STATE-OF-THE-ART REPORT on

FATIGUE AND FRACTURE MECHANISMS IN COMPOSITE MATERIALS

PREPARED FOR

PERMANENT SCIENTIFIC COMMITTEE 58 FOR STRUCTURAL & CONSTRUCTION ENGINEERING

BY

HOSSAM EL-DIN MOHAMMED SALLAM, Ph.D.

November, 1998

FATIGUE AND FRACTURE MECHANISMS IN COMPOSITE MATERIALS

BY

HOSSAM EL-DIN MOHAMMED SALLAM, Ph.D.

CONTENTS

Glossary of Terms iii 1. Background and Brief Overview 1

1.1 Suggested Readings 4 2. Fracture and Fatigue Behavior of Fiber-Reinforced

Composites 6

2.1 Introduction 6 2.2 Fiber Bridging Models 7 2.3 Effect of The Specimen Geometry 14 2.4 Laminated Plates 14

3. Fracture and Fatigue Behavior of Short Fiber-Reinforced Composites

17

3.1 Fracture Behavior of Fiber Reinforced Concrete 17 3.2 Fatigue Behavior of Fiber Reinforced Concrete 22

4. Fracture and Fatigue Behavior of Particulate Reinforced Composites

24

5. Bonded Composite Patch Repair 27 6. Summary 28 7. References 31

Glossary of Terms

• angle-ply laminate. A laminate having fibers of adjacent plies oriented at alternating angles.

• cohesive failure. Failure of an adhesive joint occurring primarily in an adhesive

layer. • cross-ply laminate. A laminate with plies usually oriented at 0o and 90o only. • crack driving force. In fracture mechanics terms, the extension of a crack is

driven by the presence of a crack driving force and opposed by the resistance of the microstructure. Crack driving force is generally defined by some characterizing parameter, such as the stress intensity factor, K, or path independent integral, J-integral, which describes the dominant stress and deformation fields in the vicinity of the crack tip.

• crack tip shielding phenomena. They are means that, the effective crack-

driving force actually experienced at the crack tip is locally reduced. • damage tolerance. A design measure of crack growth rate. Crack in damage

tolerance designed structures are not permitted to grow to a critical size during expected service life.

• delamination. Separation of the layers of material in a laminate, either local or

covering a wide area. • fatigue. The failure or decay of mechanical properties after repeated applications

of stress. Fatigue tests give information on the ability of a material to resist the development of cracks, which eventually bring about failure as a result of a large number of cycles.

da/dN-ΔK curve. A plot of fatigue crack growth rate (da/dN) against the stress intensity factor range ΔK in fatigue testing. Starting with a mechanically sharpened crack, cyclic loads are applied and the resulting change in crack length is recorded as a function of load cycles to obtain da/dN and is plotted against the instantaneous ΔK, ΔK ≈ 1.12 Δσ (πa)0.5, Δσ is the applied stress range and a is the instantaneous crack length.

S-N curve. A plot of stress amplitude (S) against the number of cycles to

failure (N) in fatigue testing. • fatigue crack closure. The faces of fatigue crack could make contact even

though the component remained in tension due to plastic deformation existing in the wake of the crack, i.e. plasticity-induced crack closure, roughness of the

crack surfaces, roughness-induced crack closure, or corrosion debris, i.e. corrosion-induced crack closure.

• fatigue threshold. The minimum value of stress intensity factor range below

which a fatigue crack does not grow. This value is denoted by the threshold stress intensity factor range, ΔKth.

• fiber. It is a general term for a filament with a finite length that is at least 100

times its diameter, which is typically 0.10 to 0.13 mm. A whisker, on the other hand, is a short single-crystal fiber or filament made from a wide variety of materials, with diameters ranging from 1 to 25 μm and aspect ratio between 100 and 15000.

• fracture toughness. A measure of the damage tolerance of a material containing

initial flaws or cracks. For mode I deformation and for small crack-tip plastic deformation (plane-strain condition), the critical-stress-intensity factor for fracture instability is designated KIC. KIC represents the inherent ability of a material to withstand a given stress-field intensity at the tip of a crack and to resist progressive tensile crack extension under plane-strain conditions. Thus, KIC represents the fracture toughness of the material and has units of MPa m0.5.

• glass transition temperature (Tg). The approximate midpoint of the

temperature range over which the glass transition takes place; glass and silica fiber exhibit a phase change at approximately 955 oC and carbon/graphite fibers at 2205 to 2760 oC.

• J-integral. A parameter defines the fracture conditions in a component

experiencing both elastic and plastic deformation. Path-independent integral which is an average measure stress-strain field ahead of a crack. For elastic plane-strain conditions, JIC = KIC

2/E(1-ν2). • lamina. A single ply or layer in a laminate made up of a series of layers (organic

composites). A flat or curved surface containing unidirectional fibers or woven fibers embedded in a matrix (metal matrix composite).

• matrix. The essentially homogeneous resin or polymer material in which the

reinforcement system of a composite is imbedded. Both thermoplastic and thermoset resins may be used, as well as metals, ceramics, and glasses.

• stress intensity factor (SIF, K). Stress intensity factor is the fundamental

principle of linear elastic fracture mechanics (LEFM). In essence, SIF serves as a scale factor to define the magnitude of the crack-tip stress field. SIF is related to both the nominal stress, σ, level in the member and the size of the crack present, a, i.e. K = σ Y (πa)o.5, where Y is the geometry correction factor.

he goal of this review article is to present a sound background regarding

the development of the understanding of the fracture processes and fatigue

damage in composite materials and show how they act as a foundation for

current models. This presentation shows the importance of matrix, reinforcement,

and reinforcement/matrix interface in fatigue and fracture behavior of composite

materials. Composites exhibit an unusual combination of brittle and ductile

phenomena.

T

1. Background and Brief Overview Composites have been developed in order to reduce the weight of components in

structural applications and to improve mechanical and thermal properties.

Composite materials can be defined as a combination of two or more materials

(reinforcing elements, fillers, and composite matrix binder), differing in form or

composition on a macroscale. A strong interface bond between the reinforcement

and the matrix is obviously desirable, so the matrix must be capable of developing a

mechanical or chemical bond with the reinforcement. The reinforcement and the

matrix materials should also be chemically compatible.

Polymers, ceramics, and metals are all used as matrix materials, depending on the

particular requirements. The matrix holds the fibers together in structural unit and

protects them from external damage, transfers and distributes the applied loads to

the fibers, and in many cases contributes some needed property such as ductility,

toughness, or electrical insulation. The structure of polymers consists of long

molecules with a backbone of carbon atoms linked by covalent bonds. In non-

crystalline or amorphous polymers the molecular chains have an entirely random

orientation and are cross-linked occasionally by a few strong covalent bonds and

numerous but weaker van der Waals bonds. These weaker bonds break as the

temperature reaches a value known as the glass transition temperature, Tg,

characteristic for each polymer. Below Tg the polymer behaves as a linear elastic

solid. Creep becomes increasingly significant as the temperature increases and,

above Tg, the polymer deforms in a viscous manner under load. In crystalline

1

polymers the molecules are oriented along preferred directions, bringing with them

optical and mechanical anisotropy. Polymers are described as being either

thermosets (e.g., epoxy, polyester, phenolic) or thermoplastics (e.g., polyimide,

polysulfone, polyetheretherketone, polyphenylene sulfide).

Ceramics, such as glasses, cement & concrete, and engineering ceramics ( Al2O3,

SiC, Si3N4, ZrO2), have a wide range of engineering applications. A simple

definition of ceramics for practical purposes is that of solids which possess an

ordered arrangement of atoms bonded together by covalent or ionic forces. The

bonding in most useful ceramics is usually of a hybrid nature with extremes

represented by silicon carbide, which is practically 100% covalent, and by

magnesium oxide, which is almost completely ionic. The strong ionic and covalent

nature of the bonding in most ceramics leads to a stable crystal structure with a high

melting point and high stiffness. Many ceramic materials have very high elastic

moduli and strengths, but the advantages these properties bestow are often

outweighed by their highly brittle nature, which leads to low and unpredictable

failure stress resulting from the presence of flaws. Therefore, in order to improve

the strength of a ceramic component, two approaches are followed, in which either

extreme care is taken to minimize the presence of flaws or the ceramic is toughened

and made more resistant to cracks. Metal matrix composites typically comprise a

light metallic alloy matrix, usually based on aluminum, magnesium or titanium

alloys. The major reinforcing elements used in composites are glass,

carbon/graphite, organic, and ceramic.

With polymer matrix composites, it is almost true to say that the properties of the

composite are essentially those of the fibers, with little contribution from the

properties of the matrix. Both metal and ceramic materials have properties closer to

those of likely reinforcements and this leads to a different choice of properties for

which these composite systems are optimized. The fabrication of metal matrix

composites usually requires temperatures close to the matrix melting points and this

precludes the use of glass and polymer fibers. The driving force for most of the

applications of metal matrix composites is the potential for an increase in stiffness

2

over the matrix alloy with little or no increase in density. Such composites

fabricated from long continuous ceramic fibers behave in a manner similar to

polymer matrix composites with their strengths and stiffnesses predicted. They have

different fracture behavior for two major reasons. First, there is generally a much

stronger fiber/matrix bond than is found with polymer matrix composites. This is

believed to be because these composites are usually fabricated at high temperatures

and at these temperatures chemical reactions can occur between matrix and

reinforcements, so promoting an increased adhesion. These reactions can sometimes

form undesirable brittle intermetallic phases at fiber/matrix interface. Second, when

the metal matrix fractures in these materials it will only do so after considerable

plastic work, and therefor another term must be considered in calculating the total

work of fracture.

The major difficulty with the use of ceramic components in design applications is

their low toughness and high variability in strength. Polymer matrices, such as

epoxy resins, have a very low fracture toughness, but when combined with brittle

fibers an increase of many orders of magnitude of fracture energy occurs. Hence, it

is hoped to achieve similar increases in the fracture toughness of ceramic matrices

by the incorporation of long ceramic fibers. This has been achieved recently, with

carbon and silicon carbide fibers being used to reinforce glass and glass-ceramic

matrices. In this case the composite achieves toughnesses many times greater than

those found in monolithic ceramics by fiber bridging, frictional delamination and

pull-out, much as is found with polymer matrix composites. The reinforcement of

ceramics by short fibers or “whiskers” (short single-crystal fibers of radius < 1 μm)

has also been investigated, but toughening less efficient than has been found with

long fibers.

In recent years, composites have become more popular for critical structural

applications. The fatigue life of an engineering component is composed of the

progressive growth of an initiated or existing crack as it passes through the short

and long crack regimes. One of the problem associated with designing against

fatigue is the ability to predict the safe life of structures under practical load.

3

Obviously, there are some difficulties in using the concept of stress intensity factor

to correlate the fatigue and fracture behaviors of composites. The main mechanisms

controlling these behaviors in composites are 1- Crack trapping in particulate

reinforced composites and 2- Crack bridging in fiber reinforced composites. Both

mechanisms depend on the relative strength of the matrix and reinforcement and the

interfacial shear strength. Composites may be notch sensitive or notch insensitive

depending on their interfacial shear strength and the stress-strain field around the

crack tip, i.e. specimen geometry. Furthermore, the effect of reinforcement on

improving or degrading the fatigue life of composites is not absolutely clear. Thus,

understanding the fatigue and fracture behavior of composites presents a new

challenge.

Composite materials can be divided into classes in various manners. One simple

classification scheme is to separate them according to the reinforcement forms-

particulate-reinforced, fiber-reinforced, or laminar composites. Fiber-reinforced

composites, can be further divided into those containing discontinuous or

continuous fibers. This classification is adopted in the present study as follows:

Section 2 presents a review of fiber bridging models used in the continuous fiber

reinforced composites. The effect of the specimen geometry on the fracture and

fatigue behaviors of composites is discussed. Fatigue and fracture behaviors of

laminated plates are introduced. In Section 3 the behaviors of short fiber-reinforced

composites are introduced. The section focuses on the fracture and fatigue

behaviors of fiber reinforced concrete. Section 4 provides the concept of particulate

reinforced composites⎯how composites can be improved or degraded by the

incorporation of reinforcement particles. Section 5 presents a brief overview of the

repair of cracks by using composite materials.

1.1 Suggested Readings The fundamental principles of fracture mechanics, fatigue mechanisms, and stress

& failure analysis of composites, as well as manufacturing and applications of

composites are discussed in the following text- and hand-books

4

• M. W. Hyer (1998), Stress Analysis of Fiber-Reinforced Composite Materials,

WCB/McGraw-Hill.

• ASM Handbook (1996), Volume 19 Fatigue and Fracture, ASM International.

• R. W. Hertzberg (1996), Deformation and Fracture Mechanics of Engineering

Materials, 4th ed., John Wiley & Sons.

• R. F. Gibson (1994), Principles of Composite Material Mechanics, McGraw-

Hill.

• S. Suresh, A. Mortensen, and A. Needleman (1993), Fundamentals of Metal-

Matrix Composites, Butterworth-Heinemann.

• P. Balaguru and S. P. Shah (1992), Fiber Reinforced Cement Composites,

McGraw-Hill.

• B. Derby, D. A. Hills, and C. Ruis (1992), Materials for Engineering - A

Fundamental Design Approach, Longman Scientific & Technical.

• Engineered Materials Handbook (1988), Volume 1 Composites, ASM

International.

• L. J. Boutman (1974), Composite Materials 5, Fracture and Fatigue,

Academic Press.

5

2. Fracture and Fatigue Behavior of Fiber-Reinforced Composites

2.1 Introduction The three fundamental constituents of fracture and fatigue models for unidirectional

composites are schematically represented on Fig. 1. First, debonding occurs at

fiber/matrix interface, requiring an understanding of interface fracture mechanics in

mixed-mode. Second, fibers exert tractions on the crack surfaces, requiring a

mechanics of large-scale bridging. Third, fiber fracture may occur, usually at

locations away from the matrix crack plane, resulting in pull-out. The dominant

dissipation mechanism that allows fibers to enhance the fracture and fatigue

resistance is caused by frictional sliding along previously debonded interface. Such

dissipation occurs at both intact and failed fibers. However, the extent of zone that

provides dissipation is strongly influenced by the fiber failure site relative to the

crack plane, which governs the pull-out length. Large pull-out lengths relative to the

crack opening also lead to large-scale bridging, wherein the nominal crack growth

resistance depends on crack size and specimen geometry.

The bridging fibers carry part of the applied load and shield the crack tip.

Consequently, crack bridging enhances the fracture and fatigue behavior of

composites in comparison to their unreinforced matrix material. The mechanics of

τ

Matrix Crack

Fiber Pull-out

Wake Debonding/Sliding

Crack Front Debonding

Fiber Bridging

Figure 1. The various mechanisms that accompany mode I matrix crack propagation in unidirectional composites

6

crack bridging by frictionally constrained fibers in brittle matrix composites under

monotonic tensile loading has been established, see e.g. Ref. 1. A fundamental

assumption in the analysis is that the driving force for crack extension is the crack

tip or the effective stress intensity factor, Keff, as governed by remote stress and the

tractions acting in the crack wake. Equating Keff with the composite fracture

toughness, which usually scales with the fracture toughness of the matrix itself,

gives the stress required for matrix cracking in terms of the component geometry

and various constituent properties, as follows:

Keff = Ka + Kb (1)

where Ka and Kb are stress intensity factor due to applied stress and bridging

tractions respectively and Kb < 0.

2.2 Fiber Bridging Models In order to successfully model the influence of fiber bridging on the composite

crack growth behavior, the bridging tractions and their effect on the crack tip region

stress and strain fields have to be calculated. The bridging tractions, T, can be

represented by closure pressure function, c(x), acting in the direction opposite to the

applied stress, as shown in Fig. 2. Only by properly formulating the closure

function c(x) can the reduction of the crack tip driving force and crack opening

displacements be predicted. Telesman et al [2] reviewed the three different methods

used at NASA Lewis to account for the influence of fiber bridging on fatigue crack

driving force and crack opening displacements. Two of these methods are based on

analytical models, i.e. shear lag models and fiber pressure model, while the third is

based on an experimental approach that uses direct measurement of crack opening

displacements. Both shear lag models and fiber pressure model attempt to predict

the fatigue and fracture behavior of the composites by calculating, through the use

of very different formulations, the stresses carried by bridging fibers. The analytical

models are based on two significantly different closure pressure formulations which

reflect the differences in the approach used to model bridging tractions. Once the

7

closure pressure functions are known, both the crack tip driving force, i.e. Keff, and

the crack opening displacements can be obtained numerically either by the use of

the weight function method or by using the finite element method.

(a) Shear Lag Models

The shear lag models have been used frequently for the analysis of stress

concentrations in composites, see e.g. Ref. 3. The shear lag models are based on the

load transfer from the cracked matrix to the fibers through relative sliding between

the fiber and the matrix over a region where the interface shear stresses exceed the

strength of the interface. In the original formulation, developed by Marshall et al

[4], the closure pressure is determined via a force equilibrium of a concentric

cylinder model, as shown in Fig. 3. The fiber/matrix interface is treated as a purely

frictional interface with a constant frictional shear stress, τ, and relative

fiber/matrix sliding occurs over a debond distance, l. Beyond the distance l, no

debonding occurs and iso-strain conditions is assumed. In this formulation the

closure pressure in bridged region is proportional to the square root of the opening

displacement and the interfacial shear stress. The closure pressure is given by

5.0

)1()(2)(

2

⎥⎦⎤

⎢⎣⎡

−=mf

cffEVR

EEVxuxc τ (2)

where u(x) = half crack opening displacement, τ = fiber/matrix interfacial frictional

shear stress, Ef, Em, & Ec = elastic modulus of fiber, matrix, and composite

respectively, Vf = fiber volume fraction, and R = fiber radius.

McCartney [5] derived the above closure pressure function by performing an energy

balance calculation for a bridged fiber as opposed to the force balance approach

used by Marshall et al [4]. He showed that the above equation violated energy

balance principles. The corrected closure formulation according to his work is as

follows

8

5.0

2 2

22

)1()(2)( ⎥⎦

⎤⎢⎣⎡

−=mf

cff

EVREEVxuxc τ

(3)

Since c(x) in both equations is a function of the unknown u(x), an iterative scheme

is required to solve for these unknown displacements. In order to validate the shear

lag models, the value of interfacial shear stress, τ, has to be determined

independently.

It is questionable whether a single meaningful value of τ can be used to accurately

describe the frictional load transfer between the matrix and the bridging fibers over

the entire region of the crack wake, as is done in the shear lag models. The use of a

single value of τ over the entire crack bridged region by the shear lag models

neglects the interfacial wear that occurs during fatigue cycles. The interfaces of the

bridging fibers near the mouth of the machined notch have been exposed to

considerably more wear cycles than the interfaces of the bridging fibers near the

crack tip. It has been shown that the interfacial wear results in a decrease of τ in the

fatigued crack wake region in comparison to the virgin composite [6]. These

findings agree with the work done by Marshall et al [7] who have also shown that τ

decreases with an increase in the interfacial wear. The typical methods of estimating

τ, such as the push-out test, are typically performed on material not subjected to

σ∞

σ∞

Closure Pressure, c(x)

ao

a

Figure 2. Closure pressure function simulating fiber bridging tractions

σ∞

τ τ l

u

T = c(x)/vf

Figure 3. Schematic of the concentric cylindemodel used to determine the force-displacement

relationship for the shear lag analysis

Matrix Fiber Matrix

9

fatigue conditions. Thus the shear stress coefficient τ obtained from such tests does

not take into effect the interfacial wear or other load history effects generated

during cyclic loading. Kantzos et al [8] have shown that for individual bridging

fibers subjected to cyclic loading the amount of interfacial wear is greatest near the

crack faces and progressively decreases, and thus τ increases, along the debonded

interface length, l (see Fig. 3).

(b) Fiber Pressure Model The fiber pressure formulation originated from an analysis of fast fracture in steel

[9] and was adopted by Ghosn et al [10] to the analysis of composites under cyclic

loading conditions. The fiber pressure model considers the fiber bridged specimen

as a structure whose members in the crack wake (i.e., bridging fibers) can carry

tensile loads created by normal stresses or bending stresses, or both. The force

balance is derived through an elementary strength of materials approach to calculate

the stresses in a beam subjected to bending or tensile forces, or both. The actual

load transfer mechanism through which the bridging members are loaded is

unimportant as long as an accurate force balance can be written which fully

describes the stresses in these members. After all, in order to model the effect of

bridging on the crack driving forces and displacements, it is only necessary to

correctly predict the closure pressure function. The closure pressure in the fiber

pressure model is assumed to be equal to the stress carried by the fibers in the

bridged region averaged out over the total bridged area. The closure pressure c(x)

for a single edge notch geometry, see Fig. 2, is given by

axaforaw

axawwaaw

wxc oo

ooo

o≤≤⎥

⎦

⎤⎢⎣

⎡−

−−−+

−= ∞

3)())()(5.0(6)( σ (4)

where σ∞ is the applied remote stress, w is the width of the specimen, ao and a are

the initial notch length and the total crack length respectively, and x is the distance

along the crack measured from the free surface. This formulation is applicable to a

composite system with very stiff fibers and overcomes many of the difficulties

10

inherent in the shear lag formulation, such as avoiding the need to determine the

shear strength coefficient τ and does not require an iterative solution since c(x) is

not a function of the crack opening displacements.

The size of the fiber bridging region depends on the applied stress and the

mechanical properties of the composite constituents and can vary from zero to the

entire crack length. Therefore, Nayeb-Hashemi et al [11] modified the fiber pressure

model by considering a partial crack bridging zone of length l, i.e. l ≤ (a - ao).

Crack Driving Forces and Crack opening profiles

The closure pressure functions obtained by analytical models can be used to obtain

crack driving forces and crack opening displacements of the bridged specimens

through the use of the weight function method or finite element method.

The weight function used is based on the Bueckner formulation [12] for the stress

intensity factor calculation of a single edge notch specimen with a finite geometry.

The homogenized composite stress intensity factor, Kc, for a partially bridged

specimen is given by

⎥⎦

⎤⎢⎣

⎡

−−

+−

= ∫∫∞∞

dxxa

xaHxcdxxa

xaHKa

a

a

co

o ),()(),(2 )(

0

σσπ

(5)

where

2

2

21)()(1),(

axam

axamxaH −

+−

+= (6)

and where m1 and m2 are functions of the ratio of the crack length to the width of

the specimen given by

)8(0444.702889.32502.0

)7(7822.81844.176147.062

2

621

)()()()(

wa

wam

wa

wam

++=

++=

11

The Bueckner weight function method can be extended to calculate the crack

opening displacements. It is assumed that the isotropic displacement equation can

be applied to the composite since the difference between displacements calculated

by orthotropic and isotropic formulations is minimal [3]. The crack opening

displacements are calculated at any location xo for a crack length of (a - xo). By

incrementing the location of xo over the entire crack length, the full crack opening

profile is obtained. The bridged displacement at a location xo for an isotropic

material is given by

u xE

H l xl x

P x H a xl x

dx dl

P xfor x a

c x for a x a

oc

c

o

o

a l

o

o

xo

( ) ( ) ( , ) ' ) ( , ' )'

' (

'( ' ) '

( )

( )( )=

−− −

⎡

⎣⎢⎢

⎤

⎦⎥⎥

< <− < <

⎡

⎣⎢

⎤

⎦⎥

∫ ∫

∞

∞

2 1 9

010

2

0

υπ

σσ

where

( ' ) =

)

and where Ec and νc are the homogenized composite elastic modulus and Poisson’s

ratio respectively in the loading direction.

By a substitution of the appropriate closure function, c(x), for the shear lag and fiber

pressure models into Eqs. 5 and 9, the bridged crack driving force and crack

opening displacements are obtained. For the fiber pressure model, a direct

numerical integration of the equations gives the solution for the opening profile and

stress intensity factor. For shear lag model, an iterative scheme is required with a

small damping factor to guarantee convergence.

The fiber pressure model is used in the finite element method as a nonuniform

pressure applied in the bridged region [10,11]. For the shear lag model, the closure

pressure was applied as a nonlinear foundation pressure [10]. Thus the closure

pressure for the shear lag model is given by

12

c x K u u x

K uV E E

u x R V E

st

stf f c

f m

( ) ( ) ( ) ( )

( )( ) ( )

( )( ) .

=

=−

11

21

122

0 5τ

where Kst(u) is a nonlinear foundation constant, Em, Ef, and Ec are the elastic

modulus of matrix, fiber, and composite, respectively, R is fiber radius, and Vf is

fiber volume fraction. Finally, the composite stress intensity factor is determined

from displacement field near the crack tip. The advantage of the finite element

method over the Bueckner weight function method is the convergence speed for the

shear lag model.

Since the cracking observed in the composite material tested was limited to the

matrix only, the crack driving force is assumed to be the effective stress intensity

factor in the matrix of the composite, Keff. Assuming a condition of iso-strain

between the composite constituents ahead of the crack tip, Marshall et al[4]

postulated that the effective crack driving force in the composite is related to the Kc

of the homogenized composite (obtained from Eq. 5) by

K K EEeff c

m

c

= ( ) ( )13

In contrast, the following relationship was obtained by McCartney [5] based on his

energy balance formulations

K K EV Eeff c

m

f c

=−

( )( )

( )1

14

The validity of the previous models to predict the fatigue crack growth behavior in

metal matrix composite was examined by several researchers [2, 10-11, 13-14].

They concluded that, there is an agreement between the experimental results and the

prediction obtained by the fiber pressure model. In the case of shear lag model, the

ability to select a value of τ that accurately predicts crack opening profile may still

not adequate to fully correct the crack driving forces for the influence of bridging.

13

Thus, shear lag model overestimates the fatigue crack driving force, especially with

an increase in the applied stress. This may be due to a higher τ in the crack tip

region than the rest of the crack wake. Bakuckas and Johnson [15] concluded that,

the dependency of τ on so many factors, such as the applied stress, wear of the

debonded surfaces and crack extension length, poses restrictions on using the fiber

bridging models in a damage tolerance methodology.

2.3 Effect of The Specimen Geometry It is worth to note that, cracks grow rapidly in the composites if the interface is

either too strong (low fiber bridging) or too weak (cracks grow parallel to the fiber

and applied load). Ghosn et al [13] found that, single edge notch specimens had

resistance to fatigue crack growth more than center crack panel specimens. On the

other hand, Kantzos et al [16] found that fatigue crack grew parallel to the loading

and fiber direction in compact tension specimen while it grew normal to the loading

direction in single edge notch specimen. These observations can be explained by

examining the stress-strain field around the crack tip in each specimen geometry.

Sallam and Hashemi [17] found that, at the same stress intensity factor, T-stress or

T-strain, i.e. stress or strain parallel to the crack surfaces, at the crack tip is not only

a function of a specimen type and thickness but also on the shape and the angle of

the notch. Since fatigue behavior in fiber reinforced composites depends on the

fiber bridging zone, the extent of the bridging zone is a function of fiber/matrix

bond strength and the shear stress and T-stress around the crack tip. Therefore they

concluded that, the effect of shear and T-stress on the reinforcement/matrix

interface must be taken into consideration to predict the closure pressure, c(x), and

consequently the fatigue behavior in composites.

2.4 Laminated Plates

Unidirectional composite materials typically have exceptional properties in the

direction of the reinforcing fibers, but poor to mediocre properties transverse to the

fibers. Thus, with the exception of one-directionally loaded members (for example,

truss members), unidirectional composite materials would be expected to poorly

14

compared to conventional materials. In practice, structures made from composites

contain a series of layers of unidirectional fibers such that each layer has some

predetermined orientation with respect to the defined dimensions of the structure to

overcome the material anisotropy. Furthermore, hybrid composites (Sandwich

Laminates) showed superior fatigue crack growth resistance as compared with

conventional materials. Fiber-reinforced aluminum laminates (FRALL) is a new

class of hybrid composites, which consists of alternating layers of thin aluminum

sheets bonded by an adhesive impregnated with high strength fiber-epoxy

composites, such as aramid fiber-reinforced aluminum laminates (ARALL) and

carbon fiber-reinforced aluminum laminates (CARALL). On the other hand, when

viewed at fiber-matrix scale, fiber-reinforced composites are seen as a complex

structure rather than a basic homogeneous substance. Depending on the dimensional

scale of interest, a composite laminate is an even more complex structure. Strength

and fracture behavior of laminates depends on a host of geometrical factors, such as

fiber diameter and volume fraction, thickness and number of plies, ply angle

orientation and sequence, size and content of microvoids, and laminate thickness.

The effect of matrix resin on the mechanisms of delamination fatigue crack growth

in unidirectional carbon fiber reinforced plastics laminates under mode I loading at

different stress ratios was studied by Hojo et al [18]. They concluded that,

Laminates with toughened matrices are most resistant to fatigue crack growth. On

the other hand, the ratio of fatigue threshold to the fracture toughness in the

toughened laminates decreased in comparison with the brittle laminates.

Furthermore, the increase in fracture toughness by matrix toughness is not really

translated into the improvement in delamination resistance under fatigue loading.

Harris et al [19] found that the addition of transverse (90o) plies exerts little effect

on the fatigue response of the main load-bearing 0o plies. However, in composite

containing ± 45o plies, shear cracks will occur in these off-axis plies, the crossing

point of a pair of such crack may lead to delamination. Three different methods to

determine the effect of crack wake bridging on mode I delamination toughness were

analyzed by Jain and Mai [20]. It was shown that both Griffith energy release rate

approach and the J-integral approach underestimate the effect of bridging on crack

15

growth resistance when compared to the stress intensity factor approach though the

difference may not be large. Moreover, the energy release rate method becomes

difficult to use when the extensibility of the reinforcing thread is taken into

consideration, as the displacement profile and hence the various energy terms

cannot be determined simply. Recently, the strain energy release rate of

nonhomogeneous delaminated laminates is derived by Sheinman and Kardomateas

[21] based on J-integral. They decomposed the strain energy release rate into mode

I (tensile mode) and mode II (in-plane shear mode) based on the assumption of

equivalent orthotropic properties through the laminate thickness.

The double cantilever beam (DCB) test specimen, as shown in Fig. 4, has been used

for measurement of mode I interlaminar fracture toughness, GIC , of composite

laminates since 1960s. Since then there has been much interest in the pursuit of a

mode I standard test method and the progress towards standard fracture and fatigue

test methods, ISO standard, for mode I delamination toughness testing of fiber

reinforced polymer composites were recently reviewed by Blackman et al [22]. A

mode I standard for the delamination toughness of composites, GIC, was proposed

as a new work item at ISO in 1994. Because the Japanese Industrial standards (JIS),

American Society for Testing and Materials (ASTM), and European Structural

Integrity Society (ESIS) had all been investigating the test method, effectively three

working drafts were prepared, one by each committee, see Ref. 22. The technical

differences between these drafts reflected partly the differing experiences of the

technical committees and partly the different motivating factors which had driven

each committee to pursue a standard.

P

P

P

B 2h

(a) End-blocks

aoB 2h

(b) Piano Hinges

ao

Figure 4. The double cantilever beam test specimen with loading, P, via (a) enblocks and (b) piano hinges. Initial film length is ao, width B and thickness 2h.

P

16

3. Fracture and Fatigue Behavior of short Fiber-Reinforced Composites Many experts claim, however, that the big future for composites will be in discon-

tinuous fibers, which exhibit essentially isotropic properties and can be shaped,

machined, drilled, etc. using conventional fabrication facilities.

The fatigue and fracture properties of short fibers reinforced composites are

controlled by fiber bridging and influenced by the volume fraction, size, aspect

ratio, and distribution of the reinforcement [23]. Improvements can be gained by

use of short fibers or whisker that have aspect ratios of > 10:1, even though cracks

are initiated at whisker or fiber ends. On the other hand, Short fibers may enhance

or reduce the fracture toughness and fatigue resistance of the matrix based on the

strength of the matrix and the interface, see for example Refs. 24 & 25.

3.1 Fracture Behavior of Fiber Reinforced Concrete

The application of the concept of fiber-reinforced composites to concrete or mortar

is by no means new. In 1910 Harry Porter claimed dramatic increases in the

physical properties of concrete by adding cut nails and spikes to the mixes, see Ref.

26. Fibers in general and polypropylene fibers in particular have gained popularity

in recent years for use in concrete, mainly to enhance the shrinkage cracking

resistance and toughness of plain concrete [27]. It is generally accepted that fracture

toughness of fiber reinforced concrete (FRC) cannot be evaluated using linear

elastic fracture mechanics without modifications because of a nonlinear zone ahead

of the crack tip often termed the fracture process zone. The nonlinearity of the

process zone arises from heterogeneity inherent in concrete, i.e. microcracking

ahead of the crack tip (zone shielding), and from fiber bridging in FRC. The

presence and the important influence of the fracture process zone in concrete has

been recognized since the late 1970s [28]. Most of the fracture mechanics models in

FRC simulate the bridging effect of fibers with a closing pressure on the crack

surface, as mentioned in sec. 2.2. Hilleborg [28,29] extended the fictitious crack

model to FRC by proposing that the closing pressure to be a function of fiber

17

length, fiber diameter and interface bond strength. Wecharatana and Shah [30]

assumed a parabolic closing pressure for fiber toughening.

The following mechanism is proposed in the case of a matrix reinforced by an

identical volume and aspect ratio of large fibers and microfibers. For the volume of

fibers normally used for cementitious composites, i.e. large fibers, only a small

improvement in tensile strength is observed, as sketched in Fig. 5. This is probably

due to the fact that matrix cracking first occurs at the micro level [31]. If fibers far

apart, they have no ability to arrest microcracks. However, once the microcracks

condense into macrocracks, the large fibers can not arrest propagation of

macrocracks and substantially improve the toughness of the composite. If

microfibers are used, they can bridge microcracks, since for a given volume these

fibers are much closer together. Microfibers can thus significantly enhance the

tensile strength of the composite, Fig. 5. However, for the same aspect ratio,

microfibers are shorter and therefore may be pulled out after macrocracks are

formed, thus providing little improvement in post peak toughness. By combining

fibers of varying size into the matrix, improvement in both the peak stress and post

peak toughening can be expected.

Several approaches to the study of the fracture of cementitious materials have been

proposed recently, see e.g. Refs. [32-34]. These approaches can be categorized as

either cohesive crack models or effective crack models. In cohesive crack models,

the fracture process zone is modeled by applying traction forces across the surfaces

Microfibers

large fibers

Plain matrix

P

P

Strain

Stress

Figure 5. Illustration of different sizes fibers on crack bridging

Microcracks

18

of newly formed cracks. A basic requirement of the cohesive crack model is the

softening curve, sometimes known as the ‘stress-separation curve’, which relates

the stresses across the crack surfaces, the cohesive stresses, to corresponding crack

openings.

An analytical model based on Bueckner weight function and an iterative procedure

to match the experimentally obtained load vs. crack mouth opening displacement

curves was developed by Eissa and Baston [32]. The model simulates the behavior

of the fracture process zone as well as the length traction free crack. The model also

allows the calculation of the crack tip opening displacement and J-integral at any

load level. Hamoush et al [33] proposed a fracture model based on the superposition

technique in fracture mechanics in conjunction with an existing pullout model to

predict the stress intensity factor of FRC. The model assumes that the final slip

distance of the fibers equals the final crack opening displacement. In this model,

two basic steps are used in the solution procedure. The first step ignores the

contribution of the fiber and finds the crack opening displacement at each fiber

location. The second step finds the crack opening displacement due to one unit of

force at each fiber location. The compatibility condition, including fiber pullout

displacement, is employed to find the final pullout force in each fiber. The forces in

pulled-out fibers are restricted to the capacity of the fiber.

The effect of the specimen size, fiber volume content, fiber type, and the presence

of the notch on the fracture toughness of FRC was studied by first phase of six-

university study funded by the Concrete Materials Research Council-American

Concrete Institute (CMRC-ACI) and the National Science Foundation (NSF) [35-

36]. The variables of experimental program is shown in Table 1 . Two different

methods of measuring beam midpoint deflection were used in their project. In the

first method, Method I, the deflection of the tension face of the beam midpoint in

relation to the machine cross-head was measured. This method includes, in addition

to the true beam deflection, extraneous deformations such that the elastic and

inelastic deformation of the loading fixtures/supports and local deformation of the

specimen at its supports. A more accurate method is to measure the beam midpoint

19

deflection in relation to the neutral axis of the beam at its support. They found that,

the error in deflection measurements as a percentage of true beam deflection prior to

matrix first-crack can be unacceptably large if these extraneous deformations are

not excluded from the deflection measurements. However, after first-crack, these

extraneous deformations constitute only a small fraction of the overall beam

deflection. The main conclusions of that investigation are (i) the ASTM C 1018

toughness indexes (I5, I10, and I30) are observed to be relatively insensitive to fiber

type, fiber volume fraction, and specimen size, (ii) toughness as a measure of

absolute energy, like TJCI, is capable of distinguishing among composites with

different fiber types, different volume fractions, and different specimen sizes, and

(iii) the load-crack mouth opening displacement approach to characterizing

toughness of FRC appears to offer some promise.

Table 1. Variables of experimental program found in Ref. 35*

Specimen size, mm ** Small 102 x 102 x 356

Large 152 x 152 x 533

Specimen type *** Notched Unnotched Fiber type

Fiber volume fraction

Fiber length, mm Aspect ratio

Hooked-end steel

0.5% 1% 50 100

Crimped steel

0.5% 1% 50 50

Two types of fibrillated polypropylene 0.1% 0.5% 50

* All six participating universities conducted all of the tests. Either three or four specimens were tested for each of the 32 series at each participating location.

** Span lengths of the small and large beams are equal to 305 and 457 mm, respectively. *** The notch-to-beam depth ratio is equal to 0.125 for both small and large specimens.

The main objective of their investigation is to compare between the available test

standards and guidelines for measuring toughness indexes, such that ASTM C 1018,

JCI SF4, JSCE SF4, and ACI 544, see Ref. 35, therefore, a lack of the discussion on

the effect of the above variables on the fracture toughness of FRC is observed in

their paper. Thus, another analysis for their experimental results will be made in the

next paragraph.

20

The stress at first crack increased with decreasing the specimen depth for both

notched and unnotched specimens. However, the opposite trend is observed for

toughness, TJCI. At the same notch-to-beam depth ratio, equals 0.125, the crack

mouth opening displacement at first crack is little affected by the specimen size,

while the deflection at first crack increased by increasing the specimen depth. In the

case of small beams, stress and TJCI at first crack are not affected by the presence of

the notch, notch depth equals 12.75 mm and may be considered as a non damage

notch. In contrast, stress and TJCI at first crack of large beams are significantly

affected by the presence of the notch, notch depth = 19 mm. The effects of the fiber

type and the fiber volume fraction on the fracture behavior of FRC cannot be

distinguished due to the difference in the aspect ratio, shape, and the mechanical

properties of the fibers and the difference in the amount of increase of the fiber

contents in each type, i.e. two times in steel fibers and five times in polypropylene

fibers. At the same fiber contents, the steel fibers increase the toughness of plain

concrete more than polypropylene fibers and steel-hooked fiber reinforced concrete

specimens have the highest toughness. The energy-absorption capacity of the

composite increased with increasing fiber volume content for all types of fibers.

However, In the case of polypropylene fibers, both the toughness and the deflection

at first crack decreased by increasing the fiber volume fraction.

The effects of steel fiber type, i.e. hooked-end, deformed-end, and corrugated

fibers, fiber length of hooked-end fibers, cement content, and the presence of silica

fume on flexural toughness of FRC were studied by Balaguru et al [37]. They found

that, Toughness indexes I5 and I10 computed using the ASTM C 1018 procedure do

not provide a good indication of the variations that are present in load-deflection

responses. For a given fiber content, toughness indexes are smaller for high-strength

concrete (containing 564 kg/m3 of cement and w/c ratio = 0.26) compared to normal

strength concrete(containing 335 kg/m3 of cement and w/c ratio = 0.45). High-

strength concrete sustained higher first crack load, but the post-peak drop is steeper.

Therefore, it is advisable to use higher fiber volume fractions for high-strength

concrete. Typically, the addition of silica fume to high strength concrete makes the

material little more brittle. However, they found [37] the differences are not

21

significant. Higher fiber contents result in much higher load-retaining capacity at

large deflection. Hooked-end fiber geometry provides better results than other

geometries. Since the mechanical anchorages, provided by deformations, are a

significant factor in hooked-end fibers, the effect of fiber length is not as

pronounced as in concrete reinforced with straight fibers.

Recently, some of the fracture mechanics approaches to the prediction of failure of

FRC structures, methods used to rank the toughness of FRC, toughness

optimization, and the properties of concrete reinforced with selected synthetic and

recycled fibers are reviewed by Wang [38]. He concluded that, methods of linear

elastic fracture mechanics and elastic-plastic fracture mechanics are not applicable

to laboratory-sized specimens of FRC. Numerical methods may be used to predict

the failure of FRC structures based on the material’s stress versus crack opening

curve. For routine quality control and toughness comparisons, flexure toughness

indices and residual strength ratios are useful. However, direct comparisons should

only be made among tests under the same conditions. Since the elastic modulus and

matrix cracking strength of FRC are generally not strongly affected by the presence

of fibers, it is desirable to normalize the indices and ratios with representative

quantities, rather than with actual cracking energy and load, in order to reduce data

scattering. He found that, carpet waste fibers can effectively improve the shatter

resistance, toughness and ductility of concrete.

3.2 Fatigue Behavior of Fiber Reinforced Concrete

Hsu [39] categorized fatigue applications as follows. “Low-cycle” is the term

applied to structures exposed to earthquakes and loads less than 1000 cycles of

load. The “high-cycle” category starts with airport pavements and bridges expected

to withstand up to 100,000 load cycles, and extends to highway bridges and

pavements, railway bridges, and ties subjected to up to 10 million cycles. FRC has

been employed in some way in almost all of the applications termed high-cycle

fatigue by Hsu [39]. Fatigue behavior in flexure, or even in compression, of FRC is

not completely understood in terms of all the influential variables, such as type and

22

configuration of loading, frequency, effect of rest periods, matrix composition,

durability of concrete, and, perhaps most important of all, fiber parameters [40].

Johnston and Zemp [40] studied the effect of fiber content, aspect ratio, and fiber

type on the fatigue behavior of FRC. They concluded that, the S-N relationships

depend primarily on fiber content and aspect ratio. The 100,000 cycle endurance

limits are 84 to 89 percent of the first-crack strength under static loading for the

better combinations of fiber type and amount characterized by at least 1.0 volume of

fibers of aspect ratio of 70 or greater. However, fiber type is secondary in

importance, they used four types of steel fibers, i.e. smooth uniform wire, surface-

deformed wire, melt extract, and slit sheet. All are straight and uniform in cross

section without hooked or enlarged ends. On the other hand, Ramakrishnan et al

[41] found that, Hooked-end fibers provide better resistance to flexural fatigue than

other types of fiber. Wei et al [42] used X-ray diffraction to analyze and calculate

the orientation of Ca(OH)2 crystal at the interfacial zone and they also used

microhardness to determine the thickness of the interfacial layer, forming,

vanishing, and restrengthening, and the effect of superimposing-strengthening of

interfacial layers, to understand the fatigue damage mechanism of FRC. They found

that, the fatigue process is relative to the space of fibers, performance of cement

matrix, and forming, strengthening, and vanishing (which means that the orientation

index, orientation range, average crystal size, crystal curve range of Ca(OH)2, and

the regularity of variation in microhardness in the interfacial zone are the same as

that in the cement matrix), and restrengthening of the interface. The key to increase

in fatigue resistance for high strength concrete is increase of crack-arresting ability.

Resistance to crack arrest comes in two ways: 1) reduction of size and amount of

original crack sources; and 2) capacity of inhibiting initiation and extension of

crack. Owing to the addition of silica fume and steel fiber, interfacial structure is

improved effectively, interfacial weakness is removed, and the effective range of

both interface and fiber is extended. Both silica fume and steel fiber reduce the

number and size of crack sources from different angles and resist the initiation and

extension of crack. By double or multiple effects, they increase various

performance indexes of fatigue resisting.

23

4. Fracture and Fatigue Behavior of Particulate Reinforced Composites Spectacular properties obtainable in a continuous-fiber-reinforced composites are

not expected for particulate reinforced composites; however, particulate

reinforcement can provide reasonable improvements in strength together with the

additional advantages of isotropic properties and allowing fabrication. Although

particulate reinforcement is less efficient than short fibers and whiskers, significant

improvements in specific strength and stiffness, compared with matrix materials,

can be still obtained. The low cost of particles is attractive. Recently, Velasco et al

[43] studied the effect of particle size on the fracture behavior of polymer matrix

composites, i.e. aluminum hydroxide polypropylene. They found that no significant

differences between the fracture toughness, KIC, value of unfilled matrix and those

of the composites. Nevertheless, the fracture energy, GIC, of the composites was

clearly lower than that of the unfilled matrix. Such reduction depends on the particle

size, i.e. the composites filled with the finest grade Al(OH)3 showed higher

stiffness, tensile yield strength, fracture toughness and fracture energy than the

composite filled with coarser particles. On the other hand, ductile particles, i.e.

rubber or metallic particles, were used to enhance the toughness of brittle matrix,

such as glasses, ceramics, and polymers [44-46]. An increase in the volume

fraction of metallic particles results in an increase of the fracture resistance and the

measured fracture toughness level of composites [44]. The observations of crack

propagation in epoxy resin containing dispersed rubber particles are summarized

schematically in Fig. 6. A notched sample is loaded in tension, Fig. 6.a; at the

fracture stress of the brittle matrix, a crack extends, Fig. 6.b, by-passing the rubbery

particles without penetrating them (crack bridging); as the crack propagates, Fig.

6.c, the particles bonded to the matrix are stretched between the opening crack and

fail when they reach a critical, large extension.

24

(a) (b) (c)

Figure 6. Schematic diagram showing the stages of crack propagepoxy resin containing a dispersion of rubber particles, Ref. 46.

In metal matrix composites, ceramic particles, such as SiC and Al2O3, may enhance

the resistance of the matrix to fatigue crack initiation and early growth. Fatigue life

behavior of metal matrix composites can be improved or degraded by the

incorporation of reinforcement particles, depending on many factors such as

fabrication processes, particle type, size, volume fraction and distribution, and

matrix properties [47]. It is difficult to make generalizations about the effects of

these factors on fatigue and fracture behavior of particulate reinforced metal matrix

composites [47-54]. Hung et al [47] concluded that, large particle size and, aging

defects, and machine-induced defects reduce fracture toughness of composites.

Beck et al [48] found that, the fracture toughness of all tested composites was

affected by changes in the matrix microstructure produced by aging. The fracture

toughness was adversely affected by increases in particle volume fraction. The

relation between particle size and fracture toughness is not clear.

Ogarevic and Stephens [49] found that fatigue crack growth rates were higher and

ΔKth values were lower in the composite compared to those of the unreinforced

material. Increasing the volume fraction of reinforcement has been observed to

increase the fatigue life under stress-controlled conditions in wrought aluminum

alloys as well as a magnesium alloy. This can be attributed to the decreases in

elastic and plastic strains that result from the increasing modulus and apparent work

hardening, both which increase with increasing volume fraction. Experimentation

on wrought aluminum alloys clearly indicates that particle size does indeed have a

25

significant influence on fatigue life of metal matrix composites. Near crack

initiation, particles are unsuitable obstacles for short crack growth, but brittle

fracture of reinforcing component may occur [50]. Kumai et al [51] found that, the

fatigue crack avoids SiC particles at low stress intensity factor, ΔK, ranges, but at

high ΔK ranges the crack appears to proceed by linking fracture SiC particles ahead

of the main crack front. Kumai et al [52] found that, fatigue cracks initiate mainly at

matrix-particle interface in molten-metal-processed composite because of degraded

interfacial strength. On the other hand, applications relating to the shot peening of

metal matrix composites are, until now, rare, and it is not known if this treatment

can be successfully applied to these materials in terms of actual improvements to

the fatigue limit. Recently, Baragetti and Guagliano [53] found that, the effect of

shot peening is more evident if a steep stress gradient (e.g. due to notch) is present.

An improvement in the fatigue limit can be over 22%. For smooth specimens, the

improvement is less evident even if shot peening shifts the crack initiation point

from the surface to an internal defect, thus improving the surface fatigue strength.

Shang and Ritchie [54] concluded that, after allowing for crack closure, the

effective threshold stress intensity factor range, ΔKeff,th, is intrinsic thresholds and

intrinsic thresholds are solely a function of the effective mean particle size and to be

independent of volume fraction. In contrast, to measured low load-ratio ΔKth

thresholds, intrinsic thresholds are found to be somewhat higher in fine particles

composites. Reinforcing particles which interact with the crack path are considered

to impede near-threshold crack extension in two ways: (i) by promoting crack

deflection (in avoiding the particles) and hence enhanced roughness-induced crack

closure at low load ratios, and (ii) by crack trapping, i.e. arrest of a crack at a

reinforcing particle. Since the process of crack trapping must involve plastic flow

at the crack tip, crack extension cannot be completed unless the plastic zone engulfs

the particle. Accordingly, a limiting condition for fatigue crack advance, i.e. the

intrinsic fatigue-threshold condition, can be represented by the assertion that the

maximum plastic-zone size at the crack tip must at least exceed the average particle

size. Therefore, crack-tip shielding phenomena such as crack deflection, roughness-

26

induced crack closure and crack trapping have a direct and significant impact on

fatigue behavior. This has provided an insight into otherwise contradictory results

related to particle size and volume fraction effects.

Finally, the most recent work in particulate reinforced composites involves

systematic investigations of the effects of particle size and volume fraction on the

fatigue crack growth behavior using composites and matrices produced by the same

fabrication routes. However, in the most of the previous studies, various kinds of

composite with different matrix compositions and different fabrication routs have

been examined, with the result that it is difficult to compare the reported behavior.

This is because of the choice of materials was controlled by availability rather than

by the requirements of a planned research program. Thus it has been difficult to

clarify the general role of microstructural factors in fatigue in these materials. In

some studies, models have been proposed for the effect of particles on fatigue crack

growth, but still they are generally poor because of a lack of adequate data.

Accordingly there is a need of further intensive research in this area.

5. Bonded Composite Patch Repair The repair of cracks or post-strengthening existing structures by advanced

materials have attracted the interest of scientists and engineers, see for example

Refs. [55-57]. Based on the world-wide research and development work carbon

fiber reinforced plastics strips to rehabilitate structures is already routine for many

firms in North America, Europe, and Japan. However, even in the future, fiber

composites will not replace traditional construction materials, such as steel,

concrete, and wood, but will be used instead to supplement them as needed

[56,57]. In metallic aircraft structures, the repair of fatigue cracks has been

received much attention in recent years [55].

Although extensive theoretical and experimental research on bonded composite

patch repairs has been carried out, and service experience with such repairs has

been good, it is evident that further work is required to assess the full potential and

27

limitations of this method of repair, and to develop optimum repair schemes for a

wide range of applications. For example, further research is required to establish

the effects of impact damage, service temperature and long term exposure to hot-

wet environments on the efficiency and durability of repairs carried out with

various types of patch. Various models have been developed for predicting the

efficiency of bonded patches in retarding the growth of fatigue cracks. In general,

the efficiency of repairs to thin flat sheet can be predicted accurately using

analytical closed form expressions, but for complex or thick section repairs three-

dimensional analyses are necessary. Unfortunately, a suitable model is not yet

available for predicting the development of debonding [55], and therefore

measured levels of debonding have to be used in patch efficiency predictions.

6. Summary

A brief review of the fatigue and fracture mechanisms in composites has been

given. Here, all the probable crack-tip shielding mechanisms in composites are

summarized. Sources of shielding are described in terms of mechanisms relying on

the production of elasticity constrained zones which envelop the crack (zone

shielding), on the generation of wedging, bridging, or sliding forces between the

crack surfaces (contact shielding) and on crack deflection and meandering. Under

small-scale yielding condition, the crack-driving force in composites can be

expressed as

Ktip = KI - Ks (15)

where Ktip, KI, and Ks are the local near-tip stress intensity, the applied or nominal

stress intensity, and stress intensity due to shielding respectively. The objective of

extrinsic toughening is thus to enhance Ks. It is possible to categorize mechanisms

of extrinsic toughening into several distinct classes, as illustrated schematically in

Fig. 7. These classes involve crack tip shielding from:

(a) crack deflection and meandering, whereby the mode I crack-driving force is

locally reduced by deviations of the crack path from the surface of maximum

28

tensile stress, has been shown to play a significant role in governing the fracture

and fatigue behavior in particulate reinforced Composites,

(b) inelastic or dilated zones surrounding the wake of the crack, termed “zone

shielding”. Zone shielding mechanisms include (i) microcrack toughening &

crack field void formation, which serve to relax crack-tip triaxiality stress and

diffuse the intensity of crack-tip stress singularity, and (ii) crack wake plasticity

& residual stress field, which develop a favorable compressive residual stress,

(c) wedging, bridging and/or sliding between crack surfaces, termed “contact

shielding”. A more general source of contact shielding during cyclic crack

growth arises from the wedging action of fracture surface asperities an/or

corrosion debris, where the crack tip opening displacements are small. Crack

bridging is most prominent in whisker- and fiber-reinforced composites. A

prominent characteristic of non-mode I crack growth is interaction between

sliding surfaces, i.e. rubbing. This phenomenon has been shown to be a very

potent shielding mechanism during fatigue crack growth in shear modes, and

(d) Plasticity-induced crack closure and phase-transformed-induced crack closure

are considered as a combined zone and contact shielding. Plasticity-induced

crack closure is generally considered to be more prevalent under plane stress

conditions and is thus more significant at higher stress intensity levels in metal

matrix composites. On the other hand, Analogous to transformation toughening

in ceramic matrix composites, an additional crack closure mechanism can result

in materials which undergo a stress-or strain-induced phase transformation.

All the above models based on linear elastic fracture mechanics (LEFM). However,

LEFM sometimes conflicts in some details with experimentally observed

phenomena of fatigue crack growth rate due to the failure of stress intensity factors

to provide an adequate representation of crack stress or strain fields. Thus, any of

the above models, i.e. based on LEFM, can not be generalized to explain or predict

the fatigue failure in composites. As mentioned by Sallam and Hashemi [17], the

correlation of fatigue crack growth behavior in composites by a single parameter,

such as effective stress intensity factor or crack tip opening displacement, may not

be appropriate. Further work is required to improve the above shielding

29

mechanisms by using two- or three-dimensional nonlinear micro-analysis taking

into consideration the strength of matrix, reinforcement, and interface.

Figure 7. Schematic representation of mechanisms oshielding in composite

Crack deflection and meanderi )a( Zone shieldin )b(

- microcrack toughenin

Conta )c(

- wedging:

combined zone and contact shieldin)d(

* corrosion-induced crack closur

* roughness-induced crack closur

- plasticity-induced crack closur

- bridgin

30

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8. Kantzos, P., Eldridge, J. I., Koss, D., and Ghosn, L. J.(1992), “The effect of fatigue loading on the interfacial shear properties of SCS-6/Ti-Based MMC”, Proceedings of MRS spring meeting, San Francisco, CA, USA.

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