parr)'

TABLE 2 Failure Criteria for Isotropic Materials, e.g. Glass, of Poisson's Ratio, v, and their Dependences on Hydrostatic Pressure, - H; o.v is the Failure Stress at Atmospheric Pressure Criterion and condition

Pressure dependence of principal stress

Tensile stress O.I =O.T

(71 = O . T

Shear stress O.I

--

0"3

=

O'T

o.t = O ' T + H

Tensile strain O.I - - 'J/(O.2 Jr" 0"3) = O"T

Deviatoric tensile stress or strain 2o.t - ( a , + o.s)= 2O'T

o't = O.T+ 2vH o. t = O.T + H

Deviatoric strain energy (O.I - - 0"2) 2 + (O.2 - - 0"3) 2 + (O"3 - - 0"1) 2 ~--- 20-2

o.t = O . T + H

Strain energy (o.~ + o.~ + o.~)- 2,,(o.,o.~ + o.~o.~ + o.~o.,) = o.~

(71(O"l -4vH) = o.r - 2H"(1 - v)

and total and deviatoric stress energies (for isotropic materials)--are listed in Table 2, and their pressure dependences are presented in dimensionless form in Fig. 8, together with experimental data. As the critical stage in failure was fracture of glass fibres, the Poisson's ratio of glass (rather than those of the composite) was used in determining the loci of constant strain and strain energy of Fig. 8. The latter naturally does not predict a linear a 1 vs H dependence. The decrease of m a x i m u m principal stress with H with a slope of - 1 (possible for materials 4 and 5) can be interpreted in terms of a deviatoric tensile strain or stress or deviatoric strain energy, as shear stress has to be excluded for fractographic reasons (fibre failure being extensile). These criteria, or additionally the critical strain energy criterion (possible for materials 1 and 2), have to be examined for the glass-polyester composites. Although glass fibre failure at atmospheric pressure is usually considered to be a critical-stress-controlled process, Griffith is in fact used strain energy considerations in deriving his fracture criterion for uniaxial tension. He went on to consider biaxial loading, but changed to a critical local tensile stress. Bridgman x6 carried out a series of tests on glass rods under superimposed hydrostatic pressures up to 2.7 GPa. Waisted rods of a minimum diameter of 2 m m were covered by a copper sheath to exclude pressurizing fluid, and were then loaded in tension along their longitudinal axis. The rods failed in a tensile manner, either as a clean break at the neck, or by separating into thin discs, still hanging lightly together. These failures occurred at applied

405

Tensile failure of pultruded composites I

"%

I

I

\

i

la)

\

e

A_

1.0

\ \

A

\ _....-1 b 1~

A-co-"-"

/

\

•

V

•

A

/e

v

08

~--~e"" R/

~\-"

A (d)

•

j{C )j"

x

0.6

x.

3.t, /

\

".?.

~2

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MATERIALS

"I

-1.0

I

~, ~,.~ ,

-O.B

N

,

,

-0.6

-0.4

,

-0.2

D.O -0.0

~H/(7T

Fig. 8. Failure criteria (for isotropic materials, i.e. including glass, but not GRP) defined by constant (a) tensile stress, (b) tensile strain, (c) deviatoric strain, stress, strain energy and shear stress, (d) total energy; plotted in normalized stress space plane defined by 0"2 "~- 0"3"The data points for all materials tested are plotted normalized to their respectiveaverage atmospheric fracture strengths. tensile stresses of about 1.6 GPa, that is, at principal compressive stresses of -,- 1 GPa. In interpreting these results, Bridgman emphasized that fracture could not occur unless it was an energy-releasing process. He considered that two energy-releasing processes were involved; the tensile force doing work and the pressure itself doing w o r k - - i n particular, the transverse c o m p o n e n t of the pressure, which could penetrate incipient cracks in the glass surface. He suggested that, at the high pressures involved, the covering sheath would be forced into these cracks. In effect, brittle failure under a superimposed hydrostatic pressure initiated at the specimen surface (because of sensitivity to surface conditions) could not be represented in terms of a single stress criterion; Bridgman did not attempt to derive an energy criterion. ~6 For polymers, Duckett 1~ proposed a theory involving pressurizing fluid penetration of surface cracks to account for extensile failure in a nominally compressive stress field. However, work on coated and uncoated epoxides 18 showed that crack propagation and failure could take place from an internal flaw when all principal stresses, although unequal, were compressive. Penetration of glass fibre surface microcracks by polyester at the low pressures not exceeding 300 MPa is unlikely. When coated and uncoated

406

R. H. Sigley, A. S. Wronski, T. V. Parry

specimens of materials 1 and 2 were tested, no significant differences in their behaviour were found; this again implies that penetration of composite surface flaws was not an influence on failure mechanisms. The question of the failure criterion of glass under complex loading is open, especially, as Swedlow 19 has pointed out, because there is no general direct equivalence between energetic and maximum stress fracture criteria. A strain or energy criterion, unlike that of critical principal tensile stress, could further account for Bridgman's observation of extensile failure in glass rods under a net compressive stress. ~6 Extensile failure under a net compressive stress is not u n c o m m o n in polymers, as well as in ceramics, as has recently been pointed out by Wronski; 2° failure criteria in brittle solids under complex loading have been discussed by Wronski and Howard. 21 They proposed that different fracture criteria might operate in different parts of stress space. Using the argument of Huber zz that tensile straining ofinteratomic or intermolecular bonds was important, and that total strain energy was relevant in the case of a tensile hydrostatic component of stress, whereas distortional strain energy was relevant for a compressive hydrostatic component, Wronski and Howard z~ suggested the following failure conditions: Hydrostatic component of stress

Relet'ant parameters

Tensile

Strain energy Deviatoric tensile strain

Compressive

Distortional strain energy Tensile strain

It should be noted that for the majority of our tests the hydrostatic component of stress, a , = ~(a~ + a2 + a3), was tensile. The data in Fig. 8 were analysed statistically in an attempt to correlate material behaviour with the various failure criteria. These analyses showed no significant differences between all the experimental data and the total strain energy criterion, and no significant difference between results on materials 3, 4 and 5 and the deviatoric stress, strain or strain energy criterion. Thus it was not possible to identify a particular criterion for a given material; more data and less scatter are required in order to distinguish between the criteria. (The a2 = a3 (experimental) condition also prevents discrimination between critical shear stress and deviatoric tensile strain, strain and strain energy criteria.) However, it is clear that the one criterion not satisfied by the data is that of m a x i m u m principal tensile stress, and it is therefore concluded that the failure criterion for glass, when it controls the composite fracture, cannot be that of a critical stress, as is usually assumed. Possible criteria are

Tensile failure of pultruded composites

407

those of deviatoric strain, stress or energy, or total strain energy. The total strain energy criterion is unlikely to hold for negative ~zH, as one o f its predictions, experimentally disproved, is failure under (pure) hydrostatic pressure. Huber's model 22 predicts a change of failure criterion as aH changes from positive to negative, i.e. for the case a~ = a 2 as the a 1 = 2Hline of Fig. 8 is crossed. Thus the strain energy and three deviatoric criteria remain for further experimentation and analysis. Within the limitations of the present 300-MPa apparatus, if the same mechanisms were to operate, critical experiments would have to be carried out with Vr reduced to below 20%. In extensile failure of a fibrous composite the composite tensile stresses, strains and strain energies are determined predominantly by the fibres. At moderate pressures, as used in the experiments described, the resin acts to some extent as a pressure-transmitting solid. To illustrate the general point that analysis of glass fibre failure approximates well to consideration of the anisotropic solid, calculations of tensile strains in the fibres and the composite will now be presented for the system where a 2 = ~z3 = H. For fibres with Young's modulus, Eg,

~1(f)= ~rl

2vH

E,

E,

(1)

and for the composite with longitudinal and transverse moduli, E, and E,, and the relevant Poisson's ratio, v,,

et(c) =cr 1

2v, H

&

(2)

&

For these to be the failure criteria, in the case of the fibres,

a I = el(f)Eg + 2vH

(3)

i.e. there is a linear relationship between at and H which has a slope of 2v, approximately 0.44. For the case of the composite,

a 1 = Elel(C ) + 2(E'~vt,H \EtJ

(4)

i.e. there is a linear relationship between a~ and H with a slope of

\ E , jV,,

(5)

Typical figures for G R P z3 give E~ ~ 5E~ and v~ = 0-05, i.e. a slope of ~0-5 is predicted. It should be noted that this calculation is extremely sensitive to the value o f v,,, which is difficult to determine and extremely small. F o r our G R P materials the tensile strain criterion in fact lies at the 'upper bound' of

408

R. H. Sigley, A. S. Wronski, 7". V. Parry

data in Fig. 8. Assuming no transition in the failure criterion from the compression-compression-compression to the tension-compressioncompression octant of stress space for glass, Bridgman's results t6 would predict atmospheric strengths in the range 80-250MPa, rather than the recorded range of 50-70 MPa, when the Griffith failure criterion is expected to have operated. It is tentatively suggested that for a~ positive, in the tensioncompression-compression octant of stress space, materials 1 and 2 obey the total strain energy criterion, and materials 3, 4 and 5 the deviatoric tensile strain criterion, both consistent with suggestions of Huber 22 and Wronski and Howard, 2~ who pointed out that a 'mechanism' (strain or deviatoric strain) and an "energy' (total or deviatoric) condition must independently be satisfied. Current results suggest that further testing of unidirectional composites in tension under superimposed hydrostatic pressure, also in the compression-compression-compression octant of stress space, could also be used to discount/determine failure criteria of other brittle fibres, such as ceramic filaments. If a sufficiently high volume fraction of fibres is incorporated into a composite, a polymer matrix will act primarily as a binder, and the properties in many loading geometries will be dominated by the fibres. This could provide a means of testing brittle materials which can be produced flaw-free only in fibrous form. Under complex loading, when all principal stresses, though unequal, are compressive, some ceramics (and polymeric) materials fail by extensile cracking. This is of particular relevance to design with 'engineering' ceramics and the application of fracture mechanics to complex loading geometries, z°

A C K N O W L E D G E M ENTS The authors acknowledge the assistance of Dr M. M. Rebbeck with fractography, the support of SERC through an award of a research studentship to one of us (R.H.S.), and the assistance of Pultrex Ltd and RBJ Reinforced Plastics in supplying materials.

REFERENCES 1. Zweben, C., Tensile failure of fiber composites. A I A A J., 6 (1968) 2325-31. 2. Barry, P. W., The longitudinal tensile strength of unidirectional fibrous composites. J. Mater. Sci., 13 (1978) 2177-87. 3. Manders, P. W., Bader, M. G. & Chou, T. W., Monte Carlo simulation of the strength of composite fibre bundles. Fib. Sci. Tech., 17 (1982) 183-204.

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