1

APPLICATION OF FRACTURE MECHANICS TO THE

IMPACT BEHAVIOUR OF POLYMERS

by

EVANGELIA PLATI

B.Sc.(Eng.), M.Sc., D.I.C.

A thesis submitted for the degree of

Doctor of Philosophy .

of the

University of London

Department of Mechanical Engineering

July 1975 Imperial College of Science and Technology London SW7 2BX

ABSTRACT

In conventional types of impact tests the impact strength is reported

in terms of the energy to fracture W divided by the ligament area A. It

is well known that such an analysis of the data is not satisfactory,.

mainly due to the fadt that w/A has a strong geometrical dependence.

The research work described in this thesis dealt with the

examination of these geometrical effects for polymers in the Charpy and

Izod loading situations, and, by employing the fracture mechanics concepts,,

the critical strain energy release rate, Gc, was deduced directly from

the energy measurements.

The success of this approach to the field of impact testing has been

clearly indicated throughout the thesis, since the same Gc value was

obtained for both Charpy and Izod tests.

The effect of temperature on the impact behaviour of polymers was

also examined. The concept of the plane strain fracture toughness Gcl

and the plane stress fracture toughness Gc2 with yield stress changes

gave a good picture of variations with temperature and specimen thickness.

Finally, the analysis of blunt notch data showed that the fracture

mechanics idea of a plastic zone provided a method of describing blunt

notch impact data in terms of the sharp notch result Gc and the plane

strain elastic energy gyp?.

3

ACKNOWLEDGEMENTS

The author is grateful for the encouragement and invaluable help

received from her supervisor, Professor J.G. Williams, during the course

of this study.

The generous financial support of BP Chemicals (UK) Limited for the

full duration of this study is gratefully acknowledged.

The author also wishes to thank Mr L.H. Coutts for his valuable

assistance on the technical aspects of the experimental work.

For their assistance and advice throughout this project, the author

expresses her gratitude to Dr G.P. Marshall, Mr P.D. Ewing and

Mr M.W. Birch. -

Special thanks are also given to Miss E.A. Quin for accomplishing

the considerable task of typing the manuscript.

To my beloved parents

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CONTENTS

Page

Abstract 2

Acknowledgements 3

Contents 5

Notation 11

Abbreviations 14

Introduction 15

CHAPTER 1: LITERATURE SURVEY 17

1.1 HISTORICAL INTRODUCTION TO IMPACT TESTING 17

1\,, 1.2 IMPACT TESTING OF PLASTICS 18

1.3 SPECIFIC IMPACT TESTS 19

1.3.1 Limiting Energy Impact Testing Methods 20

1.3.2 Excess Energy Impact Testing Methods 20

1.4 TENSILE IMPACT TEST 22

1.5 CHARPY AND HOD TESTS 22

1.5.1 The Effect of Notch Tip Radius on the Impact

Strength 24

1.5.2 Notch Stress Distribution for Charpy and

Izod Tests 25

1.5.3 Effect of Clamping Pressure for the Izod

Test 26

1.6 BRITTLE AND DUCTILE IMPACT FAILURES 27

1.7 IMPACT STRENGTH - ENERGY TO FRACTURE 28

1.7.1 Energy to Initiate and to Propagate Fracture 28

1.7.2 Energy Lost in Plastic Deformation 31

1.7.3 Kinetic Energy of the Broken Half 32

Page

1.7.4 Energy Lost in the Apparatus 35

1.8 EFFECTS OF TEMPERATURE ON IMPACT STRENGTH 36

1.9 THERMAL STABILITY - MECHANICAL LOSSES OF POLYMERS 38

1.9.1 Dynamic Mechanical Losses and Impact Strength

of Polymers 39

1.10 FRACTURE MECHANICS APPROACH TO IMPACT 43

1.10:1 The Griffith Approach 44

1.10.2 Strain Energy Release Rate 46

1.10.3 Stress Intensity Approach 46

1.10.4 The Relationship Between Fracture Toughness

and Absorbed Energy for the Charpy Impact

Test 49

1.10.5 Plastic Zone Size 54

1.10.6 Fracture Toughness and Specimen Thickness 55

1.11 INSTRUMENTED IMPACT 56

1.11.1 The Fracture Mechanics Approach to the

Instrumented Impact Test 57

CHAPTER 2: CALIBRATION FACTORS (I) 59

2.1 INTRODUCTION 59

2.2 COMPUTATION OF THE CALIBRATION FACTOR 4 FROM THE Y

POLYNOMIAL FOR THE CHARPY TEST 60

2.3 THE FACTOR AND THE COMPLIANCE RELATIONSHIP 60

2.4 EXPERIMENTAL CALIBRATION OF (1) FOR THE IZOD TEST 62

2.4.1 Specimens and Test Procedure 62

2.4.2 Experimental Results - Discussion 63

7

Page

2.5 CORRELATION BETWEEN COMPUTED AND EXPERIMENTALLY

DETERMINED CHARPY CALIBRATION FACTORS (1) 64

2.6 DERIVATION OF (I) FROM THEORETICAL COMPLIANCE BY

APPROXIMATION TO VERY SMALL CRACK LENGTHS 65

2.6.1 The Charpy Case 65

2.6.2 The Izod Case 67

2.7 COMPARISON BETWEEN THEORETICAL AND EXPERIMENTAL

CALIBRATION FACTOR 4) 68

2.7.1 (1) for the Charpy Test 68

2.7.2 for the Izod Test 68

CHAPTER 3: IMPACT MACHINE 72

3.1 INTRODUCTION 72

3.2 DESCRIPTION OF THE APPARATUS 73

3.3 ZERO AND VICE OFFSET - WINDAGE AND FRICTION LOSSES 75

3.3.1 The Zero Offset 75

3.3.2 The Vice Offset 75

3.3.3 Windage/Friction Losses 76

3.4 EFFECTIVE RELEASE POINT OF THE TUP 77

3.5 POTENTIAL ENERGY OF THE TUP 78

3.6 ENERGY TO FRACTURE - CALIBRATION TABLES 79

3.7 SOME CHECKS OF PERFORMANCE OF THE MACHINE 80

CHAPTER 4: CHARPY AND IZOD IMPACT FRACTURE TOUGHNESS OF POLYMERS 82

4.1 INTRODUCTION 82

4.2 MATERIALS 83

4.3 THE CHARPY TEST - EXPERIMENTAL PROCEDURE 84

Page

4.3.1 Test Conditions and Apparatus 84

4.3.2 Specimens and Notching Technique 85

4.3.3 Testing Procedure 86

4.4 ANALYSIS OF EXPERIMENTAL DATA 87

4.5 EXPERIMENTAL RESULTS- DISCUSSION 88

4.5.1 Low Impact Fracture Toughness Polymers 89

4.5.2 Medium Impact Fracture Toughness Polymers 89

4.5.3 High Impact Fracture Toughness Polymers 91

4.6 ANALYSIS FOR HIGH TOUGHNESS POLYMERS 91

4.6.1 The Effective Crack Length Approach 91

4.6.2 The Rice's Contour Integral Approach 92

4.7 EXPERIMENTAL RESULTS FOR HIGH TOUGHNESS MATERIALS 94

4.8 THE IZOD TEST - EXPERIMENTAL PROCEDURE 95

4.8.1 Specimens and Notching 95

4.8.2 Testing Procedure 95

4.9 ANALYSIS OF THE 'HOD TEST DATA 96

4.10 IZOD TEST RESULTS - DISCUSSION 96

4.11 CONCLUSION ON THE CHARPY AND IZOD IMPACT TESTS OF

POLYMERS 98

4.12 SOME FACTORS AFFECTING THE IMPACT FRACTURE TOUGHNESS

OF POLYMERS 99

4.12.1 Effect of Molecular Weight on the Impact

Fracture Toughness of PMMA 99

4.12.2 Materials Tested 100

4.12.3 Molecular Weight and Relative Viscosity

Relationship 100

4.12.4 Experimental Procedure 101

Page

4.12.5 Experimental Results - Discussion 101

4.13 EFFECT OF MOISTURE CONTENT ON THE IMPACT FRACTURE

TOUGHNESS OF NYLON 66 102

4.13.1 Experimental Results - Discussion 103

CHAPTER 5: EFFECT OF TEMPERATURE ON THE IMPACT FRACTURE TOUGHNESS

OF POLYMERS 105

5.1 INTRODUCTION 105

5.2 SPECIMENS AND TEST PROCEDURE 106

5.2.1 Materials 106

5.2.2 Test Conditions and Apparatus 106

5.2.3 Specimens and Notching 107

5.3 EXPERIMENTAL RESULTS 108

5.4 THICKNESS EFFECT - THEORETICAL ANALYSIS 109

5.4.1 Plane Stress Elastic Work to Yielding and Gc

Relationship 112

5.5 YIELD STRESS AND TEMPERATURE - TEST PROCEDURE 114

5.6 EXPERIMENTAL RESULTS - DISCUSSION 114

5.7 CONCLUSIONS 116

.CHAPTER 6: EFFECT OF NOTCH RADIUS ON THE IMPACT FRACTURE

TOUGHNESS OF POLYMERS 117

6.1 INTRODUCTION 117

6.2 THEORETICAL ANALYSIS 118

6.2.1 Relation Between the Plane Strain Elastic

Work W and the Plane Stress Elastic Work pl

p2 121

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Page

6.3 SPECIMENS AND TEST PROCEDURE 123

6.3.1 Materials 123

6.3.2 Specimens and Notching Technique 123

6.3.3 Test Conditions 124

6.4 EXPERIMENTAL RESULTS 124

6.5 CONCLUSION 125

CHAPTER 7: CONCLUSIONS 127

Tables 129

Figures 143

APPENDIX I 245

I.1 THE RELATIONSHIP BETWEEN FRACTURE TOUGHNESS AND 245

ABSORBED ENERGY FOR THE IZOD IMPACT TEST 245

APPENDIX II: STRESS CONCENTRATIONS AND BLUNT CRACKS 247

II.1 INTRODUCTION 247

11.2 STRESSES AROUND AN ELLIPTICAL HOLE 247

11.3 STRESSES AROUND A BLUNT CRACK 249

Figure for Appendix II 250

References 251

Paper 1

Paper 2

NOTATION

a Crack length. In infinite plate, half crack length.

of

Crack and plastic zone length. •

A Ligament area.

B Specimen thickness.

cr

• . Count recorded.

cw/f :

Count lost due to windage and friction.

Co

Compliance for a zero crack length specimen.

Ca

Compliance for a cracked specimen of notch length a.

C : Total experimental compliance.

CT

Total theoretical compliance.

D Specimen width.

E • . Young's modulus.

G • . Strain energy release rate.

Gc

• . Critical value of G. Sharp crack fracture toughness.

Gel • . Plane strain fracture toughness.

Gc2

• . Plane stress fracture toughness.

GB

• . Blunt notch fracture toughness.

g • • Constant of gravity.

j Subscripts of tensor notation.

I Moment of inertia.

J Rice's contour integral.

Jc

Critical value of J.

K Stress intensity factor.

c Critical value of K for sharp cracks.

Kcl

Plane strain critical stress intensity factor.

c

• 2

Plane stress critical stress intensity factor.

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KB

: Blunt notch critical stress intensity factor.

L : Half span for three point bending and cantilever bending.

M : Average molecular weight.

: Mass of tup.

n. : Number of counts recorded.

P : Applied load.

✓ : Radial distance from the crack tip.

rp : Radius of Irwin plastic zone.

r p2 Plastic zone size under plane stress conditions.

T Temperature.

U Elastic strain energy per unit thickness.

u Displacement.

Elastic strain energy to fracture.

W' Kinetic energy of the fractured specimen (Charpy or Izod).

rat • • Energy to give first yielding.

/ • • Plane strain elastic energy to yielding.

WP2 • Plane stress elastic energy to yielding.

Coordinate.

Crosshead speed.

Coordinate.

Finite plate correction factor.

a, s : Constants.

: Surface energy.

Ab

: Bending deflection of a beam.

A : Shear deflection of a beam.

A : Total deflection of a beam (= Ab+ As).

• : Engineer's strain.

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: Relative viscosity.

e Angular measure.

: Poisson's ratio.

p : Notch tip radius.

a : Applied stress.

a : Yield stress. y

ac

: Stress at the tip of a blunt notch.

of : Stress at fracture.

Calibration faces for Charpy and Izod tests.

Angular measure.

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ABBREVIATIONS

ABS Acry)onitrile-butadiene-styrene

GPPS : General purpose polystyrene

HIPS : High impact polystyrene

HDPE : High density polyethylene

LDPE : Low density polyethylene

PC : Polycarbonate

PE : Polyethylene

PP : Polypropylene

PS : Polystyrene

PMMA : Poly(methyl methacrylate)

PTFE : Polytetrafluoroethylene

PVC : Polyvinyl chloride

SCF : Stress concentration factor

ZO : Zero offset

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INTRODUCTION

Impact strength is widely acknowledged to be one of the most

important properties of materials. It is considered as a major criterion

in the specification of the mechanical usefulness of any material, plastic

or metal. The importance of the impact test lies in the fact that it

provides a method of quality control, mainly for plastics, and also

provides design information for research and development. In quality

control it is used to determine the uniformity of production of a given

material. By design information is meant prediction of the relative

toughness of a material under practical conditions. Unfortunately,

although impact -testing is very popular and often discussed, it is

seldom fully understood. To quote Westover (1958) "... Out of the chaos

of two centuries of investigations of impact on metals and three decades

of impact applications to plastics, we can find little ground for

agreement among present day investigations. Notched and unnotched

specimens have been made in various shapes and sizes and have been

subjected to tensile, compressive, torsion and bending impacts.

Materials have been thrown, dropped and subjected to blows from hammers,

bullets, falling weights, pendulums, falling balls, horizontally moving

balls and projections from flywheels."

The impact strength of a material is assumed to be equivalent to the

loss in kinetic energy resulting from the momentum exchange between a

moving mass and the test specimen. In conventional types of impact tests

the impact strength is reported in terms of the energy, w, absorbed by

the specimen when it is struck and fails under the impact, and this is

generally divided by the ligament area A to give an apparent surface

energy W/4.

- 16 -

It is well known that such an analysis of the data is not

satisfactory, particularly since the parameter has a strong geometrical

dependence.

The main aim of the present research work is to examine the nature

of these geometrical effects for polymers in the Charpy and Izod loading

situations, and, by employing the concepts of fracture mechanics, to

deduce the critical strain energy release rate, Gc, directly from the

absorbed energy measurements. The work began with an attempt to

determine impact fracture toughness values using the Charpy and Izod

tests for various polymers at room temperature. Good correlation

between Charpy and Izod impact fracture toughness values would provide

a basis for studying the effects of temperature and notch tip radius on

the impact behaviour of polymers.

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CHAPTER 1

LITERATURE SURVEY

1.1 HISTORICAL INTRODUCTION TO IMPACT TESTING

Studies on the subject of impact testing can be traced back over

two centuries. A monumental report on impact testing up to 1948 was

presented by Lethersich (1948) in which more than 200 references were

quoted. Historically, impact testing originated when it was realised

that metals which appeared satisfactory when tested by the usual methods

sometimes failed when subjected to shock conditions. The impact test

was able to discriminate between good and faulty steels, and specification

of a minimum impact strength fora given size of specimen was sufficient

to provide a rational quality evaluation.

The history of impact testing for metals goes back to 1734 when a

German metallurgist, Swedenborg, tested iron bars by throwing them

against a sharp edge. In America in 1824 T. Tredgold theoretically

examined the resistance of cast iron beams to impulsive forces, and in

1874 R.H. Thurston computed the impact resistance to single and repeated

blows from the area under the static stress-strain diagram. Events in

Europe are described by Charpy (1901) at the Conference of Testing

Materials. In 1901 he designed his pendulum machine, which could be

used on specimens with three point bend or cantilever-type loading.

He then discarded the cantilever support because it was thought that the

clamping pressure would affect the results, and the three point bend

support was used and named after him. In Britain Izod (1903) developed

his pendulum machine in which one end of the notched specimen was clamped

in a vice and the other end struck by a hammer so that the notch was

opened. The Izod support is, of course, of the cantilever form and

- 18 -

although named after him, it was originally designed by Charpy.

Perhaps the most significant contribution to the subject of impact

testing of metals was made in 1923, when P. Ludwik discovered that two

types of fracture could be distinguished. If failure occurs in shear,

ductile fracture results, but if the cohesion between the molecules is

broken, brittle fracture results. In 1925, Moser (1925) was the first

to measure the volume of the plastic deformation around the notch, and

he found it to be proportional to the impact strength and independent

of the specimen size. So, for the first time, the impact strengths of

specimens of different sizes could be compared.

Until 1926, impact testing was confined to metals and particularly

to steel, but development of plastics (mainly for electrical insulation)

led to the application of impact testing to these materials.

In this manner, the controversial subject of impact testing of

plastics was introduced into the world of science and engineering.

1.2 IMPACT TESTING OF PLASTICS

One of the many properties of a plastic material which influence its

choice for a particular article or application is its ability to resist

the inevitable impacts met in day to day use. Impact tests attempt to

rank materials in terms of their resistance to breakage. Impact testing

• of plastics over the last 50 years has assumed great practical importance

due to the greatly increased use of these materials in everyday life and

in many engineering applications; however, argument and confusion among

the various investigators has grown proportionally.

The complexity of impact testing results from a number of factors.

There is a remarkably large number of different impact testing machines

and test methods. All the various types of tests measure different

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quantities, some of which are not clearly defined or understood. Tests

are made on specimens of various sizes and shapes. The specimens are

broken under different kinds of stress distributions and under different

impact velocities. Variations in the specimens themselves make it

difficult to obtain reproducible results. For example, specimens may

have varying degrees of molecular orientation, which may be parallel or

perpendicular to the stresses developed during the impact test. Plastics

are considered to be notch sensitive materials (some more than others),

so that small variations in the notch tip radius can cause wide

divergence of the impact strength values obtained in the test. Humidity

and temperature control of the laboratory where the impact test is

performed is also important, as plastics are sensitive to environmental

conditions, any variation of which may result in a different impact

strength value. A typical example is nylon which tends to absorb.

moisture from the environment. This can have a remarkable effect on

the impact behaviour of the material. (The effect of moisture on the

impact behaviour of Nylon 66 is discussed in section 4.13.)

1.3 SPECIFIC IMPACT TESTS

Many methods of measuring impact strength are in use in the plastics

industry. These methods can be broadly divided into two categories:

1. Excess energy methods

2. Limiting energy methods

The essential characteristic of the excess energy method is that the

kinetic energy of the striker is much greater than the fracture energy

of the specimens, so that the velocity of the striker can be assumed to

;. 20 -

be constant during impact. The energy absorbed is determined from the

loss of kinetic energy or the decrease in angular velocity of a flywheel

striker. In limiting energy methods, the kinetic energy of the striker

is adjusted to the point at which only a fraction of the specimen,

usually a half, is broken. A simple form of limiting energy tests

consists of dropping an article from a range of heights. In

conventional tests it is more common to alter the mass of the striker

rather than the impact velocity.

1.3.1 Limiting Energy Impact Testing Methods

The falling weight test or drop dart test falls into this category.

It is usually carried out on fabricated or semi-fabricated articles such

as sheet or piping. In the British Standard version of the test

(BS 2782:1970) the specimens are 24" discs cut from sheet, and are freely

supported on a hollow steel cylinder of internal diameter 2". The

striker consists of a 1-" diameter steel ball attached to a weight carrier,

falling freely between guides from a height of 24". • Repeated trials of

differently weighted strikers are made until the minimum weight to

produce penetration is obtained. An alternative method of repeated

trials is sometimes used in which the same weight drops from increasing

heights. An obvious disadvantage of the falling weight impact test is

that a large number of trials and samples are needed for a proper

material assessment.

1.3.2 Excess Energy Impact Testing Methods

There are three main types of pendulum impact tests that are

considered to be excess energy methods:

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1. The Charpy test, *which employs specimens supported as a

three point bend bar.

2. The Izod test, which employs specimens supported as a

cantilever.

3. The tensile impact test, which employs dumbell specimens

loaded in uniaxial tension.

The Izod and the.Charpy pendulum tests were the earliest impact tests to

be standardised for plastics and they are still the most widely quoted.

This is not surprising, as these tests were originally derived from

traditional tests for metals and in any application where plastics were

to replace metals, comparative test data was required. However, the

Izod and the Charpy tests suffer from a number of disadvantages. Both

are very sensitive to errors in forming the notch, and any small

variation of the notch tip radius could affect the result. Test values

must be obtained from a standard specimen geometry and can be compared

on the basis of that standard specimen only. The complexity of the

stress distribution around the notch is another factor that creates many

difficulties in analysing the data, since very little theoretical work

has been done on the bending of plastic materials under impact loads.

Lee (1940) showed that the deflection curve of a beam under impact deviates

widely from the static deflection curve. He stated: "... A material

test carried out at high speeds may be markedly influenced by plastic

wave propagation effects. In such a case a variation of strain occurs

along the test specimen, and the stress-strain relation cannot be

determined from measurements made on the specimen as a whole."

Finally, the broken half error, or the so-called "toss-factor", has

to be considered in the Charpy and Izod tests. In the case of the Izod

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test, the broken portion of the specimen is thrown forward by the

pendulum and in the case of the Charpy test the broken halves of the

specimen are ejected after impact. Thus, both tests involve some form

of energy loss dissipated as kinetic energy by the broken specimen.

This portion of energy loss is included in the result, so the actual

energy to failure should be less than the total energy recorded.

Since Izod and Charpy test originated for metals, metallurgists paid

little attention to this error, as it appeared to be small in comparison

to the high impact strength of these materials. For plastics, however,

because their impact strength is relatively low, the broken half error

can be considerable. Many investigators have favoured the tensile

impact test. Evans (1960), Maxwell (1952), Bragaw (1956), Westover

(1958) and (1961) argued that the tensile test is a more meaningful test,

giving results that are easier to analyse than those of the Charpy or of

the Izod test. The main attraction is that the stress system is simple,

and the strain rates are known.

1.4 TENSILE IMPACT TEST

The tensile impact test is a simple modification of the Izod test

(ASTM D1822-1964). The modification consists of replacing the Izod vice

with one that holds the fixed end of a dumbell specimen and attaching a

free metal grip to the other end. The pendulum is adapted so that it

strikes the metal grip on swinging and therefore breaks the specimen in

simple tension. If the effective gauge length of the specimen is known,

the approximate strain rate may be calculated from the pendulum velocity.

1.5 CHARPY AND IZOD TESTS

The Charpy and the Izod tests are excess energy tests in which a bar

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is broken in flexure by a blow from a pendulum type striker. A scale

records the reduction in the amplitude of the pendulum swing and hence

the energy to break the specimen. In the Charpy test the notched

specimen is supported (horizontally) and is hit at the centre behind

the tip of the notch by the pendulum striker, so that fracture takes place

by three point bending.

In the Izod test, one end of the notched specimen is firmly clamped

in the vertical position in a vice and the pendulum striker hits the other

end horizontally.

Both test methods employ a range of pendulum heads with different

masses so that various plastics having a range of impact strength can be

tested. The most commonly used apparatus for the Charpy testing of

plastics is the Hounsfield impact tester of which Vincent (1971) gives

a brief description.

Some tests are carried out on unnotched specimens, but most specimens

are notched centrally. The main purpose of the notch for both methods

of testing is to•concentrate stress at its tip and hence locate the point

of fracture initiation. The Izod test is performed in two slightly

different forms, as a British Standard (BS 2782:1970) and as an American

Standard (ASTM D256-56:1961).

Table 1.1 gives specimen dimensions for the Izod test for both the

British and American specifications, as well as the dimensions for the

standard Charpy specimen. The main difference between the BS and ASTM

Izod specimens is that of the notch radius. A notch radius of 0.040"

is specified for BS specimens whereas a notch of 0.01" characterises the

ASTM specimens. Since the ASTM notch is sharper, it is more likely to

produce plane strain conditions in the specimen, so that crack initiation

energies are lower for some plastics which are very sensitive to notch

24

tip radius. Thus, a significant increase in the impact strength can be

expected when tested to British Standard specifications. Horsley (1962)

compared the BS and ASTM Izod impact strengths of a number of plastics.

He found that the BS test gives a higher impact strength for all the

plastics tested. However, he observed that the increase was more

noticeable for some Plastics than for others.

1.5.1 The Effect of Notch Tip Radius on the Impact Strength

When plastics with a high degree of notch sensitivity are used, care

should be taken in design to avoid any points of stress concentration,

whereas using plastics with a low degree of notch sensitivity such

factors are not so critical. Stephenson (1957) examined the effect of

notch tip radius on the impact strength of PMMA by testing specimens with

keyhole notches of various notch radii, and compared the data with those

obtained from ASTM and BS specifications. The data indicated an

approximately linear increase in the impact strength with notch tip

radius. The effect of notch tip radius on the impact behaviour of

plastics has also been examined. Vincent (1971), Reid and Horsley

(1959), Hulse and Taylor (1957), Adams et al (1956).

Lethersich (1948) attributed the increase in impact strength with

notch tip radius for a given specimen size and notch depth to two factors;

the greater stress concentration that arises with sharper notches, and

the increase in the spatial stress ratio* as the radius of the notch

decreases. The latter increases the probability of brittle failure.

Petrenko (1925) found experimentally that the impact strength I and the

* The ratio of the triaxial tensile stress to the shear stress.

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notch radius p could be related by the empirical equation:

I = aDpVT f SD B2

where D and B are the width and the thickness of the specimen and a and

are constants.

Inglis (1913) showed that the tensile stress at the root of the

notch is given by:

ac

= a (14- C Va/p)

(1.2)

where a is the applied stress, a is the notch depth and p is the notch

tip radius.

The constant C was found to be nearly 2. Equation (1.2) indicates

that any increase in the notch tip radius should reduce the impact.

strength. The ratio of stress at the root of the notch to the applied

stress (a /a) is defined as the "stress concentration factor" (SCF).

1.5.2 Notch Stress Distribution for Charpy and Izod Tests

Although the notch serves the same function for both tests, the

stress distribution round the notch varies considerably. Coker (1957)

examined photoelastically the general characteristics of the stress

distribution round the notch tip for both tests, and observed a

dissimilar distribution. An aslymetrical stress distribution was

observed for the Izod test. This asiymetry was believed to be due to

the applied clamping pressure since it resulted in additional stress

round the notch tip area. It must be concluded that the Charpy and the

Izod impact strengths as defined by conventional methods, WA, cannot be

directly compared since they do not measure exactly the same quantity.

-26-

This is a very important point in the author's opinion, and it can be

considered responsible for the inconsistency between the Charpy and Izod

test data. This is the main reason for the introduction of the fracture

mechanics approach into the field of impact testing, since a single

parameter, the "fracture toughness", Gc, can be deduced from any test

(Charpy or Izod) and it is characteristic of the material and independent

of the loading configuration. The fracture mechanics approach will be

discussed in section 1.10.4.

1.5.3 Effect of Clamping Pressure for the Izod Test

The main complication of the Izod test over the Charpy test is the

effect of clamping pressure on the results. BS and ASTM do not specify

the clamping pressure to be applied to the test specimen.

Stephenson (1957) performed a series of tests in which the clamping

pressure was varied. The results indicated that there is a linear

decrease of impact strength with increasing clamping pressure, which

could be represented to a fair approximation by the formula:

Impact Strength (ft.lb/in of notch) = 0.362 - 0.000024 P'

(P!= clamping pressure in lb/in2)

Adams et al (1951) examined the effect of clamping pressure on the

impact strength of several plastics and found that some plastics are more

sensitive to clamping pressure variations than others. He noted that

styrene showed a consistent decrease in impact strength with increasing

the clamping pressure. Therefore, co-operating laboratories should

agree on a means of standardising the gripping force, for instance by

-27-

using a torque wrench on the screw of the specimen vice.

1.6 BRITTLE AND DUCTILE IMPACT FAILURES

Generally all plastics under impact conditions fail in a ductile

(tough) or brittle manner. Horsley (1962) relates each type of fracture

failure to the stress level at crack initiation with the yield stress of

the material. In the case of a ductile type of failure the material in

the fracture area yields and flows, whereas in the brittle case, only

small elastic deformations take place prior to fracture. The existence

of a ductile or a brittle type of failure depends upon whether under

specific experimental conditions, the specimen yields prior to crack

initiation or whether the crack initiates before the yield stress is

reached. A brittle type failure occurs if the stress at crack

initiation is lower than the yield stress, as the elastic energy stored

in the sample at the moment of crack initiation is usually sufficient to

propagate the crack. Conversely, if the crack initiation stress is

higher than the yield stress, a ductile failure results. So if, during

any impact test, the load/deflection curve were recorded, a material

which failed in a brittle manner would give a straight line relationship

with fracture occurring at the maximum recorded load as shown in

Figure 1.1, whereas for a ductile failure a curve would be obtained with

fracture occurring at some point after the maximum load had been recorded.

The area under each centre could give a measure of the impact strength.

Therefore, any factor that affects the yield strength, the crack initiation

stress or both can have an influence on the type of failure and the

consequent impact strength value obtained. Such factors may be either

structural changes (e.g. preferred orientation or surface imperfections)

or changes in the experimental conditioning of the test to which the

-28-

specimen is subjected (e.g. humidity and temperature variations or

some environmental changes such as the effect of various chemicals).

The effect of temperature on the impact strength of plastics, and the

brittle-ductile transition type of failure are discussed in Chapter 4.

1.7 IMPACT STRENGTH - ENERGY TO FRACTURE

In the pendulum type of impact tests the energy absorbed in

fracturing the specimen is measured by the excess swing of the pendulum.

Telfair and Nason (1943) defined the "energy to break" the specimen as

the sum of energies consumed by several mechanisms taking place during

the test. They summarised these several forms of energy as:

1. Energy to initiate fracture of the specimen.

2. Energy to propagate the fracture across the specimen.

3. Energy to deform the specimen plastically.

4. Energy to eject the broken ends of the test specimen.

5. Energy lost through vibration of the apparatus and at

its base through friction.

1.7.1 Energy to Initiate and to Propagate Fracture

Lethersich (1948) discussed the opinions of various workers who

considered that the energy required to fracture a specimen is made up of

two parts: the energy to initiate the fracture and the energy to

propagate the fracture. He stated that opinion is divided as to whether

only the first part is required or both. About a century ago F. Kick

first showed that the energy required to initiate fracture was

proportional to the volume of the specimen. Some years later Charpy

-29-

suggested that the energy required to separate the two halves of the

specimen is proportional to cross-sectional area. From the above

considerations, the total energy to fracture would he given by:

I =a1/4- S S (1.3)

where V and S are the volume and cross-section of the specimen, and a

and s are constants. It was shown experimentally that for brittle

materials 13 was zero which suggests that the propagation energy is

negligible in this case, whereas for ductile materials the constant a

becomes small.

Stephenson -(1961) showed that the above equation is true with a

slight modification in the initiation energy term aV. He showed

experimentally that the elastic energy stored in the specimen at the

time of breakage is available to propagate fracture before imparting

kinetic energy. If, however, there is not sufficient elastic energy

available, then for complete fracture, extra energy will be absorbed

from the pendulum. The energy that will then be measured will be the

sum of the energy to propagate the crack and that part of the stored

elastic energy which has been lost. The energy required for crack

propagation will be proportional to the area of the q-ew surfaces

formed, i.e. the cross-sectional area of the specimen. The stored-up

elastic energy is proportional to the volume of the specimen, therefore

if it is assumed that the energy lost is proportional to the stored-up

energy it will also be proportional to the volume. By this mechanism

the measured impact energy is given as the sum of the energy required for

crack propagation and the stored-up energy which has been lost.

Using this hypothesis, the product aV gives the amount of the crack

- 30 -

initiation energy which has been lost. Therefore, the crack initiation

energy is considered to be a criterion for impact failure. With

notched specimens which differ only in the notch radius, the energy for

crack propagation will be the same for every notch radius, whereas the

crack initiation energy will decrease with decrease in the notch radius.

Therefore, there will be a critical radius above which the measured value

will increase with notch radius because crack initiation is measured, and

below which there will be a very little dependence on the radius because

crack propagation is measured. Therefore, meaningful data on crack

initiation are obtained only if the notch radius is above a critical value.

For a PMMA Izod specimen of standard dimensions, the critical radius was

found to be aboilt that of the ASTM notch (i.e. 0.010").

Vincent (1971) states that there are clearly at least two different

physical properties (i.e. crack initiation and crack propagation energy)

underlying the impact behaviour. He considered the results of tests

which were performed on samples of rigid polyvinylchloride (PVC) and

acrolonitrile-butadiene-styrene (ABS) at room temperature with sharp

notches (tip radius 0.25 mm) and with blunt notches (tip radius 2 mm).

When the sharp notched specimens were tested it was found that ABS had a

much higher impact strength, but when the blunt notched specimens were

tested PVC had a higher impact strength. He explained these results

assuming that both crack initiation energy and crack propagation energy

can contribute to the measured impact strength. By this interpretation,

PVC must have a relatively high crack initiation energy to account for

its good behaviour with blunt notches but a low crack propagation energy

to account for its poor behaviour with sharp notches. Conversely, ABS

has a relatively high propagation energy but a low crack initiation energy.

It is clear that Vincent's explanation coincides with Stephenson's,

- 31 -

that is to say that crack initiation energy is the predominant factor in

the blunt notch case. Vincent states that when a material has a low

crack propagation energy, the impact strength measures only the crack

initiation energy; once the crack has initiated, the stored elastic

energy is sufficient to propagate the crack completely across the specimen

without absorbing further energy. The crack propagation energy is more

difficult to measure. It can be estimated in the special case of a

sharply notched specimen only partly broken in the test. In this case

the ratio of the energy lost by the weight of the pendulum to the area of

new surface created, provides an upper limiting estimate of the crack

propagation energy.

1.7.2 Energy Lost in Plastic Deformation

Although the notch in the Charpy and Izod test has mainly the -purpose

of concentrating the stress and preventing plastic deformation, it is

quite usual for plastic deformations to take place during the impact

process resulting in a ductile type failure. In this case the specimen

may break (or may not break completely - hinge failure) with obvious signs

of permanent macroscopic deformations at the fracture surface. A

whitened region observed in the fracture surface indicates that some

plastic deformation has taken place. The amount of whitening can be

varied considerably by varying some experimental conditions such as the

temperature. Generally, the impact energy increases as the amount of

whitening increases, resulting in very high impact strength values.

Vincent (1971) in his monograph discusses various types of fracture in

which plastic deformations have taken place during various stages of the

fracture process. These types can be summarised as:

- 32-

1. The specimen yields at first round the crack tip region,

a whitened region is formed and the crack continues to

propagate within this region. The specimen may break or

may not, depending on the material's resistance to crack

propagation.

2. The case in which the crack initiates and propagates in a

brittle manner. No whitening is observed in the fracture

surface but suddenly the material yields and crack

propagation stops, the ligament forming a flexible hinge.

In this case the material is significantly more resistant

to crack propagation than to crack initiation.

3. Finally, the case in which the specimen yields at first but

then the crack propagates throughout the entire fracture

area in a brittle manner, resulting in a brittle type of

fracture with a small whitened region round the crack tip.

In this case the material is more resistant to crack

initiation than to crack propagation. •

If any one of these types of fracture occurs in an impact test a high

impact energy value can be expected because of the yielding process.

Energy lost in plastic deformation is included in the measured impact

energy value.

1.7.3 Kinetic Energy of the Broken Half

Kinetic energy of the broken half, in the case of the Izod test, or

of the two broken halves in the case of the Charpy test, is one of the

most important factors assumed to contribute to the measured impact

strength. In the Izod test the broken portion of the specimen is thrown

-33-

forwards by the pendulum, taking"some energy from it. A similar energy

loss occurs in the Charpy test; in this case both broken halves of the

test specimen are ejected after impact. This energy should not be

included in the impact strength value and contributes to what is referred

to as the "broken half" error or sometimes as the "toss factor". In

order to correct the Izod impact strength value for tossing of the broken

half, the broken half of the specimen is replaced and struck again.

The energy to re-toss the broken half is considered to be the tossing

error. This method was first introduced by Zinzow (1938). The main (ICS —

advantage of this method is that the actual tossing velocity for a specimen

usually differs from the velocity of a previously broken sample. Another

point to be considered is that the above method of correction does not

include rotational energy. Lethersich (1948) noted that rotational

kinetic energies as high as / the value of the linear kinetic energy have

been reported in the Izod test during the breaking stroke.

Callendar (1942) estimated the broken half error for the Izod test

by replacing the broken piece and finding the energy required to throw it

the same distance as it flew in the test. He observed, however, that the

broken half of an ebonite specimen went further in the test that it was

knocked when it was replaced. He attributed this difference to the

kinetic energy derived from the stored-up elastic energy which should not

be regarded as an error. He stated that there is always some stored

elastic energy in a stressed specimen and there is the possibility that

some kinetic energy is derived from it. Stephenson (1961) aimed to find

the energy which would just be enough to crack the specimen. In this

case there would be no broken half error. He performed the standard Izod

test for poly(methyl methacrylate) (PMMA) in which the available energy

was varied by changing the starting height and therefore the impact

-34-

velocity. He found that when the specimen was broken, the broken half

was projected forward with some velocity, even in the case when the

available energy was just sufficient to break it. This indicates that

part of the kinetic energy comes from the stored elastic energy. His

results indicated that the height reached by the broken half is

approximately the same, irrespective of the impact velocity, whereas the

distance travelled increases with the impact velocity. This behaviour

is consistent with the assumption that the broken half always leaves the

pendulum with the same velocity relative to it. He calculated the

final velocity of the pendulum from its final energy and so obtained

corrected values for the distance travelled.

He found a -characteristic value for the height and distance to which

a broken half will go, if allowance is made for the horizontal component

of velocity of the pendulum. Stephenson's results indicate that the

energy in the broken half of the Izod specimen consists of two components.

One component of energy which is characteristic of the specimen, and

should not be considered as an error when included in impact energy, and

a second component of energy imparted by the pendulum, which should be

considered as an error. Therefore, the correction will be overestimated

if the total kinetic energy of the broken half is used.

Maxwell and Rahm (1949) presented a method of impact testing which

eliminates the toss factor in the Izod test. The standard Izod-type

specimen is attached to the periphery of a flywheel that can provide a

wide range of loading rates. An anvil obstructs the path of the free

end of the specimen and fractures it and the energy removed from the

flywheel is determined. Since the specimen is in motion prior to the

impact, it contains the kinetic energy necessary to eject itself after

fracture, and thus there is no energy lost from the flywheel for the

- 35 -

toss factor. Burns (1954) introduced the Dozi (Izod spelt backwards)

impact testing machine which differed from the Izod tester in that the

Dozi-type specimen is clamped in the pendulum. This gives results

similar to the Maxwell's machine as it eliminates the toss factor.

1.7.4 Energy Lost in the Apparatus

Energy losses due to vibration of the apparatus may be large in

testing metals but are apparently negligible for plastic materials. This

assumption is based on a statement given by Westover (1958) who pointed

out that the energy lost by the pendulum during an impact test is shared

by the specimen and the machine in an inverse ratio of their elastic

moduli. That 1s to say, the greater the modulus of elasticity of the

specimen (as in the case of metals) the greater will be the proportion

of the energy absorbed by the machine, and the smaller the modulus of

elasticity of the specimen (as in the case of plastics) the smaller will

be the proportion of the energy absorbed by the machine. Friction losses

are largely eliminated by careful design and operation of the apparatus.

For example, if was pointed out that it is important, in pendulum type

machines, that the centre of percussion of the pendulum coincides with the

point of impact. Itthis condition is not fulfilled, then energy is lost

from shock in the bearings at the top of the pendulum. Lethersich (1948)

suggested that losses due to friction at the bearings of the pendulum, due

to friction at the idle pointer, and losses due to windage can usually be

estimated by performing a blank test, i.e. a test in which the specimen is

omitted. The measured energy loss gives the magnitude of these errors.

Bluhm (1955) assumed a model in which the force acting on the pendulum

was the same as that acting on the specimen. He showed that the

discrepancies in the measurement of energy absorption from one machine to

-36-

another may be attributed to:the flexibility of the impact machine and

that flexibilities can give rise to the differential behaviour of high-

and low-strength specimens having the same toughness. He concluded that

to ensure adequate design the stiffness of the pendulum should exceed a

certain minimum value.

1.8 EFFECTS OF TEMPERATURE ON IMPACT STRENGTH

The physical properties of polymers in general show a strong

dependence on temperature. Impact strength is not an exception.

Although it is obvious that in the majority of practical applications the

impact strength at room temperature is more important, graphs of impact

strength against temperature could be very useful since they could give

a much better understanding and appreciation of the polymer impact

behaviour than a single temperature value could do.

Vincent (1971) considered the temperature effect on the Charpy

impact strength of three polymers (PMMA, polypropylene (PP), and rigid PVC).

He tested unnotched and notched specimens with two different notch tip

radii, p = 0.25 mm and p = 2 mm. His results indicated that although a

wide variation in numeric values was immediately apparent, there were

nevertheless some marked similarities in the behaviour of the polymers

tested. Their impact strength showed a low value at low temperatures

(less than -20°C) with the value staying almost constant with further

decrease in temperature. With the exception of PMMA, when tested with

sharp notches (p = 0.25 mm), all polymers showed a very sudden increase

in the impact strength, during a quite small increase in temperature.

The temperature at which this increase occurred was different for the

three polymers and it also differed from one notch radius to another for

the same polymer. He examined in detail the behaviour of the polymer

-37-

within this relatively narrow range of temperature, and the appearance of

the specimens after testing showed that their behaviour changed from

brittle at lower temperatures to ductile at higher temperatures. He

proposed that this important temperature region might be called the

"tough-brittle" transition region. Reid and Horsley (1959) compared the

Charpy notched impact strength with the falling weight impact strength

of various polymers tested in the temperature range from -40°C to +60°C.

They found that the variation of the Charpy notched impact strength with

temperature was very different from that of the sheet in the falling

weight test. Although a good correlation was observed with both types

of test at low temperatures (the impact strength values were low and

fairly constant), the temperature at which the sudden rise in the impact

strength occurred was different for both tests. However, they reported

that three polymers (cellulose nitrate, styrene-acrylonitrile rubber and

high impact polystyrene (HIPS)) showed a very similar impact behaviour

with temperature for both tests. They stated that this agreement was due

to the fact that these three polymers were identified as insensitive to

notch radius. It would seem, therefore, that notch sensitivity is

responsible for changes in the material properties in the falling weight

test. Horsley (1962) reported a tough-brittle transition region for

unplasticised PVC at about 10°C. Below this temperature a significant

drop in the impact strength was observed. He pointed out that as the

transition from tough to brittle type failures is accompanied by a marked

reduction in the impact strength of the material, the major purpose of

impact testing should be to ascertain the conditions under which such a

transition occurs, so that brittle type failure can be avoided in practice

if possible.

One generalisation frequently made, Turley (1968), is that any polymer

38 -

at a temperature above or near its glass transition temperature is ductile

(i.e. it has a high impact strength), whereas any polymer at a temperature

well below its glass transition temperature is brittle (i.e. it has a low

impact strength). This assumption created doubts when it was realised

that some polymers behaved in a more complicated manner and that the above

generalisation could not be true, Boyer (1968). It was then recognised

that most polymers had transitions and relaxations lying below the glass

transition temperature and that those secondary transitions appeared quite

important in polymers which were ductile below their glass transition

temperature.

1 .9 THERMAL STABILITY - MECHANICAL LOSSES OF POLYMERS

Over the years the thermal stability of polymers, the temperature

transitions and the relaxation processes have been well examined and

discussed in detail by various investigators in many texts and in a

large number of published articles. The aim of the present review is not

to consider molecular mechanisms and relaxation processes in polymers, but

rather to refer to some views on how the impact behaviour of various

polymers could be related to the relaxation processes and damping peaks.

Figure 1.2 shows a schematic representation of three relaxation spectra

of the same polymer, measured by three different test methods at three

different frequencies (1 Hz, 1000 Hz and 107 Hz), all as a function of

temperature (after Boyer (1968)). Generally, the same energy absorption

peaks are shown up by all three methods, moving to higher temperatures as

the frequency is increased. The low frequency dynamic mechanical test

illustrates the following characteristics of the absorption spectra:

1. The melting point, TM, is the highest observed transition

- 39 -

referred to as the primary transition.

2. The glass transition temperature, TG, frequently referred

to as the a-relaxation. It is observed at a considerably

lower temperature than the melting point. This type of

relaxation corresponds to the motion of a large number of

carbOn atoms about the main polymer chain.

3. The strong T < TG relaxation is a second order relaxation

frequently referred to as the (3 or y relaxation. This type

usually involves motion of a small number (4 to 8) of

carbon atoms about the main polymer chain. It is believed

that this is the relaxation process related with the high

impact strength of some polymers at temperatures below TG.

Many investigators have considered the possibility that

there is some relation between the short-term toughness of

polymers as defined by their impact strengths and their

moduli and mechanical losses determined by dynamic

mechanical experiments. An excellent historical review

on the dependence of mechanical properties on the molecular

motion in polymers is given by Boyer (1968). In this

article over one hundred references are quoted.

1.9.1 Dynamic Mechanical Losses and Im act Strength of Polymers

Heijboer (1968) reported the impact strength of various polymers as a

function of temperature and investigated the possibility of a

relationship between the impact strength and the damping peaks. For PMMA

he observed two damping peaks at -80°C and +10°C, respectively, for 1 Hz

frequency. The damping peak at +10°C is probably the well known (3-peak

-40-

for PMMA which starts as low as -50°C, Jenkins (1972). The impact

strength of PMMA was found to increase slightly in the -80°C temperature

region, whereas in the +10oC temperature region no change in the impact

strength was observed. The impact strength for polycarbonate (PC)

showed a broad damping peak at about -110°C and the impact strength

transition was observed at about -130°C. Therefore, for PC the impact

strength transition could be well related to the damping peak. For

polyoxymethylene a good correlation between the impact strength transition

and the damping peak was observed at about -70°C, whereas for high density

polyethylene (HDPE) the damping peak at -120°C was not accompanied by an

increase in the impact strength; the impact strength transition was

observed at a somewhat lower temperature instead. From the behaviour of

these four polymers it might be concluded that the molecular movements

may have an influence on the impact behaviour. However, the exact

location of the impact strength transition cannot be predicted from the

location of the damping peak. A point that has to be emphasised is that

the damping values have been reported for 1 Hz frequency and, since impact

failure occurs in a shorter time, one might expect a better correlation

at higher frequencies.

Oberst (1963) studies the correlation between impact strength and

dynamic mechanical properties for PVC at 1000 Hz frequency. He reported

that the high impact strength for PVC at room temperature arises from the

s-relaxation. It had been previously shown that PVC shows a low, broad

s-peak at about -30°C to -50°C. This rapidly moves to higher

temperatures with increasing frequency and disappears on the addition of

plasticiser. From the last statement it follows that if the high impact

strength of PVC at room temperature is directly related to the damping

peak, one should expect the impact strength to drop on adding small amounts

-41 -

plasticiser. Bohn (1963) reported a drop in the impact strength of PVC

from 3 (ft.lbs) to 0:3 (ft.lbs) on adding up to 10% of plasticiser

(dioctylphthaiate). Vincent (1960) also studied the impact strength of

PVC as a function of plasticiser content and observed a minimum at about

10% plasticiser.

Special attention has been given to the impact behaviour as a

function of temperature for two phase polymers, such as the rubber

modified polystyrene. The addition of rubber to the polystyrene phase

markedly improves the impact behaviour of the polymer. It has been

observed that rubber modified polystyrene has several times the impact

strength of crystal polystyrene with the degree of improvement dependent

on three variables. The amount of rubber, its type, and the method of

its addition. Boyer (1968) represented schematically the mechanical

loss curves for unmodified and rubber modified polystyrene as a function

of temperature. The point of interest is the fact that for rubber

modified polystyrene an additional peak was observed (rubber peak) at

about -50°C in addition to the f3-peak for polystyrene at the much higher

temperature of about +50°C. It is believed that the rubber peak is

related to the high impact strength of rubber modified polystyrene at

quite low temperatures. However, the mechanism of rubber reinforcement

of impact strength in polystyrene is controversial (Schmitt and Keskula

(1960), Arrends (1966)) and is not within the scope of this review.

Bucknall and Smith (1965) commented on the temperature dependence of the

impact strength of rubber modified polystyrene and he identified three

regions as a function of temperature:

a) Below -30°C the impact strength is very low and almost

constant. The specimens are brittle.

-42-

b) From -30°C to +40°C a small but increasing amount of

stress-whitening is observed near the notch and the

impact strength rises steadily.

c) Above +40°C a dense stress-whitening occurs at the fracture

surface and both the impact strength and the extent of

whitening increase rapidly with temperature. The

immediate cause of the impact strength increase is

believed to be the second order transition in the rubber

(rubber peak), whereas the continuous increase at

temperatures well above this transition region was

expected to be due to the activated nature of crazes.

Vincent (1974) considered how far the impact strength and the

damping peaks could be related in polymers, and he presented some evidence

relating damping peaks in brittle and impact strength to relaxation

processes. He stated that careful selection of the notch tip radius

may be needed to demonstrate peaks in the Charpy impact strength of

polymers associated with peaks in the dynamic losses. He explained that

if the notch is too blunt, the specimens become tough in the region of

dynamic loss and the peak in the impact strength appears as a slight bump

on the low temperature side of the steeply rising impact strength curve.

. If the notch is too sharp, the peak in impact strength may not appear.

To justify the last statement he tested polycarbonate with sharp notches

and with i mm radius notches and looked for any relation between mechanical

losses and impact strength as a function of temperature. The mechanical

loss curve showed a peak at about -70°C. The impact strength with very

sharp notches was found to be constant between -100°C and +60°C and was

apparently unaffected by the f3-process. In constrast, the impact

-43-

strength with 4 mm radius notches was nearly doubled between -100°C and

-40°C, presumably because of the presence of the R-peak. Between -40°C

and 0°C the impact strength increased even more rapidly towards the very

high impact strength at +20°C.

Vincent (1974) also tested polyoxymethylene with 4 mm radius notches,

and in this case the damping peak at -50°C did not coincide with the

impact strength peak observed at a somewhat much lower temperature. His

results on PTFE, tested with very sharp notches, showed a great similarity

between damping peaks and impact strength peaks as a function of

temperature.

From the above review on the relation between impact strength and

mechanical losses in polymers, the author concludes that low temperature

loss peaks in polymers are neither a necessary nor a sufficient condition

to guarantee peaks in their impact strength.

1.10 FRACTURE MECHANICS APPROACH TO IMPACT

The results from conventional impact testing are expressed in terms

of the specific fracture energy WA, where W is the energy absorbed to

break the notched specimen and A is the cross-sectional area of the

fractured ligament. It has been previously discussed that such an

analysis of the data is not satisfactory due to the fact that the

parameter riV4 is very dependent on the dimensions of the test specimen,

the notch length and the type of impact test used. This classical

method of analysis provides no correlation between Charpy and Izod

impact strengths for the same materials. Some recent publications

(Marshall et al (1973), and Brown (1973)) showed that assuming linear

deformations, the linear fracture mechanics theory can be extended to

impact data and Gc, the fracture toughness parameter, can be deduced

- 44 -

directly from the absorbed energy measured.

A full literature review on the theories of fracture mechanics will

not be presented here, since many good reviews are available

(e.g. Liebowitz (1968), Turner (1972), Hayes (1970)). The purpose of

this section is to give a short summary of the derivations of parameters

which are used in the main part of the thesis to describe impact failure

in polymers from a fracture mechanics point of view.

1.10.1 The Griffith Approach

The fundamental concepts of fracture mechanics were proposed in the

early 1920's by A.A. Griffith (1921) who explained why materials fail at

stress levels well below those that could be predicted theoretically from

considerations of atomic structure. He carried out several studies of

brittle fracture using glass as a model material and he suggested that all

real materials were permeated with small crack-like flaws which act as

localised stress raisers. He argued that at the tips of these flaws

stresses could be raised to'such an extent that the material's

theoretical strength would be reached and failure would result. Thus,

Griffith considered fracture to be dependent on the local conditions at the

tip of a flaw. He formulated the problem in energy terms and proposed

that crack growth under plane stress conditions will occur if:

d (_ 62 IT a2

4ay) = 0 da (1.4)

where the first term inside the parentheses represents the elastic energy

loss of a plate of unit thickness under a stress, a, measured far away

from the crack; if a crack of length 2a was suddenly cut into the plate

at right angles to the direction of a. The second term represents the

- 45 -

energy gain of the plate due to the creation of the new surface having a

surface tension y. This is illustrated in Figure 1.3 which is a

schematic representation of the two energy terms and their sum as a

function of the crack length. When the elastic energy release due to

an increment of crack growth, da, outstrips the demand for surface energy

for the same crack growth, the crack will become unstable. A critical

fracture stress could be defined from this instability condition for a

centrally notched plate of infinite dimensions, shown in Figure 1.4 as:

af ✓2Ey/Ira (1.5)

which has been shown in the form afI = constant to hold quite well for

brittle and semi-brittle metals. (af

the critical stress at fracture).

In 1944, Zener and Hollomon (1944) converted the Griffith crack

propagation concept with the brittle fracture of metallic materials for

the first time. Orowan (1945) referred to X-ray work which showed

extensive plastic deformation on the fracture surfaces of materials which

failed in a "brittle" fashion. Irwin (1948) pointed out that the

Griffith-type energy balance must be between the strain energy stored in

the specimen and the surface energy plus the work done in plastic

deformation. He also recognised that for relatively ductile materials

the work done against the surface tension is generally not significant

in comparison to the work done against plastic deformation.

Irwin and Orowan (1949) suggested a modification to Griffith's theory

to account for a limited amount of plastic deformation. Their approach

was simply to add a plastic work factor P to the surface tension y in

equation (1.5). Orowan (1955) noted that the plastic work term was

approximately three orders of magnitude greater than the surface energy

46 -

term and hence would dominate fracture behaviour. Both Irwin and

Orowan argued that, provided the zone where plastic deformation takes

place is small in comparison with crack length and specimen thickness,

the energy released by crack extension could still be calculated from

elastic analysis. Under this restriction all the analyses that were

available for Griffith's theory applied to situations where limited

plasticity took place prior to fracture, provided yp replaced y

(where yp = y f P).

1.10.2 Strain Energy Release Rate

Irwin (1948) generalised the Griffith criterion by proposing that

crack propagatiOn occurs when the strain energy release rate (W/3(2)

reaches a critical value. He named the energy release rate G (after

Griffith) and the critical value at fracture, Gc , is known as the

"fracture toughness". Because two new surfaces are formed at fracture -

each requiring surface works- the relation between F7 and yp is given

by:

Gc = 2yp (1.6)

1.10.3 Stress Intensity Approach

Linear elasticity theory provides unique and single-valued

relationships between stress, strain and energy. Therefore, a fracture

criterion expressed in terms of an energy concept has its equivalent

stress and strain criteria. Irwin (1957) produced a fracture criterion

via an analysis of the stress field in the vicinity of the crack. He

considered that fracture can also take place when critical conditions are

attained in the material at the tip of the crack. Using the solution

47 -

for an elastic cracked sheet obtained by Westergaard (1939), Irwin derived

the solution for the stresses in the vicinity of the crack tip of a

centrally notched plate (Figure 1.4) as:

a = K (27r r) 2. f.. (e) '74 Ij

(1.7)

where r and e are polar co-ordinates with an origin at the crack tip.

Equation (1.7) indicates that identical stress fields are obtained for

identical K values. The parameter K is called the "stress intensity

factor" and is a function of the applied stress and of the crack

geometry. For a crack length 2a in an infinite plate the stress

intensity factor is given by:

K = a (7r a) (1.8)

If the critical stress system under which failure occurs is characterised

by a stress intensity factor, Kc , which is in itself a material

characteristic and is referred to as the "critical stress intensity

factor" or fracture toughness, then a Griffith-type relationship results

without consideration of any energy-dissipation process involved. Kc,

in the same way as Gc, is a material property, but like most material

constants, it is influenced by temperature, strain rate and some other

testing variables. Irwin also identified a simple relationship between

K and G as:

G = K2/E' (1.9)

where E' is the reduced Young's modulus, E for plane stress, and E//-v2

for plane strain (v is the Poisson's ratio). Strictly speaking,

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equation (1.8) is only applicable for a line crack in an infinite plate

and to linear elastic materials exhibiting no more than small scale

yielding, i.e. when the crack length is very much greater than the plastic

zone size or when the ratio of the applied stress to the yield stress is

about 0.7 (Liu, 1965). To apply the Kc concept to a practical test

specimen geometry some modification has to be applied to equation (1.8) to

take into account the finite width of the test specimen. The factor

(TO i ' in equation (1.8) was replaced by Brown and Srawley (1966) by a

correction factor "Y" and the general form of equation (1.8) becomes:

K = a Y

(1.10)

The factor Y depends on the geometry and on the loading configuration of

the specimen in question. For example, for a single-edge notched .(SEN)

plate in tension Y is given by:

Y = 1.99 - 0.41 (a/D) + 18.70 (a/D)2 - 38.48 (a/D)3 4. 53.85 (a/D)4 (1.11)

For single-edge notched bend specimens the correction factor Y is

represented by fourth degree polynomials of the following form:

Y = Ao + Al (a/D) + A

2 (a/D)2 + A

3 (2/D)3 A

4 (a/D)4

(1.12)

For a three point bend test (which is the loading configuration for the

Charpy impact test specimen) the coefficients of the polynomial depend on

the span to depth ratio (2L/D) of the specimen. Brown and Srawley (1966)

derived numerical values for the coefficients for 2L/D = 4 and for

2L/D =.8.

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For:2L/D = 4:

Y = 1.93 - 3.07 (a/D) 14.53 (a/D)2 - 25.11 (a/D)3 25.80 (a/D)4 (1.13)

For 2L/D = 8:

Y = 1.96 - 2.75 (a/D) 13.66 (a/D)2 - 23.98 (a/D)3 4- 25.22 (a/D)4 (1.14)

1.10.4 The Relationship Between Fracture Toughness and Absorbed

Energy for the Charpy Impact Test

Since the conventional types of impact tests record the energy to

failure, an attempt was made by Marshall et al (1973) to develop a

relationship between the recorded impact fracture energy, W, and the

fracture toughness, G,, in polymers. They considered the Charpy impact

test because it appeared to be easier to analyse than the Izod test.

The loading pattern of the Charpy test specimen is identical to the

three point bend bar. In the following analysis, the same relationships

between bending moment, load and stress are assumed to hold as the ones

described by classical bending theory. The strain energy, U, per unit

thickness absorbed in deflecting a cracked elastic test specimen of

thickness B is given by:

U = PA/2B (1.15)

where P is the load and A is the deflection of its point of application.

If the crack a is extended by an amount da, the strain energy release rate,

G, per unit thickness is:

50 -

du dA G E (2) + cl-.)/2B (1.16)

The compliance is given by:

C = A/P (1.17)

and differentiating with respect to crack length gives:

At constant load:

dC _ 1 dA _ A dP da - P • da TP2- ' dai

dC do P = da ay

(1.18)

(1.19)

Substituting equation (1.19) in equation (1.16) gives.:

p2 c i

2B da (1.20)

Substituting equations (1.9) and (1.10) in equation (1.20) gives:

y2a2a P2 dC

- 28 (da ) (1.21)

The factor Y is given from equations (1.13) and (1.14) depending on the

(2L/D) value. From three point bend theory (Timoshenko (1951)) the

nominal stress, 0-, is given as:

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a = 6P(2L)/4BD2

(1.22)

Combining equations (1.21) and (1.22) and integrating, the compliance C

can be obtained as:

C 9(2E)2 r

j Yea da f C 2BDIIE"

(1.23)

where Co

is the compliance for zero crack length. From the conventional

theory of three point bending:

= (2L)3/4EBD3 (1.24)

Thus, if the only energy absorbed, W, were the elastic strain energy, UB,

then from equations (1.15) and (1.17):

P2 U =2 c

2B

(1.25)

then by substituting for C from equations (1.23) and (1.24), and expressing

P in terms of a from equation (1.22), equation (1.25) gives:

W = GB [f Y2a da f (2L) Tyza (1.26)

= GBD4,

(1.27)

where = [f Y2x dx + (18LD)1 /y203

(1.28)

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where x = a/D the non-dimensional crack length, referred to as the "crack

depth": From equation (1.28) it is clear that the quantity (I) is a

function of the non-dimensional crack length (a/D) as well as of (2L/D).

Marshall et al (1973) developed curves of (I) against (a/D) for

2L/D = 4, 6 and 8.

At fracture G = G and equation (1.27) become:

G = W/PD(I) (1.29)

The above equation gives a powerful relationship between the fracture

toughness Gc and the energy to fracture W. They used PMMA as a model

material and theY tested a number of sharply notched specimens with various

crack lengths in the Charpy mode of failure. The results of W versus BD4)

followed a predominantly linear pattern as expected from equation (1.29).

Contrary to expectation, however, the line did not pass through the origin,

a least square fit to the data showing that there was a positive

intercept w' on the energy axis, implying that there is some additional

form of energy to be considered. Nonetheless, Marshall et al (1973)

showed the slopes of the lines for different specimen geometries were

very consistent, thereby implying a constant value of Gc independent of

both notch length and specimen size. They considered the positive

intercept W' to be interpreted as the kinetic energy loss term. They

estimated the kinetic energy loss term from classical mechanics and

argued that it will depend on the relative sizes of the specimen and

pendulum.

From classical mechanics, a mass M (the pendulum) striking, with

velocity V, a mass m (the test specimen) at rest, will impart to it a

velocity v where:

= 53 -

v = V (n m) (1 e)

(1.30)

e is the coefficient of restitution (e = 0.58) (Paper I). Thus, the

positive intercept iv' on the energy axis can easily be evaluated from

the kinetic energy equation as:

W' = z m v2 = z m V2 (in )2 (1 4. e)2

(1.31)

Marshall et al (1975) evaluated W' for various specimen dimensions.

(Charpy data in this thesis have W' = 0.01 Joule1). Fraser and Ward

(1974) followed a slightly different approach to calculate the kinetic

energy of a bend specimen (four point bend). They assumed that at

fracture the specimen halves are thin bars rotating about their outer

support points, with the inner (striking points) moving with the same

velocity (v) as the striking pendulum. They considered an element of

thickness dy from the half broken specimen, a distance y from the outer

support. The velocity of this element is V A and its mass is given by

BD dy E where B is the thickness and D is the width of the specimen.

£ is the density of the material. The kinetic energy of the element in

this case is: Vt

15 BD dy E (1J,L)2 (1.32)

and the kinetic energy of the whole specimen is:

V2 W / = BD e f y2 dy

2,2 —x (1.33)

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(t+g) is half of the span for the three point bend case, i.e. t f g = L.

Brown (1973) also applied the fracture mechanics theory to the

ure-Mt- Charpy impact energy data for polymers. He tested math.a.Rel-, polycarbonate,

amorphous polyetheleneterephthalate (PET), high molecular weight PET and

ABS and attempted to determine their fracture toughness. The data

obtained for all the polymers tested (except ABS) when plotted followed

a predominantly linear pattern and thus the fracture toughness was easily

defined. However, for ABS the plot was not linear, making the

determination of G impossible in this case. The deviation from

linearity is due to the fact that the theory assumes linear elastic

behaviour. At this point it must be emphasised that ABS and some other

ductile polymers (e.g. high impact polystyrene (HIPS)) undergo

considerable plastic deformation even at these high impact speeds and

thus some correction has to be considered to account for small scale

yielding as it will be discussed in section 4.6.

1.10.5 Plastic Zone Size

Linear fracture mechanics provides a method of measuring the "brittle"

strength of a material by using the linear elasticity solution for a

mathematically sharp crack tip (equation (1.7)) (i.e. radius of

curvature of the crack tip is "zero"). In reality, however, it is

impossible for a mathematically sharp crack tip to be achieved and thus

some plastic yielding certainly takes place during loading and the stress

level always remains finite. If plasticity phenomena are negligible in

relation to the phenomena occurring in the elastically stressed region,

the error will be negligible. As circumstances develop which increase the

ratio of volume subjected to plastic flow to volume under elastic

conditions the error will increase. Thus it is necessary to ensure that

- 55 -

the errors introduced by plastic yielding are very small or adequately

corrected for.

Irwin (1960) proposed a plastic zone correction factor, r , to take

into account small-scale plastic yielding at the crack tip. In this

case, the stress field can be adequately described by linear elasticity

theory and the approximate plastic zone size can be obtained from

equation (1.7) by the simple yield criterion that Gyy = ay and since

fYY (0) = 1 for o.= 0, then:

1K 2 r = p 2 IT

(1.34)

Irwin then suggested that the crack length should be adjusted to include

this plastic zone estimate, and that the new crack length should be r

longer than the original crack length.

At the onset of fracture where K = K, the error introduced by

plastic yielding could be estimated from the ratio (r Az) = (1/27ra)(K/a )2

which is equal to 2(G,A1 Ys)2, where ccf. is the gross fracture stress.

From this, it is evident that fracture mechanics is a good mathematical

model as long as the gross fracture stress is small compared to the yield

stress of the material. Irwin proposed that stresses up to 0.7 a could

be dealt with. A fracture mode change, from plane stress to plane strain,

may be accompanied by a drastic change in plastic zone size and a fracture

mechanics analysis may well apply to the plane strain condition but not

to the plane stress condition. (Irwin et al (1958) and Irwin (1960)).

1.10.6 Fracture Toughness and Specimen Thickness

A fracture mode change can he caused by a change in the thickness of

the test specimen. A plane strain situation exists when B » r , where

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B i$ the specimen thickness. Irwin (1960), Bluhm (1961), Repko et al

(1962), Bluhm (1962) postulated that Kc (or Gc ) is strongly dependent on

the specimen thickness and only after a certain thickness had been

exceeded could K (or G) be regarded as a material property dependent

only on the testing environment. It has been shown that KC and Gc

increase as the specimen thickness decreases and the fracture mode

changes from plane strain to plane stress. Under plane strain conditions

the fracture toughness has its minimum value denoted by kic or G . IC

To compare the fracture mode transition behaviour of various materials

Irwin (1964) considered it convenient to express the specimen thickness

in terms of a non-dimensional parameter a where:

K a = —B

A , c*2

y

(1.35)

From equations (1.30) and (1.31) the ratio of plastic zone size to

specimen thickness is given as a/7. He showed experimentally, for a

large variety of high strength metals, that when the plastic zone size

was less than the specimen thickness, i.e. a < 7) most of the specimens

showed less than 50% shear. When the plastic zone size was greater than

twice the specimen thickness, a > 2', the shear lips occupied nearly 100%

of the specimen thickness. Irwin proposed that the fracture mode

transition from flat fracture (plane strain) to shear fracture (plane

stress) occurs at the region around a . 2.4.

1.11 INSTRUMENTED IMPACT

In conventional types of impact tests the impact strength is reported

in terms of the energy absorbed by the specimen when it is struck and fails

under impact. It has been argued that this conventional impact strength

-57-

energy could be much greater than the actual energy to failure. This

discrepancy probably arises because after the test specimen has reached

the elastic limit it does not break but it starts to yield and thus some

form of energy could be absorbed during this plastic drawing process.

It was mainly the consideration of this rather complicated yielding

process in the impact behaviour that led to the development of impact

testing equipment that would show the load time relationship of the

specimen during impact. This type of impact test is referred to as the

"instrumented impact test". Wolstenholme (1962) gave a description for

such an instrumented impact tester of the Izod type.

The equipment consists of a strain gauge transducer connected to the

specimen with an oscillascope to display the transducer output and a

camera to record the oscillascope trace. The oscilloscope y-axis

deflection is calibrated directly in load units, and the calibrated x-axis

provides the time base. It can be seen from this brief description that

most types of impact testing equipment could be modified in a similar

manner to provide the dynamic stress-time data. Wolstenholme reported

that three general types of impulse curves could be recorded for various

materials according to the degree of ductility. Schematic diagrams for

these three types are illustrated in Figure 1.5.

1.11.1 The Fracture Mechanics Approach to the Instrumented Impact Test

In recent years the fracture mechanics approach has been further

extended to the instrumented impact test. The main advantage of applying

fracture mechanics concepts to instrumented impact test data rather than

to