influence of physical aging on impact embrittlement of ... · published by maney publishing (c) iom...

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Influence of physical aging on impactembrittlement of uPVC pipes

H. A. Visser*, T. C. Bor, M. Wolters, L. L. Warnet and L. E. Govaert

Most failures of unplasticised poly(vinyl chloride) (uPVC) pipes used in the Dutch gas distribution

network originate from third party damage. Brittle pipes should therefore be replaced to ensure

safe operation of the network. In this study, the relation between physical aging and embrittlement

of uPVC is investigated using instrumented falling weight impact tests. The ductile to brittle

transition temperature was first measured for a water pipe grade uPVC at different stages of

aging. As a hypothesis, a critical stress criterion is proposed above which failure is brittle. The

evolution of the ductile to brittle transition temperature that followed from the use of this hypothesis

and a model for the polymer yield stress agrees qualitatively with the experimental data. A minor

increase in transition temperature was observed for the water pipe grade with aging. Applying the

same hypothesis to a uPVC gas pipe grade shows a more pronounced influence of physical

aging.

Keywords: Poly(vinyl chloride), Impact testing, Physical aging, Yield stress, Ductile to brittle transition, Pipes

IntroductionOne of the largest industrial applications for unplasti-cised poly(vinyl chloride) (uPVC) is its use in pipesystems. In The Netherlands, uPVC is extensively usedfor water and sewer distribution systems. Moreover, theuPVC pipes were installed in the low pressure gasdistribution network between the mid-1950s and 1974.Currently, ,22 500 km of these uPVC pipes is still inservice and will reach its initially specified 50 years ofservice life in the near future. Replacing these pipesexactly after 50 years of service would result in anextremely labour intensive, and thus costly, project inthe next decade. Postponement should, however, nevercompromise the safety of the distribution network,which emphasises the need for knowledge on the currentstatus of the network and its subsequent development intime.

The operating pressure of uPVC gas distribution pipesgenerally does not exceed 100 mbar, resulting in onlylow wall stresses in service conditions, when assuming anegligible influence of the surrounding soil on theembedded gas pipes. Consequently, failure data on theexisting gas distribution network show that spontaneousfailure of uPVC gas pipes hardly occurs, and mostfailures originate from third party damage (impactloads).1 Therefore, it is important in which way theuPVC behaves upon an impact load, more specifically,whether it fails in a ductile or a brittle way. A uPVC pipethat behaves in a ductile way upon impact can absorbsignificantly more energy before it fails. These pipes can

therefore survive heavier impact events than brittlepipes. Furthermore, it is easier to stop the gas flowingfrom a pipe that failed in a ductile way, since it allowsthe instalment of a temporary stopper without the riskof further damage. If a pipe fails in a brittle manner, arelatively large part of the pipe is usually destroyedinstantly. The sharp, irregular fracture surfaces make itmore difficult to stop the gas flow. For these reasons, theprobability of (fatal) incidents is higher for brittle pipes,making embrittlement a limiting factor for the servicelife of the pipe in a gas distribution network. It is evidentthat the uPVC pipes should have good impact perfor-mance during their entire service life and not just duringinstallation, since third party damage can occur at anymoment in service. Glassy polymers, such as PVC, areknown to become more brittle in the course of time dueto physical aging. Therefore, the influence of physicalaging on the impact behaviour of uPVC is studied in thispaper.

Since the studies of Peilstocker2,3 and LeGrand,4 ithas been known that physical aging can have asignificant influence on the impact behaviour of poly-carbonate (PC, a glassy polymer like uPVC). Physicalaging is caused by the fact that glassy polymers are notin thermodynamic equilibrium but continuously strivetowards it. Although the mobility in the glassy state(below ,80uC for uPVC) is low, the polymer chains arestill capable of small conformational changes,5 whichresults in a change in the thermodynamic state of thepolymer towards its equilibrium. The mobility of thepolymer chains increases at higher temperatures, short-ening the timescales at which conformational changesoccur. As a result of the conformational changes, thepolymer density increases, the molecular mobilitydecreases and the resistance against plastic deformation

Faculty of Engineering Technology, University of Twente, PO Box 217,Enschede NL-7500 AE, The Netherlands

*Corresponding author, email [email protected]

� Institute of Materials, Minerals and Mining 2011Published by Maney on behalf of the InstituteReceived 4 August 2010; accepted 6 October 2010DOI 10.1179/1743289810Y.0000000021 Plastics, Rubber and Composites 2011 VOL 40 NO 5 201

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increases. The latter is proven by a significant increase inthe yield stress of glassy polymers during physicalaging,6 which was also demonstrated for uPVC in aprevious publication.7

The influence of physical aging on the intrinsicdeformation behaviour of glassy polymers is schematicallyshown in Fig. 1. Annealing (defined here as a heattreatment at elevated temperatures, but below the glasstransition temperature of the polymer) accelerated thephysical aging process. The stress response on the appliedstrain shows an increase in yield stress with an unaffectedstrain hardening. This results in an increase in the yielddrop, which is known as strain softening. The interplaybetween the amount of softening and the strain hardeningmodulus determines the degree of localisation of the plasticdeformation when subjected to a tensile load.8–11 Thedegree of localisation has a strong influence on the failurebehaviour of glassy polymers. An increase in strainsoftening results in, e.g. a decrease in elongation at breakon a macroscopic scale12–14 and can eventually lead tocrazing and even brittle fracture. The latter failurebehaviour might seem counter intuitive to originate fromplastic deformation but can be understood in the followingway.15 On a microscopic scale, the formation of crazes ispreceded by local plastic deformation (e.g. near animperfection) in the plastic zone. Depending on themechanical properties of the polymer, the formation ofthe plastic zone is succeeded by global plastic deformation,or the plastic zone grows further on a local scale. In thelatter case, the hydrostatic stress within the plastic zonebuilds up because its deformation is constrained by thesurrounding material. Voiding occurs when the strain islocalised to such an extent that the local hydrostatic tensilestress (near the edge of the yield zone) surpasses a criticalvalue.16 These voids grow and interconnect with theremaining highly oriented polymer ligaments between thevoids: the craze fibrils. At this stage, a craze is nucleated.The value of the critical hydrostatic stress at which crazingoccurs is hardly influenced by physical aging, as was shownfor PC,17,18 poly(methyl methacrylate)17 and polystyrene.19

The change in failure behaviour can be related to theprocess of physical aging by calculating the thermody-namic state at which the deformation of the polymerlocalises to such an extent that the hydrostatic stress in thematerial surpasses the critical value.

The aging induced changes in intrinsic behaviour canthus lead to a transition from ductile towards (macro-scopically) brittle behaviour, which is indeed observedin studies on the influence of physical aging on theIzod13,20,21 and Charpy22 impact performance of uPVC.It is known that the decrease in impact performance leadsto a shift of the ductile to brittle transition temperaturetowards higher temperatures. Both Adam et al.9 andRyan23 reported a marked increase in the ductile to brittletransition temperature of PC after an annealing treat-ment. The goal of this paper is to investigate whether theaging induced embrittlement can be related to physicalaging via the evolution of the yield stress resulting froman annealing treatment. In the next section, the annealingembrittlement data of LeGrand4 on PC are analysed tofind that the ductile to brittle transition indeed occurs at aconstant thermodynamic state and thus a constant yieldstress. This observation is then used to pose a hypothesisthat enables the prediction of the ductile to brittle tran-sition temperature TdRb based on the influence oftemperature and physical aging on the yield stress. Theexperiments that are required to characterise the influenceof physical aging on the deformation and impactbehaviour of uPVC are described first, followed by acomparison between the experimental data and thepredictions based on the posed hypothesis. The compar-ison is followed by a discussion, where the results for thewater pipe grade uPVC used in this paper are translatedto the behaviour that can be expected for the gas pipegrade uPVC of the pipes that have been in service foralmost 50 years now.

Annealing embrittlement of PCFollowing the path outlined in the introduction, one canexpect the ductile to brittle transition to be related to thethermodynamic state and thus the yield behaviour of thepolymer. As already stated, the value of the criticalhydrostatic stress at which crazes initiate in PC remainsconstant after annealing.17,18 The ductile to brittletransition upon annealing can therefore be directlyrelated to a critical amount of strain localisation, thusa critical thermodynamic state, with a correspondingyield stress (for a given strain rate and temperature).18

Consequently, the ductile to brittle data of PC, aspresented by LeGrand,4 can be coupled to the evolutionof the yield stress upon an annealing treatment.Klompen et al.24 proposed to describe the evolution ofthe yield stress sy of PC after annealing time t atannealing temperature Ta using the following relation

sy~sy,0(:e,T)zclog

teff (t,Ta)ztini

t0

� �(1)

where c is a constant equal to the slope of the yield stressversus the logarithm of the annealing time t, tini isthe initial age, t051 s and sy,0 is the yield stress at thehypothetical case of teffztini51 s, which depends on thestrain rate

:e and the absolute temperature T. Klompen

et al. used sy,0526?1 MPa, c53?82 MPa/decade andtini57?361010 s to describe the true tensile yield stressevolution of injection moulded PC tensile bars measuredat a strain rate of 1022 s21 and a temperature of 23uC.The effective time teff is a measure for the annealing timeat the reference condition and is defined using anArrhenius type time–temperature superposition

1 Schematic representation of intrinsic behaviour of

glassy polymer, such as uPVC, as measured in com-

pression before (solid line) and after (dashed line)

annealing treatment below glass transition temperature

Visser et al. Influence of physical aging on impact embrittlement of uPVC pipes

202 Plastics, Rubber and Composites 2011 VOL 40 NO 5

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teff (t,Ta)~texpDUa

R

1

Tref

{1

Ta

� �� (2)

where DUa is the activation energy that quantifies thedifference in timescale of the influence of aging atabsolute annealing temperature Ta compared with thetimescale at which aging becomes apparent at theabsolute reference temperature (here, Tref523uC).Klompen et al. found a value of 205 kJ mol21 for theactivation energy of PC. With these values, the evolutionof the true tensile yield stress as a function of theannealing time can be described for different annealingtemperatures, as shown in Fig. 2b.

As mentioned before, not only yield but also impactproperties are influenced by physical aging. The Izodimpact data for the notched PC specimens of LeGrand4

are reproduced in Fig. 2a. The data measured afterannealing at 100–125uC are used for further analysis.The data measured at 130uC are disregarded since theannealing times at this temperature are shorter thanthe time required to obtain thermal equilibrium withinthe specimens. The solid lines in Fig. 2a represent thebest fit of the Izod impact data to the inverse tangent fitfunction employed and can be used to determine thetime frame in which the ductile to brittle transitionoccurs for each annealing temperature. The ductile to

brittle time frames are marked with vertical grey areas.The same time frames are also marked in the evolutionof the yield stress shown in Fig. 2b. Remarkably, theyield stresses corresponding to the ductile to brittletransitions at the four annealing temperatures all fallwithin the range of only 2?5 MPa. This observationsupports the existence of a critical thermodynamic state(and thus critical yield stress) at which the ductile tobrittle transition occurs. This is in line with the results ofEngels,18 who proposed the use of a critical yield stressto calculate the lifetime at a certain service temperature.It should be noted, however, that the value found for thecritical yield stress cannot be applied to predict thetransition towards brittle failure in other loadinggeometries. The critical yield stress value depends, forexample, on the deformation field imposed by theimpactor. It can merely be used as a tool to predictthe ductile to brittle transition for these specific testingconditions.

Predicting TdRb for uPVCIn the previous section, the critical yield stress was foundat which the ductile to brittle transition occurred forIzod tests performed on PC at a constant testingtemperature. In the present study, impact tests areperformed on uPVC at a range of temperatures and for

2 Influence of annealing treatments at four different temperatures on a notched Izod impact strength and b yield stress.

Izod impact data of notched PC specimens tested at room temperature after annealing treatment at 100, 115, 125 or

130uC for different annealing times (reproduced from LeGrand).4 Data at 130uC are not taken into account in analysis

and are shown in grey. Evolution of yield stress at 23uC and at applied strain rate of 1022 s21 according to equa-

tion (1), as proposed by Klompen et al.24 Vertical grey hatches correspond to annealing time at which transition from

ductile to brittle behaviour is observed in data of LeGrand,4 shown in a. Horizontal grey hatches indicate correspond-

ing yield stresses


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various annealing treatments to find the influence ofphysical aging on the ductile to brittle transitiontemperature TdRb. The evolution of TdRb with physicalaging (a change in thermodynamic state) is related to theevolution of the yield stress by posing the followinghypothesis: brittle fracture occurs when the yield stresssy of the uPVC specimens surpasses a critical (tensile)stress scr. This critical tensile stress is independent of theannealing treatment (defined by the annealing tempera-ture Ta and the annealing time t) and the testingtemperature T as long as both temperatures are belowthe glass transition temperature of the polymer. Inmathematical terms, this means that the pipe behavesbrittle if

sy(T ,t,Ta)§scr (3)

This hypothesis is used to relate the impact behaviour ofuPVC with its yield behaviour.

The proposed hypothesis can only be employed whenthe influences of strain rate, temperature and physicalaging on the yield behaviour of uPVC are characterised,as performed in previous works.7,25 In these papers, theyield behaviour of uPVC was assumed to be thermo-rheologically simple: only one relaxation mechanism, thea process related to the glass transition temperature, wasconsidered to contribute to the yield behaviour. Thisassumption holds for low strain rates and/or moderatetemperatures. At high strain rates and/or low tempera-tures, such as encountered during the instrumented fallingweight impact tests, the secondary, or b transition, alsocontributes to the yield behaviour. Roetling26–28 showedthat the strain rate

:e and the temperature T dependence of

thermorheologically complex yield behaviour of poly-mers can be described with the Ree–Eyring relation.29

This is a modification of the Eyring reaction raterelation,30 in which the contribution of two (or more)relaxation mechanisms to the tensile yield stress sy aredecomposed into two parallel contributions

sy(T ,:e)~

Xx~a,b

RT

n�xsinh{1

:e:e0,x

expDUx

RT

� �� (4)

where R is the universal gas constant, n�x is the activation

volume, DUx is the activation energy and:e0,x is the

preexponential factor that is related to the entropy of thesystem. The subscript x in the parameters is substitutedby a or b to refer to the parameter for the correspondingrelaxation mechanism. The influence of physical aging onthe yield stress of uPVC can be described by making thepreexponential factor a function of time.7 In thecharacterisation procedure, it was found that, in agree-ment with the behaviour of PC,31,32 the preexponentialfactor for the b process

:e0,b in uPVC does not change for

the range of annealing temperatures investigated in thepresent study (from 45 to 60uC). The local twisting modearound the main chain, to which the b process ispresumed to be related in PVC,33,34 is in thermodynamicequilibrium in this temperature range and therefore doesnot change upon annealing. As a result, the aging kineticscan be incorporated in equation (4) by making only

:e0,a a

function of time (similar to the procedure described in aprevious publication7)

:e0,a~b0

teff (t,Ta)ztini

t0

� �b1

(5)

where b0 and b1 are constants, t051 s and tini is the initialage of the material. The effective time teff accounts for theinfluence of temperature on the aging rate and wasalready defined in equation (2). Combining equa-tions (2), (4) and (5) gives the following expression thatrelates the yield stress with the strain rate and tempera-ture and includes the influence of physical aging

sy(T ,:e,t,Ta)~

RT

n�asinh{1S

:eexp DUa

RT

� �tb1

0

b0 texpDUa,a

R1

Tref{ 1

Ta

� h iztini

n ob1T � � �

zRT

n�bsinh{1

:e:e0,b

expDUb

RT

� �� (6)

Experimental

Material and specimen preparationA large amount of material is required for the type ofinstrumented falling weight tests used in this study. It isimpossible to obtain this amount of material from uPVCgas pipes taken out of service, as multiple pipes arerequired, and it is unknown whether these are allprocessed under the same conditions and have the samethermomechanical history. Therefore, all specimenswere made from new, unused uPVC pipes all takenfrom a single processing batch. The pipes have adiameter of 110 mm and a wall thickness of 2?7 mmand are produced for water distribution purposes.Unfortunately, the uPVC used for these pipes has adifferent grade/formulation than the gas pipes producedbetween 1960 and the mid-1970s. Therefore, thecharacterisation described elsewhere7,25 cannot be useddirectly; the yield behaviour of the water grade pipesshould be characterised for this type of uPVC as well.

The specimens for the instrumented falling weighttests were produced by cutting pipe segments with alength of 55 mm from the pipe with a lathe. These pipesegments were sawed in half (in the axial direction) toobtain two identical semicylindrical specimens. Fivedifferent sets of specimens were prepared that consistedof at least 180 specimens per set. Each set was given adifferent heat treatment (as summarised in Table 1),resulting in different thermodynamic states.

The characterisation of the yield stress behaviour wascarried out with the use of tensile tests. The tensilespecimens were produced by cutting a section of 70 mmfrom the pipe with a bandsaw. Subsequently, such asection was sawed in half in the axial direction and thenpressed into flat plates in a press at 100uC, thusapproximately 15–20uC above the glass transitiontemperature of uPVC, for 25 min at a compressivestress of ,1 MPa. Tensile bars with a gauge section of,306562?7 mm were milled from the plate material(parallel to the axial direction of the pipe). The pressing

Table 1 Heat treatments of five sets of specimens

No. Annealing time/s Annealing temperature/uC

1 As received2 26106 453 16105 604 16106 605 36106 60



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procedure erased all prior effects of physical aging. Insome cases, heat treatment above the glass transitiontemperature can change the crystallinity of the uPVC,which in turn influences the b relaxation, as shown byHarrell and Chartoff.35 They varied the crystallinitylevels between 0 and 34% by selecting specimens withdifferent amounts of stereoregularity and/or chainbranching. Here, only one uPVC formulation was used.Consequently, the increase in crystallinity during 25 minat 100uC is expected to be only minor. The influenceof the processing treatment on the b relaxation andthe associated physical aging kinetics (as studied byTsitsilianis et al.)36 was therefore neglected.

Test methodThe experimental set-up for the impact tests is similar tothe one described by Meijering37 and is (partly) schema-tically shown in Fig. 3. All impact tests were carried outon a Dynatup 8250 impact machine. The specimens wereplaced on a temperature controlled anvil and impactedwith a semispherical tup with a top radius of 7?5 mm. Thetup was mounted on a falling weight of 23 kg at a heightof 460 mm above the specimen before testing. Thevelocity at impact was ,3 m s21, resulting in a kineticimpact energy of 100 J. The force during impact wasmeasured with a 15 kN Kistler force cell (9011A) andrecorded with a Yokogawa DL 1540 digital oscilloscope.The displacement of the weight was measured using aMeter Drive ZAM 301 AAS linear encoder with aresolution of 0?1 mm.

The impact tests were carried out at various tempera-tures. Before testing, the temperature of the specimenswas controlled in a Sanyo MIR 583 Incubator. Thetemperature of the anvil was controlled by an ethyleneglycol flow through a cooling circuit inside the anvil.The temperature of the ethylene glycol was controlled ina Haake F3 thermal bath. A thin layer of vaseline wasapplied on the anvil to ensure that any ice formed at thesurface of the anvil could be easily removed beforetesting. In most cases, 30 specimens were tested pertemperature.

The uniaxial tensile tests were carried out on an MTSElastomer Testing System 810 equipped with a 25 kNforce cell and a thermostatically controlled chamber.These experiments were carried out at a constantcrosshead speed, resulting in constant engineering strainrates. The tensile tests were carried out at strain ratesranging from 1024 to 1 s21 and at temperatures rangingfrom 220 up to 40uC. The value of the yield stress wascalculated using the average of the cross-sectional

surface areas as measured at three locations in thegauge section. All stresses and strains reported in thispaper are engineering values.

CharacterisationThe uPVC pipe material used for the experimentspresented in this paper differs from the grade used inprevious publications.7,25 Moreover, the b contributionto the yield behaviour has not been characterised inthese publications. The characterisation of the tempera-ture and strain rate dependence of the yield stress andthe influence of physical aging are presented in thefollowing two sections.

Characterising deformation kineticsThe results of the tensile yield stress measurementsplotted in Fig. 4 clearly show a transition from a domi-nated yield towards azb dominated yield; at roomtemperature, the influence of the b relaxation becomesapparent at strain rates higher than 0?03 s21. The solidlines represent the result of equation (4) using theparameters summarised in Table 2. The parametersrelated to the a relaxation were calculated from theparameters as determined earlier25 for the differentuPVC grades. The parameters that account for thecontribution of the b relaxation were adopted from thestudy of Bauwens-Crowet et al.38 The pre-exponentialfactors

:e0,a and

:e0,b were obtained using a reference

3 Cross-sectional view of set-up (schematically) for

instrumented falling weight test

4 Markers show yield stress as measured in uniaxial ten-

sion at range of strain rates and temperatures: two

regimes are indicated, a regime and azb regime; solid

lines represent description of equation (4) using mate-

rial parameters given in Table 2

Table 2 Values for parameters in equation (6) for a and brelaxation mechanisms in uPVC

a b

:e0,x/s

21 1.8861038 2.216100

n�x/m3 mol21 1.2961023* 8.3961024{

DUx/J mol21 2.976105* 5.866104{DUa,x/J mol21 2.386105

b0/s21 7.3961041

b1 20.45

*Value adopted from Visser et al.25 (including pressuredependence).{Value adopted from Bauwens-Crowet et al.38



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point in the a regime and one in the azb regimerespectively. The excellent agreement of the solid linescompared with the experimental data allows twoconclusions to be made. First, for the a regime, thedeformation kinetics of the gas pipe grade uPVCcharacterised in Ref. 25 is equal to the deformationkinetics of the uPVC grade used here. Second, for theazb regime, the combination of the abovementioneddata from the a regime and the parameters adopted fromBauwens-Crowet et al. also proves to give an excellentdesciption of the experimental data presented here.

Characterising aging kineticsThe physical aging kinetics of the a contribution to thetensile yield stress of (a different grade of) uPVC wascharacterised in a previous publication.7 Both Bauwens-Crowet et al.31 and Ho Huu and Vu-Khanh32 showedthat the b contribution to the yield stress of PC is notinfluenced by its thermal history. The same behaviourcan be expected for uPVC; its b transition temperature isabout 240uC, and therefore, the mobility that is relatedto the b relaxation is in thermodynamical equilibriumat the annealing temperature of 60uC. To verify whetherthe b contribution to yield stress indeed remainsconstant during annealing treatments, the experimentaldata are compared with the predictions of the model,taking only the aging kinetics of the a contributionto the yield stress into account and neglecting the bcontribution.

The yield stress data at a strain rate of 1024 s21 and at25uC after different annealing treatments are shown asunfilled markers in Fig. 5a. From the shift between thedata at the annealing temperature of 45 and 65uC, theactivation energy DUa,a in equation (2) can be calculatedand was found to be 238 kJ mol21. With this activationenergy, the location of the filled markers in Fig. 5a canbe calculated using equation (2) to calculate the effectiveaging time at a certain reference temperature. The filledmarkers represent the yield evolution of the uPVC agedat a reference temperature (chosen to be 25uC here). Thevalues of the constants b0 and b1 in equation (6) weredetermined using a non-linear least square fitting routine

on the shifted yield stress data, resulting in values ofb057?3461041 s21 and b1520?45 respectively.

As shown above, the strain rate and temperaturedependence of the yield stress in at least the a region ofthe water pipe grade used here is identical to that of thegas pipe grade used in earlier publications.7,25

Remarkably, the aging kinetics is significantly different.The activation energy for the gas pipe grade is abouthalf the value found for the material used in this paper.Moreover, the constant b1 is about half the value foundfor the gas pipe grade, resulting in a twice as steep slopeof the mastercurve for the gas pipe grade. Apparently,the cooperative motions of the polymer chain segmentsthat are related to yielding are identical for the twogrades, whereas the mechanism that enables smallconformational changes of the polymer chains, whichare related to the aging behaviour, differs significantly.The physical background behind this difference isunknown at this stage, but a few possible explanationscan be given.

First of all, the difference might be related to thedifferent contents and types of additives and fillers in thePVC grades used for the two pipes. A small amount ofplasticiser in the water pipe grade could cause an‘antiplasticisation’ effect.39,40 The small amount ofplasticiser can (partly) suppress the secondary transitionand therewith increase the modulus and yield stress andcan also affect the aging kinetics.41 If the ‘antiplasticisa-tion’ effect is present, one would also expect a change inthe contribution of the secondary transition to yieldstress: the azb regime should shift towards highertemperatures and lower strain rates. Future yield stressmeasurements in the azb regime of the gas pipe gradeare required to confirm this explanation.

Second, the difference in aging kinetics can alsooriginate from a difference in polymerisation process forthe PVC powders used for the production of the pipes.The tacticity of PVC chains polymerised from a suspen-sion is different from that of PVC polymerised from anemulsion. Assuming that the PVCs used for the twopipes were indeed polymerised via the two differentroutes, a difference in tacticity can be expected, leading

5 Influence of physical aging on deformation kinetics of uPVC. a yield stress at 1024 s21 and 25uC versus annealing time.

Unfilled markers represent yield stress versus aging time at specific annealing temperature Ta. Filled markers represent

same measurements, where annealing time is calculated for reference temperature of 25uC [effective time in equation (2)].

Master curve that follows from equation (6) is shown as solid black line. b tensile yield stress versus strain rate at 0uC for

two sets of uPVC specimens. One set did not receive heat treatment after production (‘as manufactured’) and one set was

annealed for 2?76106 s at 60uC (‘annealed’). Solid lines represent predictions using equation (6)



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to a difference in the molecular arrangement of theamorphous phases and therefore the aging kinetics.

Third, although unlikely, the differences in the crystal-line structures could also explain the observed differencein aging kinetics. Despite the low crystallinity of PVC,its crystalline structure can influence the aging kinetics.36

Differences in the crystalline structure can originatefrom differences in tacticity, leading to a different pri-mary crystalline structure.42 Furthermore, the proces-sing conditions during pipe extrusion determine the levelof destruction of the primary crystaline structure and thelevel of recrystalisation43 and will thus also affect thecrystalline structure and consequently might influencethe aging kinetics.

Fourth, a last explaination could be the difference inthe level of gelation of the water and gas pipeinvestigated. This level of gelation (the level of primaryparticle structure breakdown) of the PVC is also closelyrelated to the processing conditions.43,44 Currently, aresearch programme is being carried out at laboratiesinvolved in the present study that addresses the influenceof gelation on the aging kinetics of PVC pipes.

The influence of the strain rate on the yield stress at0uC was measured for specimens that were annealed for2?76106 s at 60uC and specimens that did not receiveheat treatment. The results are shown in Fig. 5b. Thesolid line for the annealed specimens is predicted usingequation (6) and the parameters listed in Table 2. Notethat the b contribution to yield stress was consideredto be independent of the thermodynamic state ofthe material. The quantitative agreement between theprediction and the experimental data supports theassumption that the b contribution to yield stress isnot influenced by physical aging. Hence, only thephysical aging kinetics of the a contribution is takeninto account.

Impact results

Types of failureThe conditions during the instrumented falling weighttests were such that an excess kinetic impact energy wasexerted to ensure that all the specimens failed. Thebehaviour of the specimens during impact can be divided

top: ductile failure; middle: semiductile fracture; bottom: brittle fracture6 Typical force versus displacement signals including video stills from high speed camera for three failure types

encountered during falling weight tests: letters indicated on top of figures on left correspond to video stills displayed

on right



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into three categories: ductile, semiductile and brittle. Atypical force–displacement diagram for each of thesethree types of failure is shown in Fig. 6. At critical pointsin the force–displacement curves, the correspondingimage, obtained using a high speed camera, is shown.

The force–displacement diagram of a ductile failure(Fig. 6, top left) shows a continuous increase in force upto a value between 5 and 6 kN. A ‘shoulder’ can bedistinguished during the start of deformation, betweenthe first two image stills (a and b). The deformationoccurring before this shoulder can be ascribed mainly toelastic deformation, whereas the deformation occurringafter the shoulder is mainly plastic. A considerableamount of stress whitening takes places in the materialunderneath the tup. At the moment the force reaches itsmaximum value, the sides of the specimen have deflectedupwards and lose contact with the anvil. Furthermore,the material underneath the tup is drawn into the anvilin a similar way as the ductile failures described byChivers and Moore.45 In the highly drawn regions, thematerial starts to rupture locally. These ruptures growand coalesce, followed by the formation of a crack thatis large enough for the tup to penetrate the specimen.The material folds around the tup, between the tup andthe hole in the anvil. The force does not decrease directlyto zero after the puncture of the tup as a result offriction between the moving tup and the stationaryspecimen.

The semiductile specimens follow the same path as theductile specimens up to the point where the force reachesits maximum. After this point, at still c, the tup punchesout a piece of material that has roughly the size of thehole of the anvil. This part of the fracture is still ductile,but the remaining part of the specimen fractures in abrittle way. As a result of the build-up of elastic energy,the fractured pieces scatter around at high velocity.

Brittle fracture occurs somewhere on the (left side ofthe) curve of the ductile specimens, long before themaximum force is reached. Most of the brittle fracturesoccur before the shoulder can be distinguished, thusbefore a significant amount of plastic deformation hasbeen built up. After fracture, dynamic effects cause someoscillations in the force signal, although no forces areexerted on the (fractured) specimen anymore (see thebottom left graph of Fig. 6).

Impact energy analysisDuring impact testing, the kinetic energy of the impactoris partly stored as elastic energy and partly dissipated inthe specimen as a result of plastic deformation, frictionand fracture. The amount of energy absorbed by thespecimen E is a measure of the ductility of the specimenupon impact. When all frictional losses are neglected,the absorbed energy can be calculated with

E~

ðs tfð Þ

s(tcontact)

F sð Þds (7)

where F is the force exterted on the specimen, s is thedisplacement of the tup head, tcontact is the time at whichthe tup makes contact with the specimen and tf is the timewhen failure occurs. The latter time depends on thedefinition for failure that is employed. Here, failure isdefined as the moment at which the exerted force reachesits maximum value. The amount of energy that followsfrom this criterion is referred to as the energy up to themaximum force Emax throughout this paper, and itsdefinition is graphically shown in Fig. 7. Other definitionsof failure can be employed, but will eventually lead tosimilar results and conclusions. The force displacementsignals of ductile failures are identical to those ofsemiductile failures up to the maximum force. The Emax

of these two types of failure are therefore identical, makingit easy to distinguish brittle fracture on the one side from(semi)ductile failures on the other side. This is illustrated inFig. 8 (left), which shows a histogram of Emax as calculatedfor all experiments carried out during this study. The figureclearly shows the existence of two distinct populations. Thepopulation of brittle fractures has a mean energy up to themaximum force of ,3 J. As the force–displacementbehaviour during a semiductile failure is equal to that ofa ductile failure up to the maximum force, thesepopulations coincide and are brought together under theductile population. The mean energy up to the maximumforce of this population of failures is ,34 J.

The energy up to the maximum force Emax wasdetermined for a range of test temperatures for each setof specimens listed in Table 1. All the determined valuesare plotted versus the test temperature in Fig. 9 for theas received specimens (Fig. 9a) and the specimens thatwere annealed for 36106 s at 60uC (Fig. 9b). As already

7 Typical force versus displacement signal for ductile

failure: energy up to maximum force Emax is defined as

surface area of filled, grey areas

8 Histogram of energy taken up by specimens up to

maximum force in force–displacement plot Emax of all

tested specimens



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stated, the difference between ductile and brittle failuresis very distinct, as can be seen in Fig. 9 as well. Thetransition from ductile failures at higher temperaturestowards brittle fractures at lower temperatures is,however, not very distinct. In the transition range, bothbrittle and ductile failures occur, causing large standarddeviations around the average of Emax at temperaturesin this transition region (also for the temperatures atwhich a large number of experiments were carried out).Nonetheless, it is clear from the experimental data thatthe as received specimens do show a transition towardsbrittle fracture at a lower temperature than the annealedspecimens. An attempt to quantify this shift of theductile to brittle transition temperature as a result ofphysical aging is presented in the following section.

Ductile to brittle transition analysisA failure is categorised here as ‘brittle’ when Emax,25 J.The choice for this value is rather arbitrary as theanalysis that follows is not sensitive for values between10 and 30 J. The percentage of ductile failures at eachtest temperature is shown in Fig. 10 for the as receivedspecimens (Fig. 10a) and the specimens that wereannealed for 36106 s at 60uC (Fig. 10b). The transition

temperature is obtained by fitting an error function (erf)to the percentage of ductile failure at each temperature

Percentage of ductile failures~50z50 erf d0zd1Tð Þ (8)

using d0 and d1 as fit parameters that determine thetemperature at which the transition occurs and the widthof the transition range respectively. The number ofexperiments differs per testing temperature, as can beseen in Fig. 9. The non-linear fitting routine was carriedout on all individual experimental data points toaccount for this difference in number of data pointsper temperature. The resulting best fits are shown as asolid line for the as received (Fig. 10a) and annealedspecimens (Fig. 10b).

The ductile to brittle transition is defined here as thetemperature region in which the percentage of ductilefailure is between 30 and 70%. This transition tempera-ture region can be calculated with the fitted function andis shown as the darker grey area in Fig. 10. Thetransition temperature is found to be between 23?5and 21uC for the as received specimens and between 0?4and 2?8uC for the annealed specimens, thus showing anincrease in ,4uC of the average TdRb as a result ofphysical aging. The transition regions for the specimensthat received intermediate annealing treatments (sets 2, 3

a as received specimens; b specimens annealed for 36106 s at 60uC9 Energy taken up by specimens up to maximum force Emax in force–displacement plot during falling weight versus test

temperature

a as received specimens; b specimens that were annealed for 36106 s at 60uC10 Percentage of (semi)ductile failures versus test temperature. At even temperature values, five measurements were

conducted. At uneven temperature values, 30 measurements were carried out. Solid lines are best fit to equation (8)



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and 4 in Table 1) were calculated using the sameprocedure and are shown as grey areas in Fig. 11. Onthe abscissa of the figure, the aging time at 10uC (theaverage service temperature of uPVC gas pipes) is given.This aging time at 10uC was calculated from theannealing treatment of each set, equation (2) and theactivation energy DUa,a as found during the character-isation of the aging kinetics (see above). The transitiontemperature region for the as received specimens isshown as a light grey area as its aging time at 10uC is 0 s,which cannot be shown on a logarithmic scale. Theexperimental data do not show a significant, increasingtrend of the transition temperature with an increase inaging time.

The evolution of TdRb resulting from an annealingtreatment can be predicted assuming that the ductile tobrittle transition occurs when a critical, temperatureindependent, tensile stress is reached (equation (3)). As afirst step, the value for this critical stress scr, pertainingto the conditions of the current impact experiments, wasdetermined. From equation (6) and the parameterslisted in Table 2, the tensile yield stress at any givenstrain rate and temperature can be calculated as afunction of the thermal treatment. The yield stress forthe specimens of set 3 at its TdRb was calculated to be113 MPa for a strain rate of 102 s21, which is a roughestimate of the overall strain rate of the material duringimpact (neglecting local differences) (The value of thestrain rate has an influence (albeit small) on the resultingevolution of TdRb, as the lines in Fig. 4 are not exactlyparallel in both the a and the azb-region.). This yieldstress value is assigned as the critical stress scr. Onceagain, it should be emphasised that scr is not a materialparameter, but is merely a tool to calculate the evolutionof TdRb for these specific experimental conditions.

The procedure to obtain the evolution of TdRb withthe age of the material is outlined in Fig. 11b. The TdRb

for specimens with a different annealing treatment wasdetermined by calculating at which temperature the yieldstress of these specimens is equal to the critical stress.For this calculation, it is necessary to know the thermalhistory of the material, expressed as tini (initial age) inequation (6). The initial age was estimated from the age

of the pipe material; at the time of testing, the pipematerial was 3 years old. Assuming a storage tempera-ture of 23uC, the initial age was estimated to beequivalent to ,225 years at the service temperature of10uC using equation (2). The solid line shown inFig. 11a is the result of employing the hypothesis onthe yield evolution and qualitatively agrees with theexperimentally obtained TdRb in the sense that theincrease with age is marginal. The predicted gradient ofTdRb versus the logarithm of age is somewhat higherthan the gradient found experimentally, but is still agood estimate. Furthermore, the predicted transitiontemperature of the as received specimens (the level of theinitial plateau of the solid line) is lower than themeasured value. A possible explanation for this differ-ence is that the initial age of the pipe material wasactually higher than expected because of a higherstorage temperature or a slow cooling rate afterprocessing. Another explanation is that the posedhypothesis is not valid. Ishikawa et al.46 showed thatthe critical hydrostatic stress at which crazes nucleatedecreases with temperature, which contradicts thehypothesis posed in this paper. Employing a decreasingcritical stress with temperature would, however, result inan even more pronounced increase in TdRb with(effective) annealing time, as it would mean that thehorizontal line in Fig. 11b would have a negative slope.This would result in a wider range of TdRb for the fourthermodynamic states shown. The posed hypothesis thusresults in a better description of the evolution of TdRb

and is used to describe the evolution throughout the restof this paper.

The practical implication of these results is thatphysical aging does not lead to embrittlement during50 years of service life for this water pipe grade of uPVCat unloaded pipe conditions. The 50 years of service at10uC only adds ,0?2uC to TdRb for the prediction basedon the estimated initial age of 225 years (see above). Asalready stated, the yield behaviour of the uPVC gradethat was used for gas distribution pipes is much moreinfluenced by physical aging. In the next section, theconsequences of this difference are discussed. It should,however, be emphasised that the observed difference in

11 a ductile to brittle transition temperature range (grey patches) versus calculated age at 10uC in years (using equa-

tion (2)). Solid line represents prediction using equation (6) and hypothesis given by equation (3). b tensile yield stres-

ses of uPVC specimens at four ages (1, 100, 10 000 and 1 000 000 years at 10uC, shown in grey towards black lines

respectively) and strain rate of 102 s21 versus test temperature are shown in solid black lines. Critical stress scr is

shown as horizontal, dashed black line, and resulting TdRb for each age is shown as vertical dashed grey lines



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aging kinetics relates only to the specific PVC grade ofpipes used in this study. A more extensive study on awide range of PVC pipe grades used for water and gasdistribution pipes is required before fundamentaldifferences between water and gas pipes can beconfirmed.

DiscussionBoth experimental and modelling results show that theinfluence of physical aging has but a small effect on theTdRb of the uPVC water pipe grade: 50 years of aging at10uC hardly changes the TdRb, independent from theinitial age of the material (see also Fig. 11). The agingkinetics of this water pipe grade were found to differsignificantly from a pipe grade used for gas distributionpipes, which was characterised elsewhere.7 For theoperators of the gas distribution network, the influenceof this difference on the prediction of the ductile tobrittle transition is of interest. As a first approximation,the same critical yield stress was used to calculate theevolution of the transition temperature. This choice forthe critical yield stress determines the temperature atwhich the transition occurs at a given state of aging, butnot the rate at which TdRb changes with the age of thepipe. The initial age of the uPVC gas pipe material waschosen to correspond to a yield stress of 50 MPa (at astrain rate of 1023 s21 and at an ambient temperature of23uC) and a moderate cooling rate after processing. Theresulting relation between age and TdRb for the gas pipegrade is shown in Fig. 12. Note that both the time andthe temperature range along the axes in Fig. 12 aredifferent from those in Fig. 11a.

The model predicts that the transition temperature forthe gas pipe grade is clearly more sensitive to physicalaging than the water pipe grade; TdRb increases by5?7uC/decade for the gas pipe grade and 2?5uC/decadefor the water pipe grade. Within a service life of 50 yearsat 10uC, the ductile to brittle transition temperature canbe expected to increase by ,7uC (Nonetheless, the effectof aging on the embrittlement of this grade of uPVC isstill much less pronounced than the annealing induced

embrittlement reported for PC.9,23), depending on theinitial age of the pipe at the moment it is installed. In thiscase, the initial age was chosen such that it complies withthe cooling rates encountered during the extrusionprocess of PVC pipes. Storing the pipe for 3 years at23uC (as assumed for the water pipe grade) results in anincrease in 5uC of the TdRb. Subsequent aging in theground (at 10uC) only results in minor changes as thechanges in TdRb occur on a logarithmic timescale. Thestorage time and the temperature before installation ofthe pipes therefore have an important influence on thequality of the pipe at the moment it is installed.

For the operators of the gas distribution network, it isimportant to determine a criterion for the uPVC pipes atwhich the pipes become too brittle. In this study, it isshown that this criterion can be related to the age, andthus to the thermodynamic state, of the material. Thenetwork operators are advised to create a procedurecomparable to the one used by LeGrand4 to determinesuch a criterion. First, a temperature should be chosenat which the uPVC pipe should still be ductile. Animpact load comparable to that encountered by diggingactivities should be applied on specimens of the uPVCpipe material at this temperature. Subsequently, the ageof the specimens is increased until a brittle failure isencountered. The thermodynamic state of this brittlespecimen corresponds to the critical age. The experi-mental data presented in the present paper can be usedto estimate at which age this transition occurs.

ConclusionsInstrumented falling weight tests have been used tomeasure the influence of physical aging on the ductile tobrittle transition temperature of uPVC pipes. Experi-ments that were carried out on a water pipe grade ofuPVC show that this transition temperature is hardlyinfluenced for the range of aging times tested: an increaseof only 4uC was observed after prolonged annealing ofthe specimens for 36106 s at 60uC, which is equivalent toalmost half a million years at the service temperature ofuPVC gas pipes. This marginal increase was found tocomply at least qualitatively with the description of theevolution of TdRb with physical aging using the hypoth-esis that the transition from ductile to brittle behaviouroccurs when the tensile yield stress surpasses a critical,temperature independent stress value. The calculatedincrease in TdRb is 0?2uC for a water pipe grade after50 years of service at 10uC. It can thus be concluded thatthe physical aging during the service life of the pipe willnot affect the fracture behaviour of the pipe, but thethermal history of the pipe before installation willdetermine the fracture behaviour of the pipe during itsservice life. Applying the same hypothesis on theevolution of the yield stress of the uPVC gas pipe gradeupon aging suggests that the TdRb for these pipes is muchmore influenced during service life; an increase of ,7uC ispredicted. Additional impact tests on this pipe grade arerequired to determine whether the yield stress is indeed akey parameter in determining the residual lifetime ofuPVC gas pipes that are currently in service.

Acknowledgements

The authors wish to express their gratitude to CogasInfra B.V., Enexis, Liander and Stedin for their financial

12 Prediction of ductile to brittle transition temperature

of uPVC gas pipes using aging parameters as deter-

mined elsewhere,7 assuming initial age that corre-

sponds to tensile yield stress of 50 MPa (at strain rate

of 1023 s21 and ambient temperature of 23uC) and

same critical yield stress as used for water grade

uPVC from Fig. 11



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support, which made it possible to carry out thepresented research programme. Furthermore, the help-ful discussions with Dr D. J. van Dijk are appreciated.

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