Methods and models for fibre–matrix interface characterisation in fibre-reinforced polymers: a review

ABSTRACTThe fibre–matrix interface represents a vital element in the development and characterisation of fibre-reinforced polymers (FRPs). Extensive ranges of interfacial properties exist for different composite systems, measured with various interface characterisation techniques. However, the discrepancies in interfacial properties of similar fibre–matrix systems have not been fully addressed or explained. In this review, first, the interface-forming mechanisms of FRPs are established. Following a discourse on three primary factors that affect the fibre–matrix interface, the four main interface characterisation methods (single-fibre fragmentation, single-fibre pull-out, microbond and fibre push-in/-out tests) are described and critically reviewed. These sections review various detailed data reduction schemes, numerical approaches, accompanying challenges and sources of reported scatter. Finally, following the assessment of several infrequent test methods, comprehensive conclusions, prospective directions and intriguing extensions to the field are provided.KEYWORDS: Carbon fibreglass fibreepoxythermoplasticinterface characterisationinterfacial shear strengthinterfacial fracture toughnessinterfacial friction coefficient Disclosure statementNo potential conflict of interest was reported by the author(s).List of abbreviations and symbols45FBT=45° fibre bundle tensile testAE=Acoustic emissionAFM=Atomic force microscopyANN=Artificial neural networkBAM=Federal institute for materials research and testingBEM=Boundary element methodCF=Carbon fibreCFRP=Carbon fibre-reinforced polymerCKT=Cottrell–Kelly–Tyson modelCMC=Ceramic matrix compositesCNT=Carbon nanotubesCT=Computed tomographyCTE=Coefficient of thermal expansionCZM=Cohesive zone modelDEM=Discrete element methodEPZ=Embedded process zone modelFBG=Fibre Bragg gratingFE(M)=Finite element (method)FRP=Fibre-reinforced polymerGF=Glass fibreGFRP=Glass fibre-reinforced polymerHM=High modulus carbon fibreIFFT=Interfacial fracture toughnessIFNS=Interfacial normal (radial) strengthIFSS=Interfacial shear strengthIFSSapp=Apparent interfacial shear strengthILSS=Interlaminar shear strengthIMD=Intermediate modulusLRS=Laser Raman spectroscopyMB (MBT)=Microbond testMFFT=Multi-fibre fragmentation testMRS=Micro-Raman spectroscopyPA=PolyamidePC=PolycarbonatePEEK=Polyether ether ketonePEI=PolyetherimidePP=PolypropylenePPS=Polyphenylene sulphideSCF=Stress (or strain) concentration factorSEM=Scanning electron microscopySERR=Strain energy release rateSFFT=Single-fibre fragmentation testSLM=Shear-lag modelTFBT=Transverse fibre bundle tensile testTP=ThermoplasticAemb=Embedded areaa=Crack lengthbi=Interface effective thicknessda=Change in crack lengthdC=Change in compliancedf=Fibre diameterdU=Energy summation proposed by Marshall and OliverdUe=Change of the elastic energy inside the fibredUf=Work of friction in the interfacedUGi=Debonding energy associated with the new debonded areadUl=Potential energy of the loading systemdUm=Change in matrix elastic energyE1=Longitudinal Young's modulus of the model compositeEf(Ef1)=Axial Young's modulus of the fibreEm=Matrix Young's modulusET=Transverse Young's modulus of the fibreF−δ=Force–displacementFb=Initial post-debonding forceFcat=Catastrophic failure loadFd=Debonding forceFfric.,max=Maximum frictional forceFmax=Maximum loadFs=Shear forceG=Strain energy release rate (fracture toughness)Gi=Interfacial fracture toughnessGint.=Shear modulus of the interfaceGm=Matrix shear modulusGprop.=Strain energy release rate for debond propagationGicII=Interfacial mode II fracture toughnessH=Height in contact angleK=Slope of the force-displacement curveKf=Fibre free length stiffnessKi=Cohesive stiffnessL=Droplet lengthl=Fibre length, axial location of the crack frontlavg=Arithmetic mean of the fragment lengths at saturationlc=Critical fibre lengthlcat=Fibre embedded length shorter than lmax,catld=Debond lengthlemb=Embedded fibre lengthlemb,c=Critical embedded lengthlfree=Fibre free-lengthlm=The point where the results of FEM, variational mechanics and SLM convergelmax=Maximum fragment lengthlmax,cat=Maximum fibre length beyond which catastrophic debonding does not occurlmax,friction=Maximum fibre length to surpass the frictional dissipation of energym=A parameter acquired from the slope of the u against Fs2 plot in push-in testsP=Applied loadPc=Critical load at the debond initiationPd=Debonding loadqo=Normal pressure exerted on the fibre due to the matrix shrinkage during cureR=Axial distance at which τm=0Req=Equivalent cylinder radiusRi=Indentation position to the fibre centreS0=Slope of the linear region in a push-in load-displacement curveTf=Tensile force on fibreTg=Glass transition temperatureTm=Tensile force on matrixUθ=Deformation in θ direction in a cylindrical coordinate system (rθz)u=Total recorded displacement throughout the push-in testuep=Elastoplastic indentation of the fibre surfaceuf=Fibre surface displacement due to the fibre compressionVdroplet=Droplet volumeVf=Fibre volume fractionVm=Matrix volume fractionUθ=Deformation in θ direction in a cylindrical coordinate system (rθz)WA=Work required to separate the two neighbouring molecular layers of the fibre and the matrix, Work of adhesionw=Thickness of a push-out specimen (equal to the fibre length)w2=Cross section area of a square specimenz=Fibre axial axisz∗=The z-coordinate where the stress is evaluatedαfL=Axial thermal expansion coefficients of the fibreαfT=Transverse thermal expansion coefficients of the fibreαm=Thermal expansion coefficient of the matrixβ=Shear-lag parameterβCox=Cox shear-lag parameterβgeom.=Geometrical correction factorβNayfeh=Nayfeh shear-lag parameterΔEelastic=Elastic deformation energy of the fibre, matrix and bending of the sampleΔEfriction=Work of frictionΔEplastic=Plastic deformation energy of fibre, matrix, and interfaceΔT=Temperature differenceδ=Separation in traction-separationϵ=Applied strain, Fibre axial strain distributionsϵf=Fibre strainϵm=Matrix strainθ=Contact anglek=Frictional stress transfer rateλ=Effective normal displacement between the contacting surfaces required for their separationμi=Interfacial friction coefficientνf=Fibre Poisson's ratioνfL=Axial Poisson's ratios of the fibreνfT=Transverse Poisson's ratios of the fibreνm=Poisson's ratio of the Matrixσ0=Net axial stress, Axial stress at the minimum cross-section of the specimenσc1=Longitudinal stress in a model compositeσd=Debonding initiation stress, Adhesion pressureσf=Fibre failure strengthσi=Interfacial tensile stressσn=Normal stressσrr=Radial stress in variational mechanicsσrrcritical=Critical radial stressσult=Critical radial stress value at the onset of the debond initiationσ¯z=Cross-sectional average axial stress of fibreτy=Matrix shear yield strengthτapp=Apparent interfacial shear strengthτd=Local interfacial shear strengthτf=Interfacial frictional sliding stress (post-debond frictional shear stress)τi=Interfacial shear stressτic=Interfacial shear strengthτm=Shear stress of the matrixτmax=Maximum interfacial shear stressτmaxact=Actual interfacial shear strengthτmaxLRS=Maximum interfacial shear stress obtained from laser Raman spectroscopyτmaxSLM=Interfacial shear strength obtained with the shear-lag modelτmax,ths=Maximum residual shear stressτrz=Interfacial shear stress in variational mechanicsτthermal=Residual thermal stressesτult=Ultimate interfacial shear strengthAdditional informationFundingThe effort that has been put into this research is within the framework of the HyFiSyn project, which has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 765881. M. Mehdikhani would like to acknowledge his FWO Postdoc Fellowship, project ToughImage (1263421N).