868
Views
0
CrossRef citations to date
0
Altmetric
Full Critical Review

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

, , &
Pages 1245-1319 | Received 16 Nov 2022, Accepted 23 Jun 2023, Published online: 07 Nov 2023
 

ABSTRACT

The 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.

Disclosure statement

No potential conflict of interest was reported by the author(s).

List of abbreviations and symbols
45FBT=

45° fibre bundle tensile test

AE=

Acoustic emission

AFM=

Atomic force microscopy

ANN=

Artificial neural network

BAM=

Federal institute for materials research and testing

BEM=

Boundary element method

CF=

Carbon fibre

CFRP=

Carbon fibre-reinforced polymer

CKT=

Cottrell–Kelly–Tyson model

CMC=

Ceramic matrix composites

CNT=

Carbon nanotubes

CT=

Computed tomography

CTE=

Coefficient of thermal expansion

CZM=

Cohesive zone model

DEM=

Discrete element method

EPZ=

Embedded process zone model

FBG=

Fibre Bragg grating

FE(M)=

Finite element (method)

FRP=

Fibre-reinforced polymer

GF=

Glass fibre

GFRP=

Glass fibre-reinforced polymer

HM=

High modulus carbon fibre

IFFT=

Interfacial fracture toughness

IFNS=

Interfacial normal (radial) strength

IFSS=

Interfacial shear strength

IFSSapp=

Apparent interfacial shear strength

ILSS=

Interlaminar shear strength

IMD=

Intermediate modulus

LRS=

Laser Raman spectroscopy

MB (MBT)=

Microbond test

MFFT=

Multi-fibre fragmentation test

MRS=

Micro-Raman spectroscopy

PA=

Polyamide

PC=

Polycarbonate

PEEK=

Polyether ether ketone

PEI=

Polyetherimide

PP=

Polypropylene

PPS=

Polyphenylene sulphide

SCF=

Stress (or strain) concentration factor

SEM=

Scanning electron microscopy

SERR=

Strain energy release rate

SFFT=

Single-fibre fragmentation test

SLM=

Shear-lag model

TFBT=

Transverse fibre bundle tensile test

TP=

Thermoplastic

Aemb=

Embedded area

a=

Crack length

bi=

Interface effective thickness

da=

Change in crack length

dC=

Change in compliance

df=

Fibre diameter

dU=

Energy summation proposed by Marshall and Oliver

dUe=

Change of the elastic energy inside the fibre

dUf=

Work of friction in the interface

dUGi=

Debonding energy associated with the new debonded area

dUl=

Potential energy of the loading system

dUm=

Change in matrix elastic energy

E1=

Longitudinal Young's modulus of the model composite

Ef(Ef1)=

Axial Young's modulus of the fibre

Em=

Matrix Young's modulus

ET=

Transverse Young's modulus of the fibre

Fδ=

Force–displacement

Fb=

Initial post-debonding force

Fcat=

Catastrophic failure load

Fd=

Debonding force

Ffric.,max=

Maximum frictional force

Fmax=

Maximum load

Fs=

Shear force

G=

Strain energy release rate (fracture toughness)

Gi=

Interfacial fracture toughness

Gint.=

Shear modulus of the interface

Gm=

Matrix shear modulus

Gprop.=

Strain energy release rate for debond propagation

GicII=

Interfacial mode II fracture toughness

H=

Height in contact angle

K=

Slope of the force-displacement curve

Kf=

Fibre free length stiffness

Ki=

Cohesive stiffness

L=

Droplet length

l=

Fibre length, axial location of the crack front

lavg=

Arithmetic mean of the fragment lengths at saturation

lc=

Critical fibre length

lcat=

Fibre embedded length shorter than lmax,cat

ld=

Debond length

lemb=

Embedded fibre length

lemb,c=

Critical embedded length

lfree=

Fibre free-length

lm=

The point where the results of FEM, variational mechanics and SLM converge

lmax=

Maximum fragment length

lmax,cat=

Maximum fibre length beyond which catastrophic debonding does not occur

lmax,friction=

Maximum fibre length to surpass the frictional dissipation of energy

m=

A parameter acquired from the slope of the u against Fs2 plot in push-in tests

P=

Applied load

Pc=

Critical load at the debond initiation

Pd=

Debonding load

qo=

Normal pressure exerted on the fibre due to the matrix shrinkage during cure

R=

Axial distance at which τm=0

Req=

Equivalent cylinder radius

Ri=

Indentation position to the fibre centre

S0=

Slope of the linear region in a push-in load-displacement curve

Tf=

Tensile force on fibre

Tg=

Glass transition temperature

Tm=

Tensile force on matrix

Uθ=

Deformation in θ direction in a cylindrical coordinate system (rθz)

u=

Total recorded displacement throughout the push-in test

uep=

Elastoplastic indentation of the fibre surface

uf=

Fibre surface displacement due to the fibre compression

Vdroplet=

Droplet volume

Vf=

Fibre volume fraction

Vm=

Matrix volume fraction

Uθ=

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 adhesion

w=

Thickness of a push-out specimen (equal to the fibre length)

w2=

Cross section area of a square specimen

z=

Fibre axial axis

z=

The z-coordinate where the stress is evaluated

αfL=

Axial thermal expansion coefficients of the fibre

αfT=

Transverse thermal expansion coefficients of the fibre

αm=

Thermal expansion coefficient of the matrix

β=

Shear-lag parameter

βCox=

Cox shear-lag parameter

βgeom.=

Geometrical correction factor

βNayfeh=

Nayfeh shear-lag parameter

ΔEelastic=

Elastic deformation energy of the fibre, matrix and bending of the sample

ΔEfriction=

Work of friction

ΔEplastic=

Plastic deformation energy of fibre, matrix, and interface

ΔT=

Temperature difference

δ=

Separation in traction-separation

ϵ=

Applied strain, Fibre axial strain distributions

ϵf=

Fibre strain

ϵm=

Matrix strain

θ=

Contact angle

k=

Frictional stress transfer rate

λ=

Effective normal displacement between the contacting surfaces required for their separation

μi=

Interfacial friction coefficient

νf=

Fibre Poisson's ratio

νfL=

Axial Poisson's ratios of the fibre

νfT=

Transverse Poisson's ratios of the fibre

νm=

Poisson's ratio of the Matrix

σ0=

Net axial stress, Axial stress at the minimum cross-section of the specimen

σc1=

Longitudinal stress in a model composite

σd=

Debonding initiation stress, Adhesion pressure

σf=

Fibre failure strength

σi=

Interfacial tensile stress

σn=

Normal stress

σrr=

Radial stress in variational mechanics

σrrcritical=

Critical radial stress

σult=

Critical radial stress value at the onset of the debond initiation

σ¯z=

Cross-sectional average axial stress of fibre

τy=

Matrix shear yield strength

τapp=

Apparent interfacial shear strength

τd=

Local interfacial shear strength

τf=

Interfacial frictional sliding stress (post-debond frictional shear stress)

τi=

Interfacial shear stress

τic=

Interfacial shear strength

τm=

Shear stress of the matrix

τmax=

Maximum interfacial shear stress

τmaxact=

Actual interfacial shear strength

τmaxLRS=

Maximum interfacial shear stress obtained from laser Raman spectroscopy

τmaxSLM=

Interfacial shear strength obtained with the shear-lag model

τmax,ths=

Maximum residual shear stress

τrz=

Interfacial shear stress in variational mechanics

τthermal=

Residual thermal stresses

τult=

Ultimate interfacial shear strength

Additional information

Funding

The 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).

Log in via your institution

Log in to Taylor & Francis Online

There are no offers available at the current time.

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.