Fracture Appearance - Damage Micromechanisms

At quasi-static strain rates, the fibre pull-out and fibre fractures are regarded aa failure processes which occur predominantly under tension loading o f unidirectional com posites along the fibre direction[! ']. These fibre dominated failure modes require greater energy. For tensile testing of off-axis unidirectional composites the failure is matrix dominated.

On the other hand, the splitting and delamination that have been reported to occur under com ­ pressive loading, require less energy and result in reduced structural integrity! I]. Delamination and splitting failures are also reported to occur due to stresses concentrated between the laminate

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Strain rate effects on G FR TP properties plies (interfaces) [1 Oil].

Mamalis et al. [1 ] have reported on the effect o f the fibre orientation on the compressive behaviour of a laminate comprised of unidirectional thermoset composite lamina. They reported that axially aligned fibres were bent inwards or outwards without fracturing according to their flexibility and the constraints provided by adjacent fibres. Fibres aligned transversely can only expand outwards by fracturing and inwards by fracturing or buckling. El-Habak[l 27] suggested that under quasi­

static and impact loading, the ultimate failure mechanism of unidirectional GRP was transverse tensile fracture owing to fibre debonding and matrix tensile failure.

Fan and Slaughter] 12 ] report that microbuckling is an important failure mechanism for polymer debonding and fibre pull out. Similar fracture appearance was observed at intermediate rates but the damage was more extensive and the specimen shattered on fracture. It was suggested that at impact loading rates the fibre matrix interfacial bond strength was exceeded before the tensile failure strength o f the glass fibres (which increases with increasing strain rate).

Espinosa et al.jl II] carried o u t tests on woven S2-glass/epoxy composite using a pressure-shear recovery experiment to determine the out-of-plane dynamic shear resistance o f composites. They reported matrix cracking and interfacial debonding in both high and low velocity impacts, while only fibre microcracking and breakage was observed at higher impact velocities. No indication of

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Strain rate effects on G FRTP properties the observed strain rates were given.

Xia et al.[7(i] suggested that the main failure mechanism for tensile impact testing is the cumulative breakage o f fibres which is caused by the statistical distribution of the strength o f brittle fibres similar to that of a brittle fibre bundle. A model was proposed based on the following assumptions:

• Every fibre behaves linearly up to fracture.

• The strength of the coated fibres is satisfactorily given by a particular probabilistic distri­

bution.

• If the event o f a single fibre failure, adjacent fibres are not affected by the event.

The third assumption implies that upon breakage o f a fibre the load/stress is redistributed evenly amongst the remaining unbroken fibres and therefore no stress concentrations are present. This is not representative of the physical failure mechanisms, especially at high tensile speeds - where the system has less time to reach an equilibrium (still dynamic) stress state.

McGee and Nasser[ I I '] have carried out bi-axial compressive testing on glass/epoxy systems using a split Hopkinson bar at a strain rate range between .0001 and 1000[l/sec]8. They reported that kink formation was the final stage of the failure mechanism at low strain rates. Their observations indicated that kink formation was preceded by extensive micro-mechanical damage that tended to initiate at defects (e.g. voids) - although some distributed damage was recorded with no correlation to pre-existing defects. Also for dynamic testing, multiple crossing and parallel kink bands were reported.

"There were inconsistencies in the paper stating in one occasion that the maximum compressive strain rate wax 1000[l/sec] and in other occasion 500[l/sec]

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Thiruppukuzhi and Sun] 12,] carried out tests on unidirectional S2-glass/8553-40 material system and determined that the ultimate failure occurs always along the off-axis angle parallel to the fibre direction whilst fibre breakage occurs only for the 0° specimens. They concluded that the failure mechanism for off-axis specimens is matrix dominated. T h ey choose accordingly a decoupled form for the implementation o f the failure criteria. The failure criterion for the transverse and shear properties (matrix based) uses one parameter to determine shape - which they found to be rate independent-, and another parameter which determines size. They found that the size parameter was found to be rate dependent, i.e. the failure strengths are dependent on strain rate.

Similar tests on woven E-glass fabric materials (eight harness satin weave construction) were performed] I]. The failure mechanism observed was dominated by shear, however no distinct modes of failure where identified with orientation. Therefore, Thiruppukuzhi and Sun concluded that for woven composites the failure modes cannot be decoupled. intra-laminar delamination promoted by shear stresses between the plies.

Khan et al.[l.'i l] has carried out compressive tests on S2-glass/polyester resin systems using a split Hopkinson bar at a strain range between .0001[l/sec] and 1250[l/sec]. They reported that the failure modes for dynamic loading were similar to the quasi-static loading failure modes.

Okoli]! ] carried out tensile tests on woven glass/epoxy 3[mm] thick composite systems using Strain rate effects on G F R TP properties

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a servo-hydraulic machine. He found that the failure modes were strain rate dependent. Okoli attributed his observation to the differences between the strain rate sensitivity o f the constituent phases and the properties at their interface. Because, the fibre, matrix and the fibre/matrix in­

terface are not expected to show consistent strain rate dependency the failure will be dominated by the yielding o f the weakest link. Okoli[l Hi] reported similar findings for 3 point bend impact testing.

Generally, the published research on the fracture appearance o f composite materials suggests that the fracture surface and failure mechanisms are strain rate dependent. Further, to the author’s knowledge no work has been carried out on thermoplastic composite systems.

2 .4 .4 .2 Strain Rate Effect O n The Longitudinal Tensile Properties failure tensile strength o f GRP materials. Kammerer and Nemo] J!>] reported that on cyclic tensile tests in the direction o f the fibres on a E-Glass/polyester system in the range o f 10“ 5 —» 10~3, the material showed no strain rate dependence (they also reported linear elastic behaviour and brittle fracture).

T h e work by Kawata et al.[ 1 ■ ’>'■'] has been criticised by Hamouda and Hashmi] ] and Okoli] •].

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Hamouda and Hasmhisuggested that the specimen fixing method had a undesirable effect on the true state o f stress, and Okoli suggested that Kawata el al. ignored the inertia which affects high speed testing.

Rotem and Lifshitz[ ■] found that at a strain rate of 30[sec_1] the dynamic modulus of glass/epoxy systems is 50% higher than the quasi-static modulus, whilst the dynamic tensile strength increases as much as three times the quasi-static strength. Later, Lifshitz [00] while investigating angle ply laminates observed that the elastic modulus was unaffected, and the increase of longitudinal tensile failure stress was only 20-30%. In both occasions a hydraulic (soft) powered universal machine was used to carry out the testing. As mentioned in §2.3.2, soft machines contribute a significant portion of the measured deformation at high strain rates.

Hayes and Adams[ ] carried out Charpy tests on glass/epoxy systems and found that the initial modulus and ultimate stress increased.

Welsh and Harding [ ' I , 7 ] observed an increase o f fracture strength and fracture strain with the increase o f strain rate on woven GFRP specimens, using split Hopkinson bar test method.

Also, the stress vs. strain curves departure slightly from a linear elastic response at the quasi­

static rate (10- 4 [sec-1]), while at higher rates (10 to 103[sec-1 ]). A greatly extended region of non linear deformation is observed leading to a markedly increased value of both the maximum stress and strain to fracture. The non linear deformation has been associated with successive bursts of damage.

Agbossou et al.[l II ] carried out tensile tests using a servo-hydraulic machine on unidirectional glass fibres/epoxy composite system (10 and 40% volume fraction). They found that for strain rates lower than 1 [.sec” 1) the maximum tensile stress varied linearly with the log of strain rate,

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whereas for strain rate higher than l[se c-1 ] the failure strength appeared to follow an exponential modulus and failure stress increased for increasing strain rate. They also reported contradictory conclusions for shear modulus depending on the orientation o f fibre to the principal direction of loading test chosen (10° and ±45°).

Xia et al.[7> ] carried out tests on unidirectional G F R P composite materials using a split Hopkinson bar and observed an increase o f the initial stiffness modulus and strength with increasing strain rate. From their observations, the quasi-static strain curves exhibited a linear behaviour, while the dynamic curves exhibited a non linear behaviour, however no explanation was given for this observation. Xia et al. used a load/unloading testing variation o f the Hopkinson bar, but the following problems were identified:

• The secondary reflective stress waves make it impossible to obtain the complete stress strain curve after a critical strain.

• At a constant strain rate, only one loading/unloading strain rate cycle is possible.

They proposed that the nominal tensile stress (a n c ) when n fibres have broken is given by:

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Strain rate effects on G FRTP properties

0b c = E^o£c — -jy 'j (2.7)

Eo: the initial modulus o f a coated fibre;

Ec : the strain at point where n fibres have broken;

n: the number o f broken fibres;

N : the initial number o f unbroken fibres in the bundle.

Using a least squares method, they fitted a linear model to the experimental results for initial modulus (£ ? ,) in the range up to the unstable strain9 (e/,), versus strain and substituted in eq.2.7.

They arrived at an elastic brittle damage-rate-dependent constitutive equation for a range of strain rates, which has the following form:

a = (^Er + kE \og e e x p j - a • -I- fcglog j (2.8)

where:

er , Er: the reference strain rate and the initial modulus at the strain rate;

a , (3: Weibull distribution parameters as defined by Eqn. 2.6;

k E: is a linear regression coefficient with units of stiffness modulus.

Wang and Xia ( I ] proposed a modified version o f the elastic brittle damage constitutive equation o f Xia [7i.], by introducing a double Weibull distribution function. The modified function improved correlation with the experimental results, in particular after the onset of unstable strain (which

“ The test required that the specimens did not fail.

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was a limitation in the original model). Although, the results correlated well for different types of reinforcements (Kevlar, graphite and glass), no physical explanation was offered for the adoption of a double Weibull distribution approach.

Lifshitz and Leber [v '] tested E-Glass/epoxy specimens using a split Hopkinson bar at 100 —>

200[m/sec]. They used a Hill-like failure criterion and compared the failure envelope for the quasi­

static and dynamic rates; finding clear evidence o f the effect of strain rate sensitivity on the failure envelope. They reported an increase of the failure envelope profile by 30%.

Todo et al.[ ¡] investigated woven cloth glass reinforced composites and studied the effect of different matrix material phases on the micro-level damage mechanisms which develop and the effect on the fracture properties. It has been established that fracture properties increase with increasing strain rate but stabilise beyond a critical strain rate; e.g. in the case of the examined system (modified polyamide) the increase o f the fracture properties stabilised at rates close to l[sec-1 ]). For the strain rate effects on the tensile properties a simple regression function was assumed, defined by:

Strain rate effects on GFRTP properties

M = a lne + /3 (2.9)

The problem with the use o f the natural logarithm is that the conversion o f strain rate is not as intuitive as it would be with the use of logarithm with base 10.

Pardo et al.[l I ] carried out 0° and 90° tensile tests on woven E -glass/epoxy systems on a servo- hydraulic machine and reported that at a strain rate range between 10~4 —» l()0[l/scc]. T he tests exhibited significant increases in the maximum tensile and threshold stresses, but suggested that the modulus remained constant.

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In conclusion, there are contradicting reports regarding the longitudinal mechanical properties of polymer com posite systems. Armenakas and Sciatnarcllaf '1)] found a decrease in the tensile in ultimate strength contradicting the findings of Rotem and Lifshitz[ '], Hayes and Adams[l li]

all of whom observed a measurable increase. Daniel and Liber[ I ] suggested that there was no strain rate dependency. Regarding the longitudinal modulus, a measurable increase was established by some researchers while other researchers found the longitudinal modulus to be equal for the static and dynamic case. Most o f the research work agrees that the longitudinal properties are dominated by the fibre reinforcement. The majority o f the research work on glass reinforced composite systems reports increase in stiffness and in strength, contrary to graphite reinforced composite systems which exhibit little or no strain rate sensitivity.