1 Introduction to Creep, Polymers,
`Plastics and Elastomers
`
`1.1 Introduction
`
`In an earlier book of this series, The Effect
`of Temperature and Other Factors on Plastics
`and Elastomers [1], the general mechanical prop-
`erties of plastics were discussed. The mechanical
`properties as a function of temperature, humidity,
`and other factors were presented in graphs or
`tables. That work includes hundreds of graphs
`of stress versus strain, modulus versus tempera-
`ture, and impact strength versus
`temperature.
`However, when one starts designing products
`made of plastic, these graphs do not supply all
`the necessary information. This is because these
`graphs show the results of relatively short-term
`tests. The value in design is in the initial selec-
`tion of materials in terms of stiffness, strength,
`etc. Designs based on that
`short-term data
`obtained from a short-term test would not predict
`accurately the long-term behavior of plastics.
`This is partly because plastics are viscoelastic
`materials. Viscoelastic by definition means pos-
`sessing properties that are both solid-like and
`liquid-like. More precisely in reference to plas-
`tics, viscoelastic means that measurements such
`as modulus,
`impact strength, and coefficient of
`friction (COF) are not only sensitive to straining
`rate,
`temperature, humidity, etc. but also to
`elapsed
`time
`and
`loading
`history.
`The manufacturing method used for the plastic
`product can also create changes in the structure
`of the material which have a pronounced effect
`on properties.
`The rest of this chapter first deals with the types
`of stress and a short introduction to creep. Then the
`chemistry of plastics is discussed and because plas-
`tics are polymeric materials the focus is more on
`polymer chemistry. The discussion includes poly-
`merization chemistry and the different
`types of
`polymers and how they can differ from each other.
`Since plastics are rarely “neat,” reinforcement, fil-
`lers, and additives are reviewed. This is followed
`
`by a detailed look at creep, including creep-specific
`tests and creep graphs. The discussion takes a look
`at what happens at
`the microscopic level when
`plastics exhibit creep.
`
`1.2 Types of Stress
`
`the time-dependent change in the
`Creep is
`dimensions of a plastic article when subjected to a
`constant stress. Stress can be applied in a number
`of ways. Normal stress (σ) is the ratio of the
`applied force (F) over the cross-sectional area (A)
`as shown in Eq. (1.1).
`
`σ 5 F
`A
`
`(1.1)
`
`1.2.1 Tensile and Compressive
`Stress
`
`When the applied force is applied directed away
`from the part, as shown in Figure 1.1, it is a tensile
`force inducing a tensile stress. When the force is
`applied toward the part it is a compressive force
`inducing a compressive stress.
`
`1.2.2 Shear Stress
`Shear stress (τ) is also expressed as force per
`unit area as in Eq. (1.2).
`The shear force is applied parallel to the cross-
`sectional area “A” as shown in Figure 1.2.
`
`1.2.3 Torsional Stress
`Torsional stress (τ) occurs when a part such as a
`rod for shaft is twisted as in Figure 1.3. This is also
`a shear stress, but the stress is variable and depends
`how far the point of interest is from the center of
`the shaft. The equation describing this is shown
`in Eq. (1.2).
`
`McKeen: The Effect of Creep and other Time Related Factors on Plastics and Elastomers.
`DOI: http://dx.doi.org/10.1016/B978-0-323-35313-7.00001-8
`© 2015 Elsevier Inc. All rights reserved.
`
`1
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`THE EFFECT OF CREEP AND OTHER TIME RELATED FACTORS ON PLASTICS AND ELASTOMERS
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`τ 5 Tc
`K
`
`(1.2)
`
`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.
`
`T 5
`
`θKG
`L
`
`(1.3)
`
`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. 6376].
`
`1.2.4 Flexural or Bending Stress
`
`stress commonly
`flexural
`Bending stress or
`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.
`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
`many are published [2, pp. 4653, 547555].
`
`Figure 1.1 Illustration of tensile stress and
`compressive stress.
`
`Figure 1.2 Illustration of shear stress.
`
`Figure 1.3 Illustration of torsional stress.
`
`Figure 1.4 Torsional constants for rods or beams of common geometries.
`
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`1: INTRODUCTION TO CREEP, POLYMERS, PLASTICS AND ELASTOMERS
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`3
`
`Figure 1.7 Illustration of hoop stress.
`
`circumferentially. Figure 1.7 shows stresses caused
`(P)
`by pressure
`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):
`
`σh 5 Pr
`t
`
`(1.5)
`
`where:
`
`P 5 the internal pressure
`t 5 the wall thickness
`r 5 is 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 (σl) on the same pipe
`wall. The longitudinal stress under the same condi-
`tions of Figure 1.7 is given by Eq. (1.6)
`σh
`2
`
`σl 5
`
`(1.6)
`
`Figure 1.5 Illustration of flexural or bending stress.
`
`Figure 1.6 Picture of a three point flexural or
`bending test being done in an Instron universal
`testing machine [3].
`
`A picture of a supported beam bending test in an
`Instron is shown in Figure 1.6.
`
`σ 5 Mc
`I
`
`(1.4)
`
`1.2.5 Hoop Stress
`Hoop stress (σ
`h) is mechanical stress defined
`for rotationally symmetric objects such as pipe or
`tubing. The real world view of hoop stress is the
`tension applied to the iron bands, or hoops, of a
`wooden barrel. It
`is the result of forces acting
`
`There could also be a radial stress especially
`when the pipe walls are thick, but thin-walled sec-
`tions often have negligibly small radial stress (σ
`r).
`The stress in radial direction at a point in the tube
`or cylinder wall is shown in Eq. (1.7).
`
`
`σr 5 a2P
`b2 2 a2
`
`
`
`
`1 2 b2
`r2
`
`
`
`(1.7)
`
`where:
`
`P 5 internal pressure in the tube or cylinder
`a 5 internal radius of tube or cylinder
`
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`THE EFFECT OF CREEP AND OTHER TIME RELATED FACTORS ON PLASTICS AND ELASTOMERS
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`b 5 external radius of tube or cylinder
`r 5 radius 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):
`
`σe 5
`
`where:
`
`q
`ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
`σ2
`1 σ2
`2 σlσh 1 3τ2
`l
`h
`
`c
`
`(1.8)
`
`σl 5 longitudinal stress
`σh 5 hoop stress
`τc 5 tangential shear stress (from material flow-
`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-
`tial shear stress and radial stress when present.
`
`1.3 Basic Concepts of Creep
`
`As noted earlier, creep is the time-dependent
`change in the dimensions of a plastic article when
`subjected to a constant stress. Metals also possess
`creep properties, but at room temperature the creep
`behavior of metals is usually negligible. Therefore,
`metal design procedures are simpler because the
`modulus may be regarded as a constant (except at
`high temperatures). However,
`the modulus of a
`plastic is not a constant. Provided its variation is
`known then the creep behavior of plastics can
`be compensated for using accurate and well-
`established design procedures or by modification of
`the plastics composition with reinforcing fillers.
`For metals, the objective of the design method is
`usually to determine stress values which will not
`cause fracture. However, for plastics it
`is more
`likely that excessive deformation will be the limit-
`ing factor in the selection of working stresses. This
`book looks specifically at the deformation behavior
`of plastics.
`
`Figure 1.8 Illustration of flexural creep.
`
`Figure 1.9 Illustration of tensile creep.
`
`the time-dependent change in the
`Creep is
`dimensions of a plastic article when subjected to
`stress. This is shown schematically in Figure 1.8
`for flexural creep. A given load is shown on a plas-
`tic plaque supported at the ends. The weight or
`load along with gravity supplies a constant stress
`on the plastic plaque. After 10 h in this condition
`there is very little deflection or sagging of the plas-
`tic plaque. However, after 100 h the deflection, or
`strain, has increased. It is deflected even further
`after 1000 h. The creep measured by the method in
`Figure 1.9 is called tensile creep. If the force
`squeezes on the plastic plaque then the creep mea-
`sure would be compressive creep.
`If one plots the deflection versus time a plot like
`the first part (AB) of that shown in Figure 1.10
`might be obtained. If the stress (or weight) is
`removed at point B,
`the strain or deflection
`
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`1: INTRODUCTION TO CREEP, POLYMERS, PLASTICS AND ELASTOMERS
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`
`Figure 1.10 Illustration of elastic recovery, viscous recovery and permanent deflection or creep.
`
`recovers partially very rapidly to point C. That part
`is called the elastic recovery. After point C, there is
`a slow viscous recovery to some final point D. The
`plaque is no longer flat and that remaining deflec-
`tion is permanent. Creep is the permanent deforma-
`tion resulting from prolonged application of stress
`below the elastic limit.
`properties
`creep-related
`Creep
`and
`other
`important
`(discussed later) are among the most
`mechanical characteristics of plastics. Plastics that
`have significant time sensitivity at use temperature
`will have limited value for structural applications
`or applications demanding dimensional stability.
`
`1.3.1 Categories, Stages,
`or Regions of Creep
`
`When one does a tensile creep experiment, such
`as that shown in Figure 1.9, and the data are
`graphed, a plot like that shown in Figure 1.11 may
`be obtained. Creep data in this plot can be subdi-
`vided into three categories (also called stages or
`regions): primary, steady state, and tertiary creep.
`These occur sequentially as shown in Figure 1.11.
`Initially, when the stress is applied, there is an ini-
`tial strain which is an elastic component
`to the
`strain. For that portion, if the stress is removed the
`material returns to its original shape and dimen-
`sions. Considering that the slope of the curve gives
`the strain rate, the three categories correspond to
`a decreasing strain rate (primary), approximately
`
`constant strain rate (steady state) and increasing
`strain rate (tertiary).
`The first stage of creep shown in Figure 1.11 is
`named the primary creep region, but
`it
`is also
`known as transient creep stage. Primary creep strain
`is often less than 1% of the sum of the elastic, stea-
`dy state, and primary strains. The second stage of
`creep shown in Figure 1.11 is the steady state
`region or secondary creep. This region is so named
`because the strain rate is constant.
`When the amount of strain is high creep fracture
`or rupture will occur. This is called the tertiary
`region and is also known as accelerating creep stage.
`The high strains in this region will start to cause
`necking or other failure in the material. Necking will
`cause an increase in the local stress of the component
`that further accelerates the strain. The importance of
`the tertiary region to normal operation and creep
`design criteria is minimal, as plastic parts are
`designed to avoid this region as failure is imminent.
`In Figure 1.11, the timescale of the tertiary region is
`greatly expanded for
`the purpose of
`clarity.
`Considering the small amount of time in addition to
`the fact that the tertiary region develops a plastic
`instability similar to necking, operating in the tertiary
`region is not feasible. Therefore, it is a conservative
`estimate to approximate the end of serviceable life of
`any component to coincide with the end of the steady
`state creep region.
`Whether these regions have any significance other
`than as arbitrary divisions of the curve is an arguable
`
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`THE EFFECT OF CREEP AND OTHER TIME RELATED FACTORS ON PLASTICS AND ELASTOMERS
`
`Figure 1.11 Strain versus time creep behavior.
`
`point. However, this region concept is commonly
`discussed in the literature. However, creep data are
`rarely found that exhibit a true straight line over a
`substantial region of the creep curve. In the past
`many of the analyses that have been made of stress
`problems for creep have been based on an assump-
`tion that the entire creep curve could be represented
`by a straight line, that is, a constant rate of creep.
`While this may be an adequate way of treating
`design problems involving creep at low stresses over
`long periods of time, it is hardly adequate for many
`present-day problems which often involve high stres-
`ses, high temperatures, and short times.
`The curve shown in Figure 1.11 was measured
`at one amount of stress, determined by the weight
`used in Figure 1.9. Families of these curves are
`often generated at different amounts of stress and
`at different temperatures. Increasing the amount of
`stress, logically increases the magnitude of creep
`measured. Increasing the temperature has a similar
`effect. The qualitative effect of increasing the stress
`and temperature on the strain versus time creep
`curves is shown in Figure 1.12.
`
`1.3.2 Measures of Creep
`
`This section covers the various ways to plot
`multipoint creep data and the ways the data are
`obtained.
`
`Figure 1.12 The effect of temperature and stress
`on strain versus time creep behavior.
`
`1.3.2.1 Stress, Strain, and Time
`
`The most common method of displaying the
`interdependence of stress, strain, and time is by
`means of creep curves. Ideally, the display of the
`interdependence of stress, strain, and time for a
`
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`1: INTRODUCTION TO CREEP, POLYMERS, PLASTICS AND ELASTOMERS
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`7
`
`particular plastics material at a specific temperature
`is a three-dimensional (3D) plot such as that shown
`in Figure 1.13.
`In practice,
`it
`is most common to have the
`straintime data (at a given stress) since these can
`be obtained by the relatively simple experiments
`described previously in Figures 1.7 and 1.8. By col-
`lecting a series of the straintime curves at differ-
`ent stress levels the 3D plot can be constructed. 3D
`plots are hard to work visually or practically so
`
`Figure 1.13 Hypothetical stressstraintime plot
`for a typical plastic material.
`
`is represented by a series of two-
`the 3D plot
`dimensional (2D) plots of these data.
`Some of the measured curves that were used to
`construct the 3D plot are shown in Figure 1.14. The
`curves at low stress are not shown. The relationship
`of these curves to the 3D plot is shown by the pla-
`nar slices shown in Figure 1.15.
`If the 3D plot is sliced by a series of planes that
`correspond to constant
`time, such as shown in
`Figure 1.16, a plot known as an isochronous creep
`plot is obtained. An isochronous plot of the data
`used to construct Figure 1.12 is given in
`Figure 1.17. Isochronous plots are commonly avail-
`able from manufacturers of engineering plastics and
`are very familiar to engineers. Besides being useful
`plots that data can be obtained by experiment rela-
`tively easily because they can also be obtained
`experimentally by performing a series of mini-
`creep and recovery tests on a plastic. These mini-
`creep and recovery tests are less time consuming
`and require less specimen preparation than creep
`curves. To do this a stress is applied to a plastic
`test plaque and the strain is recorded after a time, t
`(often at 100 s). The stress is then removed and
`the plastic plaque is allowed to recover, generally
`for a period of 4t. Next a larger stress is applied
`to the same test specimen and after recording the
`time t,
`strain at
`this stress is removed and the
`material allowed to recover in the same manner.
`
`Figure 1.14 Measured creep plots used to construct Figure 1.13.
`
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`
`THE EFFECT OF CREEP AND OTHER TIME RELATED FACTORS ON PLASTICS AND ELASTOMERS
`
`Figure 1.15 A plane at constant stress slices the
`stressstraintime plot.
`
`Figure 1.16 A plane at constant time slices the
`stressstraintime plot.
`
`Figure 1.17 Isochronous creep plot obtained from Figure 1.13.
`
`This procedure is repeated until enough points have
`been obtained for the isochronous graph to be plot-
`ted. Additional times may be run, but they are typi-
`cally increased by an order of magnitude, so usually
`only one or two curves are measured by this method.
`When the plane is at constant strain as shown in
`Figure 1.18,
`the plots shown in Figure 1.19 are
`obtained. These are called isometric curves. Isometric
`curves are an indication of the relaxation of stress in
`the material when the strain is kept constant. Isometric
`data are often used as a good approximation of stress
`relaxation in a plastic since stress relaxation is a less
`common experimental procedure than creep testing.
`
`Isometric and isochronous plots are the most
`common graphical
`representation of creep data.
`They can be measured in flexure, tension, or com-
`pression. They are also measured at a specific tem-
`perature, so it is common to have families of these
`curves at different temperatures.
`
`1.3.2.2 Creep Modulus
`
`to stress divided by
`Elastic modulus is equal
`strain as shown in Eq. (1.9). However, when creep
`has occurred there is an amount of strain that gets
`added into the denominator of the equation, the
`
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`1: INTRODUCTION TO CREEP, POLYMERS, PLASTICS AND ELASTOMERS
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`9
`
`Figure 1.18 A plane at constant strain slices the stressstraintime plot.
`
`Figure 1.19 Isometric plot obtained from Figure 1.13.
`
`modulus so calculated is called the apparent creep
`modulus as shown in Eq. (1.10).
`Elastic modulus 5 stress=strain ðwith no creepÞ (1.9)
`Apparent creep modulus 5 stress=ðstrain 1 creepÞ
`(1.10)
`
`A plot of apparent creep modulus (often shortened
`to just creep modulus) versus time is a common way
`to show creep performance. A generic creep modulus
`versus time plot is shown in Figure 1.20. If the data
`
`are obtained from an isometric (constant strain,
`Figure 1.19) curve then this is a relaxation modulus.
`The creep modulus curve may be obtained from con-
`stant stress curves (Figure 1.14) by dividing the con-
`stant creep stress by the strain at various times.
`Both the creep and relaxation modulus will
`decrease
`as
`time
`increases,
`as
`shown
`in
`Figure 1.20. The plot
`is usually shown using
`loglog scales. Creep modulus is sometime called
`apparent modulus or apparent creep modulus. The
`reason “apparent” is used is to be more explicit
`about how the calculation of creep or relaxation
`modulus is done.
`
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`THE EFFECT OF CREEP AND OTHER TIME RELATED FACTORS ON PLASTICS AND ELASTOMERS
`
`Figure 1.20 Typical variation of creep or relaxation modulus with a wide range of time.
`
`Figure 1.21 Apparent modulus versus time at various temperatures for a typical plastic material.
`
`Figure 1.21 shows the apparent modulus versus
`time for a plastic material at various temperatures at a
`given stress level. This figure does not cover as wide
`a range in time as Figure 1.20. As the temperature
`goes up, one would expect the creep part of the
`deflections to be larger (and the modulus to be lower)
`and this is shown in the figure. This plot is one of sev-
`eral common ways to plot the effects of creep.
`
`1.3.2.3 Creep Strength and Rupture
`Strength
`
`Creep strength and rupture strength are com-
`monly used when designing or using pipe or tubing.
`Rupture strength is defined as the stress at specified
`environmental conditions (temperature, humidity and
`sometimes chemical environment) to produce rupture
`in a fixed amount of time usually given in hours.
`
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`11
`
`Figure 1.22 Graphical explanation of creep rupture, stress rupture, and creep rupture envelope.
`
`creep strain is the sum of the permanent creep
`strain (Figure 1.10, also called permanent deflec-
`tion) plus the recoverable creep strain. The creep
`failure deformation can be defined by the design
`engineer as the point at which the part ceases to
`function as intended. Stress rupture often is defined
`as onset of the third stage of creep (Figure 1.20).
`Creep rupture extends the creep process through
`stage 3 to the limiting condition where the stressed
`part actually breaks into two parts. Many engineers
`often use stress rupture interchangeably with creep
`rupture. Figure 1.22 illustrates these differences.
`Figure 1.23 shows a plot of creep rupture envel-
`opes at several temperatures. These plots are very
`common for materials that are use in pipes. Creep
`rupture analysis generates a time to failure data for
`different constant stress levels. These data can be
`used to predict the life of a component and can be
`used in design calculations.
`load,
`Over a long period of time at constant
`most polymers will creep,
`leading eventually to
`failure. Aggressive environments, such as humid,
`oxidizing, or acidic atmospheres, generally acceler-
`ate failure as shown in Figure 1.24.
`It is important to keep in mind that creep mea-
`sures on pipes generate a time to failure curve
`under static stress conditions. Pipe usually has
`material flowing through it that can also have an
`effect on creep. This was mentioned in the discus-
`sion of hoop stress and equivalent
`stress
`in
`Section 1.2.5.
`
`Figure 1.23 Creep rupture stress (envelopes)
`versus time of a typical polycarbonate at various
`temperatures.
`
`Creep failure occurs when the accumulated
`creep strain results in a deformation of the machine
`part that exceeds the design limits. Accumulated
`
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`THE EFFECT OF CREEP AND OTHER TIME RELATED FACTORS ON PLASTICS AND ELASTOMERS
`
`Figure 1.24 Typical creep rupture curves in air and environment.
`
`of plastic pipes. The superposition technique starts
`out by measuring creep rupture curves at several
`temperatures above the temperature for the long-
`term plot. Timetemperature superposition implies
`that the response time function of the elastic modu-
`lus at a certain temperature resembles the shape of
`the same functions of adjacent temperatures. An
`example of this stress/time to failure data is shown
`in Figure 1.25.
`Then starting the highest temperature curve, T5
`in the figure, is shifted to the right until most of it
`fits over the next highest temperature, T4. Then the
`combined T5 1 T4 curve is shifted to fit over the
`T3 curve. This is all done “by eye” and the process
`is shown in Figure 1.26.
`The final master curve, shown in Figure 1.27,
`can then be used to establish the failure stress of
`the plastic pipe material in the environment at the
`service temperature and at the desired life of the
`component.
`Creep strength is defined as the stress at specified
`environmental conditions that produces a steady
`creep rate, such as 1%, 2%, or 5%. A plot of creep
`strength of polyethylene pipe at 20°C is shown in
`Figure 1.28. In this case, the creep strength is shown
`in areas due to uncertainty coming for limited exper-
`imental data. Creep strength values are determined
`from isometric plots such as shown in Figure 1.14.
`An alternate term is creep limit. As a rule, creep
`strength is expressed as the creep rupture strength
`
`Figure 1.25 Typical creep rupture curves for a
`plastic pipe at various temperatures.
`
`Many time to fail type plots run out to 50 years
`or more. Creep experiments have not been run for
`that length of time. Long-term creep is generally
`predicted by tests that are carried out at elevated
`temperature. Then, the long-term data are predicted
`using timetemperature superposition techniques.
`Timetemperature superposition is well established
`(ISO 1167 Standard) and is used extensively in the
`assessment of the long-term (50 year) design stress
`
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`
`Figure 1.26 Creep rupture curve shifts at various temperatures used to produce a long-term master curve.
`
`Figure 1.27 Typical creep rupture master curve used to assess the long-term failure stress of a material.
`
`(i.e., the stress that causes rupture after 10,000 or
`100,000 h).
`
`1.3.2.4 Temperature Shift Factors
`
`Often the modulus is found to be reasonably inde-
`pendent of stress level [4]. Plots of modulus versus
`time at various temperatures will produce a series of
`parallel straight lines as shown in Figure 1.29.
`temperatures above 23°C in
`The data for
`Figure 1.29 can be shifted to the right to create a
`single line that extends the time to many more
`hours. This is shown in Figure 1.30, the master
`
`curve of creep modulus versus shifted time cover-
`ing the full range of available data. Therefore, a
`shifted time span of 109 hours is covered.
`The amount of time that each temperature line gets
`shifted in generating the line in Figure 1.30 is noted
`and a separate graph is plotted versus that tempera-
`ture. This produces the temperature shift factor plot
`such as that shown in Figure 1.31.
`The temperature shift factor plot in Figure 1.31
`can be used to estimate the flexural creep modu-
`lus at any temperature within the range of the
`original data. The temperature shift factor at the
`desired temperature is read as indicated with
`
`ClearCorrect Exhibit 1061, Page 13 of 41
`
`

`

`14
`
`THE EFFECT OF CREEP AND OTHER TIME RELATED FACTORS ON PLASTICS AND ELASTOMERS
`
`Figure 1.28 Creep strength and creep rupture comparison for polyethylene pipe measured at 20°C.
`
`Figure 1.29 Flexural creep modulus in three point bending for acetal copolymer at five different temperatures [4].
`
`the dotted lines in the figure. The temperature
`shift factor is essentially a time multiplier that
`shifts the time axis for the reference creep modu-
`lus curve in Figure 1.30 to the predicted time axis
`at
`the desired temperature. The actual
`time of
`interest is multiplied by the temperature shift fac-
`tor to give shifted time that is used in Figure 1.30
`to determine the appropriate modulus. For exam-
`ple,
`to estimate the flexural creep modulus at
`60°C and 20,000 h, the temperature shift factor is
`about 1600 (from Figure 1.31). The desired time
`
`of 20,000 h is multiplied by 1600 to give a shifted
`time of 3.2 3 107 hours. At 3.2 3 107 hours, a
`flexural modulus of 590 MPa
`is
`read from
`Figure 1.30.
`
`1.3.2.5 Compression Set
`
`Compression set is often a property of interest
`when using elastomers. Compression set
`is the
`amount of permanent deformation that occurs when
`a material is compressed to a specific deformation,
`
`ClearCorrect Exhibit 1061, Page 14 of 41
`
`

`

`1: INTRODUCTION TO CREEP, POLYMERS, PLASTICS AND ELASTOMERS
`
`15
`
`Figure 1.30 Flexural creep modulus in three point bending for acetal copolymer at 23°C by timetemperature
`shifting [4].
`
`Figure 1.31 A temperature shift factor plot for acetal copolymer [4].
`
`for a specified time, at a specific temperature.
`ASTM D395 Standard Test Methods for Rubber
`Property—Compression Set is the test method used
`and it calls for the material to be 25% deformed
`(compressed) for a given period. After a 30-min
`recovery time, the sample is measured. The value
`derived is the percentage a material sample fails to
`recover of its original height. For example, a com-
`pression set of 40% states that the thermoplastic
`
`elastomer regained only 60% of its uncompressed
`thickness. A compression set of 100% says that the
`thermoplastic elastomer never recovers—it remains
`compressed. Often creep is confused with compres-
`sion set. However, compression set is the amount
`of deformation under a constant strain, whereas
`creep is the amount of deformation under a con-
`stant stress. Data on compression set were included
`in this work for this reason.
`
`ClearCorrect Exhibit 1061, Page 15 of 41
`
`

`

`16
`
`THE EFFECT OF CREEP AND OTHER TIME RELATED FACTORS ON PLASTICS AND ELASTOMERS
`
`chemical
`irreversible
`occur without
`These
`changes in the polymer(s) in the plastic material.
`ESC is differentiated from stress corrosion cracking
`(SCC), which by definition must involve stress and
`polymer degradation.
`It is important to note that the fluid only acceler-
`ates the mechanism as stress cracking will eventu-
`ally occur in the absence of an active fluid. It will
`eventually occur in air.
`The maximum applied stress (σ) is given by the
`following equation:
`
`σ 5 6FL
`wt2
`
`(1.11)
`
`where:
`
`F 5 the applied load in Newtons
`w 5 beam width in mm
`L 5 effective beam length in mm
`t 5 beam thickness in mm.
`
`The maximum applied stress ordinarily should
`be as high as possible.
`It should exceed the
`expected service stress. If this is not known a rea-
`sonable starting point of 20 N/mm2 should be
`applied. A dry control should always be run at the
`same time. If the vapor pressure of the contact fluid
`is high enough that evaporation occurs, then the
`fluid must be periodically or continuously replen-
`ished. The surface in contact with the fluid and the
`control surface should be compared periodically
`using a magnifying glass.
`
`1.3.2.6 Environmental Stress Cracking
`
`Environmental stress cracking (ESC) is a com-
`mon cause of plastic product failure. ESC may be
`defined as the acceleration of stress cracking by
`contact with a liquid or vapor without chemical
`degradation of the plastic. An illustration of the
`simplest test helps define ESC better.
`There are many tests for ESC [5, pp. 1319]
`and they are summarized in the following sections.
`
`Single Cantilever Test
`This simple test is a single cantilever beam test and
`is illustrated in Figure 1.32. This test requires essen-
`tially no investment. As shown in Figure 1.32 a strip
`of the plastic material is clamped to the edge of a
`sturdy bench. The test fluid is applied to the upper
`surface of the test plaque. Viscous nonvolatile fluids
`such as oils and greases can be smeared onto the sur-
`face. Volatile test fluids need to be applied continu-
`ously. A weight is applied to the end to provide a
`constant stress. A control is recommended to be run
`concurrently in the absence of the fluid. The area
`under the test fluid is examined periodically for the
`formation of cracks or other defects. Details on this
`test will be provided later in the ESC testing section.
`The mechanism of stress cracking is purely
`physical. The interactions between the fluid,
`the
`stress, and the plastic polymer include:
`
`1. Local yielding
`
`2. Fluid absorption
`
`3. Plasticization
`
`4. Craze initiation
`
`5. Crack growth
`
`6. Fracture.
`
`Figure 1.32 Single cantilever beam, ESC test
`under constant stress.
`
`Three Point Bending Test
`The three point bending test imparts a deflection
`to the middle of a test plaque or beam. Two com-
`mon devices are shown in Figures 1.33 and 1.34.
`Figure 1.33 shows a device that can impart a vari-
`able deflection by means of a screw adjustment.
`The device in Figure 1.34 is deflected by a pin.
`The pin can be machined to different diameters
`allowing for different strain levels. The test device
`can be placed in the test fluid.
`The maximum surface strain (εmax) can be calcu-
`lated using the equation:
` 
`εmax 5 6δt
`
`3 100%
`
`(1.12)
`
`L
`
`ClearCorrect Exhibit 1061, Page 16 of 41
`
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`

`1: INTRODUCTION TO CREEP, POLYMERS, PLASTICS AND ELASTOMERS
`
`17
`
`Figure 1.33 Three point bending ESC test device
`with variable imparted strain.
`
`Figure 1.34 Three point bending ESC test device.
`
`Figure 1.35 Three point bending ESC test of a plastic in contact with tri-n-butyl phosphate.
`
`where:
`
`δ 5 the midpoint deflection in mm
`L 5 effective beam length in mm
`t 5 material thickness in mm.
`
`Strains are typically less t