report

CASE STUDY 2 – DESIGN OF A NATURAL GAS DELIVERY SYSTEM

Questions to help set up the final report.

1. What density of polyethylene (high, medium, or low) would you select if you wished to

have:

a. The highest yield stress and Young modulus

b. The maximum number of intercrystalline links and high orientation hardening

after yielding

2. How do the requirements of the extrusion process affect the molecular weight of the

polyethylene used and how is the mechanical behavior of the pipe affected by extrusion?

(Warning – an extensive answer beyond the class discussion is required for the second

part of this question – document your statements with references).

3. In a thin-walled pipe of external diameter D and wall thickness t, what are the magnitudes

of the principal stresses that result from an internal pressure? If the deformation is elastic

write down an expression for the hoop strain in terms of p, D, t and the elastic constants E

and .

4. An HDPE pipe having a ratio of external diameter D to wall thickness t of D/t=11 must

have a hoop strain of less than 3% after 50 years. Use the tensile creep data of Fig. 21, to

calculate the maximum permissible internal pressure. Assume that Poison ration is 0.4

and remains constant with time. How sensitive is your answer to the exact value of the

Poison ratio?

5. For a polyethylene pipe that is installed at a temperature of 35oC, and its ends are

anchored when it is stress-free, calculate the longitudinal thermal stress 1000 hours after

burial, if the temperature falls to 10 oC when it is buried. Use the stress relaxation curve

for MDPE at a strain of 1.82% in Fig. 24 as the basis of your calculation.

6. For a buried HDPE pipe of mean diameter 200 mm and wall thickness of 10 mm, what is

the change in the pipe diameter after 10,000 hours? The vertical soil pressure is

estimated to be 20kN/m-2 and the “modulus” of soil reaction is 8MN/m-2.

7. A MDPE pipe in a trench experiences a line load of magnitude of 20D kN/m-1. where D

is the diameter of the pipe. The load acts for 1 hour and the MDPE has a yield stress of

12 MPa after that time. What is the maximum ratio of diameter to thickness that can be

used without the pipe being crushed.

8. The standard deviation of log10σ in Fig. 31 is 0.16. Does this particular MDPE meet the

company specs? The specs require that (a) the average life at 50 years should be higher

than 8.3 MPa, and (b) at a stress of 8.MPa there should be a 95% probability that the

lifetime exceeds 100,000 hours (11.4 years).

9. What is the factor of safety when a SDR 11 pipe is used for gas at 2 bar pressure? Use

the specs of question 8 as a basis for the calculation.

10. By extrapolation of the data in Figure 36 find the brittle failure lifetime of the HPDE at 20 oC under a stress of (a) 5 and (b) 3 MPa. Recommend an upper limit to the creep stress that will allow a 50 year life.

11. Read about Environmental Stress cracking. Based on what you know:

(a) Does the selection of polyethylene for good ESC resistance corresponds to the one for

good resistance to brittle creep rupture at 20oC?

(b) Should special care be taken about the use of leak detection fluids which make soap-

bubbles form when testing joints in polyethylene pipes for leakage?

12. If the fracture toughness of an MDPE is 2.7 MPa m1/2 and =0.45, what is the maximum

size of SDR 11 pipe that can be used at a test pressure of 6 bars without a runaway crack

growth being possible?

From experimental data to models

3

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v.. súainl%a Fígure 23 100 sec ísochronorc stresystrah ctroe for RtgU"; PC n2q IIDhE ín t-ertíã*ot 23"C

ltWre 2l ,Sres.r relamtÍon ctræs hbndins for MD pE p Þ;' ;ü -h,

øre labelled w¡th the åàx¡mri'swfæe strain ùn %

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.for measùred tífetímesa, i, it hoop s:tress o

lower gg.S%confi dence,, r,J- tì

10.24 MN r-2 ì

r 200 r 000

800

ó00 400

200

1.0 lc l# tOr l0 105 time to failure hours

Figure 34 Stress rupture of 950 densítyt polyetltylene at 60 oC in water curL)es labelled with MFI

Hoechst 5010 type I

Risidex 002/60

creeP rupture time/ hours

Figure 35 Creep rupture data ot 80"C,' showing the minimum lifetime required by the BGC

a.

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type 2

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. 'brittle' failure

\ t\'t\--f-.t l*trtìt- lHoìchst 5010

..)uar, Ua :-:'20 0c

400

600

800

Figure 36 Creep rupture data of Hostalen GM5010 HDPE pipe

-t û 6 .lt 'à0 o

a

predicted 100¡rm flaw pipe failures points

at I

z ¿ <,.. 6- attjt¡

u,

.,¡¡j'.

¿

,, ,,i,, , . log(time/h)

Fgwe 4I Predictedød acual hrínle pipe fujþres for AÛffi' HDPE @'rw'ot"

tr, at:

.Ei .tËÊ.äâ: Éi: Gr'

Fr$q 4t Croü gtotrth daø:for Unq MDPE at B|"C

. .. -0.8 ,-0,.6 -0r4 -O¡!,',. .:,. .,-,. ,. :.. .-:

Fîgwe 39 Crock growth dalaþr M rrDPE ínwater at th¡ee

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Fq.+Y_ , Creep rupture data of Hostalen GM50l0 HDPE; solid line r:àpresents minimum life, dashed line the auerage life

2.8

2.9

3.0

3.1

3.2

3.3

3.4

l0r 102 l0r 104 105 106 time,/h

Amhenius plot of the creep rupture ltfe of Hostalen GM50l0 HDPE at a stress of 5 MN m-2

80

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_150 _ t00 _50 0 temperatures,/oC

Figure 56 Plane strainfracture toughness os. temperaturc for Rígídex HDPE

heated rcgion B

heated region ,a¡

l0 + 0.05 mm

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Figure 57 Gull-winged specimenfor fracture toughness tests (made by opmíng out the circurnference of a pipe)

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loading time r/ms

Figure 58 Toughness as afunction of loadíng time for HDPE at 0 "C

807-55 HDPE.

55 t 0.5 mm