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 - 5-
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 121 p2 - 10 -
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 • 2
NOTATION
a Crack length. In infinite plate, half crack length. of Crack and plastic zone length. • A Ligament area.
B Specimen thickness. c .• Count recorded. r c Count lost due to windage and friction. w/f : Compliance for a zero crack length specimen. Co C Compliance for a cracked specimen of notch length a. a C : Total experimental compliance.
C Total theoretical compliance. T D Specimen width.
E .• Young's modulus.
G .• Strain energy release rate.
.• Critical value of G. Sharp crack fracture toughness. Gc Gel .• Plane strain fracture toughness.
G .• Plane stress fracture toughness. c2 G .• Blunt notch fracture toughness. B g • Constant of gravity.
j Subscripts of tensor notation. I Moment of inertia. J Rice's contour integral.
J Critical value of J. c K Stress intensity factor.
Critical value of K for sharp cracks. c K Plane strain critical stress intensity factor. cl Plane stress critical stress intensity factor. c -12-
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. r : Radius of Irwin plastic zone. p Plastic zone size under plane stress conditions. r p2 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. / • Plane stress elastic energy to yielding. WP2 Coordinate.
Crosshead speed.
Coordinate.
Finite plate correction factor.
a, s : Constants.
: Surface energy.
A : Bending deflection of a beam. b A : Shear deflection of a beam.
A : Total deflection of a beam (= Ab+ As).
• : Engineer's strain. - 13
: Relative viscosity. e Angular measure.
: Poisson's ratio. p : Notch tip radius. a : Applied stress. a : Yield stress. y a : Stress at the tip of a blunt notch. c of : Stress at fracture.
Calibration faces for Charpy and Izod tests.
Angular measure. - 14 -
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 - 15 -
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. - 17 -
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 -19-
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: -21 -
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 -22-
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 -23-
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. -25-
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:
a = a (14- C Va/p) (1.2) c
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 o region, whereas in the +10 C 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:
(_ 62 IT a2 d 4ay) = (1.4) da 0
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:
a 2Ey/Ira (1.5) f ✓ which has been shown in the form afI = constant to hold quite well for brittle and semi-brittle metals. (a the critical stress at fracture). f 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:
G = 2yp (1.6) c
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) (1.7) '74 Ij
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, -48-
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' ini 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 = A + Al (a/D) + A (a/D)2 + A (2/D)3 A (a/D)4 (1.12) o 2 3 4
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. -49-
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) + l-.)/2Bc (1.16)
The compliance is given by:
C = A/P (1.17)
and differentiating with respect to crack length gives:
_ 1 dA _ A dP dC (1.18) da - P • da TP2- ' dai
At constant load:
do P dC = (1.19) da ay
Substituting equation (1.19) in equation (1.16) gives.:
p2 c i (1.20) 2B da
Substituting equations (1.9) and (1.10) in equation (1.20) gives:
y2a2a 2 P dC (1.21) - 28 (da )
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: - 51 -
a = 6P(2L)/4BD2 (1.22)
Combining equations (1.21) and (1.22) and integrating, the compliance C can be obtained as:
9(2E)2 r C j Yea da f C (1.23) 2BDIIE" where C is the compliance for zero crack length. From the conventional o 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):
2 c U = P2 (1.25) 2B
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:
a da f Tyza (1.26) W = GB [f Y2 (2L)
= GBD4, (1.27)
where = [f Y2x dx + (18LD)1 /y203 (1.28) -52-
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 ) (1 e) (1.30) m
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 (1,JL)2 (1.32)
and the kinetic energy of the whole specimen is:
V2 W / = BD e f y2 dy (1.33) 2,2 —x -54-
(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 = (1.34) p 2 IT
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 )2, where ccf. is the gross fracture stress. Ys 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 -56-
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 , c*2 a = —B (1.35) y
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 the conventional impact energy data is that the former test provides means for evaluation of both fracture parameters Kc and Gc, whereas the latter test enables only the Gc evaluation since in this case the load 58 -
and hence the stress level at fracture is unknown. Turner (1969) commented on the measurement of fracture toughness ' Charpy impact test for various types of steel tested in the temperature range -200 C to +80°C. He analysed the data by linear fracture mechanics and the fracture toughness was calculated from equation (1.10). Turner expressed some doubts about the interpretation of some oscillations in the load-time diagram. He emphasised that a full understanding of these load oscillations recorded due to specimen vibration is important. Johnson and Radon (1975) carried out a series of instrumented Charpy impact tests for rigid PVC over the temperature range from -200°C to +20°C. They tested two impact speeds simply varying the angle of swing of the pendulum. They analysed the data by the fracture mechanics approach and evaluated the fracture toughness, Kc, by two methods: from equation (1.10) directly from the maximum recorded load, and from equation (1.9) via Gc. Comparison of Kc values by both methods showed that for the lower impact speed a fair agreement was obtained, whereas at the high impact speed a wide variation was apparent: The good correlation at the lower impact speed was due to the almost perfect triangular load deflection relationship recorded. The poor correlation at the high impact speed was due to some distortions observed and some divergence from the expected triangular shape. L-59- CHAPTER 2 CALIBRATION FACTORS (I) 2.1 INTRODUCTION In Chapter 1 a relationship was derived (equation (1.29)) between the fracture toughness Gc and the fracture energy for the Charpy test. Parameters involved in this relation are the specimen dimensions and the factor (1). The factor (I) is expressed in equation (1.28) in terms of the Y2 polynomial. Y values have been computed by boundary collocation and they are given in a series form for 2L/D = 8 and 2L/D = 4 (Brown and Srawley (1966)). From the Y2 polynomial the factor (1) can easily be computed for the Charpy test as a function of the crack depth a/D. In the first part of this chapter the calibration factor (I) will be computed from Y2 values for a wide range of 2L/D values, and it will be plotted as a function of the crack depth a/D. Y2 values have not been computed for the Izod test (cantilever bending), mainly because the cantilever test specimen analysis is amore complicated problem. Thus, since the Izod calibration factor (1) cannot be computed via the 72, it can only be determined experimentally. A series of cantilever bending tests performed in the Instron Testing Machine will be discussed herein. A simple method of analysis will be applied to the data so that the factor (I) is derived from direct compliance measurements. In addition, some experimental checks will he made on the computed values of cb. for the Charpy test by performing a series of three point bend tests in the Instron Machine. Finally, a theoretical approach to check values of will be discussed, but in this case the compliance will be derived from the classical theory of mechanics, approximating for very small crack lengths (i.e. Y2 = Tr). 60- 2.2 COMPUTATION OF THE CALIBRATION FACTOR (I) FROM THE A' POLYNOMIAL FOR THE CHARPY TEST Equation (1.28) expresses the calibration factor c for the Charpy test in terms of the geometric factor Y2. This equation can be used to compute values for the factor (t, as a function of the crack depth (a/D) for various span to depth ratios simply by substituting the corresponding values for Y2. The general form of the Y polynomial in terms of the crack depth is given in equation (1.12). Values for the coefficients of this fourth degree polynomial have been computed by Gross and Srawley (1965) by boundary collocation for various 2L/D values. Table 2.1 tabulates numeric values for the coefficients of Y for nine span to depth ratios. It is -clear that the coefficients vary very little from one span to depth ratio to the next one and thus little variation in the Y values should be expected. The values of Y are substituted in equation (1.28) to give the corresponding values for (I). The integral equation (1.28) has been solved by means of a simple'computer program that performs the integration between the limits from a/D = 0.01 to a/D = 0.6. These results are plotted in Figure 2.2 in the form of (I) versus crack depth for the nine span to depth ratios. These plots indicate that the rate of decrease of (1) with crack depth is very much higher for smaller crack depths (up to about a/D = 0.1) than for larger ones. The computed values for the factor (I) have been presented in a tabulated for in Paper I, Table 1A. 2.3 THE FACTOR q) AND THE COMPLIANCE RELATIONSHIP In deflecting a cracked elastic test specimen of thickness B, if the crack a is extended by an amount da, the strain energy release rate G per unit thickness is given by equation (1.20), i.e. G =(P2/2B)(dC/da), and - 61 - at fracture the condition becomes: p2 = — ) (2.1) Gc 2B da The above equation holds for both Charpy and Izod tests. If the only energy absorbed in a test, w,-were in fact the elastic strain energy, UB, then from equations (1.15) and (1.17): p2c W (2.2) - 2 From equations (2.1) and (2.2) the condition at failure becomes: 4C G = ( ) (2.3) c B C da where w = the energy to failure G = critical strain energy release rate (fracture toughness) c B = the specimen thickness a = the crack length C = the specimen compliance Equation (2.3) can be written in the general form: G (2.4) c B14. where the calibration factor cp is given by: C (2.5) (I) dC/d(a/D) The above relation indicates that values for the Charpy and Izod -62- calibration factor (I) for various crack lengths can be determined from the ratio of the compliance to the compliance differential with respect to crack length. The compliance, C, can either be determined experimentally or derived theoretically from the conventional theory of mechanics. 2.4 EXPERIMENTAL CALIBRATION OF (1) FOR THE IZOD TEST From equation (2.5) the factor 4 for the Izod test can be defined directly from compliance measurements. The compliance of a test specimen is impossible to measure under Izod impact test conditions, when the conventional energy type test is performed, since the fracture energy is the only value recorded during the test. The load/deflection behaviour during the test, which is essential to define the compliance, is unknown. The only possible solution to this problem is to test Izod specimens at slow strain rates in the Instron Testing Machine, so that the load/deflection relationship can be recorded. The cantilever bending test specimen at slow rates has the same loading configuration as the Izod test specimen. At this point it must be assumed that the compliance variation with crack length (when specimens of various crack lengths are tested) for the cantilever test is the same as that for the high rate Izod impact test. Thus, from the compliance/crack length relationship derived from a series of cantilever bending tests in the Instron Machine, the calibration factor 4) can be directly deduced from equation (2.5). 2.4.1 Specimens and Test Procedure The material selected to be tested in cantilever bending was PMMA supplied in sheet form of 6.5 mm nominal thickness. PMMA was considered -63- more suitable than other polymers due to the fact that it is a brittle material and no complex yielding phenomena were expected to occur during the fracture process. Specimens were machined to the dimensions given in Table 2.2. Five series of tests were performed to consider five 2L/D values. About 30 specimens were tested in each series, three of them unnotched to define the zero crack length compliance and the rest notched to various crack lengths at regular intervals up to a/D = 0.6. The notches were milled with a very sharp cutting tool, which was regularly examined under a shadowgraph to ensure that its sharpness was adequate. Extra care was taken choosing the speed of the cutting tool in order to achieve a smooth crack tip to avoid any possible formation of crazes. The tests were performed in the Instron Testing Machine at a crosshead speed of 5 cm/min. Each test specimen was rigidly clamped in a horizontal position in a vice firmly attached to the head of the Instron machine, with the knife edge striking vertically on to the specimen, as shown schematically in Figure 2.1. 2.4.2 Experimental Results - Discussion Load/deflection diagrams were recorded on the InStron chart. These diagrams were never perfectly straight (as would be the case for an ideal linear elastic material). The deviation from the straight line was observed to be greater for shallow cracks than for deep ones. Typical load/deflection curves are shown in Figure 2.3. The more noticeable deviation from the straight line for the shallow cracks can be attributed to slow crack growth, the existence of which was evident simply by examining the fracture surface of the broken specimens. In the case of -64- small crack lengths a considerable slow crack growth zone was observed at the crack tip region, whereas for large cracks there was no trace of slow crack growth. The lack of a perfect straight line relationship for the load/ deflection diagram created some problems in determining the compliance C. Several methods were attempted but the most reliable was to record the load and deflection at failure and then measure the slow crack growth after failure to determine the appropriate crack length. For every 2L/D value the compliance, c, was plotted as a function of the crack depth. A typical plot of C versus a/D is shown in Figure 2.4. The compliance differential with respect to crack length, dC/d(a/D), was derived from the slope of the tangent to the C versus a/D curve. Figure 2.5 shows the dC/d(a/D) versus a/D relation derived from Figure 2.4. Figure 2.6 shows the results plotted as (I) (evaluated from equation (2.5)) versus crack depth for span to depth ratios, 2L/D = 4, 6, 7, 9 and 11. 2.5 CORRELATION BETWEEN COMPUTED AND EXPERIMENTALLY DETERMINED CHARPY CALIBRATION FACTORS (1) The Charpy calibration factor (1) was also determined experimentally and the results were compared with the computed ones. Two series of three point bend tests (2L/D = 4 and 6) were performed in the Instron machine. Specimens were made of PMMA and were machined to the dimensions given in Table 2.3. Values of (I) were derived from compliance values using equation (2.5). An excellent correlation was obtained between the computed and the experimental data as shown in Figure 2.7. -65- 2.6 DERIVATION OF FROM THEORETICAL COMPLIANCE BY APPROXIMATION TO VERY SMALL CRACK LENGTHS 2.6.1 The Charpy Case From conventional beam theory the compliance C is defined as the ratio A/P where A is the deflection of the beam and P is the load. For an unnotched (zero crack length) three point bending bar the bending deflection is given by: P(2L)3 A (2.6) b 48E1 and the corresponding shear deflection by: _ P(2LE)I3 A 3 (1 4. -\1) (2 ) 2 (2.7) s 48 2 2L Thus, the total deflection of the beam is: P( P L )3 v A = A ÷ A [1 + 3(1 t –2)(9--)d (2.8) s 48 E 2L where 2L and D are the span and the width, respectively, of the bending bar (shown in Figure 2.1). v is the Poisson's ratio and I is the Seto-vtAk moment of iae-r< of the beam, which is given from the theory as: I = (BD3/12) (2.9) Substituting equation (2.9) into equation (2.8) the total deflection of • the unnotched three point bending beam is given as: 2L 3 v A = (—) 4EBP [1 + 3(1 + 2 (2.10) D L - 66 - Therefore, the compliance co for zero crack length is given as: 1 C 3 [/ 3(1 —v (D—)2] (2.11) o = (DL) 4EB 2 2L When the beam is notched, as is the usual case for a Charpy test specimen, then an extra compliance Ca has to be included in equation (2.11) to account for the crack length a. From equation (1.23) this extra compliance is given as: 9 (2L)2 C - Yea da (2.12) a 28,04E Therefore, the total compliance for a cracked three point bending beam is given from equations (2.11) and (2.12) as: 9 (2L)2 r 2L 3 v D j I-a da ( — — [1 + 3(1 + —) (T-)-1 (2.13) D 4EB 2 L 2BD14E Using the approximation for short cracks, i.e. Y2 = 7r, as a 4- 0 (section (1.10.3)), equation (2.13) can be simplified as: 9 (2L)2N a2 .2 C - 3 + 3(1 4- )(E----)2] (2.14) ( L) 4EB 2 2L 4BD4E D Differentiating equation (2.14) with respect to the crack depth a/D and substituting into equation (2.5), the Charpy calibration factor (1) is given as: a 1 D 2L 1 D (1 4- v/2) D (13 = 1 (—) (– ) (2.15) D 181- (-c-)(i L7) 6 (2L) Tr a - 67 - 2.6.2 The Izod Case From the conventional beam theory the bending deflection for a zero crack length cantilever beam is given as: 4PL3 A - (2.16) b EBD3 and the corresponding shear deflection is: 3PL3 =A (1 v) (-)2 (2.17) s EBD3 Thus, the total deflection for the cantilever beam is: A 4PL3 [7 + (1 + v)(2)2] (2.18) EB 3 D and the compliance Co at zero crack length: = 4 L v) (2.19) ' C ? + 4 (1 + (Li I EBD3 For a notched cantilever beam, as is the case for an Izod test specimen, the extra compliance term coc (Appendix I, equation (I.5)) has to be included in the equation (2.19) and thus the total compliance for a cracked cantilever beam is given by: 72L2 Ye 4 L3 f a da 4 • [1 4- - 4(1 v)(IEDPi (2.20) EBD4 EBD3 Making the same approximation as for equation (2.13), i.e. assuming short cracks, the equation (2.20) becomes: -68- E2a2 u 4 L3 36 [1 + v) (--)21 (2.21) C L EBD4 EBD3 and finally, the Izod calibration factor (1) is given from equation (2.5) as: (1 + v) D (1 E ( ) ( (2.22) = z D) 367r( a( D "--) .4- 127r 2L a 2.7 COMPARISON BETWEEN THEORETICAL AND EXPERIMENTAL CALIBRATION FACTOR (1) It is interesting to compare the data for the Charpy and for the Izod calibration factor (1) derived from the theoretical compliance (equations (2.15) and (2.25)) with the corresponding data obtained from experimental compliance measurements. 2.7.1 ,1) for the Charpy Test Figure 2.8 shows the theoretical, experimental and computed data for the Charpy calibration factor plotted as (I) versus 2L/D for various a/D values. The plots indicate a very good correlation for small crack depths, that is to say up to a/D = 0.2, but for higher a/D values the theoretical points give (I) values much higher than the computed and experimental ones. It is clear that the difference increases as a/D increases. This inconsistency with the larger crack lengths was expected, since the assumption was made in the theory that a is very small (a 0). 2.7.2 4, for the Izod Test Similar plots for the Izod calibration factor are shown in -69- Figure 2.9. An interesting fealure of these plots is that the experimental points are much higher than the theoretical ones for the smaller crack lengths, that is to say up to a/D = 0.4, whereas good correlation is observed for the larger crack lengths. The poor correlation for small crack lengths creates a problem. The point to be emphasised is that the difference in q) between the experimental and the theoretical values is independent of 2L/D and is only a function of the crack depth. This statement can be expressed in a form of an equation as: A¢ = c1)1, = f (a/D) (2.23) (1)E where (pE, is the- experimental value of (p and ,1)2, is the theoretical value of qa. It is expected that equation (2.23)-should give a maximum A¢ for a/D = 0. Figure 2.10 indicates a straight line from the A¢ versus D/a plot. The line has a negative intercept and can be expressed by the equation: A¢ = 0.0813 (D/a) - 0.1626 (2.24) It appears at this point that a way to understand the problem is to compare the experimental and theoretical compliances at zero crack length as shown in Figure 2.11. From this plot it is evident that the experimental compliance is much higher than the theoretical one, the reason being the conventional theory assumes that the specimen is clamped in an ideally rigid way, but this is not the case in practice. In the practical situation some form of rotation takes place in the clamped specimen, that in effect gives an increased compliance value. To account for this effect the theoretical compliance has to be -70- increased by an additional compliance C1, and for a notched test specimen: CT = C C (2.25) 1 where C is the corrected theoretical compliance and C is the original T theoretical compliance as given by equation (2.21). The additional compliance term C1 can be expressed in terms of the crack depth. Substituting equations (2.23), (2.24) and (2.25) into . equation (2.5) gives: C 1 - 0.0813 (D/a) - 0.1626 (2.26) dC/d (a/D) Differentiating equation (2.21) with respect to a/D gives: _ 72 Lea n dC (2.27) d(a/D) EBD3 and substituting in equation (2.26) gives: 72 n L a C = (T) 2 (0.0813 - 0.1626 (2.28) 1 EB Substituting equations (2.21) and (2.28) in equation (2.25) gives: 36 L2a2n 4 L3 C .1_1(i+v)(2)2].,_ 72 n ( E)2 (0.0813 - 0.1626 (I-) (2.29) T L EB D EBD4 EBD3 For an unnotched specimen (a = 0) equation (2.29) simplifies to: -71 - 4 L3 7 (P 0.0813 (2.30)* T(0) - [i ÷ ) ) 4,2-3-2T- EBD 3 C values are derived from equation (2.30) for several 2L/D values and T(0) the results are compared with the experimental data for the zero crack length case as shown in Figure 2.11. An excellent correlation is obtained between the theory and the experimental data. 2. * E = 3,500 MN/m , v = 0.35. -72- CHAPTER 3 IMPACT MACHINE 3.1 INTRODUCTION The nature of the impact test is such that extra care should be taken in its execution if reproducible results are to be achieved. Driscoll (1953) has established that reproducibility of the experimental data for the Charpy test is indeed possible, provided certain minimum safeguards that he describes are maintained. However, it has often happened that in spite of all the suggested precautionary measures tests have failed to give reproducible results from one machine to another. Under these circumstances, it is commonly suspected that the main source of this discrepancy is the basic design of the impact machine. For example, one customary design problem to be mentioned is in properly locating the centre of percussion. In ASTM D256-56 it is emphasised that the dimensions of an impact pendulum type machine must be such that the centre of percussion of the striker is at the point of impact, that is, the centre of the striking edge. The centre of percussion for a rigid body rotating about a fixed axis and struck a blow not on that axis is defined as the point at which the blow should be applied to produce zero reaction at the pivot. The exact position for the centre of percussion with respect to the pivot is given by Swanson (1963). An equally substantial problem is that of friction. Friction losses on the pointer that reads off the energy to failure in the conventional pendulum type machine can be quite significant, particularly when testing plastics. These materials are much more sensitive than metals to small variations in conditions during the test, since they have considerably lower impact strengths. Thus, friction losses resulting from a poor -73- machine design affect the results and create a large amount of scatter when testing polymers. In this chapter an apparatus will be described which overcomes most of these problems, so that machine-generated scatter is largely eliminated. All the experimental data presented in this thesis were derived from impact tests performed using this machine. 3.2 DESCRIPTION OF THE APPARATUS The impact testing machine used for the present research is of the conventional pendulum type. The machine was made in the Mechanical Engineering Department of Imperial College from a design supplied by BP Chemicals (UK) Limited. It is designed in such a way that three types of test can be performed on plastics: 1. The Charpy test 2. The Izod test 3. The tensile impact test The experimental programme of this thesis was based on the testing of various polymers in the Charpy and Izod impact modes. The tensile impact test was not attempted, mainly because the Charpy and Izod tests are more popular in the plastics industry - although results from the more straightforward tensile impact test are easier to analyse. A set of four tups with different masses enables plastics of various impact strengths to be tested in the Charpy mode, and a further set of three tups of a different configuration enables plastics to be tested in the Izod mode. All tups are marked with an identifying letter to avoid any confusion. The four tups for the Charpy test are marked D, E, F and A in the order of their masses, and the three tups for the Izod test are -74- lettered G, C and B. Figures 3.1 and 3.2 show an outline of the impact machine, set for the Charpy and for the Izod tests, respectively. The tups are fitted (screwed on from the top) on an horizontally rotating low friction shaft so that a free swing is allowed. Each tup can be released from four different positions (positions 1, 2, 3 and 4) corresponding to four impact velocities. The method of fixing the release mechanism to obtain the four release positions is shown schematically in Figure 3.3. The velocity variation from one release position to the other is rather small and within the limits of scatter the impact strength of polymers was found to be the same for the four release positions. The angular measurements of -the tup are made using a photo-electric device and a transparent disc marked at 9' of arc intervals. The angular displacements are indicated as a number on a digital counter; they are then converted • into energy values. This method of recording the data is more favourable than the conventional one, in which a pointer moves on an energy scale, since it eliminates completely the friction in the pointer. The total angular displacement is measured during the first upswing and downswing of the tup. A switch is provided on the control box which enables two modes of counting: Mode I and Mode II. In the Mode I or "trigger mode" the first upswing and downswing of the tup is recorded, following which the counter is inhibited. In the Mode II or "counting mode" the counter continues to record and to add the angular displacements for the first, second, third, ...., swing of the tup until the tup is completely stationary. The counting mode was only used to evaluate the windage and friction losses of the machine. The potential energy of the tup can be derived from the angle corresponding to the first free swing of the tup by conventional theory. The corresponding mass values for the tups are given 4 !Sec, tkAtse_c, %IA /Sec A-kistc. -75- in Tables 3.1 and 3.2. 3.3 ZERO AND VICE OFFSET - WINDAGE AND FRICTION LOSSES In preparing the calibration tables account was taken of the following: i) the zero offset, and ii) the vice offset of each tup, and iii) the windage/friction losses for each tup for each release position. 3.3.1 The Zero Offset The zero offset is the number of counts recorded before the centre of gravity (CG) of the tup reaches the point vertically below its point of suspension. This is determined by allowing the tup to hang stationary in this position, then setting the counter to zero, and moving the tup smoothly back up towards the release position until the count stops. The indicated count is the "zero offset". This must be multiplied by a factor of 2 and the product subtracted from all indicated counts using that tup. 3.3.2 The Vice Offset The vice offset is the number of counts recorded before the tup strikes the test specimen and is only different from the zero offset if there is a verticality error in the vice, or if the vice is not correctly positioned. The recorded counts for the zero and for the vice offsets for each tup are reported in Tables 3.1 and 3.2. The difference between -76- zero offset and vice offset for each tup is not significant, and only the zero offset was used in the calibration procedure. 3.3.3 Windage/Friction Losses The losses due to windage and friction were determined dynamically for each tup for each release position. The switch on the control box was switched to Mode II and the tup was released and allowed to swing freely, noting the count for each swing and resetting the counter after each complete swing. The count displayed on the counter after each complete swing and before reset was recorded on a tape recorder. The tape recorder technique was used because the swinging time is so short that it was made impossible for the count to be written. Indicating by n, n_i, n 2, n (n_1), n_n, the first, second, third, ...., nth count recorded and corrected for the zero offset, the number of counts lost per swing is given as: n n n n -1 n -2 -71 3 (3.1) 2 2 2 and the total count is given as: n n n n -1 -1 -2 n-(n-1) -n 3 3 • • • • (3.2) 2 2 2 An example is given in Table 3.3 for the tup D released from position 1. The same procedure was repeated for each tup for each release position. Finally, the results were plotted as n- - n_n/2 versus (n-1) n n /2. Typical plots are shown in Figures 3.4 and 3.5 for _(n-1) -n every tup for the Charpy and Izod test released from position 1. Thus, for any count recorded, the count lost due to windage and friction is read -77- off these graphs. These relationships were expressed in a series form by means of a "curve fit" program, and some fourth degree polynomials were found to be the best approximation. To express the windage and friction losses in a polynomial form is useful for the calibration procedure. 3.4 EFFECTIVE RELEASE POINT OF THE TUP An example of the determination of the effective release point of the tup is illustrated by considering the tup D released from release position 1. The count recorded during the first, second and third swing was plotted against the corresponding swing interval as shown in Figure 3.6 and an imaginary swing was defined. Figure 3.7, which is derived directly from Figure 3.6, indicates the count for this imaginary swing and it determines the "effective release point" R . The imaginary value for the count in A, read off from Figure 3.7, is: A E 2,200 Count during R 4- 1 = A/2 = 1,100 P P Count during 1 ÷ S = B/2 = 1,053 P P Count during R ÷ S = A/2 + B/2 . 2,153 P P Thus, 2,153 Effective R .÷ I - = 1,027 P P 2 R ,I ,S ,AandBare shown on Figure 3.7. P P P The count of 1,027 corresponds to an angular displacement of = (1,027 . 9/60) = 154°. 1p is used to evaluate the potential energy of the tup, as will be discussed in the following section. -78- 3.5 POTENTIAL ENERGY OF THE TUP The potential energy, PE, of the tup is given by conventional theory as: PE = m . g . (x y) (3.1) where m is the mass of the tup and g is the constant of gravity. The distance (x y) is indicated on a schematic diagram as shown in Figure 3.8. y is the distance of the centre of gravity from the pivot, and x can be evaluated from the right angle triangle as: x = y cos (3.2) where e = 180° - was determined as previously discussed from the effective release point of the tup. Substituting equation (3.2) in equation (3.1) gives the potential energy of the tup as: PE = m . g . y . (1 cos 8) (3.3) Values for m and y for each tup are given in Tables 3.1 and 3.2. Considering the example of the tup D released from position 1, 8 = 180° - 154° = 26°, and by substituting the corresponding values for m and y in equation (3.3) the potential energy of the tup D released from position 1 is given as: -3 909 x 10 (PE)D = Joule (3.4) The same procedure to define the effective release point R and hence to P evaluate the potential energy was repeated for each tup and for each z- 79 - release position. 3.6 ENERGY TO FRACTURE - CALIBRATION TABLES The energy absorbed to fracture a test specimen is equivalent to the energy lost by the pendulum in the momentum exchange between the moving tup and the test specimen. (The term "fracture" energy may include some other secondary forms of energy such as the kinetic energy of the broken test specimen in addition to the actual fracture energy, as was discussed in Chapter 1, section 1.7.3). The recorded count after impact corresponds to an energy value PE', which is less than the potential energy, PE, of the tup given in equation (3.1). The difference between these two energy values gives the equivalent energy to fracture as: W = PE - PE' (3.5) The energy term PE' can be evaluated from an equation similar to equation (3.1) as: PE' = m. g . (r' y) (3.6) where (x' y) is less than (x y) as shown in Figure 3.8. Substituting equation (3.1) and (3.6) in equation (3.5) gives: W = rn. g. (x- x') (3.7) x' can be derived from the corresponding count value, c. The corresponding count c will be the recorded count corrected for the zero offset (ZO) Cr .1.80 and for the windage/friction losses c (as given in Figures 3.4 and 3.5). w/f This relationship can be expressed in the form of an equation as: c = C — 2(ZO) c (3.8) r w/f Any possible recorded count crn was converted into fracture energy Wn from equation (3.7) via a computer program. This procedure was repeated for each tup for each release position and finally calibration tables were developed, which gave the fracture energy values directly from the recorded count. An example of such a calibration table is given in Table 3.4. 3.7 SOME CHECKS OF PERFORMANCE OF THE MACHINE The control unit can be used to check on the performance of the bearings and the condition of the tups. If, in the absence of a sample, a tup is allowed to swing from any release point and the count obtained differs from the data, one of the following fault conditions can be suspected: 1. Faulty bearings 2. Inaccurate release point/bend tup 3. Faulty electronics If the bearings are at fault the difference between the count obtained and the data can be expected to increase as the mass of the tup used for the, check decreases. Faulty electronics would probably lead to large and variable errors between the count displayed and the data. Small errors which remain constant, irrespective of the tup chosen, would tend to cast suspicion on the release mechanism. Small errors which seem to - 81 - be .associated with individual tups may be the result of the tup being bent. The switch provided on the control box enables a check to be made on tup straightness. With this switch in the Mode II position the suspect tup is tilted and allowed to come to its vertical rest position. The number displayed on the control box is noted. The tup is then displaced by hand towards the release mechanism. The new count indicated is greater than the original figure by a amount equal to the zero offset which may be compared with the data. -82- CHAPTER 4 CHARPY AND IZOD IMPACT FRACTURE TOUGHNESS OF POLYMERS 4.1 INTRODUCTION Impact strength is one of the most important qualities of a polymeric or "plastic" material. The interest in the impact resistance of a plastic is not only scientific but also economic. This is apparent when one realises the major uses of plastics: packaging, textiles, appliances, etc. When thus used, a plastic must be able to withstand drops, kicks or all of the abusive treatment of which a person or even a machine may be capable. It has been proved that many plastics which are tough and ductile under conditions of the tensile test appear to be brittle when subjected to impact loadings, particularly when the structure contains some stress concentrators, as for example sharp notches. This phenomenon presents one of the most important and difficult problems in the field of engineering design with polymers. A large number of tests are commonly used to assess the impact resistance of polymers. The very existence of so many alternative test methods emphasises the unsatisfactory present state of the subject and the need for a better understanding of it. The aim of impact testing by conventional methods is to characterise the fracture resistance of materials by measuring the energy required to break "standard" specimens. It must be emphasised that the impact strength derived by such methods is not a fundamental parameter of the material but an arbitrary index of toughness relating to a particular test method and to a specific specimen geometry. It therefore follows that these results cannot be used to make quantitative predictions about the impact behaviour of specimens of different geometries. -83- To overcome these difficulties and to give a meaningful answer to the general question: "Is material A tougher than material B?", the fracture mechanics approach was introduced into the field of impact testing. The good or bad impact behaviour of a polymer is characterised by a single parameter, Gc, the "impact fracture toughness", which is independent of the test method and of the specimen geometry, therefore G is a material property. The main aim of this chapter is to justify the last statement and to give emphasis to the great value of this new approach. Experimental data on a wide range of polymers tested in the Charpy and Izod impact modes of failure at room temperature will be reported here. Analysis of these data will - clearly show that a single value impact fracture toughness is obtainable for both the Charpy and the Izod tests. The Charpy test will be discussed firstly since it involves a simpler experimental procedure. The Izod test will follow and the data from both tests will be compared. The same polymers have been tested in both tests so that a direct comparison of the results is attained. Finally, some factors that may affect the impact fracture toughness of polymers will be examined. For example, the effect of molecular weight on the impact fracture toughness of PMMA and the effect of moisture content on the impact fracture toughness of Nylon 66 will be discussed. 4.2 MATERIALS 1. Poly(methyl methacrylate) (PMMA): ICI compression moulded sheet, 6.4 mm thick. 2. Polycarbonate (PC): Bayer Makrolon extruded sheet, 4.9 mm thick. -84- 3. Poly(vinyl chloride) (PVC): a) Unplasticised ICI Darvic 110 compression moulded sheet, 5.9 mm thick. b) Modified BP Breon PVC injection moulded sheet, 6.4 mm thick. 4. Polyethylene (PE): a) BP Rigidex 075-60 injection moulded sheet, 5.7 mm thick. (Density = 0.960 gm/ml; Melt index = 7.5 g/10 min). b) BP Rigidex 002-55 injection moulded sheet, 5.8 nu thick. (Density = 0.955 gm/ml; Melt index = 0.2 g/10 min). c) BP Rigidex H0-60-45P injection moulded sheet, 5.7 mm thick. (Density = 0.945 gm/ml; Melt index = 6.0 g/10 min). 5. Acrylonitrile-butadiene-styrene (ABS): Monsanto LUSTRAN ABS 244 injection moulded bars (in x .x 5"). 6. Nylon: ICI Nylon 66 (Maranyl AD151) injection moulded sheet, 4.6 mm thick. 7. Polystyrene (PS): BP UPS general purpose polystyrene injection moulded sheet, 6.4 mm thick. 8. Toughened polystyrene: a) BP CP-40 injection moulded sheet, 6.4 mm thick. b) BP HIPS 2710 - a higher impact grade - injection moulded sheet, 6.3 mm thick. 4.3 THE CHARPY TEST - EXPERIMENTAL PROCEDURE 4.3.1 Test Conditions and Apparatus All tests were performed in an air-conditioned laboratory in which -85- o + the temperature was maintained at 20 - 1°C and the relative humidity at 50% t 5%. Specimens were normalised in this atmosphere for some weeks before use. The testing was performed on the impact machine described in Chapter 3. 4.3.2 Specimens and Notching Technique The specimens were manufactured from the sheet as supplied, by machining to the-required specimen thickness (6 t 0.01 mm) as shown in Figure 4.1. Extra consideration was given in notching the specimens, since one of the requirements of the fracture theory is that artificial cracks should be made as sharp as possible, as the theory presumes zero tip radius. At first the razor notching technique was applied to PMMA specimens. This technique involves the use of a razor bladeto sharpen a saw cut of approximately the required crack length. The razor blade, mounted in a Vickers hardness tester, was pushed slowly into the material, so that a very sharp crack was produced. Although this technique has the advantage of producing an infinitesimal crack tip radius the main disadvantage is that it is time- consuming, particularly when a large number of specimens have to be notched, as is the case for impact testing. Another disadvantage of the razor blade notching technique is that the crack length is unknown; •only a very rough estimate could be made. It was suggested that machined notches could be preferable for impact test specimens, if extra care was taken to ensure that the sharpness was close enough to that produced by a razor blade. A set of PMMA machined notch specimens were tested and the results were compared with those obtained from razor blade notched specimens. A very good correlation of the results from both notching techniques was apparent as shown in Figure 4.2. This excellent agreement -86- provided no doubts about adopting machine notching as a standard method of notching impact specimens. In machining the notches extra attention was given to the following points. The cutting tool (a single point fly cutter) was regularly examined for sharpness and a greatly enlarged projection checked for correct dimensions and against irregularities in the profile. This check was repeated after notching about 60 to 80 specimens. A notched sample was also enlarged projected on the shadowgraph to ensure that the crack tip was of the required radius. A crack tip of 0.03 mm radius was specified to meet the test requirements. A single point cutter was used, as shown in Figure 4.2a, the existence of only a single cutting edge to sharpen facilitating the maintenance of the required profile. The speed of the cutting tool must also be suitable for the material, since it is essential that the surface of the notch where the crack is initiated has not been heated by the act of cutting, nor chipped if the material is brittle. Anything altering the physical properties of the material at the notch surface, or causing some stress concentration, must be excluded. The maximum length for a single cut at any one time was 0.010", and the cutting procedure was repeated until the required crack length was cut. It was observed that a crazed crack tip was obtained if cuts were taken too deep. 4.3.3 Testing Procedure The notched specimen was rested on the supports (span of 45 mm) and before testing extra care was taken to ensure that the striking point of the tup was in line with the tip of the crack. This was achieved by a simple check. The tup was slowly moved by hand from the release position and was allowed to rest stationary under gravity behind the crack tip of the specimen rested on the supports. A microscope or magnifying - 87 - glass was used to ensure that the point of impact was exactly at the crack tip. Any small deviations could affect the results considerably, resulting in a much higher fracture energy and a badly twisted fracture surface. This is illustrated in Figure 4.3 which shows the effect of varying the point of impact a distance x from the actual crack tip. The distance x was increased up to 2 mm, and was measured by means of a travelling microscope. The increase in the fracture energy is small for small variations up to x = 0.3 mm, but thereafter the fracture energy shows a drastic increase with further increase in the distance x. After the impact point/crack tip check was made, the tup was moved by hand backwards and attached to the release mechanism, the counter was switched to the trigger mode and made ready to count (i.e. set to zero). The tup was then released and allowed to strike on to the supported specimen, which fractured into halves. The indicated count on the. control box was then noted and the corresponding fracture energy value was read off from the calibration tables. After impact, the crack length was measured to ±0.01 mm by means of a travelling microscope. The width and thickness of the specimen were also checked by micrometer. It was found that accurate measurements of the crack length, specimen width and specimen thickness are necessary to ensure good results. Normally, twelve to fifteen specimens of various crack lengths (from a/D = 0.06 to a/D = 0.6) were tested from each material. 4.4 ANALYSIS OF EXPERIMENTAL DATA The impact fracture toughness, Gc, as defined in equation (1.29) was determined from the slope of the expected straight line relationship between the fracture energy and the product (B14). Values of BN for every specimen tested were computed by means of a computer program that -88- calculates (1) from equation (1.28) via the 12 polynomial. The kinetic energy loss (see Chapter 1, equation (1.31)) has not been included in the program. Thus, a positive intercept for the straight line of about 0.01 Joule (calculated from equation (1.31)) on the energy axis has to be considered. The slope of the best straight line through the experimental points gives the Gc value in J/m2. For some ductile polymers such as HIPS and ABS the analysis of the experimental data can be slightly more complicated due to some plastic deformation that takes place during the test. This matter will be discussed in section 4.6. 4.5 EXPERIMENTAL RESULTS - DISCUSSION The polymers tested can be classified in three categories according to the impact fracture toughness value: 1. Low impact fracture toughness polymers, such as GPPS, PMMA and PVC (Darvic 110), having Gc values in the 2 2 region from 0.8 kJ/m to 1.4 kJ/m . 2. Medium impact fracture toughness polymers such as PC, Nylon 66 (dry)*, PE and PVC (modified). Gc values for * Since nylon is a material that absorbs moisture from the environment extra care was taken to keep the material as dry as possible. The nylon sheets supplied from ICI were kept tightly sealed in polyethylene bags containing crystals of silica gel, so that any trace of moisture was avoided. A regular inspection was carried out to check if there was any change in the blue colour of the silica gel crystals. The colour change is an indication that some moisture has been absorbed and, if so, the crystals were replaced. -89- 2 these materials lie in the region from 3.5 kJ/m to 2 10 kJ/m . 3. High impact fracture toughness polymers, such as HIPS 2 2 and ABS. G ranges from 16 kJ/m to as high as 50 kJ/m . c The experimental results for each category of polymers will be discussed separately. 4.5.1 Low Impact Fracture Toughness Polymers Plots of the fracture energy W against BD4 for the polymers in the first category - GPPS, PMMA and PVC (Darvic 110) - are shown in Figures 4.4, 4.5 and 4.6. The impact fracture toughness Gc was determined from the slope of the best straight line through the points which, as expected, shows a positive intercept of 0.01 J (section 1.10.4) on the energy axis. The straight line fit is very good for these three polymers. The scatter of the points is very small considering the fact that since these polymers are relatively weak they are expected to be over-sensitive to small variations that may occur during the test. Examination of the fracture surfaces of these polymers indicated a flat, entirely brittle fracture without any trace of plastic deformation. Fracture surfaces for GPPS, PMMA and PVC (Darvic 110) are shown in •Figures 4.7, 4.8 and 4.9, respectively. 4.5.2 Medium Impact Fracture Toughness Polymers The corresponding plots of W against BD(1) for polymers in the second category (i.e. PC, Nylon 66 (dry, PE (075-60, 002-55 and HO-60-45P) and PVC (modified)) are shown in Figures 4.10, 4.11, 4.12, 4.13 and 4.14. The experimental points again fall on a straight line with a little 1.90- scatter, and the slope of the line, as before, determines the impact fracture toughness value. Examination of the fracture surfaces for the polymers in this category showed some interesting features of their fracture behaviour. Broken specimens of PC and Nylon 66 (dry) appeared completely brittle, as shown in Figures 4.15 and 4.16. There was no evidence of whitening, permanent macroscopic deformation or yielding on the fracture surface. Thus, there is no evidence of good resistance to either crack initiation or crack propagation for these polymers. Examination of the fracture surface of the broken specimens of PE (075-60) and PE (002-55) indicated clearly that the specimens cracked first in a brittle manner, but then the material yielded and the crack stopped. This is illustrated in Figures 4.17 and 4.18 where a whitening region, which seems to interrupt the brittle fracture pattern, can be observed at the bottom of the specimens. From this fracture behaviour it can be deduced that PE (075-60) and PE (002-55) are not resistant to crack initiation but they are significantly resistant to Crack propagation. The fracture surface of PE.(H0-60-45P), illustrated in Figure 4.19, shows a slightly different pattern than the ones observed previously for PE (075-60) and PE (002-55). Here, in addition to the whitening at the bottom of the specimen, some yielding can also be observed round the tip of the crack. This indicates that PE (H0-60-45P) yields prior to crack initiation, then cracks in a brittle manner, and finally the crack stops. PE (H0-60-45P), according to its fracture behaviour can be characterised as a material which is resistant to both crack initiation and crack propagation. The last polymer in this category to be discussed is PVC (modified). Examination of the fracture surface for tested specimens of this material indicated an extended whitening, starting at the crack tip and spreading - 91 - evenly throughout the fracture area up to a point very near to the end. The fracture mode then suddenly changes, yielding to a very small portion of brittle fracture area as illustrated in Figure 4.20. This pattern of fracture surface indicates that first the material yields, then the crack propagates within the whitened region and finally yielding stops and the material fractures in a brittle manner. Thus, it can be deduced that PVC (modified) is more resistant to crack initiation than to crack propagation. 4.5.3 High Impact Fracture Toughness Polymers When high toughness materials are tested the stresses induced at fracture tend to increase, so that considerable plastic yielding occurs. Linear elastic fracture mechanics (LEFM) assumes elastic behaviour and is thus not capable of describing large degrees of plastic deformation. LEFM cannot be applied to high toughness materials such as toughened polystyrene (CP-40), HIPS (2710) and ABS, as shown in Figures 4.21, 4.22 and 4.23. The results plotted as W versus BD(1) do not fall on a straight line and G cannot be determined for these materials. A solution to this problem can be achieved by: 1. the effective crack length approach, or 2. the Rice's contour integral approach. 4.6 ANALYSIS FOR HIGH TOUGHNESS POLYMERS 4.6.1 The Effective Crack Length Approach It is possible to extend the useful range of the LEFM theory by using the effective crack length, af, where: -92- a = a -I- r (4.1) a is the original crack length and r is the plastic zone size from equation (1.34). In impact testing the correction factor is not easy to apply since the yield stress (a ) and the Young's modulus (E) are unknown, but they can be estimated from low rate values. Better estimates may be made by varying r in the W versus BD(1) plot to give the best straight line fit to the data. 4.6.2 The -Rice's Contour Integral Approach When full yielding occurs the elastic analysis is no longer valid and the concept of Jc, the Rice's contour integral*, a more general fracture energy criterion, must be invoked. By definition, Jc Gc for the elastic case, but it is applicable for all degrees of plasticity and it may be written in terms of the yield stress and the crack tip * Rice (1968a,b) developed a path independent integral, J, which related the variation in potential energy due to growth of the crack or void in an elastic or elastic-plastic body obeying displacement plasticity theory. This live integral is often called the Rice's contour integral and it is given in a general form as: Du . J = f [ra dy - T r ax The derivation of this integral is discussed in detail by Hayes (1970). -93- displacement, u*, at fracture as was discussed by Ferguson (1973) as, J = a . u (4.2) c If full yielding is assumed in bending and this criterion is used then assuming solid body rotations, we have: W = -"! . a . B a) (4.3) 12 y - Substituting equation (4.2) in equation (4.3) gives: B (D - a) W = J . (4.4) c 2 If the ligament area is taken as A = B (D - a) then equation (4.4) becomes: (4.5) jc The factor 2 arises because the average displacement in bending is u/2 compared with u in tension. The parameter W4 provides, of course, the traditional method of analysing fracture data, but it should be emphasised that it is only appropriate for high energy fractures with gross yielding, * The crack opening displacement (COD) is associated with the mathematical model proposed by Dugdale (1960). For the general case of an infinite plate the COD was given by Burdekin and Stone (1966), and recently Hayes and Williams (1972) determined solutions for most of the practical test geometries by means of a finite element analysis. -94— and the factor 2 must be introduced in bending to give valid comparisons with G. 4.7 EXPERIMENTAL RESULTS FOR HIGH TOUGHNESS MATERIALS • Figures 4.21, 4.22 and 4.23 shows the corrected data for the three high toughness polymers. The effective crack length o was evaluated f from equation (4.1)., The plastic zone size was varied in steps of 0.5 mm to give the best W versus BD(1) straight line. For all three polymers it was found that the best straight line fit was obtained for r p = 1 mm. The positive intercept of 0.015 still holds and Gc was determined from the slope of the straight line. Figures 4.24, 4.25 and 4.26 show straight lines for the results plotted as W versus A for the three high toughness polymers. J was determined from the slope of the line given by equation (4.5). Jc values agree very well with the Gc values derived from the effective crack length. J and G values are given in Table 4.1. It must be emphasised that the J concept is appropriate only for high energy fractures with gross yielding and is not valid for low energy brittle fractures. This is illustrated in Figures 4.27 and 4.28 where the Jc concept was attempted on PMMA and PE (002-55). Figures 4.29, 4.30 and 4.31 show the fracture •surfaces of high toughness polymers, PS (CP-40), HIPS (2710) and ABS. The entire fracture surface shows a stress whitening, which is a clear indication of the large scale yielding that has taken place. G values for all the polymers tested in the Charpy mode of failure are given in Table 4.1. -95- 4.8 THE IZOD TEST - EXPERIMENTAL PROCEDURE 4.8.1 Specimens and Notching Specimens were manufactured from as-supplied sheet material (the same materials were tested in the Izod mode of failure as in the Charpy) by machining to the required dimensions as shown in Figure 4.32. The same notching technique was applied here as in the Charpy test, that is to say, the notches were carefully machined by a very sharp fly cutter. The same precautions were taken during the notching procedure as those discussed in section 4.3.2. 4.8.2 Testing Procedure Specimens were clamped rigidly in the vice of the machine by a torque spanner so that the same clamping pressure was applied to all specimens. This technique eliminates the problem of any variation in the clamping pressure that it might affect the results (Stephenson (1957)). However, some tests were performed on PMMA and PC by clamping the specimens with less than the normal pressure and no effect was apparent in the results. Extra care was taken so that the specimens were clamped vertically square in the vice. If there was an angle between the surface of the specimen to be struck and the hanging vertical tup, a higher fracture energy value would be expected due to torsional stresses set up in the specimen. A typical Izod specimen clamped in the vice of the impact machine is shown in Figure 4.33. The actual testing procedure here was the same as for the Charpy test: the counter was set to zero, the tup released and allowed to strike and break the specimen. The indicated count on the control box was then recorded and converted into energy from the calibration tables for the Izod test. 96 - 4.9 ANALYSIS OF THE IZOD TEST DATA The Izod impact fracture toughness is defined by equation (2.4). As in the Charpy case, Gc was determined from the slope of the straight line obtained from the W versus BD(1) plots. Values of ¢ in this case were read off directly from the graphs shown in Figure 2.5 for any particular crack depth a/D. The kinetic energy loss W' defined in equation (1.31) has also to be considered. The W' value for the Izod test is expected to be different from the one evaluated for the Charpy test since the tup and the specimen masses differ. In this case W' was calculated again from equation (1.31) by substituting the corresponding mass values, and e (coefficient of restitution) was taken as 0.58 (section 1.10.4). W' was found to be -2 -2 4 x 10 Joule in this case, as compared with 1 x 10 Joule for the Charpy case. 4.10 IZOD TEST RESULTS - DISCUSSION Plots of the fracture energy W versus BD4) for the low and medium impact fracture toughness polymers tested are shown in Figures 4.34-4.38. From these plots it can be seen clearly that the experimental points fit very well on a straight line with a positive intercept of 0.04 Joule, as expected. The slope of the best straight line fit through the points determines the Izod fracture toughness for each polymer. From examination of the fracture surfaces of the broken specimens, and comparison with the broken Charpy specimens, it appeared that the same fracture behaviour characterises each polymer for both tests. As in the Charpy test the gross yielding problem was evident when high toughness polymers were tested, and LEFM failed to analyse the experimental data, as shown by Figures 4.39, 4.40 and 4.41. The results - 97 -- (for PS (CP-40), HIPS (2710) and ABS) do not fall on a straight line with an intercept of 0.04 J, and if a line is put through the points a much greater positive intercept is given. Points are also shown with the correction of rp = 1 mm which had been found to work quite well with the Charpy data. However, for the Izod test the problem seems to be slightly more complicated, since although the Izod results give a line of about the same slope, the intercept is now negative and the result must be judged unreliable. The fact that the Charpy data give more satisfactory behaviour here may be explained by considering the ratio of the energy to fracture W to that to give first yield W1. The latter is defined as: a 2 W (4.6) 2 E Substituting for a,2 from equation (1.34), equation (4.6) becomes: K 2 1 • W = c (4.7) 1 2 E' 2Tr r p Substituting for Kc from equation (1.10), K = a Y 14i, equation (4.7) becomes: / y2a2a W (4.8) 1 2 E • 2ff r p •where 6 is the stress at fracture. The fracture energy w is given by: (4.9) 2E Hence, from the equations (4.8) and (4.9) the ratio WW1 is given as: W =_ 2Tr • (4.10) W1 y2 a - 98 - Since r tends to be large for these materials it is necessary to keep • P Yea as large as possible for W < WI. Y2 is larger for the Charpy test (as indicated by the (1). functions) so that in general the energy levels at fracture will be lower in that geometry and the corrected elastic solution would be expected to be more appropriate. The J concept is more appropriate for the Izod case. Plots of W versus ligament area A are shown in Figures 4.42, 4.43 and 4.44. These results give reasonably straight lines, with an intercept of 0.04 J as expected. The values of Jc determined from the slope of these lines are in very good agreement with the corresponding Jc values determined for the Charpy test as shown in Table 4.1. 4.11 CONCLUSION ON THE CHARPY AND IZOD IMPACT TEST OF POLYMERS The data presented here indicate clearly the power of this method of analysing impact data. The use of the appropriate calibration factors gives the same result for both Charpy and Izod tests. Values of G for the Charpy and Izod tests for all the polymers tested are presented in Table 4.1. Care must be exercised for high toughness materials because of gross yielding, but the use of the Jc concept provides a good basis for analysis and comparison with Gc values. Thus, the methods described here are capable of defining the fracture toughness of all the polymers tested under impact conditions using only energy measurements. This method is clearly preferable to conventional testing for evaluating impact strength. 99 - 4.12 SOME FACTORS AFFECTING THE IMPACT FRACTURE TOUGHNESS OF POLYMERS 4.12.1 Effect of Molecular Weight on the Impact Fracture Toughness of PMMA It is well known that molecular weight variations affect the strength of polymers. It is a fact that the brittle strength of polymers decreases with decreasing molecular weight. Vincent (1960) refers to Flory who has found that the tensile strength of cellulose acetate fractions and blends and butyl rubber vulcanizates depends on the average molecular weight, M, according to the relation: Tensile Strength = A — B/M (4.11) and he has suggested that this form of equation may apply to all high polymers. Since the impact strength increases as the average molecular weight of the polymer increases, the impact fracture toughness should also be expected to increase. It is certainly true that at very low molecular weights all polymers are very fragile. Berry (1964) has reported that the dependence of the fracture surface energy (y) of PMMA on molecular weight, M, can be represented by the equation: = A — B/M (4.12) where A and B are arbitrary constants. By extrapolation of experimental data obtained for values of M in the range 0.9 x 105 to 60 x 105 he concluded that y should become zero for Pi = 2.5 x 104, but he stated that "... in view of the uncertain validity of that extrapolation, it would clearly be desirable to determine directly the fracture surface energy and - 100 - other ultimate properties of samples with molecular weights extending down to the critical values". He tested notched bars of PMMA of various molecular weights in tension in the Instron machine and evaluated the fracture surface energy value, y, from Griffith's equation (discussed in Chapter 1, equation (1.5)) for the plane strain case as: 2E y crf = (4.13) Tr a (1 - v2) where o is the stress at fracture. Here, Charpy tests on four types of f Diacon (low molecular weight PMMA) and the development of a relationship between impact fracture toughness and molecular weight will be reported. These results will be compared with Berry's data. 4.12.2 Materials Tested 1. Diacon CA602 with relative viscosity 0.72*. 2. Diacon 1/3300 with relative viscosity 1.27. 3. Diacon DA100 with relative viscosity 3. 4. Diacon DP300 with relative viscosity 8. 5. Commercial grade PMMA with relative viscosity 40. The Diacon was supplied by ICI in compression moulded sheets of 3 mm nominal thickness. 4.12.3 Molecular Weight and Relative Viscosity Relationship Values of molecular weight were evaluated from the relative * The relative viscosity values were supplied by the manufacturers. Information was given that they were determined from 1% solution in CHC13. -. 101 - viscosities from the empirical relation*: 1.13. 5 M. = 1.7 n /0 (4.14) where M is the molecular weight and n is the relative viscosity. Values of molecular weight calculated from equation (4.14) are recorded in Table 4.2. 4.12.4 Experimental Procedure The four types of Diacon were tested in the Charpy mode. The commercial grade PMMA had already been tested, as previously discussed, 3 2 and its G value is 1.28 x 10 J/m as recorded in Table 4.1.. The c normal Charpy testing procedure was repeated here and the fracture energy values for a number of specimens from each Diacon were recorded. 4.12.5 Experimental Results - Discussion The fracture'toughness'values were determined from the i1 versus BN plots for each Diacon. Values of G are shown in Table 4.2. The c fracture toughness/molecular weight relation is shown in Figure 4.45. The results fall on a straight line which by extrapolation gives zero Gc for a molecular weight about 22,000. The results are in very close agreement with Berry's prediction that Y, and thus Gc, "... should become zero for a polymer of molecular weight 25,000". Figure 4.45 shows also the surface energy, y, variation with M. The dependence of y on the reciprocal of molecular weight is illustrated in Figure 4.46, where the results are compared with Berry's E.L. Zichy, ICI Welwyn Garden City, private communication. -102- data, and a good correlation between both sets of data is apparent. The results here indicate clearly that the impact behaviour of PMMA is considerably improved by increasing the molecular weight of the polymer. Low molecular weight Diacon has comparitively low impact fracture toughness values. Consequently, raw material manufacturers make considerable effort developing their products to ensure that such very low molecular weight materials are avoided for practical applications. 4.13 EFFECT OF MOISTURE CONTENT ON THE IMPACT FRACTURE TOUGHNESS OF NYLON 66 Nylons absorb more or less water depending on the type of nylon, the relative huMidity and the crystallinity of the part (Kohan (1973)). The absorption of water can significantly change the mechanical behaviour of the polymer. It is well known that absorbed water in nylon decreases its modulus and yield strength at room temperature and increases its elongation at break, that is to say, the material becomes tougher. Thus, since the absorbed water improves the toughness of the material improvement in its impact behaviour should be expected. The effect of water content on the impact strength of nylon is well established, and has been discussed by Vincent (1971) and Ogorkiewicz (1970). There are several ways that the moisture content may be increased: 1. By boiling in water. 2. By soaking in hot potassium acetate solutions. 3. By immersion in cold water. 4. By conditioning to the required humidity. The first two methods are not very much in favour, because some surface -- 103 oxidation follows these treatments. In the present work the moisture content of Nylon 66 was increased by the third method, i.e. by immersing the specimens in cold distilled water for a period of time until the required percentage water content was reached. The effect of moisture content on the fracture toughness of Nylon 66 tested in the Charpy test was then examined. 4.13.1 Experimental Results - Discussion To establish the percentage-water-content/time relationship for Nylon 66 a sample was immersed in sold distilled water for a long period of time. The weight of the sample was carefully checked by means of an electronic balance at the end of each week, so that the % water content was recorded at each time, as shown in Figure 4.47. This plot shows that the saturation level (9% water content) was reached after a period of 42 weeks, i.e. after about 7,000 hours. A set of five Charpy tests were performed on Nylon 66 with five different moisture contents: 1%, 1.85%, 3%, 3.35% and 4%. The specimens were machined to the required dimensions from sheets of material as supplied, and they were machine-notched when they were still dry. The notched specimens were then immersed in cold distilled water until the required moisture content was achieved, as shown in Figure 4.47. For example, for 1% water content the specimens were immersed for a period of 50 hours. The time of immersion to achieve the required moisture content for the test is recorded in Table 4.3. When the required moisture level was achieved the specimens were removed from the water and immediately tested in the Charpy test. The effect of water content on the impact fracture toughness of Nylon 66 is shown in Figure 4.48, in which the results are plotted as Gc versus percentage water content. At 4% water content the material becomes - 104 - ten times tougher than when it was dry, i.e. Gc increases tenfold. It was impossible to test Nylon 66 in the Charpy mode for a water content greater than 4%, since the material became very tough, quite flexible and impossible to break. The results indicate clearly that the existence of water significantly increases the impact behaviour of the material and as a result considerably improves its engineering use. -105- CHAPTER 5 EFFECT OF TEMPERATURE ON THE IMPACT FRACTURE TOUGHNESS OF POLYMERS 5..1 INTRODUCTION In the majority'of applications•of plastic materials, the impact behaviour at room temperature will be the most important factor. However, this is•not a good reason for measuring impact strengths at one temperature only. Some plastics are affected more than others by even relatively small changes in temperature, and as a result their impact behaviour can vary considerably. A common example of temperature changes that may affect the performance of thermoplastics is climatic variations that occur from one country to another. Graphs of impact fracture toughness against temperature for various polymers is not only of academic interest simply to provide a comparison between the representative materials, but also play an important role in choosing a plastic for a particular application. Some polymers that are defined as tough at room temperature such as HIPS, ABS or modified PVC appear to behave in a brittle manner at low temperatures, say about -40°C. When in practice a brittle type failure replaces a ductile one due to some drop in the service temperature the problem is quite serious and must be very carefully •considered. In this chapter the effect of temperature on the impact fracture toughness of polymers will be discussed by testing various polymers in the Charpy test in the temperature range -100°C to +60°C. The results are analysed in terms of the concept of plane stress and plane strain Gc and changes in Gc with both temperature and specimen thickness are described in terms of yield stress changes. This method of analysis is very similar - 106 - to the technique described by Bluhm (1961) and (1962) who relates similar results for metals to a bimodal fracture model. 5.2 SPECIMENS AND TEST PROCEDURE 5.2.1 Materials The polymers selected to be tested in the Charpy mode over the temperature range -100°C to +60°C are: 1. PMMA : ICI 2. PC : Bayer Makrolon 3. PVC : ICI - Darvic 110 4. PE : (a) BP Rigidex 002-55 (b) BP Rigidex HO-60-45P 5. ABS : Monsanto LUSTRAN ABS 244 6. Nylon 66:. ICI - Maranyl AD151 7. GPPS : BP 8. HIPS : BP - HIPS 2710 Specifications for each of these polymers were given in Chapter 4. 5.2.2 Test Conditions and Apparatus All Charpy tests to be reported were performed in a well insulated temperature cabinet, designed to fit on the base of the impact machine. The box, made of polystyrene foam, was split in half so that the front half could be pulled out to allow the tup to strike the specimen as soon as the specimen reached the required temperature. Specimens were normalised in this environment for a few hours before the test. Figure 5.1 shows the temperature cabinet closed and fitted on the base of -107- the impact machine, and Figure 5.2 shows its interior. A thermocouple was embedded in a dummy specimen located as close as possible to the supports and its temperature was recorded on an electronic digital thermometer. Some checks were made to assure that the recorded temperature of the dummy specimen was the same as or very close indeed to the temperature of the actual specimen rested on the supports. This check was achieved by means of a second digital thermometer with a thermocouple embedded in the actual specimen. The temperatures recorded on the two thermometers were noted and no difference was apparent, that is to say the temperature of the dummy specimen corresponds to the temperature of the actual specimen rested on the supports. Temperatures above ambient were achieved with heaters on the back walls of the temperature cabinet. For low temperatures nitrogen gas was used to blow in liquid nitrogen, and the resulting vapour was circulated by a high speed fan. A "Eurotherm" control unit, working from a thermocouple embedded in a second dummy specimen located very close to the first, controlled both the nitrogen flow and the heaters. The range -100°C to +60°C was used and a control of ± 1°C was achieved. The box is opened for a very short period (< 1 second) in order to break the specimen and no appreciable temperature change was observed. This technique of temperature control provides a very satisfactory way to achieve temperatures above and below ambient. A schematic diagram of the temperature control mechanism is illustrated in Figure 5.3. 5.2.3 Specimens and Notching Specimens were made from each material in sets of 15 having an even distribution of notch lengths between a/D = 0.06 and a/D = 0.6. The same notching technique was used as was discussed in section 4.3.2. -108- 5.3 EXPERIMENTAL RESULTS The 0 values for the polymers tested are shown in Figures 5.4, 5.5 and 5.6 for the temperature range -100°C to +60°C. The polymers tested are classed as low, medium or high impact strength according toothe value of their impact fracture toughness. 2 In the low strength group (= 1 kJ/m ) we have crystal polystyrene and PMMA, as expected. The PVC is also included in this group, since the PVC tested was the unmodified Darvic 110 which behaves as a glassy amorphous polymer, but PVC would be expected to be in a higher group when plasticisers are added. Figure 5.5 (= 4 kJ/m2) includes polycarbonate and dry Nylon 66 which are classified as medium impact strength materials. 2 Figure 5.6 gives the high impact strength materials (= 20 kJ/m ), and very large changes with temperature are apparent. Factors of variation of the order of ten are observed here as compared to two or less in the low and medium groups. There is a noticeable similarity between the curves in that all are sigmoidal in form between high and low temperature values. In the temperature range T < -60°C and T > +20°C the impact fracture toughness for all polymers stays almost constant. Examination of the fracture surfaces of the broken specimens of the low and medium impact strength materials showed a brittle fracture for the whole temperature range. However, some interesting points were observed when the fracture surfaces of specimens from the high strength materials were examined. All four high strength polymers showed brittle fractures for temperatures < -60°C while ductile fractures were observed for temperatures > 0°C. The ductile fracture for HIPS and ABS for T > 0°C was more pronounced than for the two PE grades. Figures 5.7, 5.8, 5.9 and 5.10 show the fracture surfaces of PE (002-55), PE (H0-60-45P), o HIPS (2710) and ABS over the temperature range -100°C to +60 C. From -109 - these figures it is evident that somewhere between -60°C and 0°C the fracture mode change-s from ductile to brittle; this temperature region is sometimes referred to as the "ductile-brittle" transition region, as emphasised in particular by Vincent (1971) and (1960). From the plots in Figures 5.4, 5.5 and 5.6 there is no evidence of peaks in any of the polymers tested. This has been a point for discussion by many investigators as was discussed in section 1.9.1, who considered the possibility of some relation between the impact strength of thermoplastics and their dynamic mechanical losses (damping peaks). The reason that no peaks were apparent in the results here is probably because the notches were too charp and as Vincent (1974) stated: "If the notch is too sharp, the peak may not appear". In the next chapter similar tests with blunt notched specimens will be discussed and in this case the results for PMMA will show some obvious peaks. 5.4 THICKNESS EFFECT - THEORETICAL ANALYSIS It is postulated here that a polymer exhibits different fracture strengths depending on the stress system imposed. The lowest value appears when the material is heavily constrained, as in the centre of a notched specimen, and this is termed Gel. The highest value corresponds to zero constraint, as near the surface of the specimen, and is the plane stress value Get. This concept has been used for metals (Bluhm (1961) and (1962)) and has been extended to polymers by Parvin (1975) and (1975a) but in the form of fracture toughness K. Following the same line of argument, however, similar relationships may be derived for Gc. The extent of the plane stress region is assumed to be the plastic zone size rp2 which is given by equation (1.34): -110 - K2 1 c2 r 0 (5.1) P2 11. a 2 y where K is the plane stress fracture toughness and a is the yield c2 stress. Since K 2 = E Gc2, equation (5.1) becomes: E Gc2 r = • (5.2) p2 2 Tr 2 y where E is the Young's modulus. The specimen may therefore be considered as a sandwich of a plane strain region between two plane stress regions of r as shown schematically in Figure 5.11. Since energy is thickness p2 measured in this test, an average Gc will be determined related to Gel and G c2 by: G B = G (B - 2r ) G 2r (5.3) c cl p2 c2 p2 where B is the specimen thickness. The Gc, Gcl and Gc2 relationship (equation (5.3)) is derived by simple considerations from the schematic diagram shown in Figure 5.11. Rearranging equation (5.3) it becomes: 2r 0 G = G + P- (G - G ) (5.4) c el c2 el Substituting for r from equation (5.2) gives: p2 E G c2 G = G - G ) (5.5) c el IT a 2 B (Gc2 cl y Since impact fractures are at high speeds they would be expected to be adiabatic and therefore Gel and G would not be expected to depend on c2 temperature, that is to say Gel and Gc2 are material constants independent of temperature. Similarly, E, which relates Kc and Gc would also be expected to be insensitive to temperature. ay, on the other hand, refers to the plastic deformation away from the actual fracture and it should be affected by tempei-ature changes. It would be very difficult to determine the a appropriate to impact speeds but the form of the temperature dependence would be expected to be similar to slower rate data obtainable from the Instron Testing Machine. If 1/a 2, as determined in ordinary slow rate tests at various temperatures, is plotted as a function of G , equation (5.5) would indicate a straight line extrapolating to Gel with a slope: E G c2 a (G - G ) (5.6) c2 01 B The Gel extrapolated value should be a reasonably accurate estimate since it is not derived from the particular a values used. It is also clear from equation (5.5) that in the limiting case, when the plastic zone occupies the whole specimen thickness, i.e. when 2r = B, then: p2 G G c c2 (5.7) In this case the measured fracture toughness corresponds to the plane stress value Gc2' Since a increases with decreasing temperature the form of the curve expected would be Gc remaining at Gc2 with decreasing temperature until 2rp2 < B, when dependence on a comes into force and G would tend to G . c cl Since the dependence of a on temperature is similar (i.e. approximately linear) for most polymers an explanation is provided for the similar form -112- of.curves noted previously. Figure 5.12 shows the form of equation (5.5) schematically and the effect of a thickness change is also indicated. This diagram indicates that Gcl and Ge2 values are independent of the specimen thickness. Equation (5.6) indicates that when the slope S is plotted as a function of i/E a straight line passing through the origin should be expected (i.e. S = 0 as B ca). The validity of this statement was justified from the experimental data obtained for PC and PE as will be discussed in the next section. 5.4.1 Plane Stress Elastic Work to Yielding and Ge Relationship The deformation properties of the polymer are expressed in the term o 2/E in equatiOn (5.5), and this may be written as the plane stress elastic work to yielding: a 2 1 y Pt = (5.8) p2 2 Substituting for a 2/E from equation (5.8), equation (5.5) becomes: G c2 G = G (5.9) c cl (Gc2 Gcl) 2T1- B W p2 which, solving for w , gives: p2 G (0 - G ) c2 c2 cl W - (5.10) p2 2u B (G - G ) c cl From equation (5.10) the plane stress elastic work to yielding, Wp2, can be evaluated as a function of temperature simply by substituting the numeric values for Ge, Gel and Gc2 and for the corresponding specimen thickness, B. The plastic zone size, r is related to w 2 by p2' - 113 - substituting equation (5.8) in equation (5.2), thus: G c2 r (5.11) p2 4u W p2 The actual plastic zone size will be 2r as shown schematically in p2 Figure 5.11, thus: G c2 2r = (5.12) p2 2T1- W p2 From equation (5.12) the plastic zone size can be derived as a function of temperature from the corresponding w 2/ temperature relationship as given in equation (5.10). Since W is expected to decrease with p2 increasing temperature (from equation (5.8)), r should be expected to p2 increase up to a limit denoted by (2rp2)m. This value corresponds to the temperature at which the measured fracture toughness Gc becomes the plane stress fracture toughness Gc2, i.e. when Gc = Gc2, and in this case equation (5.10) becomes: G c2 (5.13) W102 = 2Tr B Substituting in equation (5.12) the maximum plastic zone size is given as: (2r ) = B (5.14) p2 M Therefore, for the pure plane stress case the plastic zone occupies the whole thickness of the specimen. This result was expected from the diagram in Figure 5.11, which in this case takes the form of the diagram shown in Figure 5.13. 114 - 5.5 YIELD STRESS AND TEMPERATURE - TEST PROCEDURE Test to determine the yield stress of various polymers such as: PMMA, PVC (Darvic 110), PC, Nylon 66, HIPS (2710) and PE (002-55), as a function of temperature were carried out in the Instron Testing Machine at a crosshead speed of 0.5 cm/min over the temperature range -100°C to +20°C. All the tests were performed in a temperature cabinet designed to fit on the Instron Machine. The low temperatures required for the tests were achieved by applying the same principles as discussed in section 5.2.2. The specimens were machined to the normal dumbell shape to the dimensions specified by ASTM D638. The yield stress was determined from the ratio of the maximum load (the load at which the material starts toyield) to the cross-sectional area of the specimen. The load to yielding was read off from the Instron chart. It was impossible to evaluate the yield stress in tension for PMMA, since it is a very brittle material and it does not yield but fractures instantly. In this case the yield stress in compression was used and the corresponding data were supplied by Ewing*. 5.6 EXPERIMENTAL RESULTS - DISCUSSION Figures 5.15 to 5.19 show yield stress versus temperature plots for all the polymers tested in tension, and Figure 5.14 shows the corresponding data for PMMA tested in compression. The cs dependence on temperature is similar for all polymers, i.e. a increases with decreasing temperature and the relation is approximately linear. Figure 5.20 shows data for PMMA and PVC (Darvic 110) plotted as * P.D. Ewing, private communication. -115- G (obtained from Figure 5.4) versus 1/ay e and the expected linear c relationship is apparent. The straight line was extrapolated to give Gc/' the "plane strain fracture toughness", and Gc2, the "plane stress fracture toughness", is also given for the case when 2r = B as p2 expressed by equation (5.5) and schematically shown in Figure 5.12. Figures 5.21 and 5.22 show the G versus 1/ay e plots for Nylon 66 and c HIPS (2710) respectively; the data for these two materials are also perfectly fitted. by equation (5.5). Figure 5.23 shows data for two thicknesses of polycarbonate (3 mm and 6 mm) and Figure 5.24 for three thicknesses of polyethylene (PE (002-55): 3 mm, 6 mm and 11 mm). The results clearly indicate the specimen thickness effect on the slope of the line d (given by equation (5.6)) as predicted from the theory and shown schematically in Figure 5.12. When the slopes are plotted versus //13 as shown in Figure 5.25, good straight lines result. It would seem that equation (5.5) is a good description of the data given here. Table 5.1 gives values of Gel and G for the materials tested. The effect of specimen c2 thickness reported by Wolstenholme (1964) is also in accord with equation (5.5), indicating a decrease in energy per unit area with increasing thickness. Since G is found by extrapolation and Get is known, it is possible c/ to deduce the parameter TV from equation (5.10). Figure 5.26 shows P2 plots of W versus temperature for the materials tested. P2 Having established the w /temperature relation the plastic zone P2 size, can be deduced from equation (5.12), substituting for at 2rp2, P2 each temperature. Figures 5.27 to 5.32 show plots of 2r versus p2 temperature for each material tested. -- These plots show clearly that 2r13,2 = B for Gc =Gc2. -116- 5.7 CONCLUSIONS The basic hypothesis that impact strength (i.e. impact fracture toughness) is strongly influenced by the constraint imposed by the specimen geometry seems to provide a good description of the sharp notch data discussed herein. The concept of Gc/ and c2 coupled with yield stress changes gives an accurate picture of variations with temperature and specimen thickness. The fact that the yield stress away from the actual fracture zone does show changes with the temperature while Gal and Gc2 do not is the basis for the observed variations with temperature. -117- CHAPTER 6 EFFECT OF NOTCH RADIUS ON THE IMPACT FRACTURE TOUGHNESS OF POLYMERS 6.1 INTRODUCTION It is common practice to perform impact tests on specimens with blunt notches since the5e are considered a more realistic assessment of material properties than those using sharp notches. It is a fact that the impact strength of materials increases with the notch radius. This is attributed to the greater stress concentration that arises with sharper notches, according to a relationship derived by Inglis (1913). Considerably better understanding of the impact behaviour of a material can be obtained by making tests on specimens with two or more different notch radii than by using sharp notches only. Some polymers are • considered to be more sensitive to notch radius variations than others. The degree of notch sensitivity depends mainly on the toughness of the polymer. For example, brittle polymers, such as crystal polystyrene and PMMA, are considered as very notch sensitive materials whereas tougher polymers are less so. For rubber modified materials, the addition of rubber tends to decrease the notch sensitivity of the polymer. It is evident that the designer should pay more attention to rounding corners and increasing radii in materials whose impact behaviour changes steeply with notch radius than with materials which are less affected. By testing specimens with several notch radii, it is possible to arrange that the test is as severe, or as relatively mild, as desired. Plots of impact strength versus notch tip radius for a number of polymers can be of a great practical significance. In this chapter, the effect of notch tip radius on the impact fracture - 118 - toughness of polymers will be examined, by testing blunt notched specimens for several polymers in the Charpy test at room temperature. The blunt notch data will be directly related to the sharp notch data by the use of the appropriate fracture mechanics analysis. Finally, this work will be extended to measure the impact fracture toughness for blunt notches for several polymers over a range of temperatures below ambient down to -100°C. 6.2 THEORETICAL- ANALYSIS It has been observed that impact strength data may be correlated in terms of the stress at the notch root (using a stress concentration factor (SCF)), and two failure criteria have been used. A fracture toughness will describe sharp notch data while a critical stress criterion is needed for blunt notch data (Fraser and Ward (1974)). However, if an analysis is performed in terms of the stresses at some distance away from the notch tip, separate criteria do not appear to be necessary. By approximating a blunt notch as an elliptical hole, Williams (1973), the stress at the tip of a blunt notch of depth a and root radius p may be estimated from the Neuber (Inglis) formula, Neuber (1958): a = a ( 1 + 2 kW.) (6.1) where as is the stress at the tip of the blunt notch and a is the nominal applied stress. For p « a equation (6.1) may be written as: a = 2a147P (6.2) c and an 'apparent' Gc, say GB, at failure may be defined as: -119- Y2c2a G (6.3) B so that: Yea 2p G (6.4) B 4E and if a is taken as constant, a G value for any p may be found. This B result is not satisfactory since GB = 0 for p = 0 instead of the expected G = G which is the case with sharp cracks. This difficulty may be B c overcome by postulating that failure occurs when the stress reaches a at a distance r from the notch tip. This is equivalent to setting the fracture criterion as being the formation of the same plastic zone as in the sharp crack. Equation (6.2) now becomes, (see Appendix II, equation (II.7)); 1 t p/r ay = a Va/2r . (6.5) 3/2 P (1 p/2r ) so that for sharp cracks (p = 0) we have: = a la/2r (6.6) This relationship should be expected forthe sharp crack case, derived from equation (1.34). If it is postulated that fracture occurs at a stress level ay at a distance rp from the notch tip, then the fracture criterion may be re-written in terms of KB and Kc as: -120- (6.7) K c a 127 r y p or, in terms of G and Gc the fracture criterion is: B G G27a B (6.8) G c a 227T r where GB is the blunt notch fracture toughness and G is the sharp crack fracture toughness. Substituting equation (6.5) in equation (6.8), it becomes: (1 + p/2r )3 G = G (6.9) B c (1 4. p/ rp)2 or p/rp 1- G = G 1,--) (6.10) B c Br 2 p 1 4- 4 p/2r (p/r )2 and for p » r , it gives: G = G (6.11) B c Br 2 An energy, wp1, defined as the elastic energy to yield under plane strain conditions at the notch tip, is given by: a 2 W = 2 . y (6.12) pl E should not be confused with W given by equation (5.8) and defined p1 p2 - 121 - as the elastic energy to yield under plane stress conditions. Substituting for Gc from equations (1.34) and (6.12) in equation (6.11) gives: / G - FIT° p G B (6.13) 2 Thus, for determining GB for a range of p values, the slope at large p values can be used to determine w and with G we may find P1 rp from a relationship similar to equation (5.11), given as: G c r (6.14) p 4Tr p1 6.2.1 Relation Between the Plane Strain Elastic Work W and the p1 Plane Stress Elastic Work W p2 It has been proposed by Timoshenko (1951) that the elastic strain energy can be split into two parts, one due to the change in volume and the other due to the distortion. In the present case, assuming that there is no lateral deformation in the constrained region, that is to say that the elastic strain energy is due to the change in volume only, W pl and w 2 may be expressed in terms of the Poisson's ratio, v, from the stress/strain relationships known as the 'Hooke's law'. The action of a normal stress a in the x-direction of an isotropic material is x accompanied by an elongation ex in the x-direction and by lateral contractions eY and E in the y- and z-directions, given as: a X as v and 6 = — aZ X (6.15) For plane strain conditions (6z = 0): -122- — v) e e _ a (6.16) X IL Y X For plane stress conditions: (1 — 2v) EX a (6.17) 6 6 X The elastic plane strain energy is given as: (e 4. e )2 E X Y (1 — v)2 a 2 (6.18) 2 X 2 and the elastic plane stress energy is given as: (E E E )2 E x Y Z (1 — 2v1 2 a 2 (6.19) p2 2 X 2 From equations (6.18) and (6.19) the ratio W01/p2 is given as: w p1 1 — 2 ) (6.20) P,/, / - 2v P2 From equation (6.20) W co as v > 2 this is expected since complete p/ constraint has been imposed on an incompressible material. However, for most polymers v is around 0.4 giving Pip1/Wp2 = 9, so that Wpi will be expected to be much larger than w . This will be verified by the 2 comparison of wp/ and 1-17102 values for several polymers as determined by experiments. 123 - 6.3 SPECIMENS AND TEST PROCEDURE 6.3.1 Materials The polymers tested in the Charpy test at room temperature for a range of notch radii were: 1. PMMA* : ICI 2. PVC* : ICI Darvic 110 3. PE : (a) BP Rigidex 075-60** (b) BP Rigidex 002-55** 4. PC* : Bayer Makrolon 5. ABS : Monsanto LUSTRAN ABS 244 6. HIPS : BP HIPS 2710 6.3.2 Specimens and Notching Technique Specimens were machined from each material to the normal dimensions and were then notched in sets of 15 for each notch radius. The notching of the specimens was done on a milling machine by means of a fly cutter. Six fly cutters were used, each one having a different radius of curvature: 0.08 mm, 0.1 mm, 0.25 mm, 0.5 mm, 0.8 mm and 1 mm. Regular checks were made to ensure that the radius of curvature of each cutter was within the required limit. It should be noted that for materials prone * PMMA, PVC and PC were also tested for a range of temperatures below ambient down to -100°C at 20°C intervals. ** Density and melt index values for PE are given in Chapter 4, section 4.2. - 124 - to cracking (e.g. PMMA and polystyrene), care must be taken in forming the blunt notches since crazing induced during machining results in GB not increasing as expected since a large r is induced. This is illustrated in Figure 6.1 for PMMA in which milled notches gave a flatter curve. This is a very clear example of the detrimental effect of crazes. 6.3.3 Test Conditions Charpy tests• on blunt notched specimens of a wide range of polymers were performed at room temperature, 20°C ± 1°C. A series of tests were also performed on blunt notched specimens (p = 0.25 mm, 0.5 mm and 1 mm) of PMMA, PC and PVC (Darvic 110) in the temperature range -100°C to +20°C. 6.4 EXPERIMENTAL RESULTS Figure 6.2 shows data for PMMA, PVC and PE (075-60) plotted as GB versus p with equations (6.10) and (6.13) fitted with the corresponding G values as listed in Table 4.1. The slope of the straight line from equation (6.13) determines the plane strain elastic energy wp1, and thus the plastic zone size, r , can be deduced from equation (6.14). Figure 6.3 illustrates similar data for PE (002-55), PC, ABS and HIPS 2710. From the plots it is apparent that equations (6.10) and (6.13) are fitted with the G values for these materials as well. Values of Wpi, rp and G at p = 1 mm for the range of polymers tested are listed in Table 6.1. B For HIPS there was no increase in G with p up to 1 mm, which would he expected since the gross yielding of the section is independent of the notch geometry. A similar result was expected for ABS. This material did not show any substantial increase in GB with p up to 1 mm. The importance of W in determining the impact performance of materials in pl the absence of sharp flaws is apparent from the range of GP values listed I - 125 - in Table 6.1. Those materials with high values give substantial p increases in the fracture toughness, which is perhaps not surprising since high energy to yield constitutes high resilience. Figures 6.4, 6.5 and 6.6 illustrate the temperature effect on the blunt notch data for PVC, PC and PMMA, and the GB/temperature behaviour is compared with the G /temperature behaviour for the sharp notch case. PVC and PC show the expected elevation of the curves, and they remain similar in form. For PMMA, however, a peak appears at -60°C which increases in magnitude with the blunter notches and is totally absent in the sharp notch data. There is no significant evidence of peaks in the other materials for any notch radius. The blunt notch data for PVC, PC and PMMA were plotted in accordance with equation (6.13) so that was obtained and this is shown for three materials in Figure 6.7. wp1 is much greater than Wp2, as expected, and corresponds to v values of around 0.45 from equation (6.20). Values of and TV for PVC, PC and PMMA over the temperature P2 range -100°C to +20°C are listed in Table 6.2. w also decreases with P1 temperature decrease and there is evidence of peaks in all three materials. Peaks in impact data have been widely reported and Vincent (1974) has observed that they are more usually found with blunt notches. The pronounced peak at -60°C for PMMA and the lesser one for PVC at -20°C could be equated with the 13. process (Johnson and Radon (1972)). The more modest peak for PC does not seem to correspond to any tan 6 peak which agrees with the findings of Heijboer (1968). 6.5 CONCLUSION The analysis of the data presented here show clearly that the fracture mechanics idea of a plastic zone affords a method of describing blunt notch impact data in terms of the sharp notch result Gc and the plane -.126 - strain elastic energy to yielding Tipl. Blunt notch data highlights the plane strain yielding process at the notch root and although the plane stress energy T17 shows the dependence on temperature typical of slow 202 rate data the plane strain values, p1, show marked peaks. The strong dependence on volume change is believed to be important here since it seems that changes in v dominate over those in ay. Data for v is scarce but it seems likely that there would be some correlation between tan 6 peaks and volume changes. However, the origins of the effect may be in others, such as those of absorbed fluids, which are apparent in tan 6 and have a strong influence on volume changes. For example, in PMMA a peak at -60°C is sometimes ascribed to the presence of water. This sensitivity of the fracture behaviour of polymers to volumetric effects is likely to be of importance to a deeper understanding of the fundamental processes involved. -127- CHAPTER 7 CONCLUSIONS Specific conclusions relating to the tests and results have already been given at the end of each of the preceding chapters of this thesis. The discussion here 1;r-ill be limited to a few general comments on the work as a whole and on possible future research. The results' presented in Chapter 4 shows clearly that fracture mechanics, which defines the fracture toughness of polymers under impact conditions using only energy measurements, can be a powerful tool for the analysis of impact test data. The use of the appropriate calibration factors gives the same result for both Charpy and Izod tests. The results presented in Chapter 5 indicate that the Gcl and Gc2 concept coupled with the consideration of yield stress changes, gives an accurate picture of variations with temperature and specimen thickness. Worthwhile future research along these lines could be to extend the o temperature test range to below -100°C and greater than +60 C, and to investigate whether the curves of Gc versus temperature are still sigmoidal in form without any pronounced peaks. From the results presented in Chapter 6 it is apparent that the fracture mechanics idea of a plastic zone affords a method of describing blunt notch impact data, so that the 'fracture toughness for any notch radius may be described in terms of the sharp notch result G and the plane strain elastic energy to yield, W c pl. For future work it would be of interest to test blunt notched specimens at various temperatures for a wider range of polymers, and to examine the plane strain elastic energy values, FITL01, for any marked peaks. Future research of significant importance could concentrate on the instrumented impact testing of polymers. Fracture mechanics analysis - 128 - could also be applied to the data and the results could be compared with those obtained from energy measurements. TABLE 1.1 Specifications for Notched Impact Tests ASTM Izod Test BS Izod Test Charpy Test in 2.50 2.50 1.75 Specimen length cm 6.36 6.36 4.45 in 0.50 0.50 0.25 Specimen width cm 1.27 1.27 0.64 in 0.125 - 0.50 0.25 - 0.50 0.06 - 0.25 Specimen thickness cm 0.32 - 1.27 0.67 - 1.27 0.15 - 0.64 in 0.10 0.10 0.10 Notch depth cm 0.025 0.025 0.025 in 0.010 0.040 0.010 Notch radius cm 0.025 0.102 0.025 -130- TABLE 2.1 Coefficients of Y polynomial for several 2L/D values Coefficients of Y 2L/D A Al A A A o 2 3 4 4 1.93 -3.07 14.53 -25.11 25.80 5 1.937 -2.99 14.312 -24.827 25.655 6 1.945 -2.91 14.095 -24.545 25.510 7 1.952 -2.83 13.877 -24.262 25.365 8 1.96 -2.75 13.66 -23.98 25.220 9 1.967 -2.67 13.442 -23.697 25.075 10 1.975 -2.59 13.225 -23.415 24.930 11 1.982 -2.51 13.007 -23.132 24.785 12 1.990 -2.43 12.790 -22.850 24.640 - 131 - TABLE 2.2 Specimen dimensions for the cantilever bending test D B 2L 2L/D (mm) (mm) (mm) 4 12 6.5 48 6 6.5 12 39 7 6.5 12 45.5 9 12 6.5 108 11 12 6.5 132 -132- TABLE 2.3 Specimen dimensions for the three point bend test D B 2L 2L/D (mm) (mm) (mm) 4 6.5 6.5 26 6 6.5 6.5 39 TABLE 3.1 Data for each tup for the Charpy test Mass Distance of CG from pivot Total Energy (milli-Joules) in: Tup Zero Vice Offset Offset (kgs) (metres) Pos. 1 Pos. 2 Pos. 3 Pos. 4 D 0.152 19 18 0.321 909.00 730.87 547.16 381.57 E 0.280 23 22 0.325 1,742.13 1,365.58 1,021.28 712.55 . F 1.144 24 23 0.311 6,812.31 5,317.39 3,972.54 2,759.29 A 2.432 24 23 0.327 15,230.91 11,894.42 8,876.11 6,179.96 TABLE 3.2 Data for each tup for the Izod test Mass Distance of CG from pivot Total Energy (milli-Joules) in: Zero Vice Tup Offset Offset (kgs) (metres) Pos. 1 Pos. 2 Pos. 3 Pos. 4 G 0.307 24 24 0.340 1,997.88 1,552.60 1,194.39 821.55 C 1.483 23 24 0.341 9,698.99 7,397.25 5,702.45 4,014.56. B 2.928 21 23 0.341 17,616.49 14,941.78 11,314.74 7,954.14 TABLE 3.3 Total number of counts and counts lost per swing derived from recorded count for tup D released from position 1 Count recorded, cr Count -2 x (zero offset) n + n_1/2 n — n_1/2 2144 2106 2053 2015 2060.5 45.5 1981 1943 1979 36.0 1921 1883 1913 30.0 1868 1830 1856.5 26.5 1821 1783 1806.5 23.5 1779 1741 1762 21.0 1739 1701 1721 20.0 1703 1665 1683 18.0 1669 1631 1648 17.0 1637 1599 1615 16.0 1606 . 1568 1583.5 15.5 1578 1540 1554 14.0 1551 1513 1526.5 13.5 1524 1486 1499.5 13.5 1500 1462 1474 12.0 - 136 - TABLE 3.4 A sample of the calibration tables for tup D released from position 1 Energy to fracture Count recorded W (milli-Joules) .2144 - 2143 0.360 2142 0.589 2141 0.819 2140 1.049 2139 1.281 2138 1.514 _ 2137 1.747 2136 1.981 2135 2.217 2134 2.453 2133 2.690 2132 2.928 2131 3.167 2130 3.407 2129 3.648 2128 3.890 2127 4.132 2126 4.376 2125 4.620 -137- TABLE 4.1 G (kd/m2 ) MATERIAL CHARPY IZOD Polystyrene (UPS) 0.83 0.83 PMMA 1.28 1.38 PVC (Darvic 110) 1.42 1.38 Nylon 66 (Dry) (Maranyl AD151) 5.30 5.00 PC* 4.85 4.83 PE (075-60) 3.40 3.10 PE (002-55) 8.10 8.40 PE (H0-60-45P) 34.70 34.40 PVC (modified) 10.05 10.00 10.2 (0C)** 10.40 (Jc) PS - rubber modified (CP-40) 11.900 ** 15.80 HIPS. (2710) (J 14.00 (jc) 16.40 (Gc)**c) 49.00 (J ) 47.00 (Jc) ABS 47.50 (Gc) ** * Specimens cut in the extrusion direction. ** Data obtained from the effective crack length. TABLE 4.2 G y (= G/2)c PMMA grade Relative viscosity, n Molecular weight, M c (kJ/m2) (kJ/m2) CA 602 0.72 0.689 x 105 0.42 0.21 1/3300/ 1.27 2.227 x 105 0.58 0.29 DA 100 3 5.882 x 105 0.76 0.38 DP 300 8 17.816 x 105 1.14 .0.57 Commercial grade 40 109.80 x 105 1.28 0.64 - 139 - TABLE 4.3 Charpy test data for Nylon 66 (Maranyl AD151) at various percentages of water content • Time immersed in cold water G C % Water content ' (hours) (kJ/m2) 0% (dry) • - 5.2 1% 50 hours 11.0 1.85% 240 hours 16.6 3% 700 hours 36.8 3.35% 1,000 hours 41.0 4.0% 1,200 hours 50.2 - 140 - TABLE 5.1 Values of G and G for several polymers cl c2 G MATERIAL G c/ c2 (kJ/m2) (kJ/m2) PMMA 1.06 1.28 PVC (Darvic 110) 1.23 1.44 PC • 3.5 5.02 Nylon 66 (Dry) 0.25 4.15 HIPS (2710) 1.0 15.00 PE (002-55)* 1.3 11.90 * Density = 0.955 gm/ml Melt index = 0.2 g/10 min -141 - TABLE 6.1 Blunt notch data at room temperature for several polymers G G B c r MATERIAL p1 P 2 3 pm = iMM (kJ/m2)M ) (MJ/m ) (kJ/m2) PVC (Darvic 110) 1.42 10.0 28 7 PC 4.85 66.5 14 62 PMMA 1.28 3.02 80 3.98 PE (075-60) 3.40 7.5 89 6.40 PE (002-55) 8.10 91.0 17 62 HIPS (2710) 15.00 (Jc) 2.9 1000* 15 ABS 49.00 (Jc) 9.5 1000* 79 * Taken from correction factor -.142 - TABLE 6.2 Data for plane strain elastic energy to yield, 11/201 ,.and plane stress elastic energy to yield, Wp2, for PVC, PC and PMMA for a range of temperatures T W p1 W MATERIAL p2 (°C) (MJ/m3) (Md/m3) -100 2.93 17.90 x 10-2 - 80 2.94 12.80 x 10-2 - 60 2.95 8.95 x 10-2 PVC (Darvic 110) - 40 3.16 6.78 x 10-2 - 20 3.80 4.86 x 10-2 0 4.14 4.43 x 10-2 + 20 7.04 4.26 x 10-2 -100 9.50 6.45 x 10-1 - 80 11.5 4.71 x 10-1 - 60 15.0 3.55 x 10-1 PC - 40 27.5 2.80 x 10-1 - 20 47.0 2.21 x 10-1 0 53.0 1.37 x 10-1 + 20 67.0 1.32 x 10-1 -100 2.07 8.33 x 10-2 - 80 2.20 7.49 x 10-2 - 60 3.40 6.82 x 10-2 PMMA - 40 2.57 5.77 x 10-2 - 20 2.07 4.28 x 10-2 0 2.30 3.94 x 10-2 + 20 3.00 3.40 x 10-2 - 143- ,B CD 0 ELONGATION Figure 1.1: Load/elongation curves for typical tough and brittle specimens - 144 - f =1 Hz A f = 107Hz Figure 1.2*: Schematic representation of the absorption spectra for an hypothetical, idealised partially crystalline polymer - measured by three common techniques. A. Dynamic energy absorption B. Dielectric energy absorption C. Nuclear magnetic resonance •* Boyer (1968) -145- A Surface. energy =1.1 C:7) L 0J w Instability Crack length Elastic strain energy release rate----- Figure 1.3: Energy balance of crack in an infinite plate -146- X Figure 1.4: Centre notched infinite plate -147- CATASTROPHIC FAILURE A Elastic time rise Yielding TEARING FAILURE / Plast ic Area w ,JA Elastic Plastic Deformaticin Deformation TEARING BUT NO DRAWING o 0 TI ME Figure 1.5: Types of impulse curves in instrumented impact - 148 - 1(-- B Figure 2.1: Cantilever bending - specimen geometry 1.6 2 L/ D= 12 1.4 Figure 2.2: The calibration factor (f) for the Charpy test 1.2 2 L/ D=4 2L / D=5 1.0 2 L/D=6 0 .8 2 L/D = 7 / 2L/ D= 8 0.6 2 L/D =9 0.4 2 L /0 =10 / 2 L/D= 11 0 .21- 0 0.1 0.2 0.3 0.4 0- 5 ( (1 / D) -150- LOAD AT FRACTURE (a) 0 DEFLECTI ON -LOAD AT FRACTURE ( b ) 0 DEFLECT ION Figure 2.3: Typical load/deflection curves for cantilever bending (a) Deep cracked specimen 'b' Shallow cracked specimen 22 2 3 5 x10- ( a 1 D ) Figure 2.4: Compliance data for cantilever bending (2L/D = 6) -152- x10 3 dC AIM) (mm/N ) 2 4 a/D) Figure 2.5: Differential compliance data for cantilever bending (2L/D = 6) 1.6 0 21./0=11 1.4 A 2L/D = 9 ❑2L/D = 7 1.2 • 21/ D = 6 2L/D.z. 4 1.0 c..n 0-8 0.6 0 . 4 1 1 4 2 (a/D) 3 5 x10-1 Figure 2.6: Calibration factor 0 for the Izod test (experimental data) 1.6 1.4 1.2 1.0 COMPUTER RESULTS 0 EXPERIMENTAL DATA 0.?) O. 6 21-/D= 4 0.4 0.2 0 1 2 3 ( a / D ) Figure 2.7: Charpy calibration factor (1) - 155 - 2.5 Solid lines— Theory without shear. • a/D= 0.1 O a/D=0.2 A a /D =0.3 Computer Data • a/D = 0.4 CD a/D=0.5 — 2.0 O a/D = 0.1 — .0 a/D = 0.2 L a / D= 0.3 Theory with shear. ❑a/D= 0.4 . CD a/ D= 0.5 Eq.( 2.15) 1.5 1.0 a/D=0.3 a/D=0.4 a /D=0.5 0.5 0 2 4 6 8 12 ( 2L1 D ) Figure 2.8: Charpy calibration factor (1) - 156 - Solid lines Theory without shear O a/D=0.1 — • a/ D=0.2 A a/D=0.3 Theory with shear 0 a/ D=0.4 Eq.(2-- 22) • a/ D=0-5_ • ct/D=o-i • a/D=0-2 Experimental • a/D=0.3 Data o a/D=0.4 13 a/D=0.5 — 40 a/D=0.1 a/D=0.2 a/D=0-3 al0=0.4 a/D=0- 5 2 4 6 8 10 12 2L/ D ) Figure 2.9: Izod calibration factor • 1.0 = 0.0813(D/a) -0.16 26 0.8 A? 0.6 0.4 0.2 0 Figure 2.10: y data for the Izod calibration factor - 158 - 2 c {oJ ( mm IN) 1 o .EXPERIMENTAL DATA ( a =0) o C() FROM Eel. (2· 21) o ( a =0 ) f::l Cl(o) FROM EQ. .. ( 2· 27) . (a=o) or e(o)'" CJ(o)l. I 1 ) . I 6 8 10 12 ( . 2 LJ 0 ) Figure 2.11: CO:~lpliance data for zero crack .1enqth cantilever bendina . -159- .1...••■■•1 • Figure 3.1: The impact apparatus set up for the Charpy test Figure 3.2: The impact apparatus set up for the Izod test -160- (a) =7:11114.110...m. 11214111111.01158==..,..9.30C Figure 3.3: Release mechanism mounted as shown in (a) for positions 1, 2, 3 and in (b) for position 4 only . TUP TUP E n- n_t 2 500 1,000 1,500 2,000 n n-1 2 Figure 3.4: Calibration data for the Charity test tups released from position 1 TUP G 30 Figure 3.5: Calibration data for the Izod test tups released from position 1 20 n - n_i 2 TUP C 10 0 500 1,0 00 n 1,500 2,000 .' • Figure 3.6: Effective release point for tup D released from position 1 RELEASE 2.000 i PO I NT I I I (RIGHT) IMAGINARY " I~ (Rp ) I I SWING\, 1,000 . ,I /1I I cr- 2(Z)) / II I ENTER~----~--~~~~-4-~~~--r-T-~-r-+~r-d ! II I~ I' I 1,000 i /1 II I I ( LEFT) ;' I I I I I I I 2,000 I I 1/ I r I I I I : I I th I " l .;;, 1st/~ ~ I ;?7/ 2nd I~ ~ 3rd tE· "'4 I I ~OUNT I CO,UNT '" '. CqUNT. . I 71COJ Nf" st ~ 1 ~ 2nd ~ 3rd~ "th I 1 SWING I~ SWING I SvyIr~G . ISWING J I I I I f I . 2400 I I I I I ' I I I I I I I I I I I I I I 2,200 I I I I I I l I l I II I I I I c;.- 2 (ZO) J I I I I I . 2,000 I ., I I I I I .~ I I I I I I I I 2n . . 3 4 . C(SV/ING No..} 0 E • Figure 3.7: Recorded count for each swing for tup 0 released from position 1 -164- Figure 3.8: Schematic diagram of the pendulum - 165 - P/2 P/2 Figure 4.1: The Charpy test - specimen geometry - 166 - x 10 9 0 8 0 0 7 6 AVERAGE Gc = 1.26 ( KJ Mb W( J ) 0 4 0 RAZOR NOTCHED SPECIMENS 3 MACHINED NOTCHED SPECIMENS. p 2 0 1 3 4 5 -5 x10 ( ) Figure 4.2: Charpy test data for PMMA - 167 - Figure 4.2a: The cutter used for notching the specimens -168- 0.2 0.15 W(J ) 0.1 0. 0 2 x ( m m ) Figure 4.3: Fracture energy as a function of distance x for PMMA Gc = 0.83 ( KJ /m21 W (J ) Bp (m'. ) Figure 4.4: Charpy test data for GPPS W 01 4 2 1 i 1 2 3 4 -5 Bog ( rn- ) x10 Figure 4.5: Charpy test data for PMMA -171 - 10 8 6 WO 1 4 2 I i I 1 0 4 -5 4Z) 6 x10 BIR( (m?` ) Figure 4.6: Charpy test data for PVC (Darvic 110) -172- Figure 4.7: Fracture surface for GPPS (magnification x10) Figure 4.8: Fracture surface for PMMA (magnification x10) Figure 4.9: Fracture surface for PVC (Darvic 110) (magnification x10) -174- 4 0 3 W(J Gc=4.85 (KJ/mi) 1 0 2 6 -s x10 Figure 4.10: Charpy test data for PC - 175 - 1 B D0 ( mz ) 2 x 10 Figure 4.11: Charpy test data for Nylon 66 (dry) -176- .3 x10 4 3 W( J ) 2 1 I I I 3 4 5 6 _5 0 1 2 x 0 B inz ) Figure 4.12: Charpy test data for two grades of PE -177- 1 0.8 0.6 W ( J 0. Li 0.2 I 0 1 2 3 ...5 BD)2r ( m2 ) X10 Figure 4.13: Charpy test data for PE (H0-60-450 ". - 178 - 1 0·8 . . 0·6 W(J) o O·L. Gc = 10·05 ( KJ Im~) &J o 0·2 a 2 6 8 -0 x 10 Figure 4.14: Charpy test data for PVC (modified) - 179 - Figure 4.15: Fracture surface for PC (magnification x10) Figure 4.16: Fracture surface for Nylon 66 (magnification x10) - 180 - Figure 4.17: Fracture surface for PE (075-60) (magnification x10) Figure 4.18: Fracture surface for PE (002-55) (magnification x10) -181 - Figure 4.19: Fracture surface for PE (H0-60-45P) (magnification x10) Figure 4.20: Fracture surface for PVC (modified) (magnification x10) 0-3 A o o 0·2 o ORIGINAL DATA ..... OJ . [ rp =1 mm] N W( J ) Gc =11·.90 ( KJ I rrf ) 0·1 O~------~1~------~2~------~3------~L---- B¥I ml. ) x 10-'5 Figure 4.21: Charpy test data for PS (CP-40) 0.3 0 0.2 0 ORIGINAL DATA A of = a+r r =1mm P P 35L, W(J ) 0.1 Gc =16-40 ( KJ/mt") 4 X10- 6 BD ( mL ) Figure 4.22: Charpy test data for HIPS (2710) 1.2 oc9 o ° 1.0 O ORI GI NAL DATA Q =0 + r [ r - 1 mm f P 0 Gc 4 7.50 ( KJ / rn41 0 2 6 8 10 -5 x10 BD ) Figure 4.23: Charpy test data for ABS -185- 0.3 0.2 W(J) 0.1 1 3 0 1 2 x10-6 A ( ) Figure 4.24: The application of the Rice's contour integral to the Charpy test data of PS (CP-40) 0.3 0.2 W(J) 0-1 1 2 3 A ( x10 5 Figure 4.25: The application of the Rice's contour integral to the Charpy test data of HIPS (2710) -187- 1.0 0.8 0.6 W( J ) Jc= 49.0 (KJIma") 0.4 0.2 1 2 3 4 5 x10 5 A CM) Figure 4.26: The application of the Rice's contour integral to the Charpy test data of ABS x -z 6 O 00 co MJ) 0 O 0 O 2 1 2 3 4 5 5 x 10 A ( mz Figure 4.27: The application of the Rice's contour integral to the Charpy test data of PMMA - 189 - 04 0 0 0 0.3 0 0 00 0 0.2 W(J ) 0 0 Q9 0 80 0.1 0 1 3 -5 A (m4 ) 2 x10 Figure 4.28: The application of the Rice's contour integral to the Charpy test data of PE (002-55) -190- Figure 4.29: Fracture surface for PS (CP-40) (magnification x10) Figure 4.30: Fracture surface for HIPS (2710) (magnification x10) -191 - Figure 4.31: Fracture surface for ABS (magnification x10) -192- D >1 B = 6 -30 mm ± 0.01 D= 11. 6 0 m m 0.01 60.00 m m Figure 4.32: Izod impact test - specimen dimensions - 193 - Figure 4.33: A typical Izod test specimen clamped in the vice of the testing apparatus -194- 0 PMMA Gc= 1.38 ( KJ/m2 ) ❑PVC — Gc= 1.38 (KJ/rat) O GPPS Gc= 0.83 (KJ/rat) 2 4 BDP ( ma Figure 4.34: Izod test data for PMMA, PVC (Darvic 110) and GPPS - 195 - 0.2 0.15 W(J ) Gc= 5.00 (KJ/d) 0.1 0.05 2 2. BD (rn Figure 4.35: Izod test data for Nylon 66 (dry) Figure 4.36: Izod test data for PC -197- 2.0 1.5 W(J) 1.0 0.5 0 PE ( HO- 60-45P)—Gc=34.4(KJ/m PVC (modified) Gc=10(KJ/m2) I 2 4 6 8 x10-s B ) Figure 4.37: Izod test data for PE (HO-60-45P) and for PVC (modified) 0. 8 0. 6 W ( J ) 0 PE (0 0 2— 5 5)—Gc=8.4 (KJ/ma ) PE (075 — 60 ) —Gc =3 1 (KJ/m4 ) 0.4 0.2 0 /1 6 10 B (m2 ) x105 Figure 4.38: Izod test data for two grades of PE - 199 - 0.4 0 c9 0.3 CO O W(J) 0.2 0 ORIGINAL POINTS 0 of =0:1+rp 0.1 2 , BD ( Figure 4.39: Izod test data for PS (CP-40) - the plastic zone correction approach 0.6 0 0 0 W( J ) 0 0.4 MOO O ORIGINAL POINTS 0 of =CI +rp' [rp =1MM] 0.2 I 0 2 4 6 8 B D95( rriz ) Figure 4.40: Izod test data for HIPS (2710) - the plastic zone correction approach 0 0 1.5 0 0 0 WU) 1.0 0 0 ORIGINAL DATA 1 mm ❑ of =a 4-rp 4) = 0. 5 1 0 2 4 6 8 10 BDcb ml) x105 Figure 4.41: Izod test data for ABS - the plastic zone correction approach - 202 - 0 0.3 WU I 0.2 0.1 0 4 6 5 x10 A Figure 4.42: The application of the Rice's contour integral to the Izod test data of PS (CP-40) 0.5 0.4 0.3 W(J) 0. 2 0.1 i I I I 2 4 6 A ( ma ) 8 xio-3 Figure 4.43: The application of the Rice's contour integral to the Izod test data of HIPS (2710) -204- 0.2 0.15 W(J) 0.10 0.05 2 6 8 x10-5 A (ma) Figure 4.44: The application of the Rice's contour integral to the Izod test data of ABS 0 1.2. ( KJ/d1 1.0 0.8 0.6 0 Gc DATA 0 0.4 0 DATA 0.2 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . le 105 106 107 10 MOLECULAR WEIGHT ( M ) Figure 4.45: Charpy test data for polymethylmethacrylate with various molecular weights 0.7 0. 6 0 PRESENT DATA 0.5 BERRY'S DATA ( KJ/m2 ) 0.4 0.3 0.2 0.1 0 1 1 2 3 X10 VMOLECULAR WEIGHT Figure 4.46: The dependence of the surface energy, y, on reciprocal of molecular weight for polymethylmethacrylate 7 6 5 2 1 Time hours 0.5 1 i 1 I 1 2 2 3 4 6 8 101 p 4 .6 8 10 103 2 3 4 6 8 104 2 3 4 Figure 4.47: Rate of water absorption of Nylon 66 (Maranyl AD151) in distilled water at 20°C 50 40 Gc(KJ/rri) 30 20 10 2 3 4 WATER CONTENT ( ° /0) Figure 4.48: The dependence of Gc on % water content for Nylon 66 (Maranyl AD151) — 209 — Figure 5.1: Low temperature control mechanism with the temperature cabinet fitted on the base of the impact machine Figure 5.2: An indication of the interior of the temperature cabinet MOTOR DEWAR FAN XX x x xx xx xx xx XX X X XX GAUGE RADIATOR c PUMP HEATER I 1=> EUROTHERM)-- CONTROL UNIT oluultuitum r=* Figure 5.3: Schematic diagram of the temperature control mechanism 1.5 1.0 Gc (KJ /m4) 0.5 0 PMMA A G P PS 0 -100 -60 -20 +20 +60 °C ) Figure 5.4: Low impact strength materials 5 Gc KJImt ) 4 3 2 O POLYCARBONATE ❑NYLON 66 1 0 -100 -BO -60 -20 +20 +60 ° C ) Figure 5.5: Medium impact strength materials 60 O , ABS • PE ( HO-60-45P A HIPS (2710) 40 O PE (002-55 ) Gc ( KJ /mz ) 20 -100 -60 - 20 +20 +60 (0 c ) Figure 5.6: High impact strength materials - L14 - Figure 5.7: Fracture surfaces for PE (002-55) tested at various temperatures (magnification x2) Figure 5.8: Fracture surfaces for PE (H0-60-45P) tested at various temperatures (magnification x2) -215- Figure 5.9: Fracture surfaces for HIPS (2710) tested at various temperatures (magnification x2) +20°C 0 °C -20°C Figure 5.10: Fracture surfaces for ABS tested at various temperatures (magnification x2) -216- Specimen thickness (B ) B- 2 rPz r Pz p2 Figure 5.11: Schematic diagram of plane strain and plane stress regions for a specimen of thickness B. Shaded area: Plane stress (G ) C2 Unshaded area: Plane strain (G ) c/ - 217 - 2r B / Pe Gcz Gc 7, Gci T ( °C ) Figure 5.12: Schematic form of toughness changes with temperature as given by equation (5.5) -218- 2 r Pz Figure 5.13: Schematic form of a specimen of thickness B under entirely plane stress conditions 500 - 219 - 400 300 or MN/m2) 200 100 -140 -100 -60 -20 +20 T (°C) Figure 5.14: Yield stress data for PMMA - 220 - 200 180 16 0 140 120 100 Y (MN/m1 80 60 40 20 I - 100 -60 - 20 +20 + C Figure 5.15*: Yield stress data for PVC (Darvic 110) * M. Parvin, private communication -221 - T (°C) Figure 5.16: Yield stress data for polycarbonate - 222 - 150 100 50 -100 -60 -20 +20 ( °C Figure 5.17: Yield stress data for Nylon 66 (Maranyl AD151) - 223 - 20 0 —100 — 60 +20 +20 T ( °C 1 Figure 5.18: Yield stress data for HIPS (2710) - 224 - 60 50 c:(Mtlirri21 40 30 20 I I —10—100 —60 —20 +20 T ( °C ) Figure 5.19: Yield stress data for PE (002-55) 0-- GC2 ❑PVC DARVIC 110 l (ni 0 PMMA 1 2 3 _z - (\411/m2")2 Figure 5.20: Variation of impact fracture toughness with yield stress for PMMA and PVC (Darvic 110) Gc (KJ/m21 0-5 1.0 1.5 x10 cr ."4 (MN/rr)-4 Figure 5.21: Variation of impact fracture toughness with yield stress for Nylon 66 20 Gc( KJ kr? ) 0— — — -- GC2 10 1 t -3 0 1 2 ) 4 x10 cfY-4 ( MN/ ma l' 3 Figure 5.22: Variation of impact fracture toughness with yield stress for HIPS (2710) - 228 - 5 Gc ( KJ / m2 4 1 1 1 1 2 3 _z , -2 A ITY (MN/Mr) Figure 5.23: Variation of impact fracture toughness with yield stress for polycarbonate for two specimen thicknesses -229- 12 0 0 0 0 z Gc ( KJ/m 0 B = 3 mm O B = 6 mm B = 11 mm 2 4 03121 MN/e l 6 x16.13 Figure 5.24: Variation of impact fracture toughness with yield stress for PE "002-55 8 x10 10 5 o PC 0 PEE 002- 55 1 2 3 4 -1 x10 134 ( mm-1) Figure 5.25: Variation of slope of G versus Vo 2 lines with specimen thicknesses -231 - 1.0 O PE [ 002- 55 1 0 PC A NYLON 66 0.8 o PVC DARVIC 110 I • PMMA Wp2(MJIrril 0.6 0.4 0. -100 -60 -20 +20 T ( °C ) Figure 5.26: Variation of plane stress yielding energy with temperature - 232 - X10-2 6 Wpa ( NINA 2rp a (mm) 4 4 2 2 0 0 100 60 20 20 T (°C Figure 5.27: Variation of plane stress yielding energy and plastic zone size with temperature for PMMA p • - 233 - 0.2 0.15 WP2 2rpa MN/ma 6 0.1 0.0 ti 0 -100 -60 -20 +20 T °C ) Figure 5.28: Variation of plane stress yielding energy and plastic zone size with temperature for PVC (Darvic 110) - 234 - 0.3 W z (MN/A) 2r Pa 0.2 (mm) 0.1 2 0 0 -100 60 -20 +20 T (°C Figure 5.29: Variation of plane stress yielding energy and plastic zone size with temperature for Nylon 66 I -235- P2 MN/m'j 6 2r (mrn 4 2 -100 -60 -20 +20 T (°C Figure 5.30: Variation of plane stress yielding energy and plastic zone size for HIPS (2710) - 236 - 08 Pz MN/Mn 0.6 2rPz mm) 0.4 4 02 2 0 0 -100 -60 -20 +20 T (°C) Figure 5.31: Variation of plane stress yielding energy and plastic zone size with temperature for polycarbonate • - 237 - 1.5 wpz MN/rri) 2rp2 1.0 ( mm ) 4 0.5 2 0 1 -100 -60 -20 +20 T (°C Figure 5.32: Variation of plane stress yielding energy and plastic zone size with temperature for PE (002-55) 4 GB (KJ/m2) 0 2 0 0 Milled notches O Drilled notches 0 0.2 0.4 0.6 0.8 1.0 0 (mm) Figure 6.1: Effect of notching method on blunt notch data for PMMA O PMMA O PVC [ DARVIC 110] A PE 075-60 Broken lines equ. ( 6. b) Solid lines equ. ( 6. 9 I 0.1 0.2 0.3 Oh 0.5. 0.6 0.7 0.8 0.9 1.0 (mm) Figure 6.2: The variation of critical strain energy release rate with notch tip radius for PMMA, PVC (Darvic 110) and PE (075-60) O ABS O PE I 002 -551 ❑PC A HIPS (2710] Broken lines equ. (6. 8 1 Solid lines equ. ( 6.9) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 j) (mm) Figure 6.3: The variation of critical strain energy release rate with notch tip radius for ABS, PE (002-55), PC and HIPS (2710) 7 6 qB(KJ/rri) 5 4 3 2 1 —100 —60 -20 +20 T (cC Figure 6.4: Blunt notch data for PVC (Darvic 110) 60 O p =1. 0 mm o p = 0.5 mm 50 L p = 0.25mm O p = 0.03mm (Shan.) notches) 40 GB (KJ/m4 30 20 10 0 — 0 -100 -60 . -20 +20 T ( °C Figure 6.5: Blunt notch data for polycarbonate - 243 - 4 3 GB IKJ/m4 ) 2 1 0 p = 1.0 mm = 0.5mm L p = 0.25mm 0 ys 7=0.03mm (Sharp notches) 0 -100 -60 -20 420 T (°C ) Figure 6.6: Blunt notch data for PMMA - 244 - A PMMA O PVC [ DARVIC 110 I 8 0 PC 80 wpl (MN/m2') 6 60 Wpi (MN/ m) 4 40 20 0 0 -100 -60 -20 +20 T (°C ) Figure 6.7: Variation of plane strain yielding energy with temperature -245- APPENDIX I I.1 THE RELATIONSHIP BETWEEN FRACTURE TOUGHNESS AND ABSORBED ENERGY FOR THE IZOD IMPACT TEST Here a relationship similar to the equation (1.29) will be derived for the Izod test specimen (cantilever bending) shown in Figure 2.1. The equation (1.20) (i.e. G = (P2/2BXdC/da) derived in Chapter 1 for the Charpy test specimen also holds for the Izod test specimen if the crack a is extended by an amount da. As in section 1.10.4, substituting equations (1.9) and (1.10) in equation (1.20) gives: y2a2a pa A7 ET- - 2B. a) where 72 is the geometrical factor introduced to account for finite width effects. In this case the Y2 polynomials will be different from those for the Charpy test, derived by Brown and Srawley (1966). a is the nominal stress, and for cantilever bending it is given by simple bending theory (Timoshenko (1951)) as: 6 P L a - (I.2) BD2 where P is the applied load, and L, B and D are the cantilever beam dimensions as illustrated in Figure 2.1. By combination of equations (I.1) and (I.2) the compliance C is expressed as: 72 L2 f Y2a da C E BD4 The constant of integration Co is the compliance at zero crack length and - 246 7- is given by conventional theory as: 4L3 (I.4) E BD3 Therefore, the compliance for a cracked cantilever beam is given as: = 72 I E1 f Er2a 4L3 0.5) E BD4 E BD3 If the only energy absorbed in a test, W, were in fact the elastic strain energy, UB, then from W = UB = P2c/2, the energy W can be derived by substituting for c from equation (15) and expressing P in terms of a from equation (I.2): W = GBD 72a da LD/18 /72a = GBDO where = f dx L/18L] /Y2x. (I.8) Comparison of equations (1.28) and (18) indicate that similar functions for the calibration factor (f) should be expected for the.Charpy and for the Izod test (see Chapter 2). - 247 - APPENDIX II STRESS CONCENTRATIONS AND BLUNT CRACKS II.1 INTRODUCTION The analysis of the stress distribution at the tip of a blunt crack in a plate subjected to a uniform tensile stress a in the y-direction (as shown in Figure II.1) is not at all a simple problem, and it involves complicated stress functions. Williams (1973) postulated that a crack with a finite radius of curvature at the tip can be approximated to an elliptical hole assuming that p « a, where p is the radius of curvature of the ellipse and 2a is the major axis as shown in Figure II.1. In this special case, the stresses along the major axis of the ellipse (y = 0) will give the stresses at the tip of the blunt crack. 11.2 STRESSES AROUND AN ELLIPTICAL HOLE The general solution for the stresses round an elliptical hole in an infinite plate in a state of simple tensile stress a was obtained by Timoshenko (1951) using complex variable theory. He expressed the stresses a and a in terms of the curvilinear n coordinates n and g. Williams (1973) expressed the results in terms of the Cartesian coordinates as ax and a by means of the variables: a -b 2B = a 4. b and m a + b (IM) and a distance parameter: a = 2B— hx/2B)2 - m - 248 - where x is the distance from the centre of the ellipse. The stresses along the major axis of the ellipse (y = 0) were given by: A2 a y = - + A 2 l and (II.3) aX = where F. en 2_ Al (m2-1) , + /),3a - a2- m L a2- m a2 _ and (II.4) 2 ('11 + A = a [1 + 2 a2_ m The stress a at the ends of the hole on the major axis, i.e. x = — a X (a = 0) is given as: X aY a (1 ÷ or, in terms of the radius of curvature of the ellipse p = b2/a, equation (II.5) gives: a1, = a (1 + 2 va-AD (II.6) This is the so-called 'Inglis formula' discussed in detail by Neuber (1958). - 249 - 11.3 STRESSES AROUND A BLUNT CRACK For the case in which the radius of the blunt notch is very small, the elliptical hole solution may be considered making the assumption that p « a. 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(1964) "Factors Influencing Izod Impact Properties of Thermoplastics Measured with Autographic Impact Test", J. Appl. Poly. Sci., 8, 119. 85. ZENER, C., and HOLLOMON, J.H. (1944) "Plastic Flow and Rupture of Metals", Trans. Am. Soc. Metals, 33, 163. - 261 - 86. ZINZOW, W.A. (1938) Discussion in "The Impact Testing of Plastics", Proceedings Am. Soc. Testing Materials, 38, 42. Paper 1 The Determination of the Fracture Parameters for Polymers in Impact E. PLATI and J. G. WILLIAMS Department of Mechanical Engineering Imperial College, London, England A method of analysis is given by which the critical strain en- .ergy release rate G, for impact tests may be deduced for both Charpy and Izod tests from normal energy measurements. Suitable calibration factors are determined and the method is applied to a range of polymers. Very close agreement is achieved between the Charpy and Izod results except for highly ductile materials for which it was necessary to use a fay plastic analysis. The method is extended to blunt notches and it is shown that the use of a strain energy per unit volume to yielding, together with a blunt notch stress analysis, gives a good description of the results. INTRODUCTION which can be directly related to the sharp notch onventional impact testing involves the measure- data by the use of appropriate fracture mechanics ment of an energy, w, to break a notched speci- analysis. men and this is generally divided b.y the ligament Linear elastic fracture mechanics (LEFM) has area A to give an apparent surface energy w/A. It been applied widely to the failure of glassy poly- is well known that such an analysis of the data is mers, e.g., ( 4-7 ). It has been shown that the con- not satisfactory, particularly since the parameter cepts of a critical strain energy release rate Gc, and plastic zone sizes as given has a strong geometry dependence. One method of fracture toughness K, improving the situation is to measure the load at by the conventional analysis are accurate descrip- failure and then employ the usual fracture mechan- tions of observations of slow crack growth in poly- ics analysis methods. This involves very difficult mers. In this work it is hoped to improve the use- experimentation and the interpretation of the re- ful range of the theory by considering energy rep- sults is complicated by dynamic effects and re- resentations for application to the impact test as cording problems. opposed to the conventional load forms. Some recently published work (1, 2) showed that FRACTURE MECHANICS IN if the assumption of elastic deformations is made ENERGY TERMS then it is possible to deduce the critical strain en- It is of value here to derive the basic fracture ergy release rate, G„ directly from the absorbed mechanics relationships in terms of energy ab- energy measurement. A preliminary study on poly sorbed at fracture rather than the maximum load, (methyl methacrylate) (PMMA) (1) showed that or stress achieved, as is conventional. This is no the method gave a constant G, for several geometries more than saying that since it is this energy which in the Charpy test. Since G, may be employed in is measured experimentally the theory should be the existing fracture mechanics analyses of prac- couched directly in these terms. If attention is tical problems the results obtained are of consider- confined to linear elastic fracture mechanics (LEFM) able value. then the specimen is assumed to deform in a totally This paper extends this preliminary work by de- elastic manner so that the compliance, C, is a func- riving calibration factors for both the Charpy and tion only of crack length and geometry. Thus, for Izod tests and determining G, for a range of poly- an applied load P resulting in a deflection x we have; mers in both tests. It was found in the course of this testing that some very tough polymers do not C(a) (1) behave in an elastic manner and consideration has been given to the case of fully plastic deformation where a is the crack length. Since the deflection in the ligament. This concept is currently under is entirely elastic, the energy absorbed will be the active consideration for metals (3) and the concept area under the triangular load-deflection diagram; of a plastic work parameter, J„ appears to be ap- 1 1 plicable to polymers also. In addition, considera- w = — Px = — P2.C (2) tion is given to testing blunt notched specimens 2 2 470 POLYMER ENGINEERING AND SCIENCE, JUNE, 1975, Vol. 15, No. 6 The Determination of the Fracture Parameters for Polymers in Impact For a specimen of uniform thickness B the strain where /3 is another geometric constant. Thus, 4) be- energy release rate G is given by; comes; dw f Y2. (a/D)-d(a/D) r ft 1 • 1 G = • (3)° — 4- I_ 2a y2 B da Y2. (a/D) 2 -I • ( a/ D ) (11) It is postulated in LEFM that fracture occurs when G = Gc, a critical value, so that a fracture For the case of very wide center notched plate of length 2L Eqs 5 and 6 give the well known Griffith P2 dC (4) equation: ce _ 2B da ra2a = (12) The conventional stress analysis is usually written in terms of the fracture toughness K, so that; For the energy case since Y2 = r, a = 1 and p = K,2 Y2- cr2 .a (5) 2L/D, we have, 1 2L 1 where a is the maximum gross stress and Y2 is a = — (a/D) + — • —_— function of crack length to specimen width D, ratio 2 2r D (a/D) (a/D) and includes finite width and free edge effects. and Go are related by; 2w Gc (13) Keg = EGe (6) 2LD B (a + for plane stress where the Young's modulus E is a replaced by E/1 — v2 for plane strain. For any A further parameter of interest in this work is geometry there will be a constant ratio between the plastic zone size rp. For polymers it is prefer- maximum gross stress and load say (o/P), a/BD, able to use the line plastic zone, or Dugdale model so that from 5 and 6 we have: Eqs 4, (8), to the more usual circular zone, so that, dC_ 2a2 Y2(a/D) 7 Kc2 d(a/D) EB ( ) rp = (14) 8 a 2 dC/d(a/D) may be found either experimentally where av is the yield stress. In energy terms we may or theoretically so that may be deduced and by r define an energy per unit volume to yield using measured values of P at failure K, may be found from Eq 5. 0a 2 If energy and not load is to be measured, how- WP = 2E (15) ever, we must return to and Eqs 2 4 so that, so that Eq 14 becomes 'Y• G, w = G, • BD.*. (8) r = (16) where 16 w9 C = (9) dC/d(a/D) THE EFFECTS OF PLASTIC YIELDING When high toughness materials are tested the If 4, is determined as a function of (a/D) and the energy measured at fracture is plotted as a func- stresses induced at fracture tend to increase so tion of BD4, for different specimen geometries a that plastic yielding may occur. LEFM assumes straight line of slope G, should result. elastic behavior and is thus not capable of describ- 4) may be determined experimentally using Eq 9 ing large degrees of plastic deformation. It is pos- by measuring C for different (a/D) values and sible to extend the useful range of the theory, how- hence finding dC/d(a/D). It may also be deduced ever (9), by using an effective crack length, a1, from Y2 since from Eq 7; where; a f = a ± r9 (17) 2a2 C= — Y2• (a/D) -d(a/D) + Co and a is the original crack length and r, is the plas- EB tic zone length from Eq 16. In impact testing, the correction factor is not where Co is the compliance for 0 and may a/D = easy to apply since w„ is unknown but can be es- be written as; timated from low rate values. More refined estimates C (10) may be varying rp in the w vs &Do plot to give the ° EB best fit to the data. When full yielding occurs, the elastic analysis is no longer valid and the concept of ( 3 ), the more • This is true for all loading conditions but is more easily derived for 1, a fixed load or displacement. general fracture energy criterion, must be invoked. POLYMER ENGINEERING AND SCIENCE, JUNE, 1975, Vol. 15, No. 6 471 E. Vat and I. G. Williams This is defined such that J, = G, for the elastic case but it is applicable for all degrees of plasticity and may be written in terms of the yield stress and the crack tip displacement, u, at fracture as: jc = cry • u (18) a If full yielding is assumed in bending and this cri- terion is used then assuming solid body rotations P/2 P/2 we have; u B(D - a) w= •creB(D -a)=1. (19) Three point bending - the Charpy Test 2 2 If the ligament area is taken as, A=B(D -a) then 2w (20) B A The factor 2 arises because the average displace- ment in bending is u/2 compared with u in tension. The use of w/A as a parameter is, of course, the traditional method of analysing fracture data but it should be noted that it is only appropriate for high energy fractures with gross yielding and the factor 2 must be introduced in bending to give valid comparisons with G, b) Cantilever bending-the Izod Test . Fig. 1. (a) Three point bending-the Charpy test. (b) THE DETERMINATION OF 4, Cantilever bending-the Izod test. The two - geometries used in impact testing are shown in Fig. 1. For the Charpy test, Fig. 1(a), Y2 Table 1A. Charpy Calibration Factor has been computed and given in a series form for several (2L/D) ratios (10) and ¢ may be deter- mined using: 2LID 2L/D 2LID 2L/D 2L/D 3L ( L )3 a/D =4 =6 =8 =10 =12 a= - and fi= 2 - D D 0.04 1.681 2.456 3.197 3.904 4.580 so that we have /3/2a2 = L/9D. For short notches Y2 0.06 1.183 1.715 2.220 2.700 3.155 0.08 0.933 1.340 1.725 2.089 2.432 fts r so that, 0.10 0.781 1.112 1.423 1.716 1.990 1 ( a ) 1 2L 1 0.12 0.680 0.957 1.217 1.461 1.688 - (21) 0.14 0.605 0.844 1.067 1.274 1.467 2 \ D 1+ 187r • \ D (a/ D) 0.16 0.550 0.757 0.950 1.130 1.297 0.18 0.505 0.688 0.858 1.015 1.161 For the Izod test, Fig. 1(b), there are no published 0.20 0.468 0.631 0.781 0.921 1.050 values of ¢ so that only the short notch value of 0.22 0.438 0.584 0.718 0.842 0.956 may be computed and since fl/2a2 = L/18D we 0.24 0.413 0.543 0.664 0.775 0.877 0.26 0.391 0.508 0.616 0.716 0.808 have; 0.28 0.371 0.477 0.575 0.665 0.748 1 ( a \ 1 ( 2L ) 1 0.30 0.354 0.450 0.538 0.619 0.694 cis = - ) - • \ -) (22) 0.32 0.339 0.425 0.505 0.578 0.647 2 D 367r D (aID ) 0.34 0.324 0.403 0.475 0.542 0.603 Values of ¢ have been computed for the Charpy 0.36 0.311 0.382 0.447 0.508 0.564 0.38 0.299 0.363 0.422 0.477 0.527 case ( three point bending) using the published Y2 0.40 0.287 0.345 0.398 0.448 0.494 functions (10) and the results are tabulated in Ap- 0.42 0.276 0.328 0.376 0.421 0.462 pendix 1, Table IA for 2L/D ratios of 4, 6, 8, 10, 0.44 0.265 0.311 0.355 0.395 0.433 and 12 and for all) values up to 0.6. Some experi- 0.46 0.254 0.296 0.335 0.371 0.405 0.48 0.244 0.281 0.316 0.349 0.379 mental checks were made on these results by test- 0.50 0.233 0.267 0.298 0.327 0.355 ing a number of specimens with various notch 0.52 0.224 0.253 0.281 0.307 0.332 lengths. The load-deflection diagrams were never 0.54 0.214 0.240 0.265 0.288 0.310 perfectly straight, mainly because of non-uniform 0.56 0.205 0.228 0.249 0.270 0.290 supporting at low loads and slow crack growth for 0.58 0.196 0.216 0.235 0.253 0.271 0.60 0.187 0.238 0.253 higher loads. Several methods of determining C 0.205 0.222 472 POLYMER ENGINEERING AND SCIENCE, JUNE, 1975, Vol. 15, No. 6 The Determination of the Fracture Parameters or Polymers in Impact were tried but the most reliable was to record the Table 2A. Izod Calibration Factor load and deflection at failure and then measure the slow crack growth after failure to determine the 4, appropriate crack length. A graph of C versus all) 2L10 21413 2L10 2L/D 2L/D was constructed and hence dC/d(a/D) determined =4 =6 =7 =9 =11 so that 4 could be found. Figure 2 shows some re- 5 0.06 1.540 1.744 1.850 2.04 - sults for 2L/D = 6 in which the computed and ex- 0.08 1.273 1.400 1.485 1.675 1.906 perimental results are compared. The agreement 0.10 1.060 1.165 1.230 1.360 1.570 is close so that either method may be considered 0.12 0.911 1.008 1.056 1.153 1.294 reliable. Equation 21 is also shown, i.e. for Y2 = 0.14 0.795 0.890 0.932 1.010 1.114 0.16 0.708 0.788 0.830 0.900 0.990 sr), and as expected there is a marked divergence 0.18 0.650 0.706 0.741 0.809 0.890 at high a/D values. 0.20 0.600 0.642 0.670 0.730 0.810 The Izod calibration factor was determined ex- 0.22 0.560 0.595 0.614 0.669 0.750 perimentally (since Y2 has not been computed) and 0.24 0.529 0.555 0.572 0.617 0.697 the results are tabulated in Appendix 1, Table 2A 0.26 0.500 0.525 0.538 0.577 0.656 0.28 0.473 0.500 0.510 0.545 0.618 for 2L/D values of 4, 6, 7, 9, and 11. It is interest- 0.30 0.452 0.480 0.489 0.519 0.587 ing to compare these results with the Charpy values 0.32 0.434 0.463 0.470 0.500 0.561 since they would be expected to be very similar 0.34 0.420 0.446 0.454 0.481 0.538 from Eqs 21 and 22. Figure 3 shows cis • (aID) plotted 0.36 0.410 0.432 0.440 0.468 0.514 versus (aID)2 for the Charpy data which from Eq 0.38 0.397 0.420 0.430 0.454 0.494 0.40 0.387 0.410 0.420 0.441 0.478 21 should be linear with a slope of 0.5. This is never 0.42 0.380 0.400 0.411 0.431 0.460 true and there are pronounced free edge and finite 0.44 0.375 0.396 0.402 0.423 0.454 width effects as shown by the comparison with 0.46 0.369 0.390 0.395 0.415 0.434 Eq 21 given for 2L/D = 6. The values of o• (aID) 0.48 0.364 0.385 0.390 0.408 0.422 for aID = 0 are also shown plotted versus 2L/D 0.50 0.360 0.379 0.385 0.399 0.411 and the straight line predicted by simple beam theory is given with a slope of 0.015 compared with the theoretical value of 0.0176. by approximately 4D. It should be noted, however, The Izod data are shown in Fig. 4 and there is that .4) • (a/D) changes very rapidly in this region clearly a very different (aID) dependence result- and is difficult to extrapolate so that some error may ing in lines which are almost straight for (aID) > be expected in this estimate. 0.2 with a slope of 0.3 ( compared with 0.5 for Y2 constant). This significantly less pronounced finite Theoretical Line For width effect compared with the Charpy data is From Equation 121) presumably due to the extra constraint at the clamped crack. The values of c • (a/D) at OD = 0 show a straight line of slope 0.0062 compared with a theoretical value of 0.0088. There is, however, a very marked effect in that the line does not pass through the origin indicating an additional term of 0.055. The simple theory assumes perfectly rigid clamping which is not achieved in practice. This results in a rotation at the clamp which is equiva- lent to the length of the specimen being increased 1.6 2L/D • 6-0 0-- Computer results 16 Experirnentot results - -0-- Simple theory equation (211 09/19f or a /D. 0 versus 2 L/D 1.2 1.0 0-6 0-6 0.4 0.2 al 02 03 os 0.1 0.2 la/D) 2 Fig. 2. The calibration factor for the Charpy test determined by computation and experiment. Fig. 3. Charpy test calibration factor. POLYMER ENGINEERING AND SCIENCE, JUNE, 1975, Vol. 15, No. 6 473 E. Plan and J. C. Williams • Charpy Test O !sod Test AVERAGE Gel-32,003 J1m2 o plak for a/D=0 versus 2L/D W*=W- k e k e .L • 3 x 1 0 2J (Izod) k e =1.0 x 10 2J (Charpy) 0.1 (a/0) 2 0 . 2 0.3 (BD9)) Fig. 4. Izod test calibration factor. Fig. 5. Charpy and Izod data for FNMA—kinetic energy corrections included. COMPARISON OF CHARPY AND MOD RESULTS A number of different polymers were tested at 23°C using both methods to compare the G, values. The data were obtained using an impact testing 6 w. machine designed by BP Chemicals which enables (.11 .WER/48 Ct. 8 10 10' lim2 measurements of high accuracy to be obtained. The 5 lines on the w vs Bat) graphs gave a positive inter- x to cept in w because of kinetic energy effects (1) and Chorpy lest direct comparison may be made by correcting AZ0 I,,, Test a the results for this kinetic energy lc, and plotting 2 0 w• = w — 1c, versus BDo. The correction may be derived (1) as: 0./: 1 I I s 1m 6 7 8 9 10 t2 13 s10_ k•= (1+e) (1+ (1-0)m( M (1313111 2 M m+ M V2 Fig. 6. Charpy and Izod data for a medium-density poly- (23) ethylene—kinetic energy corrections included. where m.-_-_- the mass of the specimen; M = the mass of the tup; V = the tup velocity; and e = the co- styrene (HIPS). The results do not fall on a straight efficient of restitution taken as 0.58 here ( 1 )°. line through the origin and if a line is put through Figure 5 gives results for PMMA which show the points a positive intercept is given. Points are close agreement for the two methods and similarly also shown with a correction of r p = 1 mm applied for a medium density polyethylene in Fig. 6. Table 1 which works quite well with the Charpy data and gives a comparison of G, values for a range of although the Izod results give a line of about the polymers as determined by both methods and again same slope, the intercept is now negative and the close agreement is indicated. The result of 4.8 kJ/m2 result must be judged unreliable. The fact that the for polycarbonate compares with 4kJ/m2 given in Charpy results give more satisfactory behavior here may be explained by considering the ratio of the (2). The behavior of materials which exhibit plastic energy to fracture and that to give first yield w' yielding is illustrated in Fig. 7 for high-impact poly- which is, w — • The equation given in (1) is in error. The change in form only af- 8 ) fP (24) fects the value of e used since m << M. w' y2 a 474 POLYMER ENGINEERING AND SCIENCE, JUNE, 1975, Vol. 15, No. 6 The Determination of the Fracture Parameters for Polymers in Impact Table 1. The Critical Strain Energy Release Rate Determined by Two Methods G,, J/m2 Material Charpy Izod Polystyrene (GPPS) 0.83 x 103 0.83 x 103 PMMA 1.28 x 103 1.38 x 103 PVC (Darvic 110) 1.42 x 103 1.38 x 103 Nylon 66 5.30 x 103 5.00 x 103 Polycarbonaten 4.85 x 103 4.83 x 103 PE (medium density)2 8.10 x 103 8.40 x 103 PE (high density)3 3.40 x 103 3.10 x 103 PE (low density) 34.7 x 103 34.40 x 103 PVC (modified) 10.05 x 103 10.00 x 103 Fig. 7. HIPS data for both Charpy and Izod test. HIPS 15.8 x 103 (.1,) 14.0 x 103 (Jo) ABS (Lustran 244) 49.0 x 103 (Je) 47.0 x 103 (4) *1 Specimens cut in the extrusion direction. Density = 0.940; MI = 0.2. Density = 0.960; MI = 7.5. Since rp tends to be large for these materials it is necessary to keep Y2.a as large as possible for w < w'. Y2 is larger for the Charpy test (as indicated by the qs functions) so that in general the energy levels at fracture will be lower in that geometry and the corrected elastic solution would be ex- pected to be more appropriate. The same data are shown plotted as w° versus A in Fig. 8 and give reasonable lines through the origin, as expected from Eq 20, with J = 15.8 kJ/ m2 for Charpy and 14.0 kJ/m2 for Izod. This is a quite close agreement with the corrected data value of 15.8 kilm2. The I, calculation is the preferable method, however, since it does not involve a cor- • Charpy rection procedure. The results given in Table 1 • Izod for HIPS and ABS, the two materials which showed evidence of plastic yielding, are derived from the w° vs A plot and are indicated as values. Reference • 3 2 (2) analyzes ABS data in this way giving J, = 28 AVERAGE J c =15 x 10 Jim kJ/m2° but suggests a distinction between initia- tion and propagation criteria which does not ap- pear to be necessary. BLUNT NOTCH TESTING It is common practice to perform impact tests 1 2 3 6 5 6 7 8 on specimens with blunt notches since these are A x10-5 m2 sometimes considered a more realistic assessment 8. HIPS data plotted in 'terms of ligament area. of material properties than those using sharp notches Fig. (11). It has been observed that the data may be correlated in terms of the stress at the notch root ing the notch to an ellipse which gives the Neuber using a stress concentration factor ( SCF) and two (Inglis) formula (8): failure criteria have been used. A fracture tough- ness will describe sharp notch data while a critical stress criterion is needed for blunt notches (12 ). u = [ 1 + 2 However, if an analysis is performed in terms of the stresses at some distance away from the notch which is essentially the solution used in the SCF tip separate criteria do not appear to be necessary. analysis (11). The stress at the tip of a blunt notch of depth a For p << a this may be written as, and root radius p may be estimated by approxirnat- 2007 crc = (25) ° The 2 in the equivalent of Eq 20 is omitted in (2). VP POLYMER ENGINEERING AND SCIENCE, JUNE, 1975, Vol. 15, No. 6 475 E. Platt and J. G. Williams and an 'apparent' G„ say GB, at failure may be de- Table 2. Fracture Parameters for a Range of Polymers fined as, Y2a2a P= GB = 1 mm Gc, Wog GB, so that, Polymer (J/m2 (J/M3 fy, (J /m2 y2o.c2 X 103) X 106) (An1) X 103) GB= (26) 4E PVC (Darvic 110) 1.42 10.0 28 7 and if cr, is taken as constant a GB value for any p Polycarbonate 4.85 665 14 62 3.98 may be found. This result is unsatisfactory since GB PMMA 1.28 3.oz, tje = G, which may be PE (high density) 3.40 7.5 89 6.4 = 0 for p = 0 instead of GB PE (medium density) 8.10 91 17 62 overcome by postulating that failure occurs when HIPS 15.00 (Jo) 2.9 1000* 15 the stress reaches cry at a distance r, from the notch ABS 49.0 (Jo) 9.5 1000* 79 tip. This is equivalent to setting the fracture cri- terion as being the fomiation of the same plastic * Taken from correction factor. zone as in the sharp crack and hence the same Table 2 lists some values obtained for a range of crack opening displacement as given by u = Gc/ci, polymers and all but HIPS and ABS exhibit be- is achieved. Equation 25 now becomes (8): havior similar in form to PVC. For HIPS and ABS — (rp P) there was no increase in GB with p up to 1 mm rry = TcrVa. (27)* which would be expected since the gross yielding (2rp P)3" of the section is independent of the notch geometry. so that for sharp cracks (p = 0) we have, The values of GB for p = 1 mm are also given in ircrVa Table 2 and the importance of w p in determining Qy = (28) impact performance in the absence of sharp flaws is apparent. Those materials with high wp values give as in Eq 14. substantial increases in the fracture toughness which Rearranging Eq 27 we have, is perhaps not surprising since high energy to yield (1 p/2r,)3 constitutes high resilience. GB = Gc (29) It should also be noted that for materials which ( 1 + P/r02 are prone to crazing (e.g. PMMA and polystyrene), and for p > > rp, care must be taken in forming the blunt notches since crazing induced during machining results in GB=Ge [--13— 4- 1 8r, 2 GB not increasing as expected since a large r, is induced. This is illustrated in Fig. 10 and from Eq 14, for PMMA 2 Gc where milled notches gave the expected form of GB = •wp•P 1- (30) curve while drilled and sawn notches gave a flatter sr 2 curve as shown. This is a very clear example of Thus, by determining GB for a range of p values, the detrimental effect of crazes. the slope at large p values can be used to determine tol, and with G, we may find rp. A typical set of CONCLUSIONS data (for PVC in this case) is shown in Fig. 9 with The data presented here show clearly the power Eqs 29 and 30 fitted with Ge = 1.42 X 103 .//m3 of this method of analyzing impact data. The use giving wz, = 10 X 10° J/m3 and thus r, = 28 pm. of the appropriate calibration factors gives the same • The factor r/2 is introduced here to give the line zone result. 7 6 Theory I Or wp=1000 6 p e 69).1.171 A A Equation 1291 re2 5. 3 A • A A • Milled notched e• A Drilled notched Equation 1301 1 1 1 1 0.1 0.2 0.3 0.4 0 5 0.6 07 06 09 0 p (rnro 0 01 02 0-3 01. 05 .06 07 06 Fig. 9. The variation of critical strain energy release rate Fig. 10. Effect of notching method on blunt notch data for with notch root radius for PVC (Darvic 110). PMMA. 71/4.14. o r CiCA 15 'Ijri"-0 )-1-(41A- POLYMER ENGINEERING AND SCIENCE, JUNE, 1975, Vol. 15, No. 6 kaL,_t_ _ct,e_ 44_ The Determination of the Fracture Parameters for Polymers in Impact result for both Charpy and Izod tests. It is possible 1c = critical stress intensity factor or fracture to correct for kinetic energy errors but this is not toughness essential. It is also apparent that the fracture me- 2L = span of beam chanics idea of a plastic zone affords a method of m = mass of the specimen describing blunt notch impact data so that the M = mass of the tup fracture toughness for any notch root radius may P = load be described in terms of the sharp notch result G, r„ = plastic zone size and the energy per unit volume at yielding w p. u = crack opening displacement Care must be exercised for high toughnesses be- V = velocity of the tup cause of gross yielding but the use of the .1, analysis to = absorbed energy provides a good basis for analysis and comparison to, = elastic energy per unit volume at yielding with Ge values. Thus, the methods described here w° = w — lc, are capable of defining the fracture toughness of to' = energy to give first yield in specimen all the polymers tested under impact conditions x = deflection using only energy measurements. The method is Y2 = correction factor for finite width effects clearly preferable to conventional testing for evalu- a, /3 = geometric constants ating impact strength. P = tip radius of blunt notch a = gross stress ACKNOWLEDGMENTS a, = stress at blunt notch tip a = yield stress The authors wish to thank BP Chemicals for their 11 = calibration function C/dC/d(a/D) generous support of this work in providing financial rk assistance and materials. REFERENCES 1. G. P. Marshall, J. G. Williams, and C. E. Turner, I. Mat. NOMENCLATURE Sci., 8, 949 (1973 ). 2. H. R. Brown, J. Mat. Sci., 8, 941 ( 1973). a = crack length 3. J. R. Rice, P. C. Paris, and J. G. Merkle, A.S.T.M., STP of = effective crack length (a + rp ) 536, 231, (1973). A = ligament area 4. J. P. Berry, J. Polym. Sci., 50, 107 (1961). 5. L. J. Broutman and F. J. McGarry, I. Appl. Polym. Sci., specimen thickness 9, 589 (1965). C = compliance (x/P) 6. R. P. Kambour, Appl. Polym. Symp., 7, 215 (1968). Co compliance for zero crack length 7. G. P. Marshall, L. H. Coutts, and J. G. Williams, J. Mat. specimen width Sci., 9, 1409 (1974 ). 8. J. G. Williams, "Stress Analysis of Polymers," Longmans, e = coefficient of restitution (1972). E = Youngs modulus 9. G. R. Irwin, Appl. Mat. Res., 3, 2 (1964). GB = apparent G, for a blunt notch 10. H. F. Brown and J. E. Srawley, A.S.T.M., STP 410 (1966). G, critical strain energy release rate 11. P. I. Vincent, Plastics Institute Monograph, ( 1971). = plastic work parameter 12. R. A. W. Fraser and I. M. Ward, J. Mat. Sci., 9, 1624 Ice = kinetic energy correction (1974). POLYMER ENGINEERING AND SCIENCE, JUNE, 1975, Vol. 15, No. 6 477 Paper 2 THE 'EFFECT OF 'TEMPERATURE ON THE IMPACT FRACTURE TOUGHNESS OP POLYMERS by E. Plati and J.G. Williams Mechanical Engineering Department Imperial College London INTRODUCTION Impact testing is of considerable practical importance but suffers from several drawbacks in the test methods currently employed. In the first place, the apparatus used is often not of a good standard resulting in considerable scatter in the data because of poor alignment and friction. Secondly, the test method is designed in such a way that the data are difficult to interpret with any logic. This paper describes an apparatus which overcomes most of these problems so that machine scatter is largely eliminated and an analysis is employed which presents the data in a concise and meaningful form. The results from conventional impact testing are usually expressed in terms of the specific fracture energy w/A, where w is the energy absorbed to break the notched specimen and A is the cross-sectional area of the fractured ligament. Such an analysis of the data is not satisfactory because the parameter w/A depends on the specimen geometry and the type of test used. There is only a rough correlation between the Charpy and the Izod impact values for the same material. However, some recent publications (1,2,3,4) have shown that if elastic deformations are assumed linear fracture mechanics theory can be extended to impact data and , the critical strain energy release rate, can be deduced directly from Gc the absorbed energy. The absorbed energy to failure, w, can be written in the form: w = G . BD(1) c where B and D are the thickness and depth of the specimen respectively and 4 is a calibration factor which is a function of crack length and may be calculated or measured experimentally. w is determined for several crack lengths and Gc determined from the linear plot of w versus 4. In (4) calibration factors have been determined for both the Charpy and Izod tests and G determined for a range of polymers at 20°C in both tests. G was c c shown to be independent of specimen geometry and identical for both test methods. For highly ductile materials a modification of the method was necessary to obtain values which are comparable with those for the more brittle materials (2,4). This work is extended here by measuring Gc for both sharp and blunt notches over a range of temperatures for several polymers using a temperature control cabinet fitted to the impact machine. The results are analysed in terms of the concept of a plane stress and a plane strain G and changes in G with both temperature and specimen thickness are c c described in terms of yield stress changes. 3 APPARATUS The impact testing machine used is shown in Figure 1 and is of the conventional pendulum type. The machine was made by the Mechanical Engineering Department, Imperial College, from a design supplied by The British Petroleum Company Limited. A set of pendulums of various weights are used to give high precision in energy measurements over a wide range of values and the usual precautions were taken to ensure that the centre of percussion is at the impact point. Different pendulums were designed such that Charpy, Izod and tensile impact tests could be performed. Special care was taken in the bearing design to ensure a minimum of friction and play since these factors were found to be of particular importance in achieving consistency (1). The angular measurements are made using a photo-electric device and a transparent disc marked at 9' of arc intervals. The angles are indicated as a number on a digital counter. Windage and friction losses were determined from free swing experiments so that each reading on the counter could be given an energy value for each pendulum and initial pendulum angle. Tables of values were produced for all counter readings. Speed variations from the four original settings available are rather small and all the data given here is at 3 m/s. The various temperatures were achieved using a split insulated box surrounding the specimen (see Figure 1). When the required temperature is reached the front part of the box is withdrawn to allow the pendulum to swing down and strike the specimen. A small fan is used to circulate air through the box from a closed loop containing a heater coil. Low temperatures are obtained by blowing liquid nitrogen into the loop. A thermocouple embedded in a dummy specimen located close to the real one controls the nitrogen flow and the heater via a "Eurotherm" control unit. o The range -100°C to +60°C was used and a control of il C was achieved. The box is opened for a very short period (< 1 s) in order to break the specimen and no appreciable temperature change was observed. 5 EXPERIMENTAL RESULTS The G values for 6 mm thick specimens notched with a very sharp (< 50 pm) cutter are shown in Figures 2, 3 and 4 for the temperature range -100 to +60°C. Each point is obtained from the slope of a w versus graph and contains the results from 15-20 specimens of various notch lengths as shown for polycarbonate in Figure 5. They are grouped as low, medium and high impact strengths and in the low group (= 1 kJ/m2) we have unmodified polystyrene and PMMA as expected. The PVC is also unmodified and behaves as a glassy amorphous polymer but PVC would be expected to be in a higher group when impact modifiers or fillers are added. Figure 3 (= 4 kJ/m2) includes polycarbonate and dry Nylon 66 which are classified here as medium strength materials. Figure 4 gives the high impact strength 2 materials (= 20 kJ/m ) and very large changes with temperature are apparent. Changes of the order of ten are observed here while in the low and medium category they are two or less. There is a noticeable similarity in the curves in that all are sigmoidal in form between constant high and low temperature values within the temperature range covered. It should be noted that all the points are for brittle failures except for some of the high impact strength materials at the higher temperatures. In these cases, ductile failure occurs and the G is calculated from 2wIA. as outlined in (4). c A series of tests were also performed on specimens with blunt notches of tip radii 0.25, 0.5 and 1 mm. The Gc determination was as in the sharp notch case and a blunt notch GC value, termed GB, was obtained. These are shown in Figures 6, 7 and 8 for PVC, polycarbonate and PMMA, respectively. PVC and polycarbonate show the expected elevation of the curves and they remain similar in form. For PMMA, however, a peak appears at -60°C which increases with the blunter notches and is totally absent in the sharp notch data. There is no significant evidence of peaks in the other materials for any notch radius. 6 THEORETICAL ANALYSIS It is postulated here that a polymer exhibits different fracture strengths depending on the stress system imposed. The lowest value is when the material is heavily contrained, as in the centre of a notched specimen, and this is termed G01. The highest value is with no constraint as near the surface of the specimen and this is the plane stress value G c2' This concept has been used for metals (5) and has been extended to polymers (6,7) but in the form of fracture toughness Rc. Following the same line of argument, however, similar relationships may be derived for G. The extent of the plane stress region is assumed to be the plastic zone size r which is given by, (6): p2 K 2 r - 1 c2 p2 2 n 0 2 y and since Kc2 2 = E c2 where E is the modulus and a the yield stress, we have: G r - E c2 1 p2 2 w • 0 Q - Y The specimen may therefore be considered as a sandwich of a plane strain region between two plane stress regions of thickness rp2. Since energy is measured in this test an average G0 will be determined (and not Kc as in (6)) such that: G B = G (B - 2r ) G 2r 01 p2 e2 p2 7 2r , i.e. c= G (G G ) el B c2 el where B is the specimen thickness. Substituting for r we have: P2 E G c2 G 4. (G G el c2 el IT a 2 B y Since impact fractures are at quite high speeds they would be expected to be adiabatic and therefore G and G would not be expected to depend el e2 on temperature. Similarly, E, which relates and Go would also be expected to be insensitive to temperature. a on the other hand, refers to the plastic deformation away from the actual fracture and should be influenced by temperature changes. It would be difficult to determine the a appropriate to impact but the form of the temperature dependence would be expected to be similar to slower rate data. If 1/(3 2 as determined in ordinary slow rate tests at various temperatures is plotted as a function of Go, equation 2 would indicate a straight line extrapolating to Gcl. This value should be a reasonably accurate estimate since it is not derived from the particular ay values used. It is also clear that when 2rp2 = B, G = G c2 Since a increases with decreasing temperature the form of curve expected would be G remaining at G with decreasing temperature until 2r < B e c2 p2 when dependence on a comes into force and G tends to G Since the cl' a dependence on temperature is similar (i.e. approximately linear) for most polymers an explanation is provided for the similar form of curves noted previously. Figure 9 shows the form of equation 2 schematically and also indicated the effect of a thickness change. The deformation properties are contained in the term a 2/E and this may be written as the plane stress elastic work to yielding: a 2 W = 1- Y 3 p2 2 E In (4) it was suggested that blunt notch data could be analysed by assuming that the same plane strain plastic zone of radius r had to form at the tip p1 of the blunt notch at fracture as in the sharp notch. For the condition that the notch tip radius p is much greater than this plastic zone then the relationship G = G (1 /(1 t (2)2 Zr )3 r B p1 ' p1 becomes: G , G = - 7" - W p B 2 p1• 4 where G p= W C 1 16 rp1 and is the elastic energy to yield under the plane strain conditions at the notch tip. Assuming that there is no lateral deformation in the constrained region the ratio of w and w may be expressed in terms of the Poisson's p/ P2 ratio v so that: (F1 — v: 2 wp1 5. wp2 / - 2v As expected, as v w m since complete constraint has been imposed p1 -9 on an incompressible material. However, for most polymers v is around 0.4 giving wp1/Wp2 = 9 so that wp/ will be expected to be much larger than wp2° - 10 - DISCUSSION OF RESULTS Figure 10 shows data for PMMA and PVC plotted as Gc versus iN2 and the expected linear relationship is apparent giving the values of Gal and G Figure 11 shows data for two thicknesses of polycarbonate and d2. Figure 12 for three thicknesses of polyethylene. The form of the data is in reasonable agreement with equation 2 and when the slopes are plotted versus 1/B in Figure 13 good straight lines result. It would seem that equation 2 is a good description of the data given here. Table 1 gives the values of G and G for the materials tested. The effect of specimen el c2 thickness reported by Wolstenholme et al (9) is also in accord with equation 2 in indicating a decrease in energy per unit area with increasing thickness. The reported proportionality of fracture load and yield stress in (9) is also consistent with equation 4. Since G is found by extrapolation and G is known it is possible to el 02 deduce the parameter w from equation 2. The E here is an adiabatic P2 value and constant while a is not so that w will be proportional to P2 a 2. Figure 14 shows w as a function of temperature and shows a rapid p2 increase with decreasing temperature consistent with this relationship. The blunt notch data were plotted in accordance with equation 4 so that was obtained and this is shown for the three materials in wP1 Figure 14. w is much greater than w as expected and corresponds to p1 P2 v values of around 0.45. w also decreases with temperature decrease pl and there is evidence of peaks in all three materials. Peaks in impact data have been widely reported (10,11,12) and Vincent (8) has observed that they are more usually found with blunt notches. Their correlation with tan 6 peaks has been widely discussed but seems to be somewhat variable. The pronounced peak at -60°C here for PMMA and the lesser one for PVC at -20°C could be equated with the 0 process (13,14). The more modest peak , 11 for polycarbonate does not seem to correspond to any tan 6 peak which agrees with the findings of Heijboer (10). - 12 - CONCLUSIONS The basic hypothesis that impact strength is strongly influenced by the constraint imposed by the specimen geometry seems to provide a good description of the sharp notch data. The concept of Gal and Get coupled with yield stress changes gives an accurate picture of variations with temperature and specimen thickness. The fact that the yield stress away from the actual fracture zone does show changes with temperature while Gc/ and G c2 do not is the basis for the observed variations with temperature. Blunt notch data in effect magnifies the plane strain yielding process at the notch root and although the plane stress energy w p2 shows the dependence on temperature typical of slow rate data the plane strain values, wpi, show marked peaks. The strong dependence on volume change is believed to be important here since it seems that it is the changes in v which dominate over those in a . Data of v is scarce but it seems likely that there would be some correlation between tan 6 peaks and volume changes. However, the origins of the effect may be in other factors such as absorbed fluids which are apparent in tan 6 and have a strong influence on volume changes. A -600C peak in PMMA, for example, is sometimes ascribed to water. This sensitivity to volumetric effects in the fracture behaviour of polymers is likely to be of importance in an understanding of the fundamental processes involved. Acknowledgement The authors wish to thank British Petroleum Chemicals International Limited for their generous financial support of this work. - 13 - REFERENCES 1. MARSHALL, G.P., WILLIAMS, J.G., and TURNER, C.E. J. Maters Sci., 8, (1973), 949. 2. BROWN, H.R. J. Maters Sci., 8, (1973), 941. 3. FRASER, R.A.W., and WARD, I.M. J. Maters Sci., 9, (1974), 1624. 4. PLATI, E., and WILLIAMS, J.G. Polymer Engng and Sci., 15, (1975), 470. 5. BLUHM, J.I. Proc. ASTM, 61, (1961), 1324. 6. PARVIN, M., and WILLIAMS, J.G. In press, Int. J. Fracture. 7. PARVIN, M., and WILLIAMS, J.G. In press, J. Maters Sci. 8. VINCENT, P.I. Polymer, 15, (1974), 111. 9. WOLSTENHOLME, W.E., PREGUN, S.E., and STARK, C.F. J. Appl. Polym. Sci., 8, (1964), 119. 10. HEIJBOER, J. J. Polym. Sci., (C), 16, (1968), 3755. 11. WADA, Y., and KASOHARA, T. J. Appl. Polym. Sci., 11, (1967), 1661. 12. TURLEY, S.G. Appl. Polym. Symp., 7, (1968), 237. 13. JOHNSON, F.A., and RADON, J.C. Engng Fracture Mechs., 4, (1972), 552. 14. BOYER, R.F. Polym. Engng and Sci., 8, (1968), 161. TABLE 1 G G cl e2 Material 2 kJ/m2. 10/mt ANA 1.06 1.28 Polystyrene 0.35 0.90* PVC 1.23 1.44 Polyearbonatel 3.5 5.02 Nylon 66 (Dry) 0.25 4.15 Polyethylene (Medium Density)2 1.3 11.90 Polyethylene (Low Density)3 5.0 35.00* HIPS 1.0 15.00 * Estimated values - no reliable yield stress data available. 1 Bayer Makrolon extruded sheet. Specimens cut in the extrusion direction. 2 Density = 0.955. MI = 0.2. 3 Density = 0.945. MI = 6.0. Figure 1 - Impact machine with temperature box 1.4 1.2 -0 1.0 G (kJ/m2) 0.8 0.6 0.4 0 PVC — 0 ❑ C5 PMMA ❑GPPS 0.2 0 -100 -80 -60 -40 -20 0 +20 +40 +60 (oc) Figure 2 - Low impact strength materials 5.0 4.0 0 0 3.0 G0 (kJ/m2) 2.0 ..a.•■••0 0 Polycarbonate 0 Nylon 66 (Dry) 1.0 -100 -80 -60 -40 -20 0 +20 +40 +60 (0C) Figure 3 - Medium impact strength materials Q Polyethylene (low density) Polyethylene (medium density) O HIPS -100 -80 -60 -40 -20 0 +20 +40 +60 • (Oc), Figure 4 - High impact strength materials 3 -5 (BD(0 ) x 10 Figure 5 - Sharp notch data for polycarbonate at three temperatures 7.0 Sharp notches 6.0 C3 p = 0.25 mm o p = 0.5 mm 5.0 () p = 1.0 mm 4.0 w.• 3.0 -0 0 2.0 1.0 0 -100 -80 -60 -40 -20 0 +20 (°C) Figure 6 - Blunt notch data for PVC ' 60 A Sharp notches C3 p = 0.25 mm 50 0 p = 0.5 mm p = 1.0 mm 40 30 20 10 1 •••••••^•••••• 0 -100 -80 -60 -40 -20 0 +20 (0C) Figure 7 - Blunt notch data for polycarbonate 4 3 2 G (kJ/m ) B 2 11.1111. 1 Sharp notches 0 p = 0.25 mm 0 p = 0.5 mm () p = 1.0 mm 0 . -100 -80 -60 -40 -20 0 +20 (0C) Figure 8 - Blunt notch data for PMMA G G c2 G c1 T (°C) Figure 9 - Schematic form of toughness changes with temperature as given by equation 2 G (kJ/m2) c 0 1 2 3 2 -2 -4 (1,/a )2 (MN/m ) x10 Figure 10- Variation of impact toughness with yield stress ()------Ga2 ❑ I 0 1 2 3 2 -2 -4 (1/a y)2 (MN/m ) x 10 Figure 11- Variation of impact toughness with yield stress for polycarbonate for two specimen thicknesses 1 2 3 4 5 6 . 2 -2 -3' (1/c )2 (MN/m ) x 10 Figure 12 - Variation of impact toughness with yield stress for medium density polyethylene for three specimen thicknesses. x 1018 10 8 dG c 6 4 0 Polycarbonate A Polyethylene 2 (medium density) 0 0.1 0.2 0.3 0.4 (1/B) (mm)-1 Figure 13 - Variation of slope of G versus 1/ay e lines with specimen thickness 0 Polyethylene (medium density) 1.0 C) Polycarbonate 0 Nylon 66 (dry) A PVC PMMA 0.8 0.6 3 w (MJ/m ) p2 0.4 0.2 -100 -80 -60 -40 -20 0 +20 (°C) Figure 14 - Variation of plane stress yielding energy with temperature wp1 (MJ/m3) 10 A PMMA 9' El PVC 0 Polycarbonate 8 7 6 5 -100 -80 -60 -40 -20 0 +20 (0C) Figure 15 - Variation of plane strain yielding- energy with temperature