Mechanical Behavior of Four Brittle Polymers
by
Rami Lokas
B. S. Mechanical Engineering, Georgia Institute of
Technology, 1998
Submitted to the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degree of
Master of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2000
@ Massachusetts Institute of Technology 2000. All rights reserved.
A u th or .................................
Department of Mechanical Engineering
May 8, 2000
C ertified by ..................................
...........
..
Ali S. Argon
Professor
Thesis Supervisor
Accepted by .
Ain A. Sonin
Chairman, Department Committee on Graduate Students
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
SEP 2 0 2000
LIBRARIES
Mechanical Behavior of Four Brittle Polymers
by
Rami Lokas
B. S. Mechanical Engineering, Georgia Institute of Technology, 1998
Submitted to the Department of Mechanical Engineering
on May 8, 2000, in partial fulfillment of the
requirements for the degree of
Master of Science in Mechanical Engineering
Abstract
Most descriptions of polymers start at room temperature and end at the melting
point. Cryogenic testing is rare for even the most common polymers. Considering
the increased use of polymers at low temperatures (eg: thermal and electrical insulations, support elements for cryogenic devices, low-loss materials for high-frequency
equipments) this seems to be a great lack. This thesis seeks to provide data on the
behavior of several polymers under low temperature testing. The polymers tested
are high density polyethylene, polyvinyl chloride, polypropylene, and polyetherimide.
The mechanical tests they underwent were compression tests and compact tension
tests. The temperature range was from -150'C to room temperature. The yield and
stiffness values as a function of temperature are presented. They were all found to be
increasing with decreasing temperature.
Several parameters determine the fracture behavior of ploymers : temperature,
time, plasticity, chain orientation, and adiabatic heating. The main topic of these
investigations is the temperature dependence. Time and loading rate where kept
constant at 2 mm/min. in all the tests. The polymers were as recieved in an almost
isotropic form. The fracture toughness of the polymers increased with decreasing
temperature except for polyetherimide. However, HDPE and PVC had a precipitous
drop at tests below the glass transition.
Fractography was used to study and understand the process of crack propagation.
In most cases there were well defined regions of ductile and brittle crack propagation with clear transitions. These regions correlated well with the load displacement
plots of the fracture tests. Explanations were ventured to explain the morphological
features of the fracture surfaces such as yielding due to adiabatic heating and crack
bifurcation due to crack velocities and stress distributions.
Thesis Supervisor: Ali S. Argon
Title: Professor
2
Acknowledgments
I want to acknowledge my mother, Dr. Olivia Shenouda, and my father, Mr. Farouk
Lokas, to whom I am eternally indebted. I cannot forget my love, Christine Chen,
who continues to cancel my debts and my brother, Karim Lokas with whom I am
currently developing my debt. I am greatly privileged to have my name written on
the same page as Prof. Ali S. Argon. I do not think I am deserving of such an honor.
I have not only learned much about materials behavior from him but I have also
learned much about life and civil human interaction.
I want to thank all the professors from whom I have learned : Prof. M. Boyce,
Prof. D. Parks and Prof. L. Anand. I am also thankful for the best office mates
anyone could ask for : Kevin Bass, Hang Qi, Heather Dunn, Franco Capaldi, Matts
Danielsson, Rebecca Brown, Ethan Parsons, Jin Yi, Steve Xia, Jeremey Gregory, Greg
Nielson, Yu Qiao, Cheng Su, Harish Rajaram, Jinchul Hong, Brian Gearing, Prakash,
Tom Arsenlis, Jennifer Shin, and the friendliest Una Callinan. They made my stay
fun and they so willingly offered their help whenever I needed it. I couldn't have done
this thesis without them (especially Qi Hang, Greg Nielson and Una Callinan).
I also want to thank my friends who encouraged me along the way and offered
me unquantifiable support: Brad Geving, Kurt Romondt, Ese Adebayo, Scott Davis,
William Ochan, the Wilson family, Tom Lin, the Boyle family, Brian Johnson with a
specially heart fealt thank you to Darbon Go a friend who is more than a brother.
Finally I want to thank my Lord and Savior Jesus Christ who made this wonderful
creation for us to study and admire and wonder about. Without whom nothing that
is, is.
3
Contents
10
1 Introduction
2
13
A Review of Polymers and Fracture Mechanics
2.1
Overview of Crystalline and Amorphous Thermoplastics
2.2
HDPE . . . ....
... . .
2.3
PVC . . . . ....
....
. . . . . . .
13
...
14
. . . . . . . . . . .
15
2.4
U ltem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
2.5
Polypropylene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
2.6
Literature Review of Polymer Fracture Testing . . . . . . . . . . . . .
16
2.7
Review of Fracture Mechanics . . . . . . . . . . . . . . . . . . . . . .
18
...
. ..
....
. . . ..
. . . . . ..
. . . . . . . ..
. . ..
.
22
3 Experimental Techniques
3.1
The Test and Equipment . . . . . . . . . . . . . . . . . . . . . . . . .
22
3.2
ASTM Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
3.3
Evaluation of Temperature Dependent Material Properties . . . . . .
23
3.4
Stress Intensity Factor Calculations . . . . . . . . . . . . . . . . . . .
25
30
4 Temperature Dependence of Fracture Toughness
4.1
4.2
HDPE .. .
.
30
4.1.1
Crack Tip Opening Displacement . . . . . . . . . . . . . . . .
33
4.1.2
Crack Velocity
. . . . . . . . . . . . . . . . . . . . . . . . . .
34
4.1.3
Modified CT Specimens
PVC ...
........
.....
...
........
. .. . .. . ...
. ..
. . . ..
. ..
. . . . . . . . . . . . . . . . . . . . .
36
. . . . . . .
37
... . . . . . . . . . . . . ..
4
5
4.3
Ultem . . . ..
. . . . . .
38
4.4
Polypropylene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
....
.. ... . . . . . . . . . ...
Fracture Surface Topographies
77
5.1
Specimen Preparation
77
5.2
HDPE . . . ...
5.3
. . . . . . . . . . . . . . . . . . . . . . . . . .
... .....
.. . ..
. . . ..
. . . . ..
. ..
. . . .
77
5.2.1
Fracture Surface Topography
. . . . . . . . . . . . . . . . . .
77
5.2.2
Adiabatic Heating . . . . . . . . . . . . . . . . . . . . . . . . .
79
5.2.3
Brittle Fracture Surface
. . . . . . . . . . . . . . . . . . . . .
81
5.2.4
Causes of Bifurcation . . . . . . . . . . . . . . . . . . . . . . .
81
. . .
86
Transition Crack Length . . . . . . . . . . . . . . . . . . . . .
87
PVC . . . . .....
5.3.1
6
... ...
....
...
. . . . . . . . . . . . . . . . . ..
5.4
U ltem
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
5.5
Polypropylene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
Conclusions and Recomendations
108
6.1
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
108
6.2
Suggestions
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
109
5
List of Figures
3-1
Comparing two methods of displacement measurements in a -50 0 C
HDPE Compact Tension Test (COD gage vs. crosshead displacement)
26
3-2
The dimensions of the compact tension specimens . . . . . . . . . . .
27
3-3
The compression test setup inside the temperature chamber (the screws
were not tightened so that the PVC placed inside can be seen so as to
understand the placement of the specimens)
3-4
. . . . . . . . . . . . . .
28
Modifying the data from the compression setup by factoring-in the
stiffness of the setup (the above plot is the unmodified data and the
lower plot is the modified data) . . . . . . . . . . . . . . . . . . . . .
29
4-1
Compression tests on HDPE at various temperatures
. . . . . . . . .
43
4-2
Temperature dependence of yield strength in HDPE . . . . . . . . . .
44
4-3
Temperature dependence of elastic modulus in HDPE . . . . . . . . .
45
4-4
Unmodified plots of fracture toughness tests on HDPE . . . . . . . .
46
4-5
Modified plots of fracture toughness tests on HDPE . . . . . . . . . .
47
4-6
The bifurcated cracks in HDPE . . . . . . . . . . . . . . . . . . . . .
48
4-7
Temperature dependence of the critical stress intensity factor in HDPE 49
4-8
CTOD as a function of temperature in HDPE . . . . . . . . . . . . .
50
4-9
Plastic zone size as a function of temperature in HDPE . . . . . . . .
51
4-10 Unmodified plots of fracture toughness tests for 1" thick HDPE (with
side grooves) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
4-11 Modified plots of fracture toughness tests for 1" thick HDPE (with side
grooves) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
53
4-12 Temperature dependence of the critical stress intensity factor in 1"
thick HDPE (with side grooves) . . . . . . . . . . . . . . . . . . . . .
4-13 Compression tests on PVC at various temperatures
54
. . . . . . . . . .
55
4-14 Temperature dependence of yield strength in PVC . . . . . . . . . . .
56
4-15 Temperature dependence of elastic modulus in PVC . . . . . . . . . .
57
4-16 Unmodified plots of fracture toughness tests on PVC
. . . . . . . . .
58
4-17 Modified plots of fracture toughness tests on PVC . . . . . . . . . . .
59
4-18 Temperature dependence of the critical stress intensity factor in PVC
60
. . . . . . . .
61
4-20 Temperature dependence of yield strength in ULTEM . . . . . . . . .
62
4-21 Temperature dependence of elastic modulus in ULTEM . . . . . . . .
63
. . . . . . .
64
4-23 Modified plots of fracture toughness tests on ULTEM . . . . . . . . .
65
4-19 Compression tests on ULTEM at various temperatures
4-22 Unmodified plots of fracture foughness tests on ULTEM
4-24 Temperature dependence of the critical stress intensity factor in ULTEM 66
4-25 CTOD as a function of temperature in Ultem . . . . . . . . . . . . .
67
4-26 Plastic zone size as a function of temperature in Ultem . . . . . . . .
68
4-27 Compression tests on polypropylene at various temperatures . . . . .
69
4-28 Temperature dependence of yield strength in Polypropylene . . . . . .
70
4-29 Temperature dependence of elastic modulus in Polypropylene . . . . .
71
. . . .
72
4-31 Modified plots of fracture toughness tests on Polypropylene . . . . . .
73
4-30 Unmodified plots of fracture toughness tests on Polypropylene
4-32 Temperature dependence of the critical stress intensity factor in Polypropylene ..........
74
....................................
4-33 Plastic zone size as a function of temperature in Polypropylene . . . .
75
4-34 CTOD as a function of temperature in Polypropylene . . . . . . . . .
76
5-1
The cavitated region and the brittle crack origin in HDPE . . . . . .
89
5-2
Closeup of the cavitations and the tapped crack front in HDPE
. . .
90
5-3
Brittle crack origin and hackle marks in HDPE at lower temperatures
91
7
ft
5-4
A schematic demonstration of (a) kinked and (b) forked crack geometries and teh associated nomenclature . . . . . . . . . . . . . . . . . .
92
5-5
Shear yielding in HDPE
93
5-6
The intermediate region during the cracks transition from ductile to
. . . . . . . . . . . . . . . .
brittle fracture in HDPE . . . . . . . . . . . . . . . .
. . . . .
94
5-7
A closeup of the intermediate region in HDPE . . . .
. . . . .
95
5-8
Typical brittle fracture surface . . . . . . . . . . . . .
. . . . .
96
5-9
PVC fracture surface photograph
. . . . . . . . . . .
. . . . .
97
. . . . . . .
. . . . .
98
5-11 A craze in PVC . . . . . . . . . . . . . . . . . . . . .
. . . . .
99
5-12 The initial crack transition in PVC . . . . . . . . . .
. . . . .
100
. . .
. . . . .
101
5-10 Stable to unstable crack growth in PVC
5-13 A closeup of the initial crack transition in PVC
5-14 The mountainuos region that defines the final stages of the high speed
brittle crack . . . . . . . . . . . . . . . . . . . . . . .
102
5-15 Brittle crack origin in ULTEM . . . . . . . . . . . . .
103
5-16 Crazing in ULTEM
104
. . . . . . . . . . .
5-17 Transition from hackle marks to wave pattern in HDPE . . . . . . . . 105
5-18 Multiple crazing at tapped crack front in PP . . . . . . . . . . . . . . 106
5-19 Microvoiding in PP . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
107
List of Tables
2.1
Material Properties of the Polymers Supplied by their Manufacturers
21
4.1
HDPE's Measured Values
. . . . . . . . . . . . . . . . . . . . . . . .
41
4.2
PVC's Measured Values
. . . . . . . . . . . . . . . . . . . . . . . . .
41
4.3
Ultem's Measured Values . . . . . . . . . . . . . . . . . . . . . . . . .
42
4.4
Ploypropylene's Measured Values
42
9
. . . . . . . . . . . . . . . . . . . .
Chapter 1
Introduction
The mechanical behavior of metals have been studied more extensively than polymers.
On the whole, their behaviour is well understood and modeled. Polymers, on the other
hand, have not had the benefit of similar intensive study and thus their behavior and
modelling is still lacking consideraly in comparison. This becomes a serious issue
when it is considered that they are becoming increasingly more widely used and
are replacing their metal counterparts in many structural engineering and biological
applications, and the like.
Considering the microstructural differences between metals and polymers, it is not
difficult to see that models developed for metals do not necessarily extend to polymers
without modifications. As an example, the theories based on the micromechanisms
of rate dependence of flow stress and toughenening, namely dislocations, in metals do
not explain the behavior in polymers since polymers do not have similar crystalline
structures as metals have.
Most of the modeling of polymers currently is based on phenomenological information rather than physical. This is clearly a disadvantage since each model would
be very limited in its application. In 1963 Geil wrote:
"Although rapid advances have been and still are being made in our knowledge of the morphology of crystalline polymers, the gaps in our knowledge
are at present ... both wide and numerous. In addition, little ... is known
10
of the morphology of noncrystalline polymers."
Although it has been nearly 40 years, much remains to be understood on polymer
morphology and behavior. Therefore, polymers need to be studied more throroughly
for them to be better understood.
The following studies have been carried out on the subject of polymer brittleness.
Fracture behavior is an essential field of study for structural applications of materials
since they have a tendency to fail in a brittle manner. Fracture toughness is studied in
this thesis to find its temperature dependence at below room temperature conditions.
This information is not readily available in the literature. When it is available the
studies do not provide the desired details nor offer sufficient explanations. Therefore
this study was undertaken to gather more needed information to supplement the
currently available literature.
Some explanantions of the observed behavior have
been attempted.
This study was performed on four polymers
" High Density Polyethylene (HDPE)
* Polyvinyl Chloride (PVC)
" ULTEM (a ployetheremide)
" Polypropylene (PP)
Their known properties and morphologies are briefly explained in Chapter 2. Included
for each material are mechanical behavior data and properties obtained from manufacturers and literature. This is followed by a review of cryogenic polymer testing
literature and fracture mechnaics principles.
The brittleness and temperature dependence of the critical stress intensity factor
for fracture in these polymers was studied by performing compression and fracture
toughness tests at temperatures ranging from room temperature down to -1450C.
These tests and the data reductions are explained in Chapter 3. This includes the
ASTM standards and the test equipment.
11
In Chapter 4 the results of the tests are presented. The results are then interpreted and used to calculate other fracture related values such as crack tip opening
displacement, plastic zone size, and crack velocity. These values are used to aid the
interpretation of the results and the understanding of the behavior of the polymer.
Through this process an explanation of the specific behavior patterns of the polymers
is formulated.
Scanning Electron micrographs were obtained of the fracture surfaces. They are
presented with explanations in Chapter 5. The features of the surfaces are pointed
out and addressed. Also their correlations with the fracture toughness information
is delineated to better understand the fracture process they underwent. In the study
of the morphologies, issues of crack propagation, ductile to brittle transitions, and
adiabatic heating are discussed. Considering local stress intensities and crack tip
stress distributions an understanding of crack bifurcation in HDPE is developed.
In Chapter 6 conclusions and suggestions for further work are formulated.
12
Chapter 2
A Review of Polymers and Fracture
Mechanics
2.1
Overview of Crystalline and Amorphous Thermoplastics
Three polymers used in this study were crystalline thermoplastics while Ultem was
a glassy polymer. The crystalline properties of certain polymers have been studied in the past but the structure and behavior of semicrystalline polymers is still a
topic of much investigation. Though many of the unit cells of crystalline phases are
well established the molecular arrangements are not. Crystallizable polymers can be
melt-crystalized or grown by precipitation from dilute solutions. Many are known
to be spherulitic with amorphous layers arranged between the lamellae rays of the
spherulite. The solution grown polymers tend to be lamellar with the chains folded
in a regular manner and the layers separated by amorphous regions.
Crystalline polymers are found in a variety of morphological forms ranging from
single crystals to semicrystalline polymers in which the non-crystalline component
can be either rubbery or glassy. They can also be oriented. Unlike amorphous polymers the fracture behavior of crystalline polymers is greatly affected by structure and
morphology and thus their fabrication is an important factor. Moreover, the applica13
i
tion of fracture mechanics is not always straightforward even for isotropic polymers
because they are not always brittle and their deformation can be non-linear with
large scale yielding in the vicinity of the crack. This however is not a concern at low
temperatures because brittleness sets in.
Above the glass transition temperature (Tg) thermoplastic polymers are able to
deform extensively in tension or compression. Below Tg the amorphous region is much
less compliant and though the material could exhibit a higher yield stress it does not
easily flow plasticaly. The variety of mechanical properties that have not always been
available makes them worthy of study.
Glassy thermoplastics have been extensively studied for their fracture behavior.
The reasons for this are many. Thermoplastics are relatively simple from a structural
viewpoint, compared with either thermosets which have a complex three-dimensional
molecular structure or semicrystalline polymers with a great variety of morphological
forms. They are also very experimentally well behaved in the sense that the behavior
is very consistent because unlike crystalline polymers their material properties are
not strongly dependent on their fabrication. Also, since their bulk deformation is
approximately linear elastic and the plastic zone is limited to the crack tip, they are
well suited for Linear Elastic Fracture Mechanics (LEFM).
A brief listing of some of the properties provided by the manufacturers of the
polymers used in this study is given in Table 2.1.
2.2
HDPE
HDPE (High Density PolyEthylene) falls under the category of olefin polymers. It is
also known as linear polyethylene. It is composed of a row of carbon atoms each of
which are surrounded by two hydrogen atoms. Its unit cell is orthorhombic. Typically
HDPE is very highly crystalline. This causes it to have a relatively high melting point,
moderate stiffness, tensile strength, and hardness. Polyethylene is used in injection
molding of housewares (eg: bottles) and toys. It is also used in piping and fabrics.
The HDPE used in this study was manufactured by Spartech Plastics (821 Clark
14
Street, Conneaut, OH 44030-1213, 1-800-325-5176)
2.3
PVC
PVC (PolyVinyl Chloride) falls under the vinyl polymers which used to be the largest
group of thermoplastics before the olefins surpassed them. They are only slightly
crystalline and the crystals are not large and not well defined. Thus, they are primarily
amorphous but tend to retain a discrete particle structure. PVC is generally unstable.
These two facts lead to the complication that PVC is rarely in pure form as other
polymers.
The PVC used in this study was manufactured by Geon Company (One Geon
Center, Avon Lake, Ohio 44012, 1-800-438-4366). The sheets were grey in appearance
due to the manufacturer injecting coloring during the compounding process. Geon
claims this has no affect on its properties and behavior.
2.4
Ultem
Polytherimide (PEI) is an amorphous engineering thermoplastic characterized by high
heat resistance, high strength and modulus, excellent electrical properties that remain
stable over a wide range of temperatures and frequencies, and excellent processibility.
It derives its trademark name, Ultem, from the General Electric Co. which is the
resin producer.
The Ultem used in this study was manufactured by AL Hyde (1 Main st., Grenloch,
NJ 08032; (856) 227-0500).
2.5
Polypropylene
Polypropylene, like HDPE, is linear and has high degrees of crystallinity which imparts
to it high stiffness and tensile strength. It is used primarily in filaments (eg: seat
covers) and fibers. It is also used for articles such as luggage made by injection
15
i
molding.
Spartech Plastics, the supplier of HDPE was also the source of polypropylene used
in this study.
Some of the relevant properties of the four polymers used in this study are listed
in Table 2.1
2.6
Literature Review of Polymer Fracture Testing
Fracture toughness as used in fracture mechanics is a material property in that it
is independent of test method and geometry. However it can be temperature dependent and because of polymer viscoelasticity it can be time-dependent too. The
characterizing parameter when considering fracture energy is Jc. In the case of linear
visco-elasticity, as is the case with polymers, it is more convenient to express this
parameter as G, or its equivalent Kc. The 'I' refers to mode I fracture which is
the only fracture mode considered in this thesis. Linear Elastic Fracture Mechanics
can be utilized for polymers at cryogenic temperatures because yielding is minimal
causing brittle fracture.
Glass transitions are important to the study of polymers because they mark significant changes in the behavior. Several of the studies Kinloch and Young referred to in
their book Fracture Behavior of Polymers [19] have found some influence of secondary
glass transitions on Gmc. However, their dependence on loading rates and material
fabrication makes them difficult to study for universal application since each material
batch will have a unique glass transition that is affected by the rate of deformation
and testing environment. This requires referring behavior to well designed standard
reference states. The fracture behavior of polymers above room temperature, where
many primary glass transitions occur in industrially interesting polymers, has been
studied extensiely. Cryogenic fracture behavior of polymers has not been well investigated and this includes secondary glass transitions. Below is a helpful summary of
the literature avialable on cryogenic fracture testing of polymers.
Marshall et. al. [24] showed that in PMMA, KI, increased with decreasing tem16
perature. Atkins et. al. [11] showed that GI, had a similar temperature dependence.
They also investigated the dependence of these parameters on crack velocity. They
found that a critical crack tip opening criterion can be applied over the entire range of
tests because it remained constant at ~ 1.6pm [24]. Prior to these studies Marshall et.
al. [25] investigated an added complication to cryogenic testing. They found that the
testing medium affects the polymer behavior. The PMMA exhibited greater craze
growth rates in active environments. The active environment used was methanol.
Parish and Brown [27] demonstrated that this was the case for liquid nitrogen and
liquid helium environments too. They showed that the results and glass transitions
presented by Johnston and Beardmore [13], and Beardmore [12] (who did not always
specify the environment) on PS, PC, and PMMA were environmentally affected.
Mai and Atkins [22] tested the dependence of Kc on low temperatures and crack
velocity in PS while Parvin and Williams [28] did similar studies on PC. Fraser and
Ward [18] showed that a constant critical crack growth criterion could also be applied
to PVC as was applied to PMMA by Morgan and Ward [26] a year earlier.
Sims [30], using a trouser leg tear test, studied the dependence of GI, on temperature in PP for temperatures between -60'C and room temperature. The relationship
between GI, and temperature was found to be positive. However, this relationship
applied to tests below the glass transition. He also found that at temperatures approaching the glass transition (-
- 15'C) there was a rapid increase in fracture energy
but he did not show the temperature dependence beyond this point. Mai and Williams
[23] showed that the plane strain KIc dependence on temperature in PP and Nylon 6
is minimal but that the plane stress Kc increased with decreasing temperature. Mai
and Williams also suggested a constant critical crack-opening displacement criterion
in the region of secondary transitions.
Fernando and Williams [17] demonstrated that K, for single edge notched PP specimens in bending and tension remained relatively constant from -150'C to -75"C
and then rose with increasing temperature.
They also showed that modified PP
had a decreasing K, with decreasing temperature until brittleness at -100 0 C was
reached, below which K, remains constant. Williams, [1] also mentions that PP has
17
an essentially constant K, (4.7 MPav/ ii) from -100
C to 201C.
Williams [21 also showed that single edge notched PVC specimens in bending and
tension had a very slowly rising negative dependence of K, on temperature down to
-1200C below which a pronounced increase is observed. He explained that this could
be due to the condensation of liquid nitrogen. In her thesis, Lee [21] pointed out that
unnotched tensile PVC specimens underwent a transition from discontinuous yielding
to a brittle failure mode at approximately -60C.
Chan and Williams [161 tested single edge notched PE in bending and found
it behaved in the same fashion as the PVC with a similar transition temperature.
However, the PE they used was not a homopolymer.
Finally, Saatkamp and Hartwig [29] used compact tension specimens with chevron
shaped crack fronts to study crack propagation in HDPE specimens at -196
0 C.
They
found a strong increase in the fracture energy associated with uncontrolled crack
propagation which they explained by local crack tip heating effects that raised the
temperature to above the glass transition causing higher crack resistance from plasticity.
There are many factors to be considered in the study of polymer fracture behavior.
As has been explained, the glass transition is very specific to the material batch,
test rate and environment. KIc has similar dependences and is influenced by the
glass transition. The dependence of KIc on temperature is a topic of controversy.
Some of the explanations given above for abrupt changes in this dependence were
environmental effects, adiabatic heeating effects, and glass transitions.
2.7
Review of Fracture Mechanics
From the theory of fracture mechanics, a quantity called the stress intensity factor,
K, can be defined that characterizes the severity of the crack situation as affected by
crack size, stress, and geometry. In defining K, the material is assumed to behave in
a linear-elastic manner, according to Hooke's Law, so that the approach used is called
Linear Elastic Fracture Mechanics.
18
i
A given material can resist a crack without brittle fracture occuring as long as
this K is below a critical value K, which is a property of the material called the
fracture toughness. Values of K, vary widely for different materials and are affected
by temperature and loading rate, and secondarily by the thickness of the member and
the environment.
Considering a crack in the center of a wide plate:
K = O-ovi
(2.1)
where
G-o = far - field stress
a = half the crack length
This equation only applies if a is much smaller than half the width of the plate.
Therefore, the critical far-field stress is:
-coG =
c
(2.2)
Hence, longer cracks have severe effects on the materials strength.
For Linear Elastic Fracture Mechanics to apply the plastic zone of the crack tip
must be small compared to the crack length and other geometric dimensions.
In general terms, K characterizes the magnitude (intensity) of the stresses in the
vicinity of an ideally sharp crack tip in a linear-elastic isotropic material. This region
is labeled the K-field. The variation of stresses around the crack tip in the K-field are
given in Sect. 5.2.4. Their general form is:
=
K1
o- 2- = fij (6)
where
-ij = the various stress components
K 1 = K in mode I (tensilemode)
r = radial distance from crack tip
fij (0)
=
angle dependent function of the K - field
19
(2.3)
Fracture toughness testing of polymers in ambient conditions cannot usually be
considered LEFM. Under cryogenic conditions, however, LEFM usually applies to
fracture testing of polymers.
20
Table 2.1: Material Properties of the Polymers Supplied by their Manufacturers
HDPE
PVC ULTEM
PP
Melt Index (g/10 min)
Density (g/cm 3 )
Tensile Strength (MPa)
Tough to Brittle Transition Temperature
Heat Deflection Temp. (A 66 psi)
21
0.31
-
-
0.06
0.949
26.06
< -76oC
720C
1.42
50.3
82 0 C
1.27
104.8
2150C
2100C
0.9
34.5
-28.8-OOC
98.9-104.4"C
Chapter 3
Experimental Techniques
3.1
The Test and Equipment
Compact tension (CT) specimens were used to test the fracture toughness of the
various polymers. To find the temperature dependence of the fracture toughness, the
CT specimens were tested at temperatures varrying from -10'C
down to -145 0 C.
The loading pin displacement rate was 2 mm/min. on a screw driven Instron machine
(Model 5582).
The chamber used to maintain temperatures was also supplied by
Instron (Model 3009). Liquid nitrogen was the cooling medium in the chamber.
An available COD gage was initially used to measure the crack opening displacement but was soon abandoned because it had neither the required extension range
nor was it usable at the low temperatures. The machine crosshead displacement was
used instead of the COD measurements. This proved to be sufficient for the purpose
(see Fig. 3-1).
3.2
ASTM Standards
The polymers were ordered as 10 mm thick sheets from which the CT specimens were
machined. The dimensions had to comply with ASTM standards (ASTM Standard
no. E399 and D5045 for polymers) as shown in Fig. 3-2 with B as thickness and W
as width. The crack length, a, was about 2.7 cm (Table 3.1) such that a/W~ 0.53.
22
A size criterion that must be satisfied to achieve plane strain conditions is:
B, a, (W - a) > 2.5(KQ/o-)
2
(3.1)
where KQ is the trial Kmc value and a-, is the yield stress for the specific temperature
and loading rate. The yield stresses for the different polymers at different temperatures are given in Sect. 3.3.
Once the above criteria (Eq. 3.1) are satisifed plane strain and limited plasticity
in the ligaments are ensured and Kc, for the testing conditions, is established. The
energy release rate GI, can then be obtained from :
=
(1
-
v 2 )K2
E
(3.2)
but for polymers, E must be obtained at the same time and temperature conditions
as the fracture test because of viscoelastic effects. Many uncertainties are introduced
by this procedure and it is considered preferable to determine GI, directly from the
energy derived from integration of the load versus displacement curve up to the same
load point used for Krc as stated in Sect. 6.2 for future work.
3.3
Evaluation of Temperature Dependent Material
Properties
Compression tests on 7 mm tall cylinders with 9.6 mm diameters were carried out
at a displacement rate of 2 mm/min. (same rate as the fracture toughness tests)
to establish the yield strength for each polymer at the chosen temperatures. This
was needed for evaluating the fracture toughness at the various temperatures. An
apparatus (Fig. 3-3) was designed to achieve compression from an Instron used in the
tension mode. The fixtures resembled a pair of links. As the displacement between
the Instron's crossheads increased the polymer, sandwiched between the fixtures, was
compressed.
23
The machine and setup stiffness (Fig. 3-4) were determined and used to correct
the data collected. True stress and true strain were calculated from load-displacement
data using the sequence of equations below:
r = initial radius (4.8 mm)
initial length (7 mm)
10 =
1
current length
=
A0
=
initial cross - sectional area
A = current cross - sectional area
Al= length increment
F = load
= engineering strain
Eeng
=
a
=
true strain
true stress
6eng
(3.3)
=
Eeng)
(3.4)
Ao = 7rr 2
(3.5)
Aoe'
(3.6)
E= ln(1 +
A
=
-=
F
-(3.7)
A
The 0.2% offset yield strength was also extracted from these plots by translating
the elastic portion of the slope 0.002 strain units to the right and taking the value of
stress at the point of intersection betwen it and the curve.
One issue that arose during testing was lubrication. To achieve this 0.05 mm thick
Teflon sheets with WD-40 lubricant were used at room temperature. This form of
lubrication fails at low temperatures. Most other lubricating materials and agents
also fail at such low temperatures. Therefore, the cryogenic compression tests were
conducted without a lubricant. The test apparatus surfaces that were in contact with
24
the specimens were polished to a 0.3pm mirror finish in order to improve slipping
between the specimens and the fixtures.
Stress Intensity Factor Calculations
3.4
The factor KQ, the conditional or trial Kc, must first be established in order to
calculate Kjc. To determine KQ, FQ must be evaluated from the load displacement
plot. where FQ is the greater of the two:
1. The load at the intersection of the load-displacement curve with a line that has
a slope that is 0.05 smaller than that of the elastic loading line.
2. Maximum load withstood by the specimen.
Once FQ is obtained, KQ is calculated using :
KQ = B
FQ
2
(3.8)
where (0.2 < x < 0.8)
f (2 + x)(0.886 + 4.64x - 13.32x 2 + 14.72x 3 - 5.6x 4 )
(1 - X)
(39)
where:
FQ = load as determined above
B = specimen thickness (10 mm)
W = specimen width from center of pinholes to edge (2")
a = crack length measured as an average of 3 measurements on diff erent crack f ronts
x =a/W
It is then determined whether KQ is consistent with the size and yield strength of
the specimen according to Eq. 3.1. If all the critera are satisfied then KQ represents
Kc25
1.4
1.2
/
1
/
/
1-
/
/
/
0.81
/
/
0
/
/
0
/
0.61
/
/
/
/
COD gage
/
0.41
-
/
Instron displacement
-
/
/
/
/
0.2
/
/
/
/
0
0
0.5
1
I
1.5
I
2
displacement (mm)
Figure 3-1: Comparing two methods of displacement measurements in a -50 0 C HDPE
Compact Tension Test (COD gage vs. crosshead displacement)
26
2.5
i
W=5.14 cm
a=2.7 cm
7
0.275W=1.4 cm
1.2W=6.1 cm
O
4.19 cm
2.79 cni
0.25W=1.27 cm
B=1.27 cm
Figure 3-2: The dimensions of the compact tension specimens
27
Figure 3-3: The compression test setup inside the temperature chamber (the screws
were not tightened so that the PVC placed inside can be seen so as to understand
the placement of the specimens)
28
400
C- 300
- -
U)
_
unmodified data using the compression settup
materials real behavior
_
_
_
_
_
_
_
_-__
_
,200
U)
100
-
-
0
C
0.1
0.2
0.3
0.4
0.5
0.6
0.7
true strain (mm/mm)
400
D-
--- -
modified data using the compression settup
materials real behavior
300
/
CO)
CD,
,200
/
-
100
O'
0
0.1
0.2
0.3
0.4
0.5
0.6
true strain (mm/mm)
Figure 3-4: Modifying the data from the compression setup by factoring-in the stiffness of the setup (the above plot is the unmodified data and the lower plot is the
modified data)
29
0.7
Chapter 4
Temperature Dependence of Fracture
Toughness
The polymers were tested in compression to first establish their temperature dependent material properties. The temperature dependence of fracture toughness for these
polymers was determined from compact tension tests. Fracture toughness calculations
(Eq.'s 3.8 and 3.9) depend on specimen geometry and loading behavior but in order
to ensure plane strain and small scale yielding the size criteria (Eq. 3.1) must be
satisfied. Flow stress is needed to verify the Kc test's validity using the size criteria.
The compression tests supplied the flow stress parameter and its variance with temperature. Thus, the temperature dependence of the polymer's fracture toughness is
determined. This is presented in the following sections with discussions.
4.1
HDPE
The compression specimens were tested to establish the material constants of specific
batches and their temperature dependence. Figure 4-1 shows the stress strain plots
of the compression tests at the various temperatures. The properties extracted from
these are listed in Table 4.1 alongside other values. As can be clearly seen from the
plots, the HDPE undergoes a brittleness transition between -70 0 C and -110'C. The
glass transition temperature of the amorphous component of the material, as stated
30
i
by the manufacturer (Table 2.1), is below -76 0 C. In most of the literature it ranges
from -73
0C
to -118
0C
for different grades of PE having different molecular weights.
This transition is evident in the material's inability to withstand much deformation as
can be seen in Fig. 4-1. At -110'C and -1451C the specimens fracture just beyond
the yield point at about 0.16 units of true strain. The slight dip in the stress strain
curve of the HDPE at -70 0 C is due to a circumferential crack that developed but
did not become unstable. This may be the result of environmental cracking. Parrish
and Brown [14] have shown that PE is affected by liquid nitrogen at increasingly low
temperatures. They observed that PE in liquid nitrogen fractured at lower stresses
than in a helium environment or vacuum. The N2 appeared to induce cracks in the
samples. The reduced surface free-energy due to the absorption of the N 2 was given as
the cause of the brittle behavior. The compression tests presented in Fig. 4-1 could
be exhibiting environementally induced brittleness but it cannot be verified unless
compared to tests in other mediums.
The temperature dependence of the yield point exhibits a very linear trend in Fig.
4-2 as does stiffness in Fig. 4-3. The yield point increases about 4.3 times from -10
0C
down to -145'C. Elastic modulus increases about 1.4 times. Brittleness is associated
with increased stiffness and strength and thus the lower temperatures should yield
lower Kic's, however, this is not the case.
The load-displacement plots of the compact tension test results for the various
temperatures are presented in Fig. 4-4. A peripheral issue that should be addressed
before proceeding is the stiffnees of the system. The fracture toughness test fixtures
lacked adequate stiffness due to many connectors (screw connectors and pinholes).
This is apparent in the initial non-linearity of the unmodified load-displacement plots
in Fig. 4-4. They were adjusted by making displacement corrections for system
compliance and loading-pin penetration into the samples. The corrections were made
by discarding the initial non-linear portion of the curves, extending the linear portion
down, and transposing to zero displacement. The adjusted plots are shown in Fig.
4-5.
The behavior is generally linear with very precipitous drops at the point of frac31
ture. The specimens failed by unstable brittle crack propagation. In the lower temperatures the crack bifurcated and developed into two unstable cracks. These two
unstable cracks caused the specimen to separate into three parts as shown in Fig. 4-6.
The angle between the two new crack fronts was roughly 570 t 50 and was relatively
unaffected by the temperature. This behavior has not been reported on by most
researchers of HDPE who performed fracture tests in cryogenic conditions. However,
several of these researchers resorted to the use of compact tension specimens with
chevron shaped crack fronts to avoid the cracks bifurcation. At the higher temperatures cracks did not branch. For example at -10'C there were no signs of bifurcation
and the material fractured along the crack plane. The load-displacement curve shows
some previous local yielding prior to fracture and the fracture surface had a distinguishable milky craze-like region in the initial stages of the crack. The test at -30
0C
failed in a similar manner to that at -10'C but had evidence of bifurcation. However,
neither of the two branched cracks became unstable. The corresponding curve also
shows some non-linearity prior to fracture.
The fracture toughness calculated from Eq. 3.8 exhibited a linear rise with decreasing temperature (Fig. 4-7) from -10'C down to -70
0 C.
This rise has been
documented by other researchers and it coincides with the crack's tendency to bifurcate. It rises from about 4.5 MPavjmi, at -10"C, to about 9 MPaj
, at -70 0 C.
However, below -70 0 C, this linearly rising trend is curtailed. The fracture toughness ceases to be temperature dependent and settles down to about 7 MPa/-T.
This
abrupt reduction in the critical stress intensity occurs below the low temperature
brittleness transition. The temperature dependence of Kc has been a matter of controversy. Hartwig 161 mentioned that some authors such as Parrish and Brown
expected that Kc is influenced by secondary glass transitions. Hartwig stated:
"Most properties of amorphous polymers are influenced by several weak
glass transitions well below the primary glass transition temperatures.
They arise from unfreezing of the mobilities of specific molecular groups
..
Glass transitions hav been found down to 30K. However, for most
polymers they do not occur below 120K."[7]
32
[271
Chan and Williams [15] showed that Kc rose with decreasing temperature. They
aslo observed a similar glass transition in the same regime. They found that the glass
transition temperature was absent from the PE copolymer.
Crack Tip Opening Displacement
4.1.1
The rise in Kc is unusual because lower temperatures generally cause materials to be
increasingly brittle and become defect sensitive. Considering the Crack Tip Opening
Displacement (CTOD, 6) some insight can be given into this negative temperature
dependence. Thus,
S 8 a n[sec(
7rE
)]
(4.1)
for plane strain
(4.2)
2a-,
which for small stresses can be simplified to give:
6=
__(
UOE
-
v2 )
where
6
Crack tip opening displacement
o=
yield strength
E
elastic modulus
o = far - field stress
a = crack length
K 1 = stress intensity factor
Inserting the values for the range of temperatures from -10
0C
to -70
0C
the
CTOD remains constant at about 400 pm. Figure 4-8 shows this constancy is maintained for the range of temperatures above the glass transition in the amorphous
component. The constancy of the CTOD has been verified in several polymers over a
range of crack velocities and temperatures and has been termed critical crack opening
displacement or a crack tip opening criterion. Marshal et. al. [24] found a 1.6 pm
critical CTOD for PMMA over a range of temperatures while Parvin and Williams
33
[28J showed that the critical 6 for PC is approximately 37 pm for a lower range of
temperatures. Though the calculation of 6 is questionable because it depends on
three temperature dependent parameters, Morgan and Ward [26] measured this constancy in PMMA. Fraser and Ward [181 repeated that work for PC with the same
conclusion. Given the constancy of the critical CTOD, the plastic resistance must
be rising at a high rate (Fig. 4-2 and Table 4.1) to compensate for the rise in the
square of the stress intensity factor (overlooking E because it does not rise much as
seen in Fig. 4-3 and Table 4.1). The increased yield strength is giving the brittle
material the ability to withstand defects through elastic means while the local crack
tip region is undergoing plasticity at higher flow stresses. Below the glass transition
this no longer continues because the material remains elastic and a fracture condition
is reached before local yielding. This also applies to the rising trends in PVC and
polypropylene as is discussed below. Ultem however is simply brittle, with no evidence of plasticity and thus it follows the downward fracture toughness trend that is
expected of brittle materials. The temperature dependence of the fracture toughness
of Ultem is understood by the occurrence of crazing that accompanies the fracture as
explained in Sect. 5.4.
4.1.2
Crack Velocity
The tendency to bifurcation of cracks in HDPE may be related to the crack velocity.
However, a more plausible explanation is given in Sect. 5.2.4. Crack velocities are an
important factor that have been studied in many like investigations. Crack velocities
affect Kmc and glass transitions. Another important outcome of the crack velocity is
heating which is discussed in Sect. 5.2.2 in relation to fracture surface features.
Although crack velocity is primarily governed by loading rate, temperature and
environmental influences are considerable. Since the loading rate was maintained at
2mm/min for all the tests the variation in crack velocity is a result of the temperature
and environmental effects. Vincent and Gotham [32] were among the first to show
that GI, rises with crack velocity. Marshall et. al. demonstrated a similar relationship
between Kc and i for various temperatures.
34
The crack velocity, 6, can be given by:
t
t
(4.3)
where t is the time elapsed and rp can be either the plastic zone (as expressed in
Sect. 5.2) or the Dugdale zone for materials that craze. Either zone is described by
the same equation:
= C_r
(4.4)
0
with the value of the constant c depending on which zone size is considered. Using
c=
y from Eq. 5.1 in Sect.
5.2, the plastic zone size is seen to be diminishing rapidly
with decreasing temperature as illustrated in Fig. 4-9. However, this does not mean
that the crack velocity is diminishing also since t ,the time elapsed, is diminishing at
a greater rate. The plastic zone size at -50
0C
was more than 85% of the plastic zone
size at -70 0C while the elapsed time for fracture at -50
0C
was less than 75% that
of -70 0 C. This can be seen more clearly if Eq.s 4.2, 4.3, and 4.4 are combined with
Eq. 5.1 to give:
K
c
(60)1/2
8o
n
Eo?"
where E0 is from a power-law dependence, o = EoEot-,
(4.5)
and n, related to molec-
ular relaxation, is a constant in the order of .1. The CTOD has been shown in Sect.
4.1.1 to remain relatively costant. Yield strain is effectively constant. Therefore all
the values in the parenthesis are essentially of no bearing to the relationship between
K, and e.
Since Kc practically doubles while E grows less than 50%, & must be
increasing.
With increasing crack velocities the maximum stress shifts to either side of the
plane of the crack causing a tendency towards forking. However, this usually happens
in the final stages of crack propagation, preceded by a significant amount of stable
crack growth, and where the velocities are approaching sonic levels. On the other
hand, the cryogenic conditions under which these cracks occur cause extremely high
35
crack velocities at the early stages of crack propagation.
Some cryogenic fracture
testing on polymers measured crack speeds up to 1/3 the speed of sound [8] [3].
Other investigations [20] have shown there is a transitional crack speed that defines
a ductile to brittle transition and that this transitional crack speed decreases with
decreasing temperature. The higher crack velocities at the lower temperatures could
cause this bifurcating behavior however this is not a sufficient explanation since this
does not occur in the other polymers that experienced similar high crack velocities.
A more cogent explanation is given in Sect. 5.2.4. Though these stress distributions
existed in the other polymers their fracture surfaces showed evidence of crazing and
initial plasticity. When HDPE showed signs of cavitation the specimens did not
fracture but in the lower temperatures, with no signs of cavitation, the specimens
bifurcated. Therefore the energy absorbing mechanisms of deformation caused the
cracks to remain in plane while their absence allowed the brittle cracks to deviate.
4.1.3
Modified CT Specimens
The measured Kc values were clearly affected by crack forking. In order to confirm
the validity of the fracture toughness values, more tests were conducted with thicker
specimens. The 1 inch thick specimens (as opposed to the prior 0.5 inch specimens)
were machined with a groove along the two sides of the specimens in order to confine
the travel path of the crack so as to not allow it to bifurcate. The thickness across the
grooved area, which is the reduced specimen thickness, was 0.5 inch. The unmodified
and modified plots are presented in Fig. 4-10 and 4-11. The temperature dependence
of the critical stress intensity factor in these specimens is commensurate to the thinner specimens thus validating them. The bifurcation does not have any significant
effect on the measure of the fracture toughness. Figure 4-12 not only demonstrates
the similarity in Kic's, it also demonstrates that there is an abrupt decrease in fracture toughness below -70 0 C re-confirming the britteleness transition in the samples
without side grooves.
36
4.2
PVC
The material properties of PVC are presented in Table 4.2. The manufacturer reports
that the glass transition temperature is about 70 0 C while the majority of the literature usually reports it to be about about 80 0 C. The tests however show that there is
another brittleness transition at lower temperatures. HDPE exhibited such a transition when the specimens in the compression tests began to fracture at small plastic
strains as explained above in Sect. 4.1. PVC showed the transition by a visible and
quantifiable increase in the modulus of elasticity. This is apparent in Fig. 4-13 when
comparing the linear slopes of the -110"C and -145
0C
tests to the remaining tests.
Fig. 4-15 emphasizes this sudden change in stiffness. The elastic modulus remains
relatively constant at 1.1 GPA from -10
1.5 GPa at -110
0C
0C
down to -70 0 C with a sudden rise to
below which it remains constant once again. The yield strength,
however, has a linearly rising trend with decreasing temperature (Fig. 4-14). Below
-700C the yield point seems to rise parabolically, though not enough data has been
collected to confirm this behavior. The yield point increased roughly 1.85 times from
77 MPa at -10
0C
to 219 MPa at -145
0 C.
This unforeseen low temperature transition also arose in the fracture toughness
tests (Fig. 4-18). There was a linearly rising relationship between Kc and temperature down to -70
0C
below which there is an abrupt drop in value from about 7
MPaV m to about 4 MPaV 7i. The unmodified curves in Fig. 4-16 and the modified
curves in Fig. 4-17 (for an explanation of the modifications see Sect. 4.1) show evidence of plasticity in the tests. The -10
0C
tests proved to be invalid Kc tests due to
excessive plastic deformation. This is obvious from the curves which also show stable
crack growth. All the tests leading down to -70 0 C had some degree of plasticity
which is confirmed by investigating more closely the linearity of the curves. This,
however, was not the case for -110'C and -145 0 C, again emphasizing a transitional
behavior.
The cracks often wandered away from the expected crack plane. They did not
always result in a clear fracture of the specimens in two pieces at the higher temper-
37
atures since the fractures did not become completely unstable. When the specimens
were then finally torn apart at very high rates in order to examine the fracture surfaces, the cracks bifurcated near the end of the specimens for high crack velocity
reasons elaborated upon in Sect. 4.1.2.
4.3
Ultem
Unlike HDPE and PVC, Ultem showed no transitional behavior. The compression
tests presented in Fig. 4-19 show slowly and uniformly rising yield strengths and
stiffness. This is better seen in Fig. 4-20 and Fig. 4-21. The yield point rises with
decreasing temperature in a linear manner from 120 MPa at -10
0C
to 185 MPa at
-145'C. The elastic modulus rose at a slower rate, from 1.2 GPa to about 1.4 GPa.
The glass transition temperature of Ultem is around 200 0 C as stated by both in the
literature and by the manufacturer. Table 4.3 contains the experimentally verified
material properties of Ultem.
Fig. 4-19 shows the stress strain plots at the different temperatures. The 201C
test showed an anomolous dip at about 0.175. This dip is due to poorly centering the
specimen in the compression chamber. This resulted in an offcentered radial plastic
expansion and contact with the wall of the compression chamber. The constraint
caused a lateral force shifting the specimen over and an associated load drop.
Ultem behaved in a very brittle manner. The curves in Fig. 4-23 are linear with
precipitous drops illustrating the instability of the cracks that signify brittle behavior.
Ultem had a relatively temperature independent Kc with no transitions throughout
the range of temperatures from -145
0C
decreased slightly from 6.5 MPaVx/
at --10C to 5.5 MPaIm at -145'C. The result
of the -110
0C
to -10 0 C, given in Fig. 4-24. The Kc values
test is attributed to experimental error.
The brittleness of Ultem can aslo be seen by its smaller plastic zone size and
CTOD shown in Fig.'s 4-26 and 4-25. The CTOD is essentially constant throughout
the range of temperatures.
The fracture surface of the Ultem CT specimens exhibited a wave-like pattern of
38
lines. The waves bowed away from the crack front and had smaller separations in the
initial stages of crack growth. As the crack propagated the spacing between the lines
diminished. These waves have the appearance of hackle and rib marks. Generally,
hackle and rib marks appear when cracks depart from their plane of fracture and are
usually relatively steep ridges but Ultem had a fairly flat fracture surface and the
ridges were not steep. These features are presented in Sect. 5.4.
4.4
Polypropylene
The temperature dependent material properties of Polypropylene are listed in Table
4.4. Fig. 4-27 show the stress strain curves of the compression tests at different
temperatures.
Much like Ultem, there is no apparent change in behavior over the
temperature range of -10'C to -145'C. The literature and the manufacturer place
the T of the amorphous component of polypropylene between 00 C and -25'C. This
is in agreement with the curves in Fig. 4-27. As explained in Sect.'s 4.1 and 4.2 the
brittleness transition correlates with a sudden rise in the stiffness and reduced strain
to fracture. Below -10
0C
the compression tests show a gradually increasing stiffness
with decreasing temperature. The highest Kc test temperature was -30
0C
and thus
no brittleness transition could be seen by the fracture toughness tests.
The 0.2% offset yield as a function of temperature is plotted in Fig. 4-28 as is
the elastic modulus in Fig. 4-29. The temperature dependence of the yield strength
follows the pattern found in PVC (Fig. 4-14). It is initially linear and then becomes
slightly parabolic. However, the rise is greater than that of PVC. The yield strength
at -145
0C
(120 MPa) is 4 times larger than the yield strength at -10'C (30 MPa).
The temperature dependence of the elastic modulus increases at a decreasing rate
and is an almost linear relationship rising from 0.7 GPa to 1.2 GPa for the same
temperature range.
As with PVC, polypropylene showed significant plasticity effects at the higher
temperatures in fracture toughness tests as seen in Fig. 4-30 and Fig. 4-31. The
temperature dependence of KIc (Fig. 4-32) also showed a very slight upward trend
39
as HDPE and PVC, but without a drop at low temperatures. This trend, as with the
stiffness trend, showed minimal temperature dependence. Fig. 4-33 shows the calculated plastic zone size as a function of temperature. It follows the trend exhibited by
the other polymers. However, the CTOD shows to be slight temperature dependence
(Fig. 4-34).
The fracture surfaces of the tested CT specimens were identical for all the test
temperatures. The cracks did not deviate from the expected crack plane path and the
fracture surfaces were smooth. At the higher temperatures, the crack did not become
unstable, yet, the surface maintained the same appearance as the fracture surface of
the specimens that underwent unstable crack growth at the lower temperatures. The
only observable difference between the specimens was a shear lip along the side of
the specimens in the higher temperature experiments which is a result of loss of the
triaxility of stresses at the surface.
40
Temperature
(OC)
-10
-10
-30
-30
-50
-50
-70
-70
-70
-70
-110
-145
Temperature
(OC)
-10
-10
-30
-30
-50
-50
-70
-70
-70
-70
-110
-145
Crack
Length
(a, cm)
2.7457
2.772
2.754
2.6387
2.69
2.661
2.63
2.63
2.752
2.685
2.725
2.705
Table 4.1: HD PE's Measured Values
Yield
Elastic
Critical Stress
Strength
Modulus Intensity Factor
(UO, MPa) (E, GPa) (K4c MPav6
)
47.36
4.63
0.94
47.36
0.94
4.73
72.47
1.1
5.93
72.47
1.1
9.96
88.32
6.73
1.3
88.32
7.62
1.3
1.48
11.02
118.4
1.48
8.81
118.4
1.48
8.25
118.4
1.48
9.59
118.4
164.71
1.41
6.89
203.86
7.13
1.56
Crack
Length
(a, cm)
2.735
2.6483
2.7103
2.6967
2.625
2.74
2.595
2.5925
2.7917
2.748
2.68
2.762
Table 4.2: PVC's Measured Values
Yield
Elastic
Critical Stress
Strength
Modulus Intensity Factor
(E, GPa) (K,,, MPav/'m)
(0-0, MPa)
76.89
1.08
6.46
5.64
1.08
76.89
3.21
1.11
90.34
90.34
1.11
3.58
1.16
4.93
105.77
1.16
5.05
105.77
8.02
1
113.95
8
1
113.95
1
5.28
113.95
113.95
1
5.16
4.1
1.48
151.64
218.96
1.48
3.83
41
Temperature
(OC)
-10
-10
-30
-30
-50
-50
-70
-70
-70
-70
-110
-145
Temperature
(OC)
-10
-10
-30
-30
-50
-50
-70
-70
-70
-70
-110
-145
Crack
Length
(a, cm)
2.624
2.6343
2.7167
2.74
2.6
2.6
2.54
2.54
2.756
2.756
2.64
2.681
Table 4.3: Ultem's Measured Values
Yield
Elastic
Critical Stress
Strength
Modulus Intensity Factor
(E,
GPa) (KC, MPa /m-)
(o, MPa)
122.78
6.5
1.18
122.78
6.56
1.18
124.68
1.22
5.76
124.68
1.22
5.69
137.41
1.28
6.46
1.28
137.41
5.42
6.04
158.36
1.2
1.2
6.35
158.36
5.92
1.2
158.36
1.2
158.36
5.46
1.44
4.27
171.28
1.31
5.64
186.5
Table 4.4: Ploypropylene's Measured Values
Elastic
Critical Stress
Yield
Crack
Modulus Intensity Factor
Strength
Length
(E,
GPa) (KIC, MPav/-j)
(a, cm) (o, MPa)
30.83
1.97
2.7303
0.73
2
2.7287
0.73
30.83
3.45
37.21
0.89
3.008
2.04
2.743
37.21
0.89
45.04
2.717
3.93
0.91
0.91
45.04
3.58
2.762
2.64
52.54
1.01
3.76
4.27
1.01
2.64
52.54
1.01
3.59
2.862
52.54
2.777
52.54
1.01
3.61
2.78
1.09
84.16
3.97
2.757
4.04
119.98
1.17
42
250
I
I
200-
o
x
+
'-i 150 1V
cn
20 0 C
-10OC
-300C
A~5000C
-704C
-1100C
-1450C
100-
H
50+-4
0
0.1
0.2
0.3
0.4
true strain (mm/mm)
Figure 4-1: Compression tests on HDPE at various temperatures
43
0.5
0.6
250
I
I
I
I
200-
'2 150 -
a..
C',
CD,
- 100 0
0
50-
0
0
1
1
1
-160
-140
-120
-100
-60
-80
temperature (OC)
-40
-20
Figure 4-2: Temperature dependence of yield strength in HDPE
44
0
20
2
I
I
I
1.8 --
1.6-
0
1.4-
01.20
-n
E
0.8-
-
0
CO 0.8-
0.6-
0.4-
0.20
-160
-140
-120
-100
-60
-80
temperature (0 C)
-40
-20
Figure 4-3: Temperature dependence of elastic modulus in HDPE
45
0
20
2500
-100C
300C
-
-30'C
2000-
1500 -700
-
-5000
_ 5000
-
~~-50'C
-70 OC
700C
-700
-70'C
-11 00C
-
4500
1000-
500-
0
0
0.5
1.5
1
displacement (m)
Figure 4-4: Unmodified plots of fracture toughness tests on HDPE
46
2
2.5
x 10-3
2500
S-
100C
-300C
-300C
2000
-500C
-7000
-700C
/1
/
I
-
-
/
-
15001
I>
~
-
700C
-70'C
-1100C
-1400
0
10001
500
0
0
0.5
1.5
displacement (m)
1
2
Figure 4-5: Modified plots of fracture toughness tests on HDPE
47
2.5
3
x 10-3
Figure 4-6: The bifurcated cracks in HDPE
48
15
S
E
10-
(U
U)
C0
0
0)
0
U,
0
CD
0
0
glass transition
-160
-140
-120
-100
-60
-80
temperature (4C)
-40
-20
0
Figure 4-7: Temperature dependence of the critical stress intensity factor in HDPE
49
20
1
1
I
1
-140
-120
-100
1
1
1
1
-60
-80
temperature (0C)
-40
-20
0.9-
0.8-
0.7-
0.6-
E
o 0.50
0.4-
0.3-
0.2-
0.1
-160
Figure 4-8: CTOD as a function of temperature in HDPE
50
0
1 .5
I
I
0
1E
a)
N
0
N
0
-160
-140
-120
-100
-60
-80
temperature (0C)
-40
Figure 4-9: Plastic zone size as a function of temperature in HDPE
51
-20
0
2500 --
2000-
1500-
0
1000-
500 -
-
-100C
..........-
400C
-400C
700C
-700C
-
-/
0
0.5
1.5
1
displacement (m)
- -----
1100C
1400C
400
Figure 4-10: Unmodified plots of fracture toughness tests for 1" thick HDPE (with
side grooves)
52
2.5
X
10-3
2500
I
I
I
I
2000-
1500-
1000~ - -00C
1
-400C
500-
0
//-40
-700C
-700C
0
0
0.2
0.4
0.6
0.8
1
~~-11 00C
--- 110 C
~-1 400C
140*C 11.4
--
1.6
displacement (m)
Figure 4-11: Modified plots of fracture toughness tests for I" thick HDPE (with side
grooves)
53
2
1.8
X
10-
15
E
x
101-
CO
x
(D>
C
x
x
x
U)
x
0
x
5
0 -150
-50
-100
temperature (0C)
Figure 4-12: Temperature dependence of the critical stress intensity factor in 1" thick
HDPE (with side grooves)
54
0
300
I
0
200C
10 c
x--100C
X
250C7
-500C
-70'C
-110C
-1 450c
200-
U)150 --
Uw
100-
50
0
0.1
0.3
0.2
0.4
true strain (mm/mm)
Figure 4-13: Compression tests on PVC at various temperatures
55
0.5
0.6
250 ---
-
200-
'@150-
a.
CD
CO)
0)0
1000
0
50-
01
-160
-140
-120
-80
-100
-60
-40
-20
temperature (0C)
Figure 4-14: Temperature dependence of yield strength in PVC
56
0
20
2
1.8-
1.6-
1.4-
- 1.20
E
) 0.8-
0.6-
0.4-
0.2-
0
-160
-140
-120
-100
-80
-60
-40
-20
temperature (0C)
Figure 4-15: Temperature dependence of elastic modulus in PVC
57
0
20
2200
2000-
-10oC
31000
-300C
-
-----
1800-
300C
-500C
1600
500C
--
1400
1200
-/
i
2-
0 1000
800
-
-700C
-700C
-700C
-700C
-11 000
0
14500
-'
600
400
200
0
0
1
I
I
2
3
I
4
5
displacement (m)
I
6
Figure 4-16: Unmodified plots of fracture toughness tests on PVC
58
7
8
9
x 10-3
2200
2000
1800 I
16001
--
1400
~
-1-
I1OI
-Z 1200
/-300C
-300C
~~ -500C
II
0 1000
-
-
-I
-
800
600
-50*C
- -700C
-700C
-'700C
-70OC
-1100C
145G-
-/
400
-(
2001
0
0
1
2
4
displacement (m)
3
5
6
Figure 4-17: Modified plots of fracture toughness tests on PVC
59
7
8
x 10-3
10
I
I
9-
8-
7E
a. 6-CO,
50
20
C,
3-
2-
2epeaur
(C
1
-160
-140
-120
-100
-60
temperature (00)
-80
-40
-20
0
Figure 4-18: Temperature dependence of the critical stress intensity factor in PVC
60
20
300
I
250-
200-
a150-
1005
X
+
200C
-1 04C
-30'C
A
V
-500C..
-700C
-110oC
-145 0C
50 -
0
0
0.1
0.3
0.2
1
0.4
true strain (mm/mm)
Figure 4-19: Compression tests on ULTEM at various temperatures
61
1
0.5
0.6
250
200-
'R 150-
a.
,5100--
00
0
0
01
50--
-160
-140
-120
-80
-100
-60
-40
-20
temperature (4C)
Figure 4-20: Temperature dependence of yield strength in ULTEM
62
0
20
2
1.8-
1.6
1.4-
0
E
u0.8-
0.6
0.4-
0.2-
0
-160
-140
-120
-100
-80
-60
-40
-20
temperature (0C)
Figure 4-21: Temperature dependence of elastic modulus in ULTEM
63
0
20
1600
-10
-
-
~- 500C
-700C
-
-700C
12001
-700C
-700CC
-1100C
10001
0
-O 04C
-300C
-30 0 C
-500C
14001
U)
-
0C
14500
8001
"A
/
/
7
-
/
0
-.
600
~
/*
400
/
,-~
/
200
0
0
0.2
0.4
0.8
0.6
1
1.2
1.4
displacement (m)
Figure 4-22: Unmodified plots of fracture foughness tests on ULTEM
64
1.6
1.8
x 10-3
1500
/
1
/
>NI
/
II
/
j*j
/ ///
/
10001
i~
~
~
4'
/
/
ii
H
"
K
I
/
~~/7
I--,
7
0
-L;"
7
-100C
1/
500
-30*C
//
-
-300
-0C
-500C
/
//
-504C
-700C
-700C
-700C
/
/
_700C
I
I
0
0
0.2
0.4
0.6
0.8
1
1.2
displacement (in)
Figure 4-23: Modified plots of fracture toughness tests on ULTEM
65
-11 000
1-4500
1.8
2
x 10-3
15
C
E
I
I------
10-
0z
CL
to
0)
C
5
0
00
50
20
0
-160
-140
-120
-100
-60
-80
temperature (SC)
-40
-20
0
Figure 4-24: Temperature dependence of the critical stress intensity factor in ULTEM
66
20
I
1
I
I
1
1
0.9-
0.8
0.7-
0.6-
E
o .5
0.5-0
0.4-
0.30
0.2-
0.1 --
00
-160
-140
-120
-100
-60
-80
temperature (SC)
-40
Figure 4-25: CTOD as a function of temperature in Ultem
67
-20
0
0.5
0.45-
0.4-
0.35E
E 0.3-
-
N
0.25 0
N0
Cu)0.2-0
0.15-
0.1 -
0.05 --
0
-160
-140
-120
-80
-100
-60
-40
temperature (4C)
Figure 4-26: Plastic zone size as a function of temperature in Ultem
68
-20
0
160
140-
120-
100-
c 0-)-
60--
40-0
20 --
S0.1
0.2
0.3
true strain (mm/mm)
0.4
20"C
-10C
+-300C
-500C
S-700C
V-11 00C
-
Figure 4-27: Compression tests on polypropylene at various temperatures
69
45
.6
1000
C')
CO)
U)
U)
50-
00
-160
-140
-120
-100
-60
temperature (0C)
-80
-40
-20
Figure 4-28: Temperature dependence of yield strength in Polypropylene
70
0
20
2
I
I
I
1.8-
1.6-
1.4-
a- 1.2-
0
0
0
0.6-
~0.2-8
0.4-
0.2-
-160
-140
-120
-100
-80
-60
-40
-20
temperature (OC)
Figure 4-29: Temperature dependence of elastic modulus in Polypropylene
71
0
20
1000-1
- 10*C
-300C
- -300C
-- -500C
500C
900-
800
-
700-
-
6700C
-700C
110 C
600\
Q
2
- -700C
500
1
/-
400
-
300
200-~
100
0
0
0.5
2
1.5
displacement (m)
1
2.5
Figure 4-30: Unmodified plots of fracture toughness tests on Polypropylene
72
3
3.5
X10-3
1100
10000
9000
900
-100 0
--1 C
r
-300C
-300C
I500C
800
\
~~~-704C
-700C
600 -/3
-
~50'C
700
-700C
-700C
-1100C
500 400-/..
-
300 -
14
200
100
0
-
/
0
0.5
1
1.5
2
displacement (m)
2.5
3
Figure 4-31: Modified plots of fracture toughness tests on Polypropylene
73
3.5
4
X 10-3
10
I
I
9-
8-
7E
Cz
CO,
0
63-0
23-
2-
1
-160
-140
474
-120
-100
-80
-60
-40
-20
0
temperature (00)
Figure 4-32: Temperature dependence of the critical stress intensity factor in
Polypropylene
74
20
1
0.9 _
0.80
0.7-
E 0.6 a)0
N
(0.5-
0
N
C)
0.3-
0.2-
0
-160
-140
-120
-80
-100
-60
-40
temperature (0C)
Figure 4-33: Plastic zone size as a function of temperature in Polypropylene
75
-20
0
1
0.9-
0.8-
0.7-
0.6E
o 0.50.4 --
0.4
0.3 0
0
0.1 -
0
-160
-140
-120
-80
-100
-60
-40
temperature (CC)
Figure 4-34: CTOD as a function of temperature in Polypropylene
76
-20
0
Chapter 5
Fracture Surface Topographies
5.1
Specimen Preparation
A LEO 438VP environmental scanning electron microscope was used to study the
fracture surfaces. The specimens were machined to fit in the SEM and the sputter
coater. 200
A
of gold/palladium was vapor deposited on the fracture surfaces of
the samples enhancing the image contrast and eliminating charge buildup on the
surface. The samples were pressed down on copper tape and mounted on metal studs.
Silver paint was along the sides and edges of the samples improved conduction from
the gold/palladium coating to the stud draining the charge build-up. A computer
interface was used to produce digital images at several locations on the fracture
surfaces.
5.2
5.2.1
HDPE
Fracture Surface Topography
The fracture surfaces of HDPE had three well defined regions very similar to that
found from impact loading notched standard HDPE. The first was a small milky crazelike region that was more readily observed in the higher temperature tests where crack
bifurcation did not occur. The second was a 'mountainous' region that had ridges
77
extending out from a central point delineating an origin of crack growth. The third
was a very smooth usually curved surface.
The first region was of particular interest beacuse it was only observed clearly in
the samples where the crack did not bifurcate. Under closer inspection the topography
of the region resembled indpendent sites of cavitation (Fig. 5-1 and Fig. 5-2), a
process that usually accompanies ductile fracture.
Most cavities had centeral foci
that indicated sources. The cavities were smaller in size and greater in number near
the crack front of the razor tapped crack yet greater in size and less in number
away from the crack front. Therefore, the earlier cavities were nucleation controlled
as opposed to the latter ones being growth controlled. This is due to the greater
tensile stresses experienced by those nearer to the crack front. The boundaries of
these cavities were bowed out towards the crack. In ductile fracture, cavities occur
just beyond the crack front and grow towards the crack causing the crack to travel
forward. If the plastic zone size is considered, an interesting correlation is found.
Using the Irwin approximation:
(5.1)
r, = 37 ( a,, )2
where
plastic zone ahead of the crack
r=
K1
o=
=
stress intensity factor
yield stress
A rough estimate of the plastic zone size can be calculated.
Using the values
obtained at -10 0 C (K 1 = 4.7 MPaV-\Y and -o =- 47 MPa) the plastic zone size
is found to be 1.05 mm. The cavitated region measures about 1.1 mm (Fig. 5-1).
Here the initial form of fracture was by ductile cavitation. At -30
0 C,
the plastic zone
size is approximately 700 Mm. Since the cavities are, on average, 200pam in diameter
the plastic zone size would have about 2-3 cavities. Figure 5-3 shows this to be true.
There is virtually no evidence of cavitation at -70
0C
or below.
A fracture surface feature that appeared at the lower temperatures involved lo-
78
calized shear. This can be seen in Fig. 5-5 which is a fractograph of the crack front
on the specimen tested at -50
5.2.2
0 C.
Adiabatic Heating
Between the first and second regions is a very short intermediate stage (Fig. 5-6)
that appears to be the result of a temperature rise-induced softening due to plastic
cavitation prior to the unstable crack growth. This transitional softening is better
seen in Fig. 5-7. Saatkamp and Hartwig [291 demonstrated that adiabatic heating
increased crack tip plasticity in fracture tests using chevron shaped CT specimens.
They concluded that the increased level of plastic flow raised the fracture toughness.
Kausch [4] also noted this in impact loaded notched HDPE. Local heating at a crack
tip can be induced by friction, chain scission, or other dissipative processes. This
effect is especially strong at low temperatures where the specific heat is small, and
even low heat pulses raise the temperature drastically. Adiabatic conditions exist at
unstable crack propagation where the rate of heat generation is lower than for its
removal by thermal conductivity. Since the crack undergoes a significant velocity
increase between the region of ductile stable crack growth and unstable brittle crack
growth, adiabatic heating would have occured.
Hartwig [9] showed that the ratio
between thermal relaxation time and heat generaion time is 10 - 500, meaning that
fully adiabatic conditions exist for unstable crack propagation for polymers in low
temperatures.
Marshall et. al. [241 showed that the abrupt rise in crack velocity during the
transition from stable crack gowth to unstable crack growth is due to an adiabatic/isothermal transition. Below the transitional crack velocity an isothermal state
of heat dissipation accompanies the stable crack growth whereas above the transitional crack velocity there is adiabatic heating at the crack tip and the material in
that region is thermally softened.
79
Marshall et. al. [241 showed that adiabatic conditions can occur at relatively low
crack velocities because of relatively low thermal conductivities using:
c
(ATad) 2 PCk
(60 K;e)2
(5.2)
where
=
unstable crack velocity
ATad =
T
=
T=
adiabatictemperature rise
T - To
temperature at the crack tip
test temperature
p = density
c
k
specific heat
=
thermal conductivity
Kj*c= value of K 1 e at the instability
Saatkamp and Hartwig [29] argued that the temperature rise in front of the crack
tip can be estimated using the fracture energy as the upper limit for the heat source.
About 60% of GI, is consumed in the plastic zone and thus converted into heat (from
studies by Weichert and Schonert [33]). Under these assumptions one obtains, for the
adiabatic case:
A\Tad
<
0.6 Gjc
pcrp
(5.3)
This reasoning showed that ATad can range from 50 K to 100 K. This temperature
rise can develop added yielding at the crack tip. In some cases the crack tip can
be experiencing above glass transition temperatures while the bulk is below glass
transition [19] [29] [9].
80
5.2.3
Brittle Fracture Surface
The SEM micrograph in Fig. 5-1 shows characteristic river markings of brittle fracture
surfaces.
Figure 5-8 is a sketch of the region examined on the SEM image. The
fracture surface is divided into four regions:
1. The flaw is the defect that acts as the cracks source. The fracture origin is normally due to machining, impact, or material defects such as pores or inclusions.
The material defects can be inherent defects that exist naturally in a material
or are introduced in processing.
2. The mirror region is an area with a smooth, glossy appearance that surrounds
the initiation region. This region marks the beginnings of unstable crack propagation. The crack velocity is relatively slow in this region but it has begun to
accelerate.
3. The mist region has been described as having a 'matte appearance'. This region
is substantially rougher than the mirror region because the crack travels faster
creating parabolic markings giving it the 'matte appearance'.
4. The hackle region appears to be the roughest area due to highest crack velocity.
Macroscopic crack branching initiates at the end of the hackle region.
This sequence of processes is observed in Fig. 5-3
5.2.4
Causes of Bifurcation
Cavity formation is driven by the hydrostatic tensile components of stress and this
intrinsically causes the crack to propagate in a plane perpendicular to the maximum
tensile stress. This typically results in slow cavity expansions followed by crack extension through the cavitated regions. At the higher temperatures where there was
a well developed plastic zone and cavitation occurred, the crack did not deviate from
its expected plane. However, at the lower temperatures the crack was more affected
by shear yielding which occurs at a 450 ± 8' angle as is explained in Sect. 5.2.4 below.
81
Local Stress Intensities on Bifurcating Cracks
Clarification of the stress distribution around the crack tip is important to understand crack behavior. Suresh [10] showed that crack bifurcation and kinking can be
understood by the measure of the angle of deviation and local stress intensity factors:
K 1 = a11 (oz)K
+ a12 (a)KII
(5.4)
K 2 = a2 1 (OZ)Kj + a22 (a)Kr-
(5.5)
1
where K, and KI, denote the mode I and mode II stress intensity factors for
the main crack in the absence of any bifurcation and a is the angle between the
two new crack fronts as demonstrated in Fig. 5-4. K1 and K 2 are the local stress
intensity factors for the bifurcated cracks.
They are, respectively, transverse and
along the path of bifurcated crack propagation. To a first approximation in a, the
dimensionless factors for a kinked crack are:
I
al (a) =
a
3a\
(3cos - + cos
32\
3 /8, a
4 si
+ sin
1 /
a
.3a\
stn + sin
a21(ce) =
a12(a)
-
all (o) =
(cos
+ 3cos 2a
(5.6)
(5.7)
(5.8)
(5.9)
With only a mode I applied to the crack in these experiments Eq.s 5.4 and 5.5
simplify to:
K1 = a11 (c)KI
(5.10)
K 2 = a21 (a)Kr
(5.11)
The tapped cracks are hardly, if ever, in the same plane as the machined crack.
This is due to the tipping of the blade during the tapping process. The tipping angle
82
depends on the geometry of the specimen (specifically the machined groove) and the
blade dimensions. In these experiments the blade tapping produced a crack at a 50
angle away from the crack plane. Applying equations 5.4 and 5.5 to this crack:
al
~ 0.997
a 2 1 ~ 0.044
The angle subscribed by the two crack fronts is initially 30±50. As the cracks grow
apart the angle increases to 90' with the average being about 57" ± 5'. With similar
derivations for finite kinked cracks, Suresh and Shih [31] showed that k 2 vanishes
at 2a = 32' whereas k, reaches a maximum while still remaining smaller than K1 .
Therefore, the phenomena of crack forking improves the fracture toughness. This
improvement, however, is not significant as demonstrated in 4.1.3
83
Crack Tip Stress Distributions
Although the initial 50 angle caused by the blade tapping did not have a significant
affect on the macroscopic stress intensity it does alter the stress distribution around
the crack tip. Considering :
0
=
angle from crack plane
r = distance from crack tip
For Mode I
1
301
2
4
2
/5r [4
V2
301
0
1
K1 3
- cos- + -cos - I
2
2 4
/2irr 4
1 . 30
K1 1 . 0
+ -smn-sn2
4
2
/2irr 4
0=
-rO
5
K1
o-r =
=
0
cos-
-cos-
-
(5.12)
(5.13)
(5.14)
For Mode II
K
-rr =
[
3
301
5 . 0
-- sin- + -si-I
4
2 4
2
3
3 . 0
2
V/2 ir
.301
K2
C
K
rO =
-- sin-
4
2
2
-
221sin-
4
0
3
1
r -cos- 2 + -sin2
4
4
.301
84
(5.15)
(5.16)
(5.17)
Superposition gives:
K1
gr-K,
_~r
UOs
V/2 7K1
5-osCo 0
-
2
4
3
0
-Cos- +
2
0027rr 4
K1
1 0
01-ro =4sn2
2
=
1-s-+
o 30]
4
2
1
30~
12[--siri--+
5
K2
.
42
K2
3 .
sin - 2
4
-/r
r
K2
1
0
+
+-Cos-/2
4
2
/2Fr
-Cos2
4
1.
4
30
2
+ -sin-
3 sin-30]l
4 2
3 .30
-sin2
4
3
30
-sin-4
2
(5.18)
(5.19)
(5.20)
with
K1
=
0.997Kr
K 2 = 0.044K 1
from Sect. 5.2.4.
Differentiating to get the angles of maximum tensile and shear stress:
0
=
0 =
d
d
d
3
0
1
301
(0.997 [4 cos2 + 4 cos 2
1l
0
5 .0
3
301
3
3
+ 0.44 [-4sn2 + 4 sin 2
1.31
0.997 -sin- + -sin
+ 0.044
cos
+ 3sin
(5.21)
(5.22)
The maximum tensile stress is alligned 50 away from the crack plane while the
maximum shear stress is 430 away from the crack plane. This places the plane of
maximum shear stress along the same plane as the shear bands.
Local stress intensities and stress distributions explain the negative temperature
dependence of fracture toughness but fail to explain the cause of crack bifurcation.
Considering the other polymers did not experience bifurcation the difference must
lie in the difference of structures between HDPE and the remaining polymers or the
unquantifiable environmental effects that could affect HDPE and not the other polymers. HDPE is significantly more crystalline than PVC or PP and Parrish and Brown
114] showed that PE becomes markedly crack sensitive in liquid nitrogen environments
at low temperatures.
"Changes in crack path are generally induced by such factors as multiaxial far-field
85
streses, interaction of the crack tip with microstructural inhomogeneities, abrupt load
excursions, or the embrittling effect of an aggressive environment."[31] Therefore the
crack may have bifurcated due crystalographic structure and environmental effects.
The local stress intensties coupled with the crack's velocity result in the higher K1 c's
with continued bifurcation.
5.3
PVC
Much like HDPE, PVC had 3 well defined fracture surface regions that varried in size
with temperature (Fig. 5-9). The PVC fracture surfaces had a clear correspondence
between the behavior observed on the fracture toughness plots and the fracture surface
topography of the specimens.
The first region was a dull flat surface that was featureless to the naked eye. This
region marks the stages of ductile stable crack growth defined by the linear portion
and of the curve and the onset of non-linearity. As the temperature was reduced this
region became less visible. At -145oC
the region is absent and the corresponding
curve in Fig. 4-17 exhibits minimal displacement.
The second stress whitened region (from grey to milky grey) is defined by ridges
that resemble ribs. The surface was rougher than the previous one yet still flat. This
is evidence of a transition to brittle fracture. The plot bounds this region between the
point the curve reaches the maximum load and the point of a markedly precipitous
drop which indicates that the crack has transitioned from stable ductile fracture to
unstable brittle fracture. The scanning electron fractograph (Fig. 5-10) shows this
transition with a trench that spans the width of the speciman at the crack front (Fig.
5-11). It resembles the crazes reported by Lee in her study of deformation mechanisms
in PVC.
86
5.3.1
Transition Crack Length
Dowling
f5]
used a transition crack length, at, as an approximate crack length above
which the strength is expected to be limited by brittle fracture.
at =(5.23)
When comparing this calculated transition crack length to the surface measurement it is found that the transitional crack length was half of the measured length
at best. Since Dowling is using this transition crack length as an industrial criterion
for the employment of fracture mechanics a factor of safety of two - three is probably
implicitly used in Eq. 5.23. If this is true the results are reasonable.
Another interesting characteristic is the region immediately following the transition (Fig. 5-12). Many voids accompany this region which is better seen in Fig.
5-13.
The final stage of crack growth is marked by the sudden drop in the load-displacement
curve which marks complete fracture. The region returns the color of the PVC from
the milky-gray appearance of the former region. The SEM image in Fig. 5-14 shows
it as an extremely 'mountainous' region. This is the region in which the crack may
deviate from its plane due to increased crack velocities. At the low temperatures the
entire surface was composed of this region only less 'mountainous'.
5.4
Ultem
As alluded to in Sect. 4.3 the surface of the fractured Ultem CT specimens primarily consisted of a wave-like pattern that bowed out away from the crack. These
waves could be the result of the interference of the crack front with the elastic waves
released by the fracture itself. The waves become less frequent and have greater wavelength along the crack's path of propagation. This is the outcome of a crack that is
accelerating.
The fracture surface is dominated by hackle marks originating from the origin of
87
the brittle crack propagation (Fig. 5-15). The flaw, mirror region, and hackle marks
are distinguishable. A prior form of crazing can be seen in Fig.s 5-15 and 5-16. The
lower fracture toughness of Ultem at the lower temperatures is attributed to smaller
craze regions since craze initiation is an energy absorbing process.
Fig. 5-17 illustrates the transition from the hackle marks to a wavelike pattern.
5.5
Polypropylene
The macroscopic fracture surface of polypropylene was deceptively brittle in appearance. However, the polypropylene surface contained much microvoiding. Microscopically the failure was ductile on a small scale with the surface consisting of a series
of cusps with highly deformed fibrils between. The cusps form from the microvoids
which appear to nucleate from within the material. Fig. 5-18 shows a fibrillated form
of void growth at the blade tapped crack front. Voiding was prevalent throughout
the entire surface (Fig. 5-19).
Unlike Ultem, polypropylene cavitated more readily at the lower temperatures.
The active liquid nitrogen environment has been known to cause materials to tend
to craze.
The larger craze regions at the lower temperatures absorb more enrgy
causing the fracture toughness to rise. Another factor to be considered is adiabatic
heating. Adiabatic heating, as discussed above in Sect. 5.2.2, is a function of crack
velocity. At the lower temperatures the crack is travelling at greater velocities causing
increased adiabatic heating. The heating could very well have raised the crack tip
temperature above the glass transition since the glass transition is well within the
testing temperatures. The material would thus exhibit more ductility at the crack
tip.
88
.....
..
....
Figure 5-1: The cavitated region and the brittle crack origin in HDPE
89
I
- i FeEw
. -
. -,-I
-
Figure 5-2: Closeup of the cavitations and the tapped crack front in HDPE
90
- --
---
.-
- I --
- --
-
- =-- - --
.
-F-F4-
I
- - I
-
-
Figure 5-3: Brittle crack origin and hackle marks in HDPE at lower temperatures
91
I
,
-m
~-fl
I
/
/
>
do
-.-
..............
I,
'p
I
rp
Figure 5-4: A schematic demonstration of (a) kinked and (b) forked crack geometries
and the associated nomenclature
92
.I
---
-
, -- - - -
I
. -- --
I
Figure 5-5: Shear yielding in HDPE
93
---
- -
aw
-- 2
DATA
001170 1
1
0
1 1024
768
Figure 5-6: The intermediate region during the cracks transition from ductile to
brittle fracture in HDPE
94
Figure 5-7: A closeup of the intermediate region in HDPE
95
Mist Region
Flaw
Mirror Region
Hackle Region
Figure 5-8: Typical brittle fracture surface
96
lk
goIV
U:
Figure 5-9: PVC fracture surface photograph
97
Figure 5-10: Stable to unstable crack growth in PVC
98
Figure 5-11: A craze in PVC
99
Figure 5-12: The initial crack transition in PVC
100
Figure 5-13: A closeup of the initial crack transition in PVC
101
i............
Figure 5-14: The mountainuos region that defines the final stages of the high speed
brittle crack
102
Figure 5-15: Brittle crack origin in ULTEM
103
Figure 5-16: Crazing in ULTEM
104
Figure 5-17: Transition from hackle marks to wave pattern in HDPE
105
Figure 5-18: Multiple crazing at tapped crack front in PP
106
OEM
19119REArn k
''I ---
Figure 5-19: Microvoiding in PP
107
-
, ,,
-
Chapter 6
Conclusions and Recomendations
6.1
Conclusions
Fracture toughness of crystalline thermoplastics generally rises with decreasing temperature. This fracture toughness is diminished and ceases to be temperature dependent below the glass transition for polymers like HDPE. Some polymers, like PVC,
with above room temperature glass transitions may still exhibit this transition at
secondary glas transitions below room temperature. While others yet, do not have a
brittleness transition like PP. Glassy polymers like Ultem, however, have a positive
temperature dependence.
The higher KI,'s at lower temperatures is the result of many factores. Higher
yield stresses with constant CTOD predicts this negative dependence. Though less
crazing and cavitation, which are energy absorbing processes may be apparent at the
lower temperatures, higher crack velocities accompanied by adiabatic heating could
increase the energy absorbing capacity of the plastic zone.
Crazing, cavitation, and shear yielding may be present in cryogenic fracture testing. Failure by crazing or cavitation occurs at lower Kin's than failure by shear
yielding. Crazing is the dominant mechanism of fracture in glassy polymers. Temperature affects the mechanisms of deformation. More importantly environmental
factors have an unestablished effect on them such as causing HDPE to fracture in
compression tests where it would not otherwise.
108
In cryogenic fracture testing crack velocities are of such magnitude that crack tip
heating is significant. This adiabatic heating can cause the temperature in the crack
tip plastic zone to rise above the glass transition inducing greater ductility.
Bifurcation of the crack is introduced by a slight variance in the crack plane
(usually introduced by initiating through blade tapping) in the absence of energy absorbing plastic zone micromechanims of deformation. However this is not a sufficient
reason. Crystal structure and environment are probably the major causes of crack
branching.
6.2
Suggestions
More tests are required at a variety of temperatures to confirm the trends established
in this thesis. At least three tests should be conducted at each temperature. Testing
temperatures in the glass transition regime would be of interest.
More polymers
should also be considered in order to increase the available literature on cryogenic
testing of polymers.
Thicker specimens should be considered to reduce the degree of plasticity in the
higher cryogenic temperatures. In retrospect, chevron shaped specimens would be
better suited for testing. Chevron specimens have many added benefits. For example
energy release rates can be determined through direct methods because crack arrest
will occur. These crack arrests will also allow for utilization of a COD gage from
which crack velocities can be better quantified using crack tip opening displacement
rates. J-integral concepts should also be utilized.
More fractography can be implemented. Extensive studies of each of the stages
of crack propagation can be studied with special attention to transitonal points (eg:
point of crack forking and ductile to brittle transitions).
Using the chevron CT
fracture experiments, unstable crack growth could be inhibited or arrested at desired
test points. These points could be studied by cleaving the remainder of the specimen
at high rates exposing and marking those regions. Side views of the fracture surfaces
would contain much information too. A determination of the spherulite size and
109
crystal structure can be benefitial to understanding the cavitated region in the HDPE
and the cause of crack bifurcation. Measures of surface roughness would also aid the
understanding of the fracture process.
The effect of the temperature chamber environment should be considered since it
is well known that polymer behavior is drastically affected by active environments.
110
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