Table Of ContentTHE EFFECT OF CREEP AND OTHER
TIME RELATED FACTORS ON
PLASTICS AND ELASTOMERS
PLASTICS DESIGN LIBRARY (PDL)
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THE EFFECT OF CREEP AND OTHER
TIME RELATED FACTORS ON
PLASTICS AND ELASTOMERS
Third Edition
Laurence W. McKeen
AMSTERDAM(cid:129)BOSTON(cid:129)HEIDELBERG(cid:129)LONDON(cid:129)NEWYORK(cid:129)OXFORD
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Foreword
This book is a second update to an “authorless” 3. Various modulus measures (tensile, com-
work of the same title first published in 1991. As pressive, flexural) versus time at various
expected a lot has changed in the field since the temperatures
previous two editions were published. There are a
4. Hoop stress versus time at various tem-
few new plastic materials. There has been a huge
peratures
turnover and consolidation in ownership of the
5. Stress cracking and other plastics failure
plastic producing companies, which of course
versus time.
means discontinued products. This update is much
more extensive than the usual “next edition.” It is 6. Creep rupture versus time.
also the first Plastics Design Library (PDL) series
book to be published in color. The data in each plastic section are generally
Plastics of similar polymer types are grouped into organized by producer and then product. The unre-
nine chapters. As each plastic type is presented, a inforced products are at the front of each section.
brief explanation of the chemistry of the polymers Next are the reinforced grades in order of increas-
used in the plastics is included. ing reinforcement levels. Generally, glass rein-
The first chapter had been updated. It is an intro- forcement is presented before mineral and carbon
ductory chapter that summarizes the chemistry of reinforcement.
making polymers, the formulation of plastics, creep Generally, within each product usually iso-
testing and test methods, creep measures and charts, chronous plots are first, followed by creep strain.
theory and plastic selection. Subsequent to those will be modulus plots.
Most plastic products and parts are expected to be Creep rupture and hoop stress plots are usually at
usedunderperiodicorconstantstressandattempera- the end.
tures other than room temperature. Chapters 2(cid:1)10 Some data from the first and second edition
are a databank that serves as an evaluation of creep have been removed. Removed data include dis-
of plastics. Over 900 uniform graphs for more continued products and the data on mechanical
than 56 generic families of plastics are contained in property changes as a function of thermal or envi-
thesechapters.Thefollowingtypesofgraphsmaybe ronmental aging. The thermal and environmental
included. aging data are included in other books of this
series. Product names and manufacturers have been
1. Isochronous stress(cid:1)strain curves at various updated.
times and temperatures
2. Creep strain or creep deformation versus time Larry McKeen
at various stress levels and temperatures 2014
xi
Acknowledgments
This book is a second update to an “authorless” eventually led to the 1969 International Science
work by the same title. It was published in 1991. Fair. The many outstanding chemistry teachers at
Of course it was not really “authorless.” This was Rensselaer Polytechnic Institute provided the best
one of the first books published by the cofounder and most thorough undergraduate chemistry educa-
of William Andrew Publishing, William Woishnis. tion in the country. RPI continues to do so in nearly
Bill Woishnis and his staff assembled this book all the fields of science and engineering. Finally,
and it was originally offered in loose leaf and my major professor at the University of Wisconsin,
binder form. Professor James W. Taylor, was a great educator
A number of teachers have greatly impacted on and ultimately developed my teaching abilities.
my education and deserve special thanks. Ms. Anna The author is especially appreciative of the
Kruse was my high school chemistry teacher confidence, support, and patience of my friend Sina
(Lyman Hall High School, Wallingford, CT), who Ebnesajjad. The support from the Elsevier staff,
not only was a great educator but also motivated particularly David Jackson, is outstanding.
this particular young student to study chemistry My family has been particularly supportive
beyond the classroom. That included writing arti- through the long hours of writing and research
cles for an educational chemistry magazine while from my home office. My wife, Linda, has been
in high school and after school projects, one that behind this work 100%.
xiii
1 Introduction to Creep, Polymers,
Plastics and Elastomers
1.1 Introduction by a detailed look at creep, including creep-specific
tests and creep graphs. The discussion takes a look
In an earlier book of this series, The Effect at what happens at the microscopic level when
of Temperature and Other Factors on Plastics plastics exhibit creep.
and Elastomers [1], the general mechanical prop-
erties of plastics were discussed. The mechanical
properties as a function of temperature, humidity, 1.2 Types of Stress
and other factors were presented in graphs or
tables. That work includes hundreds of graphs Creep is the time-dependent change in the
of stress versus strain, modulus versus tempera- dimensions of a plastic article when subjected to a
ture, and impact strength versus temperature. constant stress. Stress can be applied in a number
However, when one starts designing products of ways. Normal stress (σ) is the ratio of the
made of plastic, these graphs do not supply all applied force (F) over the cross-sectional area (A)
the necessary information. This is because these as shown in Eq. (1.1).
graphs show the results of relatively short-term
tests. The value in design is in the initial selec- F
σ5 (1.1)
tion of materials in terms of stiffness, strength, A
etc. Designs based on that short-term data
obtained from a short-term test would not predict
accurately the long-term behavior of plastics. 1.2.1 Tensile and Compressive
This is partly because plastics are viscoelastic Stress
materials. Viscoelastic by definition means pos-
When the applied force is applied directed away
sessing properties that are both solid-like and
from the part, as shown in Figure 1.1, it is a tensile
liquid-like. More precisely in reference to plas-
force inducing a tensile stress. When the force is
tics, viscoelastic means that measurements such
applied toward the part it is a compressive force
as modulus, impact strength, and coefficient of
inducing a compressive stress.
friction (COF) are not only sensitive to straining
rate, temperature, humidity, etc. but also to
elapsed time and loading history. 1.2.2 Shear Stress
The manufacturing method used for the plastic Shear stress (τ) is also expressed as force per
product can also create changes in the structure
unit area as in Eq. (1.2).
of the material which have a pronounced effect
The shear force is applied parallel to the cross-
on properties.
sectional area “A” as shown in Figure 1.2.
The rest of this chapter first deals with the types
of stress and a short introduction to creep. Then the
1.2.3 Torsional Stress
chemistry of plastics is discussed and because plas-
tics are polymeric materials the focus is more on Torsional stress (τ) occurs when a part such as a
polymer chemistry. The discussion includes poly- rod for shaft is twisted as in Figure 1.3. This is also
merization chemistry and the different types of a shear stress, but the stress is variable and depends
polymers and how they can differ from each other. how far the point of interest is from the center of
Since plastics are rarely “neat,” reinforcement, fil- the shaft. The equation describing this is shown
lers, and additives are reviewed. This is followed in Eq. (1.2).
McKeen:TheEffectofCreepandotherTimeRelatedFactorsonPlasticsandElastomers.
DOI:http://dx.doi.org/10.1016/B978-0-323-35313-7.00001-8
©2015ElsevierInc.Allrightsreserved. 1
2 THE EFFECT OF CREEP AND OTHER TIME RELATED FACTORS ON PLASTICS AND ELASTOMERS
Tc
τ5 (1.2)
K
In this equation, T is the torque and c is the dis-
tance from the center of the shaft or rod. K is a tor-
sional constant that is dependent on the geometry
of the shaft, rod, or beam. The torque (T) is further
defined by Eq. (1.3), in which θ is the angle of
twist, G is the modulus of rigidity (material depen-
dent), and L is the length.
θKG
T5 (1.3)
L
Figure1.1 Illustration oftensilestress and
compressivestress.
The torsional constant (K) is dependent upon
geometry and the formulas for several geome-
tries are shown in Figure 1.4. Additional
formulas for torsional constant are published [2,
pp. 63(cid:1)76].
1.2.4 Flexural or Bending Stress
Bending stress or flexural stress commonly
occurs in two instances, shown in Figure 1.5.
One is called a simply supported structural beam
bending and the other is called cantilever bending.
Figure1.2 Illustration ofshearstress.
For the simply supported structural beam, the upper
surface of the bending beam is in compression and
the bottom surface is in tension. NA is a region of
zero stress. The bending stress (σ) is defined by
Eq. (1.4). M is the bending moment, which is calcu-
lated by multiplying a force by the distance between
that point of interest and the force. c is the distance
from NA (Figure 1.5) and I is the moment of inertia.
The cantilevered beam configuration is also shown
in Figure 1.5 and has a similar formula. The
formulas for M, c, and I can be complex, depending
on the exact configuration and beam shape, but
Figure1.3 Illustration oftorsional stress. many are published [2, pp. 46(cid:1)53, 547(cid:1)555].
Figure1.4 Torsional constantsfor rodsor beams of common geometries.
1: INTRODUCTION TO CREEP, POLYMERS, PLASTICS AND ELASTOMERS 3
Figure 1.7 Illustrationof hoop stress.
circumferentially. Figure 1.7 shows stresses caused
by pressure (P) inside a cylindrical vessel.
The hoop stress is indicated in the right side of
Figure 1.7 that shows a segment of the pipe.
The classic equation for hoop stress created by
an internal pressure on a thin wall cylindrical pres-
sure vessel is given in Eq. (1.5):
Figure1.5 Illustration offlexural orbending stress.
Pr
σ 5 (1.5)
h
t
where:
P5the internal pressure
t5the wall thickness
r5is the radius of the cylinder.
The SI unit for P is Pascal (Pa), while t and r are
in meters (m).
If the pipe is closed on the ends, any force
applied to them by internal pressure will induce an
axial or longitudinal stress (σ) on the same pipe
l
wall. The longitudinal stress under the same condi-
tions of Figure 1.7 is given by Eq. (1.6)
Figure1.6 Picture ofa three pointflexural or
σ
bending test being done in an Instron universal σ 5 h (1.6)
l
2
testingmachine [3].
There could also be a radial stress especially
A picture of a supported beam bending test in an
when the pipe walls are thick, but thin-walled sec-
Instron is shown in Figure 1.6. tions often have negligibly small radial stress (σ).
r
The stress in radial direction at a point in the tube
Mc
σ5 (1.4) or cylinder wall is shown in Eq. (1.7).
I
(cid:1) (cid:3)(cid:1) (cid:3)
a2P b2
σ 5 12 (1.7)
1.2.5 Hoop Stress r b22a2 r2
Hoop stress (σ ) is mechanical stress defined
h
where:
for rotationally symmetric objects such as pipe or
tubing. The real world view of hoop stress is the
P5internal pressure in the tube or cylinder
tension applied to the iron bands, or hoops, of a
wooden barrel. It is the result of forces acting a5internal radius of tube or cylinder
4 THE EFFECT OF CREEP AND OTHER TIME RELATED FACTORS ON PLASTICS AND ELASTOMERS
b5external radius of tube or cylinder
r5radius to point in tube where radial stress is
calculated.
Often the stresses in pipe are combined into a
measure called equivalent stress. This is determined
using the Von Mises equivalent stress formula
which is shown in Eq. (1.8):
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
σ 5 σ21σ22σσ 13τ2 (1.8)
e l h l h c
where:
σ 5longitudinal stress
l
Figure 1.8 Illustrationof flexural creep.
σ 5hoop stress
h
τ 5tangential shear stress (from material flow-
c
ing through the pipe).
Failure by fracture in cylindrical vessels is domi-
nated by the hoop stress in the absence of other
external loads because it is the largest principal
stress. Failure by yielding is affected by an equiva-
lent stress that includes hoop stress, and longitudinal
stress. The equivalent stress can also include tangen-
tialshearstressandradialstresswhenpresent.
1.3 Basic Concepts of Creep
As noted earlier, creep is the time-dependent Figure 1.9 Illustrationof tensile creep.
change in the dimensions of a plastic article when
subjected to a constant stress. Metals also possess Creep is the time-dependent change in the
creep properties, but at room temperature the creep dimensions of a plastic article when subjected to
behavior of metals is usually negligible. Therefore, stress. This is shown schematically in Figure 1.8
metal design procedures are simpler because the for flexural creep. A given load is shown on a plas-
modulus may be regarded as a constant (except at tic plaque supported at the ends. The weight or
high temperatures). However, the modulus of a load along with gravity supplies a constant stress
plastic is not a constant. Provided its variation is on the plastic plaque. After 10h in this condition
known then the creep behavior of plastics can there is very little deflection or sagging of the plas-
be compensated for using accurate and well- tic plaque. However, after 100h the deflection, or
established design procedures or by modification of strain, has increased. It is deflected even further
the plastics composition with reinforcing fillers. after 1000h. The creep measured by the method in
For metals, the objective of the design method is Figure 1.9 is called tensile creep. If the force
usually to determine stress values which will not squeezes on the plastic plaque then the creep mea-
cause fracture. However, for plastics it is more sure would be compressive creep.
likely that excessive deformation will be the limit- If one plots the deflection versus time a plot like
ing factor in the selection of working stresses. This the first part (A(cid:1)B) of that shown in Figure 1.10
book looks specifically at the deformation behavior might be obtained. If the stress (or weight) is
of plastics. removed at point B, the strain or deflection
