预报单向复合材料轴向强度的双尺度方法

预报单向复合材料轴向强度的双尺度方法

Abstract

Inrecentyears；theuseofunidirectionalcompositeshasincreased

invariousindustries,fromaerospacetoautomotiveandsports.The

axialstrengthofthesecompositesisacriticalparameterthatdirectly

affectsthedurabilityandreliabilityofthefinalproduct.However,

accuratepredictionoftheaxialstrengthofunidirectionalcomposites

remainsachallengingtaskduetotheircomplexmicrostructures.This

paperpresentsadual-scalemethodforpredictingtheaxialstrengthof

unidirectionalcomposites.Themethodcombinesthemicromechanical

andmacromechanicalmodels,whichaccountforthemechanical

behaviorofthecompositeatthemicroandmacroscale,respectively.

Introduction

Unidirectionalcompositesarewidelyusedduetotheirhighspecific

strength,stiffness,anddurability.Thesecompositesarecomposedof

fibers(suchascarbon,glass,oraramid)andamatrixmaterial(suchas

epoxy,polyamide,orpolyester)thatholdsthefibersinplace.The

mechanicalbehaviorofunidirectionalcompositesisgovernedbythe

mechanicalpropertiesofthefibersandthematrixmaterial,aswellas

themicrostructureofthecomposite(i.e.zfiberorientation,volume

fraction,andinterfacialproperties).Amongthemechanicalproperties,

theaxialstrengthisacriticalparameterthatdeterminesthemaximum

stressthatthecompositecanwithstandalongthefiberdirection.

Accuratepredictionoftheaxialstrengthofunidirectionalcompositesis

crucialfordesigningreliableanddurableproducts.However,thistaskis

challengingduetothecomplexmicrostructureofthecomposite.

Severalmodelshavebeenproposedtopredictthemechanical

behaviorofunidirectionalcomposites.Thesemodelscanbeclassified

intotwocategories:(i)micromechanicalmodelsand(ii)

macromechanicalmodels.Micromechanicalmodelsdescribethe

mechanicalbehaviorofindividualfibersandtheinterfacialproperties

betweenthefibersandthematrixmaterial.Thesemodelsarebasedon

themechanicsofmaterialsandcanprovidedetailedinformationonthe

microstructureofthecomposite.However,theyrequiresignificant

computationaleffortandarenotsuitableforpredictingthemacroscopic

behaviorofthecomposite.Ontheotherhand,macromechanicalmodels

describethemechanicalbehaviorofthecompositeatthemacroscopic

level.Thesemodelsarebasedoncontinuummechanicsandcanbe

usedtopredicttheoverallbehaviorofthecomposite,includingtheaxial

strength.However,theyassumeahomogeneousmaterialbehaviorand

donotaccountforthemicrostructureofthecomposite.

Inthispaper,weproposeadual-scalemethodthatcombinesthe

micromechanicalandmacromechanicalmodelstopredicttheaxial

strengthofunidirectionalcomposites.Themethodaccountsforthe

mechanicalbehaviorofthecompositeatboththemicroandmacro

scaleandprovidesaccuratepredictionswhilereducingthe

computationaleffort.

MicromechanicalModel

Themicromechanicalmodelisbasedonthemechanicsofmaterials

anddescribesthemechanicalbehaviorofindividualfibersandthe

interfacialpropertiesbetweenthefibersandthematrixmaterial.The

modelassumesthatthefibersarelinearlyelasticandthatthematrix

materialisisotropicandlinearlyelastic.Theinterfacialproperties

betweenthefibersandthematrixmaterialaremodeledusingthe

shear-lagtheory.Themethodassumesthattheloadistransferredfrom

thefiberstothematrixmaterialthroughshearstressattheinterface

betweenthefibersandthematrix.

Theaxialstrengthofthecompositeispredictedusingthefollov/ing

equation:

of=am(1-af)+Taf

whereofisthefiberstress,amisthematrixstress,afisthefiber

volumefraction,Tistheshearstressattheinterfacebetweenthe

fibersandthematrix,andafistheaxialfiberstrain.Theequation

representsthebalanceofforcesbetweenthefibersandthematrix

material,andthetransferofloadfromthefiberstothematrixmaterial

throughtheinterface.Theequationcanbesolvednumericallyusingthe

finiteelementmethod,andtheaxialstrengthofthecompositecanbe

calculated.

MacromechanicalModel

Themacromechanicalmodeldescribesthemechanicalbehaviorof

thecompositeatthemacroscopiclevel.Themodelassumesthatthe

compositeishomogeneousandlinearlyelastic.Theaxialstrengthofthe

compositeispredictedusingtheclassicallaminationtheory,which

assumesthatthecompositeiscomposedofseverallayersof

unidirectionalpliesthatarestackedatvariousanglestothefiber

direction.Thelayerv/iseapproachassumesthatthestressandstrainin

eachplyareconstantandthatthelaminatebehavesasasingle

structuralunitintheaxialdirection.

Theaxialstrengthofthecompositeispredictedusingthefollov/ing

equation:

of=om(1-af)+Elaf

whereofisthefiberstress,amisthematrixstress,afisthefiber

volumefraction,Elisthelongitudinalelasticmodulusofthecomposite,

andafistheaxialfiberstrain.Theequationrepresentsthebalanceof

forcesbetweenthefibersandthematrixmaterialandthetransferof

loadfromthefiberstothematrixmaterialthroughtheelastic

deformationofthecomposite.Theaxialstrengthofthecompositecan

becalculatedusingthefiniteelementmethodbasedonthelayerwise

approachandtheclassicallaminationtheory.

Dual-ScaleMethod

Thedual-scalemethodcombinesthemicromechanicaland

macromechanicalmodelstopredicttheaxialstrengthofunidirectional

composites.Themethodaccountsforthemechanicalbehaviorofthe

compositeatboththemicroandmacroscaleandprovidesaccurate

predictionswhilereducingthecomputationaleffort.

Themethodinvolvesthefollowingsteps:

1.Determinethefibervolumefractionandorientationdistribution

usingmicro-CTormicroscopytechniques.

2.CalculatethelongitudinalelasticmodulusandPoisson'sratioof

thecompositeusingthemicromechanicalmodel.

3.Calculatetheshearmodulusofthecompositeusingthe

macromechanicalmodel.

4.Calculatetheinterfacialshearstressusingthemicromechanical

model.

5.Calculatetheaxialstrengthofthecompositeusingthe

micromechanicalmodelandthemacromechanicalmodel.

Thedual-scalemethodprovidesaccuratepredictionsoftheaxial

strengthofunidirectionalcomposites,takingintoaccountthe

mechanicalbehaviorofthecompositeatboththemicroandmacro

scale.Themethodismoreefficientthanusingonlythe

micromechanicalmodelandprovidesmoredetailedinformationthan

usingonlythemacromechanicalmodel.Themethodcanbeusedfor

designingreliableanddurableproductsthatrequirehighstrengthand

stiffness.

Conclusion

Unidirectionalcompositesarewidelyusedduetotheirhighspecific

strength,stiffness,anddurability.Theaxialstrengthofthese

composit