Monotonic and fatigue behaviour of chopped-strand-mat/polyester composites with rigid and flexibilised matrix

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Composites: Part A 38 (2007) 234–243

Monotonic and fatigue behaviour of chopped-strand-mat/polyestercomposites with rigid and flexibilised matrix

G. Caprino *, U. Prisco, L. Giorleo

Department of Materials and Production Engineering, University of Naples ‘‘Federico II’’, Piazzale Tecchio, 80, 80125 Naples, Italy

Received 26 January 2006; received in revised form 23 May 2006; accepted 27 May 2006

Abstract

Monotonic and tension–tension fatigue tests were carried out on E-glass chopped-strand-mat/polyester composites, varying the flex-ibiliser content by weight in the matrix in the range 0–30%. The flexibilising action was due to the adipic acid monomers present in theflexibiliser.

In monotonic tests, the most marked effect of resin flexibility was in the transverse cracks formed during loading, whose critical den-sity (i.e., the density at failure) was very high for the rigid matrix, resulting in a highly non-linear stress–strain curve, and in the largestapparent strain to failure. With suitably increasing the flexibiliser content, the transverse crack formation was nearly suppressed, and theoverall stress–strain curve approached linearity.

In fatigue, the critical crack density decreased with increasing fatigue life in the case of the rigid matrix. For the flexibilised resins, thecrack density at failure was independent of the maximum applied stress, larger than observed in monotonic tests, and higher the higherwas the flexibiliser content, up to about 80% of the tensile strength. Beyond this limit, it converged through the material monotonicbehaviour. The evolution of the residual elastic modulus with elapsing fatigue cycles was qualitatively consistent with the number oftransverse cracks observed. The more flexible the matrix, the lower was the fractional modulus loss in fatigue. However, the highest elas-tic modulus along all the fatigue life pertained to the composite with rigid matrix, due to the flexibiliser adversely affecting the initialrigidity.

Despite the differences in monotonic response and crack formation features, all the materials tested exhibited very similar S–N curvesat moderately high fatigue lives. Nevertheless, appropriately treating the experimental results in terms of fatigue sensitivity, it was foundthat this parameter tends to increase with increasing matrix flexibility.� 2006 Elsevier Ltd. All rights reserved.

Keywords: A. Polymer-matrix composites (PMCs); A. Discontinuous reinforcement; B. Mechanical properties; B. Fatigue

1. Introduction

Composite materials are nowadays employed in manyengineering structures, such as helicopter and wind turbinerotor blades, boat hulls, and buildings, implying the appli-cation of variable loadings for long time spans. This raisesthe question of their fatigue behaviour, whose importanceis increasingly appreciated also in the fixed-wing aircraftindustry, where fatigue life has not been a major issue in

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doi:10.1016/j.compositesa.2006.05.006

* Corresponding author. Tel.: +39 0 817682369; fax: +39 0 817682362.E-mail address: [email protected] (G. Caprino).

the past, due to the low working strains used in practicalcomponents.

Although a large body of experimental work has beencarried out on the fatigue of composites in the past 50 years[1–8], our knowledge of this phenomenon is far from beingexhaustive. Reliable predictive methods, capable of provid-ing the material life under not only service loading spectra,but even simple loading histories, are yet needed beforecomposite laminates can be used confidently in fatigue-crit-ical applications.

Undoubtedly, a necessary step underlying the develop-ment of design tools for fatigue-critical applications is thestudy of damage mechanics, i.e., the identification of

G. Caprino et al. / Composites: Part A 38 (2007) 234–243 235

microstructural failures responsible for final collapse, andthe assessment of their evolution during time [2,4,6,7,9].From these analyses, it has long been recognised that thefatigue response of composite laminates is governed byquite peculiar rules when compared to metallic materials.In metals, a single crack nucleates at a stress concentrationpoint, and intermittently propagates up to the catastrophicfailure, the material far from the crack being negligiblyaffected by fatigue. In composites, a multiplicity of micro-cracks often develops within the entire material volume,resulting in a progressive decay of both the rigidity andresidual strength.

The earliest damage modes occurring in a compositeunder static as well as fatigue conditions involve thematrix, consisting of intralaminar and interlaminar cracks.Therefore, some authors attempted to preserve the materialintegrity by using more flexible resins [9–13]. Generally,this solution is effective in lowering the crack density,allowing a better modulus retention, which is consideredbeneficial in rigidity-critical applications. Nevertheless,adding a flexibiliser to a rigid matrix also causes a decreasein the initial modulus, so that the actual advantage of fol-lowing this route must be carefully evaluated.

The effect of tougher resins on the fatigue strength is amatter of debate so far. Some researchers [9,14] found animprovement in fatigue life associated with the adoptionof matrices having higher ductility. In other cases, it wasconcluded that the resin flexibility does not affect [10] theS–N curve, or even results in a poorer fatigue response[15–17], especially at very high fatigue cycles.

In a previous paper [18], the static and fatigue behaviourof a polyester resin with different proportions of flexibiliserwas analysed. In this work, the same resin system consid-ered in [18] was used to fabricate four chopped-strand-mat/polyester (CSM) composites, which were subjected tomonotonic and repeated-tension fatigue tests. The fibre vol-ume fraction was kept low, to highlight the role played bythe matrix in the mechanical response of the composite. Inorder to assess the influence of the matrix flexibility on thematerial response, several features, such as the shape ofthe stress–strain curve and the parameters associated, thedensity of the transverse cracks formed under monotonicand fatigue conditions, the modulus degradation in fatigue,the S–N curves and the fatigue sensitivity were analysed.

2. Materials and test methods

The basic materials employed in this work were an E-glass chopped-strand-mat 350 g/m2 in areal weight byVetrotex and a polyester orthophtalic resin typeOR155.5386 by Poolkemie.1 MEKP of 1% by weight wasused as a catalyst. The flexibiliser, FLEX AR FS56, pro-vided adipic acid monomers to the basic resin, partiallyinhibiting the cross-linking process. To verify its effect on

1 In [18], this resin was erroneously attributed to Prochima.

the composite behaviour, four different flexibiliser contentscf, i.e., 0%, 10%, 20%, and 30% by weight, were adopted inthe formulation of the matrix.

The laminates, under form of square panels 350 mm inside, were fabricated putting three layers of reinforcementon a glass plate, together with the suitable quantity ofliquid resin. The complete impregnation process and poly-merisation was accomplished under vacuum bagging, hold-ing the plate for 24 h at room temperature. After that, thelaminate was demoulded and post-cured for 24 h at 80 �Cin oven. The fibre volume fraction of the composite aftercure, measured by matrix burning, was Vf = 0.12.

From each panel, dog-bone shaped specimens, accord-ing to ASTM D 638 Standard, were cut by a diamond tool.The mechanical tests were carried out at ambient tempera-ture in an MTS 810 servo-hydraulic machine. In the mono-tonic tests, the displacement rate was fixed at 100 mm/min,to approximately match the strain rate conditions achievedin fatigue. The material strain was evaluated by an MTS634.31F-24 extensometer with 20 mm gage length. At least10 specimens were brought to failure for each flexibilisercontent.

In the fatigue tests, performed under a sinusoidal load,the stress ratio was R = 0.1, and the frequency f = 2 Hz.Some of the fatigue tests were stopped after predeterminednumbers of cycles, and the elastic modulus was measured,to appreciate possible variations of this parameter inducedby damage phenomena developing in the material. A min-imum of three specimens was tested for each experimentalcondition.

In evaluating the stresses arising in monotonic and fati-gue testing, the mean value of the thickness (t = 3.6 mm)resulting from the measurement of all the specimensemployed was used.

3. Results and discussion

3.1. Monotonic behaviour

Fig. 1 shows the effect of the flexibiliser content, cf, onthe stress–strain curve of the composites considered in thiswork.

As expected [10–13], the elastic modulus E0 steadilydecreases with increasing cf, reflecting the contribution ofthe resin to the material rigidity. In fact, in [18], wherethe same resin system used here was mechanically charac-terised, a 30% flexibiliser content resulted in a modulus lossof about 50% compared to the neat resin. The modulusdecay within the same range of cf values is less noticeable(approximately 35%) in the case of composite (Fig. 2),because the effect of matrix is partially masked by the pres-ence of reinforcement.

Apart the initial modulus, the flexibiliser content influ-ences remarkably the overall stress–strain curve evolution.When the matrix is brittle (cf = 0), a knee is clearly visibleat a stress level r � 46 MPa, beyond which the materialrigidity is considerably lowered. This behaviour is not

Fig. 1. Effect of the flexibiliser content, cf, on the stress–strain curve.

Fig. 2. Elastic modulus, E0, against flexibiliser content, cf.

Fig. 3. Tensile strength, rr, against flexibiliser content, cf.

236 G. Caprino et al. / Composites: Part A 38 (2007) 234–243

usual for mat/polyesters, which generally exhibit a moregradual departure from linearity [19,20] with approachingfinal failure. Rather, the presence of a knee-point is welldocumented in Sheet Moulding Compounds (SMCs)[3,12,21], where its presence is the more apparent, the loweris the fibre volume fraction, and the higher the filler content[22]. Beyond the knee-point, the load bearing capacity ofthe mat/polyester increases further with increasing strain,until final failure occurs for a strain exceeding 2.5%. Thishigh elongation to break has been rarely observed inCSMs, which generally fail for e values lower than 2%[19,20,22].

The evidence of knee is progressively suppressed as faras cf is increased. Indeed, no knee at all is perceivable forcf = 20% and cf = 30%, whose r–e curves sensiblyapproach linearity. Similar results were reported by Garrettand Bailey [11], who tested in tension glass fibre-reinforcedpolyester cross-ply laminates, increasing the resin failurestrain by suitably varying the proportion of flexibiliser.When a brittle matrix was used, the authors noted a knee

in the r–e curve. On the contrary, a linear behaviour wasfound for the most flexibilised laminates.

In Fig. 3, the dependence of the tensile strength, rr, onthe flexibiliser content is shown. Considering the scatterof the data, the sensitivity of rr to cf is quite limited. Amuch more marked effect of the flexibiliser on the materialstrength was reported by Owen and Rose [10,23], whostudied the mechanical properties variation of a CSM whena flexible resin was added to a general-purpose polyestermatrix. The minimum strength, pertaining to the resinwithout flexibiliser, was 79 MPa, whereas the maximumone, obtained for a 15% flexible resin addition, was foundto be 120 MPa.

The strain to failure (Fig. 4) is maximum (slightly higherthan 2.5%) for cf = 0, undergoes a large reduction goingfrom cf = 0 to cf = 10% (where it holds approximately1.8%), and then steadily increases with increasing the flex-ibiliser content. Under the same loading conditionsadopted here, the failure strain of the resin alone [18] wasa monotonically increasing function of the flexibiliser con-tent, varying from about 4% to 10% when cf was increasedfrom 10% to 30%. Therefore, as also revealed from previ-ous results available in the literature [11–13], only a littlepart of the elongation capacity of the resin is retained inthe composite, whose final failure mainly reflects the fibreproperties. However, the CSM without flexibiliser exhibitsa peculiar behaviour, because a lower resin failure straingenerally results in a correspondingly lower elongation tobreak of the composite [11–13]. The explanation of thisseemingly strange phenomenon is given by the analysis ofthe specimens during the loading stage and after final col-lapse. Some examples are shown in Fig. 5.

Irrespective of the flexibiliser content, all the sampleswere broken in two pieces, with little evidence of fibre fail-ure. However, when cf = 0 and 10% (Fig. 5(a) and (b)), thedeparture from linearity of the stress–strain curve wasaccompanied by the well documented [3,11,13,21,24] for-mation of cracks extending perpendicular to the loading

Fig. 4. Strain to failure, er, against flexibiliser content, cf.

G. Caprino et al. / Composites: Part A 38 (2007) 234–243 237

direction, quite evenly spaced, which propagated in anunstable manner until the entire specimen width was cov-ered. These cracks grew in number with increasing thedeformation, until final failure was achieved.

Comparing Fig. 5(a) and (b), the main difference is inthe crack density, which is lowered by the presence of flex-ibiliser. This justifies why the portion of the stress–straincurve beyond the knee-point is more prolonged forcf = 0: the higher tendency of the material to generatetransverse cracks increases locally the deformation, result-ing in a higher apparent strain to failure.

When cf is further increased, the crack formation is sub-stantially suppressed (Fig. 5(c) and (d)), and transversecracks are only occasionally observed (arrows in the fig-ures). Even in this case, they generally start propagatingfrom one side (probably induced by small surface defects),but are arrested before the opposite sample side is reached.Accordingly, a knee does not appear in the stress–straincurve [11,13].

Fig. 5. Specimens failed under monotonic load: (a) flexibiliser c

From the observations made, the trend in Fig. 4 is dueto two competitive phenomena, attributable to the flexibil-iser: (a) the tendency to suppress cracking, lowering theapparent elongation at break; (b) the tendency to increasethe matrix strain to failure, contributing to raise its com-posite counterpart. For low cf values, not enough flexibil-iser is present to suppress cracking, and the apparentelongation at break is high. When sufficient quantities offlexibiliser are used to limit or avoid crack formation, theeffect of the higher matrix strain to failure prevails.

The reason why the knee-point in the CSM without flex-ibiliser is particularly evident is probably dependent on thelow reinforcement content by volume (12%), which high-lights the resin brittleness. Notably, although this materialdevelops the most extensive damage state before final fail-ure, its tensile strength is comparable to the ones of theflexibilised CSMs. Consequently, a large damage propagat-ing into the material structure does not necessarily result ina poorer strength to failure.

3.2. Fatigue behaviour

The visual analysis revealed little qualitative differencesbetween the specimens broken under monotonic and fati-gue loading. The most notable dissimilarities concernedthe transverse cracks appearing in the materials with higherflexibiliser content (cf = 20% and 30%), which in fatiguewere longer and occasionally crossed the whole samplewidth (Fig. 6). From a quantitative viewpoint, however,the crack density (defined as the number of cracks crossinga straight line of unit length parallel to the loading direc-tion) was strongly influenced by the type of load (mono-tonic or fatigue), as shown in Fig. 7, where itsdependence on the non-dimensional maximum appliedstress rmax/rr is depicted. In the figure, the vertical barsdenoting scatter are not reported for clarity. The continu-ous lines were drawn by hand, to better evidence the trendof the experimental points.

ontent cf = 0; (b) cf = 10%; (c) cf = 20% and (d) cf = 30%.

Fig. 6. Specimens failed in fatigue: (a) flexibiliser content cf = 0; (b) cf = 10%; (c) cf = 20% and (d) cf = 30%.

Fig. 7. Crack density at failure against the non-dimensional maximumapplied stress, rmax/rr.

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With the exception of cf = 0, all the curves, irrespectiveof the flexibiliser content, exhibit the same general trend.When the maximum applied stress is sufficiently low (highfatigue life), and up to rmax/rr = 0.80, the crack densitystays sensibly constant. Beyond rmax/rr � 0.80 (low fatiguelife), the crack density steadily decreases, until themonotonic condition (rmax/rr = 1) is recovered. Theseobservations suggest that, below rmax/rr = 0.80, a true fati-gue-induced failure develops, whereas above this stresslevel the fracture process turns progressively to its mono-tonic features as far as the material strength is approached.

In the case of cf = 0, the dependence of the number ofcracks formed at failure on the maximum applied stress fol-lows a peculiar law. For this composite (Fig. 7), the crackdensity is stress-dependent, slightly increasing with increas-ing rmax/rr. Due to this behaviour, when the non-dimen-sional maximum applied stress is in the range rmax/

rr = 0.45–0.50, the mat/polyester without flexibiliser devel-ops at failure a number of cracks lower than the compositewith cf = 10%. This may be considered quite surprising, ifreference is made to the monotonic response of the twomaterials.

From the previous data, the presence of the flexibilisercan result in a strong change in the failure mechanisms ofthe composite, being able to drive a fatigue-dependent or,alternatively, a stress-dependent matrix crack formation.In the domain of fatigue-induced failure, the crack densityis a characteristic of the material, being independent of thestress level, i.e., of the critical number of fatigue cycles.Therefore, this Characteristic Crack Density (CCD) couldyield an easy indication of possible final collapse in fatigue.Of course, this criterion is hardly applicable to flexiblematrices: increasing the flexibiliser content from 10% to30% nearly suppresses the crack formation not only undermonotonic loading, but also in fatigue.

The concept of CCD introduced here should not be con-fused with the ‘‘Characteristic Damage State’’ (CDS), oftenobserved in studying the fatigue of composites [6,25]. Infact, assessing the existence of a CDS requires a monitoringof damage with evolving fatigue, and a verification ofwhether an equilibrium condition in the crack density isreached beyond a given number of cycles. On the contrary,the CCD simply records the number of cracks after finalfailure, without any indication of the damage evolutionduring fatigue life.

In Fig. 8, the non-dimensional elastic modulus measuredat n cycles, En/E0, is plotted against the normalised numberof cycles, n/N, with N indicating the critical number ofcycles controlling the sample collapse.

For cf = 0 (Fig. 8(a)), the decrease in modulus isstrongly dependent on the load level. At high stress, En/E0 undergoes a large decay in the first few cycles. This isanticipated from the monotonic behaviour, since the stressfor knee appearance in the stress–strain curve (Fig. 1) is

Fig. 8. Non-dimensional residual elastic modulus, En/E0, against the non-dimensional number of cycles, n/N: (a) flexibiliser content cf = 0; (b) cf = 10%;(c) cf = 20% and (d) cf = 30%.

Fig. 9. Residual modulus, En, against the non-dimensional number ofcycles, n/N. Maximum non-dimensional applied stress rmax/rr = 0.45.

G. Caprino et al. / Composites: Part A 38 (2007) 234–243 239

about 65% of the tensile strength. Therefore, when rmax/rr = 0.80, many cracks are expected to nucleate and prop-agate in the first cycle. Something similar occurs for rmax/rr = 0.60, which approximately corresponds to the stresslevel for knee formation. After the first cycles, the rate ofdecrease in modulus is lowered, until final fatigue failuretakes place. At low stress level, a slower decrease in rigidityis observed. At failure, the residual modulus of the materialis significantly affected by the stress level, being approxi-mately 75% of the initial modulus for rmax/rr = 0.45, and50% for rmax/rr = 0.80. This phenomenon is qualitativelyconsistent with the crack densities measured, which arehigher for higher applied stresses (full triangles in Fig. 7).

The effect of the stress level on the modulus evolutionsensibly disappears when the flexibilised composites areconsidered (Fig. 8(b)–(d)). Recognising that the decreasein modulus somehow reflects the state of damage, thisimplies that, in the stress domain within which a fatigue-induced failure occurs (rmax/rr 6 0.80), the damage statefor a fixed material is uniquely dependent on the portionof life spent, n/N. Comparing the results in Fig. 8(b)–(d),the final modulus of the composite is approximately 65%,70%, and 90% of E0 in the case of cf = 10%, 20%, and30%, respectively. Indeed, this correlates qualitatively wellwith the CCD of the three materials (Fig. 7), which is thelarger, the larger is the decrease in stiffness.

Although a more flexible resin preserves the materialmodulus lowering CCD, the usefulness of the flexibiliser

in stiffness-critical applications cannot be directly inferredfrom the results in Fig. 8, because higher cf values also wor-sen the initial modulus E0 (Fig. 1). In Fig. 9, some of thedata in Fig. 8, concerning rmax/rr = 0.45, are rearranged,and En (instead of its non-dimensional value) is shownagainst n/N. Clearly, a higher initial rigidity results in ahigher stiffness along all the fatigue life. Therefore, usinga flexibiliser can be inappropriate, in spite of the highermodulus retention guaranteed by an increase in cf.

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The horizontal dashed straight lines in the diagrams inFig. 8 represent the secant modulus Es resulting from themonotonic tests. Some authors [2,9] have proposed thatthis quantity could be a good indicator of an incipient fati-gue failure, which would occur when the residual elasticmodulus equals Es. From the data generated in this work,this seems to approximately hold when cf = 10% and 20%(Fig. 8(b) and (c)). In the other cases examined, En forn = N is higher than Es, so that assuming En= Es as a fail-ure criterion would yield a non-conservative estimate of thefatigue life.

In Fig. 10, the classical stress-loglife (S–N) curves for thematerials tested are collected. The extreme points on theleft are the monotonic strengths, which have been plottedat 0.5 cycle (LogN = �0.30), as usual for repeated-tensionfatigue. The lines are third-order polynomials, which werebest fitted to the experimental data to highlight theirtrends.

The general shape of the experimental S–N curvesagrees with the trends often observed in fibre-reinforcedplastics [4,26,27], where three regions can be individuated:in Region I, the curve is characterised by a slow decrease infatigue life with increasing number of cycles; then, a down-ward curvature appears, and the fatigue resistance under-goes a sensibly linear decrease with increasing LogN

(Region II); finally, the S–N curve flattens out at suffi-ciently low stress (Region III), suggesting the existence of

Fig. 10. Fatigue curves: (a) flexibiliser content cf = 0; (b) cf = 10%; (c) cf = 20polynomials.

an endurance limit. Region I is easily distinguished inFig. 10(b)–(d), associated with the flexibilised matrices,whereas it is barely visible in Fig. 10(a), pertaining to thebrittle resin. Therefore, there seems to be a correlationbetween the resin brittleness and the downward curvatureaffecting the S–N curve at high stress levels. The transitionfrom Region II to Region III is not clearly noted inFig. 10(b): probably, tests at lower loads should have beennecessary to reveal the flattening out of the fatigue curvefor this material.

To compare the fatigue response of the CSMs tested, allthe results in Fig. 10 were replotted in Fig. 11. To avoidcrowding of data, the mean value of LogN for each givenexperimental condition was calculated, and represented bya symbol in the figure.

From Fig. 11, the distinct behaviour of the four compos-ites at high stresses, anticipated from the difference in themonotonic strength, is apparent. However, beyond 102

cycles the fatigue curves for cf = 0–20% are almost super-posed, indicating a fatigue life practically independent ofcf. Only the CSM with 30% flexibiliser exhibits a slightlypoorer response in the range N = 102–104. Nevertheless,its fatigue strength is comparable to that of the other lam-inates at about 105 cycles.

It can be considered surprising that composites charac-terised by different stress–strain curves (Fig. 1), and dissim-ilar in the level of damage developed during fatigue cycling

% and (d) cf = 30%. Symbols: experimental data; lines: best-fit third-order

Fig. 11. Superposition of all the fatigue curves in Fig. 10.

Table 1Values of the constants in Eq. (2) calculated by best fitting the fatiguedata, and fatigue sensitivity of the unreinforced resins

cf (%) CSM Resin

rr (MPa) rrf (MPa) b b

0 71.5 73.3 0.121 –10 63.5 80.3 0.131 0.12320 77.6 80.9 0.134 0.11230 72.7 76.3 0.143 0.120

Fig. 12. Fatigue curves normalised with respect to the virtual monotonicstrength, rrf. Symbols: experimental data; lines: Eq. (2).

G. Caprino et al. / Composites: Part A 38 (2007) 234–243 241

(Fig. 7), display S–N curves very close with each other. Infact, this simply suggests that there is no strict correlationbetween the fractures taking place in the matrix and thefinal collapse in fatigue, which seems to be governed bythe reinforcement, rather than by the resin type. Notably,this occurs despite the fact that the CSMs tested in thiswork were characterised by a low fibre content by volume[23].

Noticing that the S–N curve follows an approximatelylinear law in the medium range of fatigue lives (102–105 cycles), Mandell [5,17] forced the experimental pointswithin this range to fit the relationship:

rmax

rr¼ 1� bLog N ð1Þ

and assumed the constant b in Eq. (1), i.e., the fractionalloss in tensile strength per decade of cycles, as a fatigue sen-sitivity parameter.

In this work, the following modified version of Eq. (1)was preferred to calculate the fatigue sensitivity:

rmax

rrf¼ 1� b½LogN � Logð0:5Þ� ð2Þ

where rrf is the intercept of the straight line best fitting thedata at LogN = Log(0.5). The substitution of Log N in Eq.(1) with the quantity in square brackets in Eq. (2) merelyreflects the difference in representing the monotonic datapoints, which were plotted at Log N = 0 by Mandell. Thereplacement of the normalising strength rrf to rr was justi-fied by the transition from the statically-induced to the fa-tigue-induced failure mechanisms. Of course, in this casethe composite behaviour in Region II is not correlated withthe monotonic strength.

To eliminate from the analysis the points pertainingto Regions I and III, all the data for which rmax/rr > 0.8and rmax/rr < 0.45 in Fig. 10 were disregarded, andthe best-fit straight lines were drawn through the remainingpoints. The resulting constants are shown inTable 1, together with the measured monotonic strength rr.

Comparing rr with rrf in Table 1, the latter is alwayshigher than the former, supporting the existence of a down-ward curvature in the S–N curve at low fatigue lives. Fur-ther, a precise trend, hardly appreciated from Fig. 11,appears from the fatigue sensitivity values, which steadilyincrease with increasing the flexibiliser content. Therefore,the use of flexible matrices seems to affect adversely thefatigue behaviour, if the susceptibility to fatigue, ratherthan the critical number of cycles determining final failure,is considered.

The straight lines in Fig. 12 are the graphical represen-tation of Eq. (2) for cf = 0 (exhibiting the lowest fatiguesensitivity) and cf = 30% (highest fatigue sensitivity). Thesymbols are the mean values of the experimental LogN

results. The agreement between theory and experiments isvery good in the range rmax/rr = 0.45–0.8, within whichthe constants of the best-fit straight lines were evaluated.This simply witnesses that the shape of the S–N curve inthe medium range of fatigue lives is well represented by alinear law. A deviation of the material behaviour fromthe linear trend is also apparent at long lives (two extremepoints on the right), anticipating the levelling off of the fati-gue curve at low applied stresses. Of course, at very longlives the usefulness of the fatigue sensitivity as defined byEq. (2) is lost.

In [18], the fatigue sensitivity for the unreinforced resinused in this work was calculated, in an attempt to find a

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correlation between cf and the fatigue response. From theresults, it was concluded that the fatigue sensitivity is nota monotonic function of the flexibiliser content, since thelowest b value was found for cf = 20%, whereas higher val-ues pertained to cf = 10% and cf = 30%. The method forthe evaluation of b used in [18] was different from theone illustrated previously. Therefore, to have a commonbasis for comparison, in this work the data in [18] were rep-lotted, and the b values for the pure resins were calculatedanew according to Eq. (2) and collected in the last columnin Table 1.

If a correlation exists between the fatigue sensitivities ofthe unreinforced resins and those of the correspondingCSMs, it does not appear clearly from the data in Table1. Notably, the b values for the resins are very close witheach other, and not far from those of their composite coun-terparts. Probably, this explains why the effect of matrix onthe fatigue response of the composites cannot be easilyhighlighted.

4. Conclusions

From the monotonic and tension–tension fatigue testsperformed in this work, carried out on E-glass chopped-strand-mat/polyester specimens whose matrix was flexibi-lised with different flexibiliser contents, the main conclu-sions are as follows:

� the flexibiliser strongly affects the monotonic response;in particular, the higher its proportion, the lower is thematerial elastic modulus, as well as the tendency todevelop transverse cracks; consequently, the stress–strain curve is highly non-linear when a rigid matrix isused, whereas progressively tends to linearity when theflexibiliser content is increased;� in fatigue, the crack density in the flexibilised composites

achieves a characteristic value, higher than found inmonotonic tests and decreasing with increasing flexibil-iser content, provided the maximum stress is sufficientlylow; when the maximum applied stress approaches themonotonic material strength, the crack density in fatigueconverges through its monotonic value;� in the composite without flexibiliser, the crack density

seems to mildly increase with increasing the maximumapplied stress, i.e., with decreasing the fatigue life;� thanks to the tendency to transverse crack suppression,

the flexibilised matrices retain a greater portion of theirinitial modulus along all their fatigue life; however, dueto the penalising effect of the flexibiliser on the initialrigidity, the absolute value of the modulus for a fixednumber of cycles is the higher, the more rigid is thematrix;� the flexibiliser content clearly affects the trend of the S–

N curves only at high stress levels (low fatigue lives),whereas has a negligible effect on the fatigue curves atmoderately high fatigue lives; nevertheless, if the fatigue

data are considered in terms of fatigue sensitivity, thisparameter seems to slowly increase with increasing theproportion of flexibiliser.

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