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MTS Adhesives Project 2:

Failure Modes and Criteria Report No. 2

EXPERIMENTAL METHODOLOGIES TO DETERMINE THE FRACTURE

PROPERTIES OF ADHESIVE JOINTS

R Davidson and R J Lee

AEA Technology

February 1995

AUTHOR: R J Lee SIGNATURE: DATE 1/2/95

REVIEWER: J C McCarthy SIGNATURE: DATE 7/2/95

Customer Ref: AH 9/2

Document Ref: AEA-ESD-0180

File No: 29569200 I

MTS Adhesives Project 2: Report 2 Experimental Methodologies

MTS ADHESIVES PROJECT 2: FAILURE MODES AND CRITERIA

Foreword

Many UK manufacturers are aware of the merits of adhesives in certain critical roles.

However the range of applications of adhesives is still limited largely due to the lack of

consistent test methods and validated test data which the engineer needs in order to specify

adhesives for a given application. In a recent survey the Centre for Adhesive Technology was

commissioned by the DTI to establish specific areas where validated test methods could

improve confidence in predicting joint life. The survey identified measurement methods for

use in design, environmental durability and process control as priority areas and five projects

were finally selected by the DTI for support through the Measurements Technology and

Standards (MTS) budget. The projects started in December 1992 and are 100% funded by the

DTI at the level of& 5.4 M over three years.

The survey also identified the need to understand adhesive joint failure modes and the

development of more robust, validated failure criteria as being critical to the development of

confidence in adhesive bonding technology. This requirement forms the basis of MTS

Adhesives Project 2 which is being carried out through a collaboration of AEA Technology,

University of Surrey and Imperial College of Science, Technology and Medicine.

The project is addressing the issue of failure criteria through initially an extensive study of

joint fracture. This forms the project’s first task aimed at providing a greater understanding of

the micro mechanisms by which adhesive failure begins and propagates through the joint. The

task makes extensive use of scanning electron microscopy and laser moire interferometry, both

techniques being used ‘in-situ’ on joints as they fail where possible and applicable. The

projects other two major tasks are to investigate and develop new and existing failure criteria,

and to investigate and develop tests for the measurement data needed to make the criteria

work. These tasks run in parallel through the second and third years of the project. All the

major loading modes will be addressed in the project - static, fatigue, creep and impact

loadings. The failure criteria should be accurate yet easy to apply; and the supporting test

methods should be sufficiently accurate to give good predictions of failure whilst being easy to

use by efficient utilisation of existing experimental equipment.

ii


1. INTRODUCTION

2. TEST METHODS FOR MEASUREMENT OF ADHESIVE BOND FRACTURE

2.1 Relation to other Programmed 2.2 Fracture Toughness Geometries 2.3 Application of Fracture Mechanics to bonded joints 2.4 Conditions for adhesive fracture 2.5 Relationship between Gc and Kc 2.6 Relationship between G and K for Adhesive Joints

3. EXPERIMENTAL TECHNIQUES

3.1 Mode I Specimen Geometry 3.1.1 DCB Specimen Analysis 3.1.2 DCB Testing issues 3.1.3 Data Reduction Methodology

3.1.3.1 Experimental Compliance (Wilkins method) 3.1.3.2 Corrected Beam Theory 3.1.3.3 Experimental Compliance (Berry’s Method) 3.1.3.4 The Area Method

3.2 The Tapered Double Cantilever Beam (TDCB) 3.3 Fracture Energy by Double Torsion 3.4 Compact Tension Geometry 3.5 Chevron Notched Geometry 3.6 Mode 11 Geometries 3.7 Mixed Mode Geometries

3.7.1 Cracked Lap Shear Joints

4. STRESS INTENSITY FACTORS FOR POLYMERS AND ADHESIVE JOINTS

4.1 Use of KIC in Adhesive Joints 4.2 Width Effects

5. FATIGUE IN ADHESIVE BONDS

5.1 Use of KIC in Fatigue 5.2 Effects of Test Frequency on Fatigue Crack Propagation (FCP)

6. CREEP EFFECTS IN BONDED JOINTS

7. CONCLUSIONS

8. ACKNOWLEDGMENTS

9. REFERENCES

TABLES AND FIGURES

1

2

2 3 4 5 6 7

7

8 9

11 11 12 12 13 13 14 15 16 17 17 19 19

20

20 22

22

23 24

25

25

28

29

APPENDIX 1: TEST SPECIMEN GEOMETRIES FOR DETERMINING

FRACTURE TOUGHNESS

. . . 111


Glossary

TAST

CGR

Gc

Kc

DCB

DT

CT

CLS

ENF

CNF

Gi, Gp

Y

Wd

u a

b

Fc

Y

E1I

n and H

XI c CFRP

d

LEFM

FCP

TDCB

Thick adherend shear test

Crack growth rate

Critical strain energy release rate

Critical stress intensity factor

Bonded double cantilever beam, tapered and untapered

Bonded double torsion specimens

Compact Tension

Bonded cracked lap shear

End notched (cracked) flexure

Centre notch flexure

Mixed Mode Bending

Strain energy release rate for initiation and propagation

Geometrical constant

work done by the external force

elastic energy stored in the specimen

crack length

specimen width.

load required for crack propagation

displacement at the load point

flexural rigidity

experimentally determined constants

Mode I correction factor

Compliance

Carbon fibre reinforced plastic

displacement

Linear Elastic Fracture Mechanics

Fatigue Crack Propagation

Tapered Double Cantilever Beam

iv


EXPERIMENTAL METHODOLOGIES TO DETERMINE THE FRACTURE

PROPERTIES OF ADHESIVE JOINTS

Roger Davidson and Richard J Lee

1. INTRODUCTION

This report was compiled as part of the activities undertaken within Task 2 ‘Development

of Test Methods ’ of the MTS Adhesives Project 2 ‘Failure Modes and Criteria’ and forms

the first deliverable from that task. The report is a review of test methods for measuring

the fracture properties of adhesive joints.

The report is a companion to the review by Crocombe and Kinloch [1] - a deliverable from

Task 3 of this project - which addresses some of the more important adhesive bond failure

criteria. Issues relating to test methods to assess environmental aspects of failure,

particularly due to the effects of moisture, are covered in reports from MTS Adhesives

Project 3 ‘Environmental Durability of Adhesive Bonds’.

The review consists of the following:

. a brief discussion of each type of test and what it measures together with references

to its development;

. overall conclusions on the tests reviewed and their suitability.

The review concentrates on tests to measure the properties of adhesive materials relevant to

fracture mechanics type failure criteria [1]. This type of criteria attempts to predict the

static strength, fatigue life or creep rupture time of an adhesive bond by the development of

a critical flaw within the bond line. The general principal behind all tests is therefore to

measure the crack growth along the adhesive bondline as a function of applied load and

hence to calculate the critical strain energy release rate (Gc) or critical stress intensity factor

(Kc).

Of the other failure criteria discussed in the review by Crocombe and Kinloch [1] only the

maximum stress/ strain criteria require material failure properties for which current tests

exist (maximum strain to failure, maximum stress at failure). Tests to measure these

material properties are being investigated in MTS Adhesives Project 1 ‘Measurement of

Basic Mechanical Properties of Adhesives for Design Use’ and have not been further

covered therefore in this review.

The review consists of some 30 pages of text plus figures and in parts is quite detailed. It is

not aimed as a primer on adhesive bond test methods but as a summary for an experienced

researcher of the current state of test development. As such the review will be used to form

the work plan for the later activities on Task 2 which, together with the results from Task 1

1


of the project ‘Detailed Studies of Joint Failure’ and Task 3 ‘Development of Failure

Criteria’, will investigate the most appropriate test methods further or develop new test

methods if they do not currently exist.

2. TEST METHODS FOR MEASUREMENT OF ADHESIVE BOND FRACTURE

2.1 Relation to other Programmed

One of the primary objectives of the current MTS Adhesives Project 2 is to examine the

most appropriate test methods for measuring the properties required for the prediction of

strength in the selected adhesives and joint configurations. From an industrial point of

view, and to permit wider application, tests should be as simple as possible to carry out

whilst providing sufficient accuracy to be useful for design purposes. Initial data has

focused on two adhesives widely used in practice representing a high stiffness and a

compliant resin system. They are:- AV119 (Ciba Polymers, Duxford), a one-part toughened

epoxide which cures at -120'C, and F241 (Permabond Adhesives Ltd. Eastleigh), a

compliant room temperature curing toughened acrylic. They have both been extensively

studied under quasi-static, creep, fatigue and impact loading within Task 1 of the project.

The work has primarily focused on two bonded joint geometries based on thick adherend

shear test (TAST) and the 180° T-peel test. The specimen geometries are illustrated in

Figures 1 and 2. Mechanical tests have also been carried out on bulk samples. In order to

ensure minimal overlap of work between other current MTS Adhesive projects there has

been appropriate liaison between workers on Project 1 dealing with characterisation of

adhesive materials (NPL, TWI, Department of Mechanical Engineering, University of

Bristol) and Project 3 (DRA Oxford Brookes University and AEA) on prediction of the

lifetime/durability of adhesive joints in hostile environments. A companion review of

adhesive bond failure criteria by Kinloch and Crocombe[ 1 ] addresses short term static

loading, cyclic fatigue loading, sustained loading and impact loading. Issues relating to tests

to assess environmental durability aspects of failure, particularly due to the effects of

moisture, are being covered in MTS Project 3 documentation.

2


2.2 Fracture Toughness Geometries

For quasi-static loading the crack growth rate (CGR) $ is measured as a function of the

critical strain energy release rate (Gc) or the critical stress intensity factor (KC) using the

adhesives and surface pretreatments of interest. The test sample geometry can be selected

from a wide variety of fracture mechanics test coupons currently used, including :

. Bonded double cantilever beam, tapered and untapered, DCB

● Bonded double torsion specimens, DT

. Compact Tension, CT

. Bonded cracked lap shear, CLS

. End notched (cracked) flexure, ENF

The approach used in fracture mechanics methodology is to conduct mechanical tests on a

particular representative test geometry to measure crack growth along the adhesive

bondline as a function of applied load. The critical strain energy release rate, or fracture

energy, (Gc) and the critical stress intensity factor (Kc) for that mode of crack opening are

calculated. The data are usually plotted as a function of the crack length to produce a crack

growth resistance R-curve from which critical values for initiation and propagation can be

obtained. The strength of other types of joints may then, in principle, be predicted using

fracture mechanics employing a standard Y-calibration factor representing the geometry of

the joint. The analysis also requires the inherent flaw size or the critical value of the

fracture energy for the applied crack opening mode.

The lifetime of other joint designs are then predicted. The fracture mechanics analysis may

require values of the inherent flaw size and final crack length in the joint to be deduced or it

may be deduced from a knowledge of the threshold value of the fracture energy. Typical

GIC and KIc values for various materials are summarised in Table 1.

Strength prediction, for static loading, based on fracture mechanics principles is not

currently widely used for joint design because of the difficulty of assuming a critical flaw

size and obtaining valid fracture toughness parameters. However, during fatigue or creep

loading, as inherent flaws propagate or other flaws are initiated, the application of fracture

mechanics principles may be more appropriate. It is clearly evident that there are many

unresolved areas in the application of fracture mechanics to the failure of adhesive joints

which are less well understood. The dependence of measured fracture parameters on joint

geometry, the effects of temperature and strain rate, and the theoretical complications

arising from cracks at, or near, the interface are clearly areas where further understanding is

required.


2.3 Application of Fracture Mechanics to bonded joints

The materials scientist’s method of analysis usually centres on measuring the strain energy

release rate for initiation, Gi, and propagation, GP, as a function of crack length whereas

the engineering approach usually calculates the critical stress intensity factor for the loading

mode using the expression :

where Y is a constant dependent on the specimen geometry and obtained from standards

and research reports, o is the remote applied stress and a is the crack length.

The energy balance approach has the advantage of avoiding theoretical difficulties

associated with analysing cracks which arise when the critical stress intensity factor

approach is used [2]. Crack blunting effects do not apply in this case and the value of G

can be measured from the applied load and crack length measured directly or by a

compliance calibration factor measured previously on a pre-cracked sample. A graph of log

— versus log G is normally linear and so maybe fitted as a power law. The basic method

of analysis is to postulate that in the bonded joint under investigation any sub-critical flaw

present will propagate slowly under the action of applied stress (and environment) until it

reaches a critical size after which it propagates catastrophically. The same principle can

also be applied with creep and cyclic loading. In laboratory fatigue experiments a simple

sinusoidal waveform or a more complex realistic, sometimes random, loading spectra can

be applied to the specimen. Crack growth data and applied loads can be monitored and

stored by computer during testing to obtain the adhesive’s crack growth characteristics.

Fracture mechanics methodology assists in the understanding of large scale service failures

and their avoidance. From an engineering point of view, fracture mechanics aims to predict

the onset of fracture of a structure containing a crack of given size and geometry. From a

materials science point of view, fracture mechanics aims to isolate material parameters of

importance to crack resistance so that materials with improved fracture toughness can be

devised. Given a quantitative knowledge of the critical driving force, the values of nominal

stress necessary for crack propagation for various size specific cracks can be estimated.

This premise is applicable only for progressive fracture spreading from a local region of

high stress. There are three major patterns of crack extension behaviour:

● Slow, stable crack growth where the forward movement of the crack border

develops gradually as a function of time and environment.

● Rapid, stable crack propagation, where the speed of creation of new fracture

surfaces is fixed by the rate of energy release and increases with time.

4


● Crack growth and arrest in a ‘stick-slip’ manner.

The failure of adhesive joints occurs by the initiation and propagation of flaws when the

joints are subjected to either mechanical, thermal, environmental stresses or combination of

these. Mechanical stresses may be applied statically or dynamically. One approach to

failure prediction is to mathematically analyse the loads at which flaws propagate and

describe the manner of their growth. Intrinsic flaws in adhesives occur naturally and may

be caused by interracial cracks from poorly wetted out adhesive, voids from entrapped

vapours or gasses and particulate matter introduced deliberately to control bondline

thickness or accidentally by poor process handling. In general these flaws may either be

present during manufacture and their precise position within the bonded area is important,

or they may develop upon subsequent stressing. The key issue is whether such defects

grow to a critical size where the defect can cause catastrophic failure. Fracture mechanics

principles are useful in characterizing the toughness of adhesive, assessing mechanisms of

failure and as an aid to the prediction the service life of cracked or damaged structures.

2.4 Conditions for adhesive fracture

For fracture to occur two conditions are necessary:

i. Sufficient strain energy is released from the stress field around the crack tip by

extension of the crack to supply the energy requirements of the new fracture

surfaces [3, 4]. The release of energy comes either from the stored elastic strain

energy or from potential energy of the loading system, including test machine.

This approach provides a measure of the energy required to extend a crack over

unit area, denoted by GIC, the fracture energy or critical strain energy release rate.

ii. The stress intensity factor caused by modifications to the stress field surrounding

the sharp crack, for a linear elastic material, must exceed a critical value Kc which

is a material property [5, 6].

The basic aim of experimental fracture mechanics is to identify fracture criteria such as Gc

and Kc which are independent of the geometry of the cracked body.

For adhesives the materials used are seldom perfectly elastic and localised viscoelastic

and/or plastic energy dispersive processes at the tips of cracks are desirable to introduce a

degree of toughness and crack blunting. Such micro-mechanisms are usually the main

source of energy absorption in the material, and indeed the microstructure of toughened

adhesives is tailored to maximise such processes and so impart enhanced toughness. Gc

includes all the energy losses occurring around the crack tip.

5

MTS Adhesives Project 2: Report 2

The fracture criteria becomes:

Experimental Methodologies

Where, Wd is the work done by the external force

U is the elastic energy stored in the specimen

a is the crack length

b is the specimen width.

For structures exhibiting bulk linear elastic behaviour the inequality gives,

where Fc is the load required for crack propagation. This equation provides the basis for

determining adhesive fracture energy for a number of specimen geometries.

2.5 Relationship between CC and Kc

Regardless of the fracture mode, values of Gc and Kc can be found by experiment as a

function of load and crack size or as a function of load and compliance. If the material is

isotropic and linear elastic, analysis shows that for ‘thick’ plane strain samples the

relationship between the adhesive fracture energy Gc and the fracture toughness Kc for

linear elastic materials is given by:

Similarly for ‘thin’ plane stress specimens:

or

where

The loading modes equivalent to G1, GII and GIII are shown in Figure 3.

6

MTS `Adhesives Project 2: Report 2 Experimental Methodologies

2.6 Relationship between G and K for Adhesive Joints

For a crack in an adhesive, which is relatively distinct from an interface, the above

expressions are still valid and the appropriate elastic values for the adhesive may be

employed to correlate G(joint) and K(joint). Thus, for plane strain:

For the case of a crack present at or very near an interface the situation is less clear and an

effective modulus, weighted between the adherend and the adhesive, has been suggested [7,

8]. For cracks very close to the interface no relations are available.

For non-linear elastic materials the concept of G is still valid but the interpretation of stress

intensity factor is not as straightforward and the above relations are not generally

applicable.

Adhesive joints must support both shear and peel forces and any crack lying in the plane of

the joint may experience combinations of Mode I, Mode II and Mode III types of loading

depending on the applied stress state. These different mixed-mode loading modes are

defined in Figure 3. For adhesive joints, the crack opening Mode I is the most critical.

However, in order to be able to design adhesively bonded structures with a similar level of

confidence as now exists for metal structures, it will be necessary to understand the fracture

behaviour under single and mixed mode conditions.

For a single mode loading the driving force for crack extension is the strain energy release

rate G = Gtotal . Under mixed mode loading Gtotal = GI + GII + GIII. The appropriate driving

force must be established experimentally and this requires the testing specimens with a

different ratio of modes. The following sections describe

and data reduction techniques which are applicable to

bonds.

3. EXPERIMENTAL TECHNIQUES

the different specimen geometries

the characterisation of adhesive

A variety of specimen geometries exist which aim to measure the fracture resistance of

structural adhesives. Most geometries have been adapted from metallic, and more recently

advanced structural composite, fracture mechanics specimens. Test geometries may be

based on bulk adhesive samples or more realistically, they are based on adhesive bonds

between metal or composite adherends. The geometries have been reviewed extensively

by Kinloch and co-workers [9, 10].


The MTS Project 2 experimental work requires that methods for fracture toughness

measurements based on static, fatigue, creep and impact loading are assessed. The tests

must be industrially relevant, simple to carry out with relatively simple specimen

geometries.

3.1 Mode I Specimen Geometry

For adhesive bonds the opening Mode I is the most critical. The simplest specimen

geometry and one of the most widely employed is the double cantilever beam (DCB)

[11, 12]. The DCB specimen has been the subject for numerous analyses based on the

classical beam theory. The crack is made to extend by applying a tensile force acting in a

direction normal to the crack face. The specimen recommended in ASTM D3433 is shown

in Figure 4. Two metallic rectangular beams are bonded together with an initial unbended

length of 25.4 mm and loaded through pins until the crack grows rapidly. The strain is

held constant and the load drop as a function of time is recorded until the crack stabilises.

The new crack length is measured and the procedure repeated until failure. The fracture

toughness is given by:

For a thin adhesive layer the compliance can be estimated from beam theory as:

Alternatively the compliance can be measured experimentally

length. The deflections can be estimated from the cross head

extensometry across the bond thickness.

as a function of the crack

movement or directly from

A modification of the DCB is used in the Boeing wedge geometry which is used primarily

in environmental resistance tests [13, 14]. Thin metal adherends are used with cracks

started by driving a wedge into the end of the bonded beam. The specimen geometry is

given in Figure 6. The advantages of these specimens are that they are simple and

inexpensive to make, they are self-contained and can be exposed without complex loading

fixtures and produce rapid results which is ideal for quality control purposes. The major

disadvantages are that the test piece is only semi-quantitative as the adherends are often

8


plastically deformed and the wedge force varies as the crack extends. Also, the rate of

change of compliance with crack length is not constant and under constant load G increases

with the crack length, and accurate measurements of the crack lengths with time are

required, In the test the crack growth as a function of time is monitored with the specimen

held in the environment of interest. Using beam theory and ignoring some of the

complicating issues mentioned above, the toughness of the adhesive is estimated from:

where y is the displacement at the load point.

3.1.1 DCB Specimen Analysis

The DCB specimen has been widely analysed as a classical encastered beam, assuming that

the loaded beams are rigidly built into the remainder of the untracked specimen and that

classical small deflection beam theory is valid [15, 16].

The compliance of the straight-sided DCB specimen may be obtained from elastic beam

theory as:

where a is the crack length and Ellis the flexural rigidity of each beam of the specimen.

The strain energy release rate is given by:

Critical conditions occur when F = Fc, and the Mode I fracture toughness GIc for plane

stress conditions is

An experimental compliance

compliance is expressed as

approach has been taken by Berry [15] where the beam

9


Where n and H are points to be determined experimentally.

The two approaches coincide if n = 3 and H = 1.5E1I. The

to this approach is given by:


critical value of GIc according

FCan c

where d is the displacement at the critical load, yields H

The Berry method is currently accepted by ASTM committee D30.02.02 as the basis for

experimental fracture toughness determination of composites. However, these equations

may need to be corrected for various effects which are not accounted for in the simple beam

theory [17]. Such effects arise as a result of shear deformation and deflection at the crack

tip, large deflections of the arms and any stiffening of the arms due to the presence of end

blocks which are often used with thin composite adherends. In Mode I the correction

factor x1, may be introduced for end rotation and deflection of the crack tip. The

potentially large deflection at the bonded end blocks, where thin adherends are used, and

other stiffening effects caused by end blocks may be taken into account by using the

correction factors Q and N. The expressions for the corrected compliance and Mode I

fracture energy for the DCB test are then given by:

Hence

crack length, a, where the intercept gives the value of the correction factor X,.

10


3.1.2 DCB Testing issues

For thin adherends load introduction tabs are required in order to transfer tensile load to the

beams and a design utilising piano hinges has been recommended [18, 19] in the ASTM

standard. The specimen geometry is shown in Figures 7 and 8. For composite adherends

the DCB should be approximately 15 cm long and 2.5 cm wide. To provide a starter crack,

thin 15-75 um insert films of PTFE or release agent coated polyimide or aluminium foil are

used. The hinge alignment is critical and may be accomplished by using a mounting jig.

Before testing, the edges of the specimen are painted with a thin coating of brittle

typewriter correction fluid. This makes the visual determination of the crack front at the

specimen edge easier and more reliable. Similar procedures may prove appropriate in the

testing of adhesive joint configurations.

The test procedure employed depends on the data reduction procedure to be used. The

classical beam approach and the area method require loading and unloading cycles for each

increment of crack growth; other methods require continuous loading of the specimen.

For crack length measurements, an optical microscope, a precision Vernier gauge or an

electrical method such as potential drop is needed. The initial crack length a, from the load

line to the tip of the starter crack on both sides of the specimen is first determined and the

real time analogue display of the load versus crack opening displacement curve for a cross

head rate of -0.5 mm/min is monitored. The DCB specimen is loaded until the crack

extends about 10 mm and the cross head is stopped. The crack length is measured and the

specimen is unloaded. The procedure is repeated until the crack is -100 mm in length.

Figure 9 shows typical results for a unidirectional CFRP composite specimen.

For continuous loading methods as the critical load is realised the crack starts to grow. The

position on the chart when the crack has grown 2.5 mm ahead of the starter crack is

marked and this procedure is continued until the crack has advanced about 40 mm [20].

3.1.3 Data Reduction Methodology

The measurement of adhesive fracture toughness depends on the method adopted for data

interpretation. Data reduction procedures are of two types :

. Direct energy methods, such as Areas method.

● Compliance methods, requiring a relationship to be found between compliance

and crack length.

Experimental data usually comprises load-displacement records for cracked samples

together with sample geometry and crack length. The choice of analysis method used to

interpret the data should be such that material or specimen behaviour must not violate the

11


assumptions of the analysis or the fracture parameter will lose its significance as a design

parameter. Some of these effects includes:

●

●

●

rotation and deflections occurring at or near the crack tip,

large displacements being present in the test sample,

stiffening effects due to the geometry of the loading points.

For discontinuous loading there are several common

including the following :

3.1.3.1 Experimental Compliance (Wilkins method)

data reduction methodologies

In the Wilkins method [16] the compliance C is evaluated from the rising portion of the

load cycle C = $-. From a log log plot of C against a, a straight line of slope 3 is fitted to

the data by linear repression analysis (Figure 10). The line is extrapolated to log a = O. 2

The corresponding compliance is equal to A1 = — In order to obtain the Mode I

fracture toughness, GIc, the critical loads Fc, at the onset of crack propagation are

evaluated from the load displacement record. The Fc versus a data are plotted on a log-log

diagram, and a line of slope -1 is fitted to the data. The line is extrapolated to a = 1 mm.

The critical load at say a = 1 mm corresponds to the constant A2 =~- hence,

GIC =

This method provides an averaged GIC value for the entire range of crack lengths, which is

appropriate if GIC is a true constant, independent of crack extension.

In order to capture any variation of GIc with crack extension (R curve effect) the equations

may be combined to give:

A, is obtained from Figure 10 but the curve fit procedure of Figure 11, which assumes a

constant GIC is circumvented; instead individual sets of Fc and a are substituted to extract a

possible crack length dependency to GIC.

3.1.3.2 Corrected Beam Theory

Simple beam theory predicts that the compliance of a perfectly built-in DCB specimen is :

where F is load, d is displacement, B is specimen width and a is crack length.

12


In practice this expression underestimates the compliance as the beam is not perfectly built-

in and a correction factor is applied. This correction treats the beam as containing a slightly

longer crack, a+D, and D may be experimentally determined by plotting W as a function

of crack length. GIC is then given by:

This approach allows the adherend modulus to be calculated, which should be independent

of crack length, and is a useful check on the procedure.

3.1.3.3 Experimental Compliance (Berry’s Method)

An alternative approach is to plot compliance against crack length on a log-log plot. The

slope of this plot, n, can be used to derive GIC as follows :

C = Kan

so

3.1.3.4 The Area Method

An alternative method to determine the fracture toughness is the area method which allows

for the direct evaluation of GIC. The critical strain energy release rate may be determined

from a loading-unloading sequence according to Figure 12.

Where AA is the area indicated and a2-al is the increment in

For linear elastic behaviour GIC is approximately [21]:

GIC maybe determined as:

crack length.

An average GIC value is obtained from the total series of loading and unloading curves.

One of the major advantages of the area method is that it quantifies the propagation

13


toughness while the compliance techniques characterise the initiation toughness. Fracture

toughness determination according to this method requires that the parameter n be

determined: from the slope of a plot of F= / 6C versus a in a log-log diagram as illustrated in

Figure 13. Once n is obtained, the fracture toughness is determined for each crack length

from;

Figure 14 shows GIC, for a rubber toughened CFRP, determined from both the classical

beam theory method and the experimental compliance method.

In some materials, stick slip behaviour is observed where unstable growth occurs [22].

3.2 The Tapered Double Cantilever Beam (TDCB)

This specimen is an adaptation of the DCB but uses shaped metallic adherends. The

specimen, designed initially by Mostovoy and Ripling [23-25], is tapered to give a linear

compliance change with crack length. To achieve this the height of the adherends is varied

such that

where m is a constant. The ASTM specimen form = 90 is shown in Figure 5a.

This feature is particularly useful in cases where difficulty is encountered in locating the

crack tip. The experimental procedure is simpler than with the DCB but the specimen

geometry is more complex and expensive to machine.

A high m number generates a geometry with a low taper angle which causes a large bending

stress in the plane of the crack. However, because of the relatively low modulus of the

adhesives used this stress is not significant. The specimen geometry is not usually suitable

for bulk specimens as the high bending stresses cause the arms to break off. The problem is

minimised for a low value of m by making the beams stiffer and adding side grooves to the

specimen to direct the crack. When the specimens are made stiffer, linear compliance is

achieved but the specimens cannot be used to determine GIC because the assumptions used

in beam theory become increasingly invalid as the height to length ratio increases. In

of m an experimental value determined from the compliance calibration designated

required. Hence the toughness of monolithic specimens having low m is defined as :

14

place

m’ is


where bn is the width at the crack plane,

b is the gross specimen width and

E is the tensile modulus of the adherend,

Mostovoy showed that by using the DCB or TDCB, a pure Mode I load can be set up on

the bond line. This fracture force is analogous to the stress intensity factor K] used to

determine the force at the crack tip in homogeneous materials where :

for plane stress

and,

An alternative design to achieve constant = uses contouring of the width of the specimen ~a

along its length. This is most often used with composite adherends which tend to have

uniform thickness and is not recommended for adhesives. It has also been shown [26] that

by using a traditional TDCB specimen manufactured with a 45° scarf angle at the bonded

faces, it is possible to investigate mixed Mode I/ III crack growth. By varying the scarf

angle the ratio of Mode I : Mode III can be investigated. Figure 5b shows the specimen

geometry for a scarf angle of 45° using a value for m of 4 in-l.

3.3 Fracture Energy by Double Torsion

This method may be used to assess either the bulk adhesive or adhesive bonds loaded

through the metal adherends. Typical dimensions are 30 x 75 x 3 mm containing a pre-

crack. By bending the end of the plate through its width in 3 or 4 point loading a crack can

be extended. The main feature of this geometry is that the specimen compliance C varies

‘c the fracture energy linearly with a so that by pre-calibrating the specimen to provide — da

may be calculated from the crack propagation load [27, 28]. Typical specimen geometry is

shown in Figure 15.

Employing this technique cracks either propagate continuously or in a ‘stick-slip’ mode.

continuous crack propagation the fracture energy is defined uniquely by the failure load.

15

In

In


the ‘stick-slip’ mode two values can be obtained - the crack initiation energy Gi at the onset

of crack jumping and the arrest energy Ga

In the case of a thin adhesive layer between metal adherends,

where dm is the length of the moment arm

b is the width of the specimen in the plane of the crack for a proved specimen,

K, is a constant which equals 0.28 when -$= 4 [25].

Alternatively the fracture toughness KIC can be obtained from,

where bn is the width of the specimen in the plane of the crack for a grooved specimen.

3.4 Compact Tension Geometry

For the case of an adhesive joint in a compact tension specimen [45] the general equation

used for metals is modified to take account of adhesive stiffness.

where

Hence,

where b is the thickness of the specimen

w is the length of the specimen in the direction of crack propagation.

16


The polynomial function Y varies considerably with specimen geometry as shown in

Appendix 1.

3.5 Chevron Notched Geometry

For fracture toughness measurements it is necessary to start with a sharp, well defined,

crack. Three techniques can be used to achieve this: fatigue pre-cracking, limited crack

growth and Chevron notching. Fatigue cracking of joints is not very reproducible due to

the non-uniform microstructure and high residual stresses which are within the joint.

Running cracks can be difficult to control and may run in an unstable fashion. Chevron

notching is designed to minimise the pre-cracking problem by initiating flaw growth at the

tip of the notch [29, 30]. The specimen geometry is somewhat complex as shown in Figure

16. Initially the stress per unit width across the crack front is very high due to the sharp

chevron notch. As the crack grows the crack width increases rapidly as the stress per unit

width drops proportionately. For a displacement or load control test the crack will grow in

a stable manner. Concurrently as the crack grows, the moment arm (and therefore the

stress intensity on the crack front) increases. In this regime the crack will be unstable in a

load controlled test although stable in a displacement controlled test. The peak load a

specimen will support occurs when the crack reaches a critical length. The critical crack

length depends only on specimen geometry and not on specific material properties. As

such, once the specimen geometry has been calibrated, either by experiment or by analysis,

the critical plane strain fracture toughness can be obtained from the maximum load. In

recent work [30] a nylon modified epoxide adhesive was studied between aluminium alloy

and steel adherends as a function of the adhesive bond thickness, temperature and crack

opening rate results are shown in Figure 17-19.

3.6 Mode II Geometries

Barrett and Foschi [31] utilised the edge notched flexure (ENF) specimen to characterise

the Mode II interlaminar fracture of cracked wood beams and Russell and Street [32]

utilised the specimen to characterise the critical strain energy release rates of advanced

composites. The test geometries are given in Figure 20 and 21. The specimen comprises a

3 point flexure bonded beam with a through-the-width crack in the adhesive running from

one end face. The delamination is placed at the end of the specimen to accommodate the

sliding deformation across the adhesive that results from flexural loading. The sample is

currently being investigated for GIC measurements in composite adherends, but may well be

applicable to adhesive bonds. The specimen is easy to manufacture, and the test fixture is

simple and data reduction is straightforward. The starter crack can be produced by

embedding a 20 um PTFE film or release agent coated aluminium film at the centre of the

bond.

17


Compliance can be measured for several crack lengths in a single ENF specimen containing

a long crack. Providing that the loads applied are not sufficient to cause the crack to

extend, various crack lengths can be achieved by sliding the specimen with respect to the

central loading point. The compliance is fitted to a polynomial of the form:

where C1 is a constant, including

data. The resulting expression

calibration is:

C= C1+ma3

machine compliance and m is the slope of the C verses a3

for the strain energy release rate based on compliance

Co for the beam with no crack:

It should be noted that alternative Mode II interlaminar

against as shown in Fig. 22.

flexural specimens have proliferated

since the introduction of the ENF specimen to composites. These include the end loaded

slit laminate [33], the cantilever beam enclosed notch (CBEN) [34, 35], the centre notch

flexure (CNF) [36] for static and impact loading and the mixed mode bending (MMB) [37].

These sample geometries which may also be applicable to adhesive bond testing are

summarised in Figure 23. A modification to the ELS test has been described in [38] where

a sliding clamp was used to eliminate the axial force generated into the specimen when it is

encastered at the clamped end. In this case:

and the compliance C is given by:

18


3.7 Mixed Mode Geometries

3.7.1 Cracked Lap Shear Joints

The cracked lap shear (CLS) specimen geometry is shown in Figure 24. It represents a

structural joint subjected to in-plane loading [39, 40]. Both shear and peel stresses are

present in the joint. The magnitude of each component of the mixed-mode loading can be

modified by changing the relative thickness of the strap and lap adherend. The ratio of G,

GII can be varied between 0.6 to 0.2; as the thickness of the shorter lap adherend is

increased. The ratio can also be changed by machining the lap adherends to tapers. For

samples with strap/ lap thicknesses of 2:1 a taper angle of less than 5°- 10° reduces the peel

effect on the bond such that pure Mode II operates [40]. Experimental data shows a

significant improvement in debond resistance for taper angles below 10°, for toughened

epoxide adhesives. Untracked specimens may be tested in fatigue to investigate the crack

initiation and growth in the adhesive bond line. Alternatively pre-cracked specimens may

be used. Data showing the variation of debond length increasing with increasing number of

fatigue cycles is shown in Figure 25 for a CLS specimen.

The cracked lap shear specimens can be analysed using finite element techniques to

determine the strain energy release rate for a given geometry, debond length and applied

load. The non-linearity associated with the large rotation in the asymmetric cracked lap

specimen must be taken into account.

The cracked lap shear specimen is one of the most commonly used comparison tests, since

it allows a range of Mode I and Mode 11 ratios. This specimen represents a simple

structural joint subjected to in-plane loading. Both shear and peel stresses are present in the

bondline of the joint. Detailed mechanisms occurring during the initiation and propagation

of cracks are amenable to study using laser moire interferometry (LMI) techniques.

Cracked lap shear joints represent mixed mode loading and large area bonds typical of

many structural applications. They are also convenient specimens for laboratory tests on

debond growth and fatigue crack growth. Analytical studies of the joint geometry provide

insight into geometric non linear effects, and the effect of adherend and adhesive material

properties. The magnitude of each component of the mixed Mode I and Mode II loading

can be modified by changing the relative thickness of the strap and lap adherends. The

typical specimen geometry consists of-200 mm long lap adherend bonded over a 250 mm

long strap adherend. Both the specimen geometry and the adhesive thickness relative to the

bonded length are important in determining the ratio of ~. II

19


According to Kinloch [10], for the CLS geometry :


{

where 1 and 2 refer to the adherends and (Esd)2 > (Esd)1.

4. STRESS INTENSITY FACTORS FOR POLYMERS AND ADHESIVE JOINTS

The critical stress intensity factor (fracture toughness) KIC for adhesive joint conjurations,

is a more useful design parameter from the stress analysis view point than fracture energy.

In homogeneous isotropic materials, K expressions for a wide range of test piece

geometries and loading configurations have been computed and are available in the

published literature [41, 42]. Appendix 1 shows a table illustrating K calibration factors, in

the form of a finite series, for various specimen geometries used for plane strain fracture

toughness. In the most general form

K =@&

where o is the applied stress and

F is the shape correction factor.

4.1 Use of KIC in Adhesive Joints

For cracks in an adhesive layer in a joint the value of K is a function of the ratio of the

moduli of the adhesive and the adherend and the thickness of the adhesive layer as well as

the overall geometry of the joint. In many geometries where the elastic energy available for

crack growth is largely stored in the adherends as in the DCB, TDCB, DT and CT the

values are similar to the homogeneous specimen multiplied by ; this assumption E

adhered

is valid for adhesive thicknesses up to several millimetres. This modification to the equation

is not directly applicable to two phase materials such as metal/ adhesion joints for ‘thick’

bond lines where the compliance contribution due to the adhesive is significant. If doubts

exist as to the value of the calibration factor it must either be ascertained using numerical

analysis or experimentally using compliance calibration [43, 11].

20


For ‘thin’ bond lines it has been shown by Trantina [43] that:

Where n is I for Mode I stressing of a compact tension specimen and n is II for Mode II

loading of a compact shear specimen [44]. Experimentally fracture loads Fc are recorded

against corresponding crack lengths, a.

All the above relationships predict infinite stresses at the crack tip; in reality plastic yielding

in a zone ahead of the crack tip will occur. Where the zone is small then it will not greatly

disturb the elastic stress field, and the assumptions of LEFM broadly still apply. Irwin [9]

suggested that the extent of crack tip plasticity for bulk material could be regarded as

shown in Figure 26. Here dt is the crack tip opening displacement and ry is the radius of

the circular plastic zone at the tip of the notional crack. The elastic stress field ahead of this

notional crack may therefore be regarded as identical to the stress distribution of a real

crack of length a with the extent of plastic zone 2ry. The size of the plastic zone radius is

given by [46]:

The corresponding crack-opening displacements at the crack tip are:

Plane strain fracture conditions are considered to be present when the plastic zone is < 2%

of both the component thickness and crack length [47].

21


4.2 Width Effects

In practice the values of GIC or KIC can, over a certain range of widths, vary with the width

of the specimen. This arises because the state of stress near the crack tip varies from plane

stress in very thin specimens to plane strain near the centre of a wide plate. The general

variation is shown in Figure 27, with the values lower for plane strain conditions. This

arises because the tensile stress at which a material yields is greater in a tri-axial plane strain

field than in hi-axial plane stress and therefore in the former a more limited degree of

plasticity develops at the crack tip. The lower conservative, plane strain value is usually

required for engineering design and life prediction studies. The width, b, necessary to

achieve this condition is:

2

where KIC is the plane strain value.

5. FATIGUE IN ADHESIVE BONDS

Early work by Mostovoy and Ripling [48] established the validity of using LEFM to

describe the fatigue crack growth when bonding aluminium alloy substrates using a range of

epoxide adhesives. They employed a TDCB joint specimen and conducted tests under

Mode I cyclic loading and measured the rate of crack growth ~ per cycle as a function of

the range of strain energy release rate, DG (Gmax - Gmin) that was imposed. It was observed

that:

i. Over the range of experimental data:

or

22


ii. The relationship between


& ~ and DG was sigmoidal in shape given by :

Crack growth rates decreased to

under short term monotonic static

lower values as DG approached GC for crack growth

loading. Subsequently there have been studies of the

effect of the thickness of the adhesive [49], the type of adhesive [50, 51] and the mode mix

[52, 53] of the loading conditions. Clearly to be of greatest advantage to the designer it is

necessary to be able to use the results of such fatigue studies to predict the fatigue life of

adhesively bonded joints. Kinloch [54] has recently published his attempts to do this.

5.1 Use of KIC in Fatigue

Once the stress intensity for a given sample is known then the critical stress intensity factor

Kc (plane stress) or KIC (plane strain), necessary to cause fracture can be obtained. In

fatigue, propagation of the crack tip usually occurs in a stable manner across the width of

the sample until the magnitude of the crack tip stress intensity factor reaches the critical

value at which point rapid unstable fracture occurs. The kinetics of the fatigue crack

propagation process can be examined by measuring the change in crack length of a pre-

cracked sample as a function of the total number of load cycles. Many monitoring

techniques have been employed such as compliance measurements, acoustic emission

detectors, Eddy current techniques, potential drop measurements and the use of traveling

microscopes. Most data on non-conducting polymers have been based on microscope

readings. A typical plot of such data is shown in Figure 28, which shows the crack length

increasing with number of fatigue cycles. The fatigue crack growth rate per cycle — can dn

be determined as a function of crack length. For most specimen configurations, the crack

growth rate increases with increasing crack length, thereby shortening the component life at

a high rate. From this it is recognised that most of the loading cycles involved in the total

life of an engineering component are consumed during the early stages of crack extension

when the crack is small and possibly, undetected.

From Figure 28 it can be observed that ~ increases with increasing stress levels such that

23


Numerous relationships have been proposed to describe the FCP behaviour of metallic and

polymeric solids, based on empirical formulations and fracture mechanics principles. The

latter approach has proven to be most flexible and has been widely adopted. Paris [55]

postulated that the stress intensity factor, itself a function of stress and crack length, was

the major controlling factor in the FCP process. From Figure 28, then the growth rate

at any arbitrary crack length would correspond to respective values of

for some fixed stress level. Paris found that the key stress variable was the stress K.

&l range (a~= – crti ) and so described — values in terms of the stress intensity factor range

dn

DK with a relationship of the form

h where — is the fatigue crack growth rate, DK the stress intensity factor range

dn

(DK = K~= - Kti ) and A, m are functions of materials variables:- environment, frequency,

temperature, stress ratio etc. Though many studies have verified the log-log linear

relationship of a variety of polymers between ~ and AK such as shown in Figure 29,

others have shown FCP plots of a sigmoidal nature. Here crack growth rates can decrease

to vanishingly low values as AK approaches some limiting threshold value and increase to

very high values as Kmax approaches KC. Sutton [56] found that an amine cured bisphenol

A epoxy resin followed the Paris law but had values for A and m higher than for

thermoplastic materials. The apparent fracture toughness and corresponding modulus of

these resins also improved with increasing amine/ epoxy ratio, r; There is, however, a

corresponding fall in Tg from 198°C to 119°C as r increases from 1.0 to 2.2 [57].

5.2 Effects of Test Frequency on Fatigue Crack Propagation (FCP)

Experiments on pre-notched samples of various polymeric materials tested over a range of

frequencies from 0.1 to 100 Hz show varying trends. Polymers such as polycarbonate,

polysulphone, nylon and PVDF show no apparent sensitivity; others including poly methyl

methacrylate, polystyrene, PVC and a poly phenylene oxide/ high impact polystyrene blend

had a decreasing FCP with increasing frequency. A sample of the data is shown in Figure

28 [58]. Usually most polymers which are susceptible to crazing exhibit a strong frequency

sensitivity. Polycarbonate, however, is an exception to this rule. Localised heating at the

crack tip of a pre-cracked FCP specimen can attenuate the fatigue crack propagation rates.

Conversely premature thermal failures can occur during the fatigue testing of unnotched

24


samples. It might be expected to record higher FCP rates in pre-cracked samples at high

test frequencies if the polymer/ adhesive possesses a high degree of damping.

6. CREEP EFFECTS IN BONDED JOINTS

Little quantitative published work exists on creep of bonded joints and the current MTS

work aims to address failure prediction of joints subjected to sustained loading. There are

several factors which must be considered when embarking on an experimental programme

to measure creep data for design purposes. The data should preferably be obtained from

realistically sized specimens and subjected to a uniform stress level as possible. Creep

effects in bonded joints would be expected to be markedly different from bulk samples

because of the effects of the non-uniform strain distribution, particularly the relatively

unstressed central region, which serves to ‘pin’ the joint and improve creep resistance.

Creep curves obtained by quantitative measurement of the shear deflection across the bond

line in TAST bonded joints in Task 1 of MTS Project 2 have shown the presence of

characteristic curves with essentially three stages:

● Stage I, a rapid initial extension developing into,

● Stage II, a linear region followed by,

● Stage III an increasing rate leading to specimen failure.

The relative proportions of these stages depend on the applied stress and temperature and

whether brittle fracture behaviour, controlled by the creation of new cracks or the extension

of existing flaws, occurs before plastic flow processes leading to deformation controlled

fracture. Linear viscoelastic creep models, based on simple springs and dampers, have been

described in detail in the Task 3 review by Crocombe and Kinloch [1]. It is proposed that a

number of these models will be examined in further detail together with the ‘Theta

Projection Method’, developed by Evans and Wilshire [59] for modelling creep of metals

and ceramics. This assumes a creep curve of the form :

7. CONCLUSIONS

1. For fracture mechanics to be appropriate and helpful in measuring and predicting the

fracture properties of structural adhesive joints the values of the critical fracture

energy Gc or the stress intensity factor Kc for a given mode of loading should be

25


2.

3.

4.

5.

6.

7.

8.

independent of the specimen geometry. They should be materials properties with

appropriate dependency at the strain rate, temperature and other environmental

conditions.

Application of structural fracture mechanics to non cracked specimens is difficult, as

an estimate of intrinsic defect size for adhesive bonds is required. The uniqueness of

this approach for a given adhesive is questionable.

Data can be regarded in two ways:

(i) as a means to assess and compare the resistance to cracking (i.e. toughness)

of different adhesive systems. This is particularly useful during the

development of new adhesive forms. Here values of Gc are most useful.

(ii) to extrapolate data from laboratory specimens and to use these in the design

and production of the service life of bonded structures. Here values of Kc

are most useful.

For adhesive joints the Mode I crack opening displacement mode is the most critical.

A double cantilever beam geometry is simple to produce but the compliance will vary dC

non linearly with crack length. A tapered DCB has the advantage of a constant — all’

making a somewhat easier test but needing a more complex and expensive specimen.

Mode II & Mode III cracking is of less importance than Mode I but usually occur in

consideration with Mode I and their influence should be studied and assessed during

CLS/ENF tests for Mode II and wedged TDCB for Mode III interactions.

Fracture mechanics principles will be of use in assessing the effect of creep loads on

cracked joints. Rates of crack growth maybe used to estimate lifetimes.

Fracture mechanics principles can be applied to joints subjected to fatigue loads

where the crack growth rate can be increased as a function of the number of fatigue

cycles provided the crack growth is not discontinuous. This technique will clearly

work best where a specimen has been pre-cracked and the crack is running within the

adhesive. For untracked specimens fracture mechanics principles will only be

appropriate in the propagation stage of crack growth and will give little information

regarding the longer duration initiation phase.

Further information is required to validate and extend existing work modelling the

strain (and hence stress) environment in the vicinity of the crack tip. A suitable joint

configuration will be examined using LMI to directly observe sub-critical crack

growth in order to determine the stress/ strain distribution in the vicinity of the crack

tip.

26


9. There is currently no suitable test geometry to study pure Mode III loading as it is not

possible to easily monitor crack growth. The effect of Mode III will be studied using

a traditional TDCB specimen manufactured with 45° and 30° scarf angles.

10. The techniques developed in the static specimen measurements should be applied as

appropriate to study long term creep and fatigue in structural bonds. In these cases

the variables should be kept to an absolute minimum.

27


8. ACKNOWLEDGMENTS

The following are gratefully acknowledged for their respective contributions.

● The support of and finding from the DTI under the Measurement Technology and

Standards (MTS) budget.

● The work of the Centre for Adhesive Technology (CAT) in proposing the original

project scope.

● The staff at AEA Technology, Imperial College and the University of Surrey for

their critical review, discussion, proof reading and typing of this work. In

particular we would like to acknowledge the helpful comments of Dr. Paul Smith

(University of Surrey), Prof. Tony Kinloch (Imperial College of Science,

Technology and Medicine), Dr Alan Espie (Centre for Adhesive Technology) and

Mr. John McCarthy (AEA Engineering) during the preparation of the review.

28


9.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

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32


LIST OF FIGURE CAPTIONS


Figure 1:

Figure 2:

Figure 3:

Figure 4:

Figure 5a:

Figure 5b:

Figure 6:

Figure 7:

Figure 8:

Figure 9:

Figure 10:

Figure 11:

Figure 12:

Figure 13:

Figure 14:

Figure 15:

Figure 16:

Figure 17:

Figure 18:

Figure 19:

Figure 20:

Figure 21:

MTS Project 2 TAST specimen geometry

MTS Project 2 T-Peel specimen geometry

Modes of crack loading:

(a) Mode I (opening Mode);

(b) Mode II (forward shear);

(c) Mode III (tearing)

Double cantilever beam flat adherend specimen geometry

Contoured double cantilever beam specimen geometry

Scarf angle (45°) contoured tapered double cantilever beam

geometry

Boeing wedge specimen geometry

Hinged DCB specimen

Resin rich region ahead of starter film

specimen

Load-displacement curves for a unidirectional CFRP DCB at various crack

lengths

Compliance versus crack length relation for a DCB specimen

Critical load versus crack length for a DCB specimen

Area method to determine GIc

Plot used to determine parameter n.

GIC determined from classical beam theory and experimental compliance

versus crack length

Double torsion specimen geometry

Chevron-notched Geometry

Influence of mouth opening rate on fracture toughness of adhesive at

different thicknesses

Influence of adhesive thickness on fracture toughness

Influence of temperature on the fracture toughness of Al bonded joints

End notch flexure specimen

ENF Compliance calibration requires specimen with long crack length

33


Figure 22:

Figure 23:

Figure 24:

Figure 25:

Figure 26:

Figure 27:

Figure 28:

Figure 29:

Figure 30:

Compliance calibration for the ENF specimen

Mode II interlaminar fracture flexural specimens

Cracked-lap-shear specimen

Typical variation of debond length with fatigue cycles at different stress

levels for CLS specimen

Irwin model of plastic zone at crack tip

Schematic representation of the variation of KIC or GIC with width of a bulk

specimen

Crack length versus number of load cycles

Fatigue crack propagation in selected crystalline and amorphous polymers

Effect of cyclic frequency on FCP rates in various polymers

34

LMI Specimen

12.5 mm

TAST Specimens (20 Carbon Steel)

6 mm

SEM Specimen

Figure 1: MTS Project 2 TAST specimen geometry

T-Peel Specimens (Mild Steel)

MI Specimen

I

Adhesive Thickness

60 mm I

Figure 2: MTS Project 2 T-Peel specimen geometry

(b)

(c)

Modes of crack loading: (a) mode I (opening

mode); (b) mode II (foward shear); (c) mode III (tearing).

Figure 3: Modes of crack loading:

adherend specimen geometry

Figure 5a: contoured

95

25.4 ,

Figure 5b: Scarf angle (450) contoured tapered double cantilever beam specimen geometry

in.

t-%-+--

Figure 6: Boeing wedge specimen geometry

Distance from

load point to

initial crack tip

Growth during

exposure

Hinged DCB specimen.

Figure 7: Hinged DCB specimen

200

150

50

0 0

STARTER FILM - RESIN RICH REGION 15-75 um 200-500 um

Resin rich region ahead starter film

Figure 8: Resin rich region ahead of starter film

AS4/3501-6 [0]24

al

a2

a3

a,

2 4 6 8 10

DISPLACEMENT, mm

Load-displacement curves for a [0]24 graphite/epoxy DCB specimen at various crack lengths

12

Figure 9: Load-displacement curves for a [0]24 CFRP DCB at various crack lengths

lx 7.5 x

5x

2.5 X

DISPLACEMENT, d

Figure 12: Area method to determine GIC

I I

log a

Figure 13: Plot used to determine parameter n.

Figure 14: GIC. determined from classical beam

theory and experiment

I

(a)

Crack-growh testing geometries,

Figure 15: Double torsion specimen geometry

T

~__

S+l l<-

ADHESIVE

SLOT

`SECTION AA

-Specimen dimensions used for chevron-notched geometry. ln this study, specimen width B = 25.4 mm.

Figure 16: Chevron-notched Geometry

)0

Figure 17: Influence of mouth opening rate on fracture toughness of adhesive

2

15

1

0.5

0

ADHESIVE THICKNESS (u/m)

Figure 18: Influence of adhesive thickness on fracture toughness

o

Figure 19: Influence of temperature on the fracture toughness of Al bonded joints

Figure 20: End notch flexure specimen

Figure 21: ENF Compliance calibration requires

specimen with long crack length

Figure 22: Compliance calibration for the ENF specimen

VARIOUS MODE II FLEXURE SPECIMEN

(c)

Figure 23: Mode II interlaminar fracture flexural specimens

254 mm r -1

Figure 24: Cracked-lap-shear specimen

DEBOND LENGTH,

mm

CYCLES (X 106)

Figure 25: Typical variation of debond length with fatigue cycles at different stress levels for CLS specimen

I I

Figure 26: Irwin model of plastic zone at crack tip

— Plane-stress value

Plane-strain value

1

Width of specimen (b)

Figure 27: Schematic representation of the variation of KIC or GIC with width of a bulk

specimen

h

Figure 28: Crack length versus umber of load cycles

Figure 29 Fatigue crack propagation in selected crystalline and amorphous polymers

1 I

o

POLYSTYRENE

/

Figure 30: Effect of cyclic frequency on FCP rates in various polymer

APPENDIX 1: Various test specimens used for the determination of plane strain fracture toughness

APPENDIX 1 (Continued)

SINGLE-EDGED NOTCHED THREE POINT BEND

T-TYPE WOL

P

Modified X-type specimen with increased width and stiffer arms to prevent bending under high loads. The overall size of this specimen has increased considerably and there fore many of the advantages have beers lost but it is felt that this type of specimen with a large width is ideal for the study of crack growth rates.

mts adhesives project 2: experimental methodologies 2/p2r2.pdf · 2014-10-30 · mts adhesives...

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