Mechanical Properties of Engineered Materials 2008 Part 10 doc

9 Introduction to Composites 9.1 INTRODUCTION Two approaches can be used to engineer improved mechanical properties of materials. One involves the modification of the internal structure of a given material system (intrinsic modification) by minor alloying, processing, and/ or heat treatment variations. However, after a number of iterations, an asymptotic limit will soon be reached by this approach, as the properties come close to the intrinsic limits for any given system. In contrast, an almost infinite array of properties may be engineered by the second approach which involves extrinsic modification by the introduction of additional (external) phases. For example, the strength of a system may be improved by reinforce- ment with a second phase that has higher strength than the intrinsic limit of the ‘‘host’’ material which is commonly known as the ‘‘matrix.’’ The result- ing system that is produced by the mixture of two or more phases is known as a composite material. Note that this rather general definition of a composite applies to both synthetic (man-made) and natural (existing in nature) composite materials. Hence, concrete is a synthetic composite that consists of sand, cement and stone, and wood is a natural composite that consists primarily of hemi- cellulose fibers in a matrix of lignin. More commonly, however, most of Copyright © 2003 Marcel Dekker, Inc. usarefamiliarwithpolymermatrixcompositesthatareoftenusedinmod- erntennisracquetsandpolevaults.Wealsoknow,fromwatchingathletic events,thattheseso-calledadvancedcompositematerialspromotesignifi- cantimprovementsinperformance. Thischapterintroducestheconceptsthatarerequiredforabasic understandingoftheeffectsofcompositereinforcementoncomposite strengthandmodulus.Followingabriefdescriptionofthedifferenttypes ofcompositematerials,mixturerulesarepresentedforcompositesystems reinforcedwithcontinuousanddiscontinuousfibers.Thisisfollowedbyan introductiontocompositedeformation,andadiscussionontheeffectsof fiberorientationoncompositefailuremodes.Theeffectsofstatisticalvar- iationsinfiberpropertiesonthecompositepropertiesarethenexaminedat theendofthechapter.Furthertopicsincompositedeformationwillbe presentedinChap.10. 9.2TYPESOFCOMPOSITEMATERIALS Syntheticcompositesareoftenreinforcedwithhigh-strengthfibersorwhis- kers(shortfibers).Suchreinforcementsareobtainedviaspecialprocessing schemesthatgenerallyresultinlowflaw/defectcontents.Duetotheirlow flaw/defectcontents,thestrengthlevelsofwhiskersandfibersaregenerally muchgreaterthanthoseofconventionalbulkmaterialsinwhichhigher volumefractionsofdefectsarepresent.ThisisshowninTable9.1in whichthestrengthsofmonolithicandfiber/whiskermaterialsarecompared. Thehigherstrengthsofthewhisker/fibermaterialsallowforthedevelop- mentofcompositematerialswithintermediatestrengthlevels,i.e.,between thoseofthematrixandreinforcementmaterials.Similarly,intermediate valuesofmodulusandothermechanical/physicalpropertiescanbeachieved bytheuseofcompositematerials. Theactualbalanceofpropertiesofagivencompositesystemdepends onthecombinationsofmaterialsthatareactuallyused.Sincewearegen- erallyrestrictedtomixturesofmetals,polymers,orceramics,mostsynthetic compositesconsistofmixturesofthedifferentclassesofmaterialsthatare showninFig.9.1(a).However,duringcompositeprocessing,interfacial reactionscanoccurbetweenthematrixandreinforcementmaterials. Theseresultintheformationofinterfacialphasesandinterfaces(bound- aries),asshownschematicallyinFig.9.1(b). Oneexampleofacompositethatcontainseasilyobservedinterfacial phasesispresentedinFig.9.2.Thisshowsatransversecross-sectionfrom a titanium matrix (Ti–15V–3Cr–3Al–3Sn) composite reinforced with car- bon-coated SiC (SCS-6) fibers. The interfacial phases in this composite Copyright © 2003 Marcel Dekker, Inc. havebeenstudiedusingacombinationofscanningandtransmission electronmicroscopy.ThemultilayeredinterfacialphasesintheTi–15V– 3Cr–3Al–3Sn/SCS-6composite(Fig.9.2)havebeenidentifiedtocontain predominantly TiC. However, some Ti 2 C and Ti 5 Si 3 phases have also been shown to be present in some of the interfacial layers (Shyue et al., 1995). The properties of a composite can be tailored by the judicious control of interfacial properties. For example, this can be achieved in the Ti–15V– 3Cr–3Al–3Sn/SCS-6 composite by the use of carbon coatings on the SiC/ TABLE 9.1 Summary of Basic Mechanical/Physical Properties of Selected Composite Constituents: Fiber Versus Bulk Properties Young’s modulus (GPa) Strength a (MPa) Alumina: fiber (Saffil RF) 300 2000 monolithic 382 332 Carbon: fiber (IM) 290 3100 monolithic 10 20 Glass, fiber (E) 76 1700 monolithic 76 100 Polyethylene: fiber (S 1000) 172 2964 monolithic (HD) 0.4 26 Silicon carbide: fiber (MF) 406 3920 monolithic 410 500 a Tensile and flexural strengths for fiber and monolithic, respectively. FIGURE 9.1 Schematic illustration of (a) the different types of composites and (b) interfaces and interfacial phases formed between the matrix and reinfor- cement materials. Copyright © 2003 Marcel Dekker, Inc. SCS-6fibers.Thehexagonalgraphitelayersinthecarboncoatingstendto alignwithaxialstress,thusmakingeasyshearpossibleinthedirectionof interfacialshearstress.Hence,theinterfacialshearstrengthsofsiliconcar- bidefiber-reinforcedcompositescanbecontrolledbytheuseofcarbon coatingsthatmakeinterfacialslidingrelativelyeasy.Suchinterfacialsliding iscriticalintheaccommodationofstrainduringmechanicalloadingor thermalcycling. Compositepropertiesarealsocontrolledbytheselectionofconsti- tuentswiththeappropriatemixofmechanicalandphysicalproperties (Tables9.1and9.2).Sincelightweightisoftenofimportanceinalarge numberofstructuralapplications,especiallyintransportationvehicles suchascars,boats,airplanes,etc.,specificmechanicalpropertiesare oftenconsideredintheselectionofcompositematerials.Specificproperties aregivenbytheratioofaproperty(suchasYoung’smodulusand strength)tothedensity.Forexample,thespecificmodulusistheratio ofYoung’smodulustodensity,whilespecificstrengthistheratioof absolutestrengthtodensity. Itisausefulexercisetocomparetheabsoluteandspecificpropertiesin Table9.2.Thisshowsthatceramicsandmetalstendtohavehigherabsolute and specific moduli and strength, while polymers tend to have lower abso- lute properties and moderate specific properties. In contrast, polymer matrix composites can be designed with attractive combinations of absolute specific FIGURE 9.2 (a) Transverse cross-section of Ti–15V–3Cr–3Al–3Sn composite reinforced with 35 vol% carbon-coated SiC (SCS-6) fibers and (b) Interfacial Phases in Ti-15-3/SCS6 composite. Copyright © 2003 Marcel Dekker, Inc. TABLE 9.2 Summary of Basic Mechanical/Physical Properties of Selected Composite Constituents: Constituent Properties Density (mg/m 3 ) Young’s modulus (GPa) Strength a (MPa) Ductility (%) Toughness, K IC (M Pa m 1=2 Þ Specific modulus [(GPa)/ (mg/m 3 )] Specific strength [(MPa)/ (mg/m 3 )] Ceramics Alumina (Al 2 O 3 ) 3.87 382 332 0 4.9 99 86 Magnesia (MgO) 3.60 207 230 0 1.2 58 64 Silicon nitride (Si 3 N 4 ) 166 210 0 4.0 Zirconia (ZrC 2 ) 5.92 170 900 0 8.6 29 152 -Sialon 3.25 300 945 0 7.7 92 291 Glass–ceramic Silceram 2.90 121 174 0 2.1 42 60 Metals Aluminum 2.70 69 77 47 26 29 Aluminum–3%Zn–0.7%Zr 2.83 72 325 18 25 115 Brass (Cu-30%Zn) 8.50 100 550 70 12 65 Nickel–20%Cr–15%Co 8.18 204 1200 26 25 147 Mild steel 7.86 210 460 35 27 59 Titanium–2.5% Sn 4.56 112 792 20 24 174 Polymers Epoxy 1.12 4 50 4 1.5 4 36 Melamine formaldehyde 1.50 9 70 6 47 Nylon 6.6 1.14 2 70 60 18 61 Poly(ether ether ketone) 1.30 4 70 3 54 Poly(methyl methacrylate) 1.19 3 50 3 1.5 3 42 Polystyrene 1.05 3 50 2 1.0 3 48 Poly(vinyl chloride) rigid 1.70 3 60 15 4.0 2 35 a Strength values are obtained from the test appropriate for the material, e.g., flexural and tensile for ceramics and metals, respectively. Copyright © 2003 Marcel Dekker, Inc. strengthandstiffness.Thesearegenerallyengineeredbythejudiciousselec- tionofpolymermatrices(usuallyepoxymatrices)andstrongandstiff (usuallyglass,carbon,orkevlar)fibersinengineeringcomposites,which areusuallypolymercomposites. Thespecificpropertiesofdifferentmaterialscanbeeasilycompared usingmaterialsselectionchartssuchastheplotsofEversus,or f versus inFigs9.3and9.4,respectively.Notethatthedashedlinesinthesefigures correspond to different ‘‘merit’’ indices. For example, the minimum weight design of stiff ties, for which the merit index is E=, could be achieved by selecting the materials with the highest E= from Fig. 9.3. These are clearly the materials that lie on dashed lines at the top left-hand corner of Fig. 9.3. FIGURE 9.3 Materials selection charts showing attractive combinations of spe- cific modulus that can be obtained from engineering composites. Copyright © 2003 Marcel Dekker, Inc. Similarly,thematerialswiththehighestspecificstrengths, f =,arethe materialsatthetopleft-handcornerofthestrengthmaterialsselection chartshowninFig.9.4.Inbothcharts(Figs9.3and9.4),polymermatrix compositessuchascarbonfiber-reinforcedplastics(CFRPs),glassfiber- reinforcedplastics(GFRPs),andkevlarfiber-reinforcedplastics(KFRPs) emergeclearlyasthematerialsofchoice.Forthisreason,polymermatrix compositesareoftenattractiveinthedesignofstrongandstifflightweight structures. Averywiderangeofsyntheticandnaturalcompositematerialsare possible.Conventionalreinforcementmorphologiesinclude:particles(Fig. 9.5),fibers[Fig.9.6(a)],whiskers[Figs9.6(b)and9.6(c)],andlayers,Fig. 9.6(d).However,insteadofabruptinterfaceswhichmaycausestresscon- FIGURE9.4Materialsselectionchartsshowingattractivecombinationsofspe- cific strength that can be obtained from engineering composites. Copyright © 2003 Marcel Dekker, Inc. centrations,gradedinterfacesmaybeusedinthedesignofcoatingsand interfacesinwhichthepropertiesofthesystemarevariedcontinuouslyfrom 100%Ato100%B,asshownschematicallyinFig.9.7.Suchgradedtransi- tionsincompositionmaybeusedtoavoidabruptchangesinstressstates thatcanoccuratnongradedinterfaces. Furthermore,compositearchitecturescanbetailoredtosupportloads indifferentdirections.Unidirectionalfiber-reinforcedarchitectures[Fig. 9.6(a)]are,therefore,onlysuitableforstructuralapplicationsinwhichthe loading is applied primarily in one direction. Of course, the composite fiber may be oriented to support axial loads in such cases. Similarly, bidirectional composite systems (with two orientations of fibers) can be oriented to sup- port loads in two directions. The fibers may also be discontinuous in nature [Figs 9.6(b) and 9.6(c)], in which case they are known as whiskers. Whiskers generally have high strengths due to their low defect densities. They may be aligned [Fig. 9.6(b)], FIGURE 9.5 Schematic illustration of particulate reinforcement morphologies: (a) spherical; (b) irregular; (c) faceted. Copyright © 2003 Marcel Dekker, Inc. FIGURE 9.6 Examples of possible composite architectures: (a) unidirectional fiber reinforcement; (b) aligned whisker reinforcement; (c) randomly oriented whisker reinforcement; (d) continuous layers. FIGURE 9.7 Schematic illustration of graded reinforcements. Copyright © 2003 Marcel Dekker, Inc. orrandomlyoriented,Fig.9.6(c).Thereadermayrecognizeintuitivelythat alignedorientationsofwhiskersorfiberswillgiverisetoincreasedstrength inthedirectionofalignment,butoverall,toanisotropicproperties,i.e., propertiesthatvarysignificantlywithchangesindirection.However,ran- domorientationsofwhiskerswilltendtoresultinloweraveragestrengthsin anygivendirection,butalsotorelativelyisotropicproperties,i.e.,properties thatdonotvaryasmuchinanygivendirection. Inadditiontothesyntheticcompositesdiscussedabove,severalcom- positesystemshavebeenobservedinnature.Infact,mostmaterialsin naturearecompositematerials.Someexamplesofnaturalcomposites includewoodandbone.Asdiscussedearlier,woodisanaturalcomposite thatconsistsofaligninmatrixandspiralhemicellulosefibers.Bone,onthe otherhand,isacompositethatconsistsoforganicfibers,inorganiccrystals, water,andfats.About35%ofboneconsistoforganiccollagenprotein fiberswithsmallrod-like(5nmÂ5nmÂ50nm)hydroxyapatitecrystals. Longcortical/cancellousbonestypicallyhavelowfatcontentandcompact structuresthatconsistofanetworkofbeamsandsheetsthatareknownas trabeculae. Itshouldbeclearfromtheabovediscussionthatanalmostinfinite arrayofsyntheticandartificialcompositesystemsarepossible.However, theoptimizationofcompositeperformancerequiressomeknowledgeof basiccompositemechanicsandmaterialsconcepts.Thesewillbeintroduced inthischapter.Moreadvancedtopicssuchascompositeplytheoryand shearlagtheorywillbepresentedinChap.10. 9.3RULE-OF-MIXTURE THEORY Thepropertiesofcompositesmaybeestimatedbytheapplicationofsimple rule-of-mixturetheories(Voigt,1889).Theserulescanbeusedtoestimate averagecompositemechanicaland physicalpropertiesalongdifferentdirec- tions.Theymayalsobeusedtoestimatetheboundsinmechanical/physical properties.Theyare,therefore,extremelyuseful inassessmentofthecom- binationsofbasicmechanical/physicalpropertiesthatcanbeengineered via composite reinforcement. This section will present constant-strain and con- stant-stress rules of mixture. 9.3.1 Constant-Strain and Constant-Stress Rules of Mixtures An understanding of constant-strain and constant-stress rules of mixtures maybegainedbyacarefulstudyofFig.9.8.Thisshowsschematicsofthe same composite system with loads applied parallel [Fig. 9.8(a)] or perpen- Copyright © 2003 Marcel Dekker, Inc. [...]... Chap 10 9.3 RULE -OF- MIXTURE THEORY The properties of composites may be estimated by the application of simple rule -of- mixture theories (Voigt, 1889) These rules can be used to estimate average composite mechanical and physical properties along different directions They may also be used to estimate the bounds in mechanical/ physical properties They are, therefore, extremely useful in assessment of the... the combinations of basic mechanical/ physical properties that can be engineered via composite reinforcement This section will present constant-strain and constant-stress rules of mixture 9.3.1 Constant-Strain and Constant-Stress Rules of Mixtures An understanding of constant-strain and constant-stress rules of mixtures may be gained by a careful study of Fig 9.8 This shows schematics of the same composite... from Pergamon Press.) be used to estimate the effects of reinforcements on many important physical properties They may also be used to estimate the bounds in a wide range of physical properties of composite materials Such rule -of- mixture calculations are particularly valuable because they can be used in simple ‘‘back-ofthe-envelope’’ estimates to guide materials selection and design Finally, in this section,... rule -of- mixture equations indicate that upper-bound comCopyright © 2003 Marcel Dekker, Inc posite properties are averaged according to the volume fraction of the composite constituents The fraction of the load supported by each of the constituents also depends on the ratio of the in moduli to the composite moduli Hence, for most reinforcements, which typically have higher moduli than those of matrix materials. .. nature We will examine the properties of composite constituents, and how the constituent properties contribute to composite behavior 9.8.1 Fibers and Matrix Materials In Chap 6, we showed that the theoretical strength of a solid is $ G=2, where G is the shear modulus However, due to the existence of defects, the actual measured strengths of solids are generally a few orders of magnitude below the predicted... longer fibers The mechanical properties of fibers, therefore, exhibit statistical variations These statistical variations are often well described by Weibull distributions (Weibull, 1951) Typical values of the strengths and moduli for selected composite fibers are compared with those of their monolithic counterparts in Table 9.1 Note that the fiber strengths are approximately one order of magnitude greater... FAILURE OF OFF-AXIS COMPOSITES So far, we have focused primarily on the deformation behavior of unidirectional fiber-reinforced composites However, it is common in several applications of composite materials to utilize fiber architectures that are inclined at an angle to the loading axis Such off-axis composites may give rise to different deformation and failure modes, depending on the orientation of the... aligned orientations of whiskers or fibers will give rise to increased strength in the direction of alignment, but overall, to anisotropic properties, i.e., properties that vary significantly with changes in direction However, random orientations of whiskers will tend to result in lower average strengths in any given direction, but also to relatively isotropic properties, i.e., properties that do not... observed in nature In fact, most materials in nature are composite materials Some examples of natural composites include wood and bone As discussed earlier, wood is a natural composite that consists of a lignin matrix and spiral hemicellulose fibers Bone, on the other hand, is a composite that consists of organic fibers, inorganic crystals, water, and fats About 35% of bone consist of organic collagen protein... ceramics are brittle, and are susceptible to failure by the propagation of pre-existing cracks For this reason, there are relatively few applications of ceramic matrix composites (compared to those of polymer matrix Copyright © 2003 Marcel Dekker, Inc TABLE 9.4 Typical Mechanical Properties of Polymer Matrix Composites and Polymer Matrix Materials Density (mg/m3 ) Nylon 66 + 40% carbon fiber Epoxide + 70% . Inc. usarefamiliarwithpolymermatrixcompositesthatareoftenusedinmod- erntennisracquetsandpolevaults.Wealsoknow,fromwatchingathletic events,thattheseso-calledadvancedcompositematerialspromotesignifi- cantimprovementsinperformance. Thischapterintroducestheconceptsthatarerequiredforabasic understandingoftheeffectsofcompositereinforcementoncomposite strengthandmodulus.Followingabriefdescriptionofthedifferenttypes ofcompositematerials,mixturerulesarepresentedforcompositesystems reinforcedwithcontinuousanddiscontinuousfibers.Thisisfollowedbyan introductiontocompositedeformation,andadiscussionontheeffectsof fiberorientationoncompositefailuremodes.Theeffectsofstatisticalvar- iationsinfiberpropertiesonthecompositepropertiesarethenexaminedat theendofthechapter.Furthertopicsincompositedeformationwillbe presentedinChap .10. 9.2TYPESOFCOMPOSITEMATERIALS Syntheticcompositesareoftenreinforcedwithhigh-strengthfibersorwhis- kers(shortfibers).Suchreinforcementsareobtainedviaspecialprocessing schemesthatgenerallyresultinlowflaw/defectcontents.Duetotheirlow flaw/defectcontents,thestrengthlevelsofwhiskersandfibersaregenerally muchgreaterthanthoseofconventionalbulkmaterialsinwhichhigher volumefractionsofdefectsarepresent.ThisisshowninTable9.1in whichthestrengthsofmonolithicandfiber/whiskermaterialsarecompared. Thehigherstrengthsofthewhisker/fibermaterialsallowforthedevelop- mentofcompositematerialswithintermediatestrengthlevels,i.e.,between thoseofthematrixandreinforcementmaterials.Similarly,intermediate valuesofmodulusandothermechanical/physicalpropertiescanbeachieved bytheuseofcompositematerials. Theactualbalanceofpropertiesofagivencompositesystemdepends onthecombinationsofmaterialsthatareactuallyused.Sincewearegen- erallyrestrictedtomixturesofmetals,polymers,orceramics,mostsynthetic compositesconsistofmixturesofthedifferentclassesofmaterialsthatare showninFig.9.1(a).However,duringcompositeprocessing,interfacial reactionscanoccurbetweenthematrixandreinforcementmaterials. Theseresultintheformationofinterfacialphasesandinterfaces(bound- aries),asshownschematicallyinFig.9.1(b). Oneexampleofacompositethatcontainseasilyobservedinterfacial phasesispresentedinFig.9.2.Thisshowsatransversecross-sectionfrom a. Inc. beusedtoestimatetheeffectsofreinforcementsonmanyimportantphysi- calproperties.Theymayalsobeusedtoestimatetheboundsinawiderange ofphysicalpropertiesofcompositematerials.Suchrule -of- mixturecalcula- tionsareparticularlyvaluablebecausetheycanbeusedinsimple‘‘back -of- the-envelope’’estimatestoguidematerialsselectionanddesign. Finally,inthissection,itisimportanttonotethatthesimpleaver- agingschemesderivedabovefortwo-phasecompositesystemscanbe extendedtoamoregeneralcaseofanyn-componentsystem(where n!2).Thisgives ðX c Þ n ¼ X m i¼1 V i ðX i Þ n ð9:16Þ whereX i maycorrespondtothephysical/mechanicalpropertiesofmatrix, reinforcement,orinterfacialphases(Figs9.1and9.2). 9.4DEFORMATIONBEHAVIOROFUNIDIRECTIONAL COMPOSITES Letusstartthissectionbyconsideringtheuniaxialdeformationofan arbitraryunidirectionalcompositereinforcedwithstiffelasticfibers. FIGURE9.9Schematicillustrationofupperandlowerboundmoduligivenby constant-strain. Inc. SCS-6fibers.Thehexagonalgraphitelayersinthecarboncoatingstendto alignwithaxialstress,thusmakingeasyshearpossibleinthedirectionof interfacialshearstress.Hence,theinterfacialshearstrengthsofsiliconcar- bidefiber-reinforcedcompositescanbecontrolledbytheuseofcarbon coatingsthatmakeinterfacialslidingrelativelyeasy.Suchinterfacialsliding iscriticalintheaccommodationofstrainduringmechanicalloadingor thermalcycling. Compositepropertiesarealsocontrolledbytheselectionofconsti- tuentswiththeappropriatemixofmechanicalandphysicalproperties (Tables9.1and9.2).Sincelightweightisoftenofimportanceinalarge numberofstructuralapplications,especiallyintransportationvehicles suchascars,boats,airplanes,etc.,specificmechanicalpropertiesare oftenconsideredintheselectionofcompositematerials.Specificproperties aregivenbytheratioofaproperty(suchasYoung’smodulusand strength)tothedensity.Forexample,thespecificmodulusistheratio ofYoung’smodulustodensity,whilespecificstrengthistheratioof absolutestrengthtodensity. Itisausefulexercisetocomparetheabsoluteandspecificpropertiesin Table9.2.Thisshowsthatceramicsandmetalstendtohavehigherabsolute and