c pipe material behaviour didier ilunga only]

8/2/2019 c Pipe Material Behaviour Didier Ilunga Only]

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DIDIER ILUNGA

Prof JE VAN ZYL &

Dr M. DUNDU

THE EFFECT OF THE PIPE MATERIALIN THE BEHAVIOUR OF

LONGITUDINAL CRACKS UNDER

PRESSURE

SERVICES (PTY) LTD


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INTRODUCTION Problem of leakage

Leakage much more sensitive to pressure

Theoretically, =0.5,

In the field, 0.5 2.8

ghACQ d 2=

( )5.0

.2 == hgACQ d

SERVICES (PTY) LTD


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Pipe material behaviour

Longitudinal cracks in water pipes


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OBJECTIVES Investigate and understand the structural

behaviour of longitudinal crack in pipe with

increasing pressure

Derive an Equation for crack opening area

-Pressure

-Material properties


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OBJECTIVES Derive an Equation for leakage flow through a

longitudinal crack in uniaxial stress state (used

as model)-Geometry of the pipe

-Pipe material

-Fluid properties

Predict an appropriate leakage Equation forpressurised pipes


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Based on

-Theoretical approach

-Experimental verification on flat plate


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Stresses in pressurised cylinders

STRESSES IN PRESSURISED THIN-

CYLINDERS

)(2)(1 2 AxialHoop =


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Behaviour of Crack due to Internal Pressure


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MECHANICAL EXPLANATION

Stress concentration around crack edges Hoop stresses dominate

Pressure assists with pushing walls open

Curvature of the pipe

Cause bulging on crack faces


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Y

x

tL

W

2aNy

Ny

Rectangular cracked thin-plate under tension

THEORETICAL APPROACH


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Apply tensile load on the plate material

Measure the resulting the strain

deformations until the crack startspropagating

EXPERIMENTAL APPROACH


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Local buckling and crack opening


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MAXIMUM CRACK OPENING AREA IN APLATE

Assuming no crack propagation, the altered

shape of the crack

2a yu

a

xa

E

Ku y

224 =


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0max, =xuy

axuy =min,

maxyu

a

maxyu

0 x

0max, =xuy

a

E

K

u y

4

max=


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RESULTS

Crack Opening Area, function of Critical

buckling load of the plate in uniaxial stress state

+= tE

vNauA crycry 1.


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+=

tE

RghvauA cr

cry

1.

Crack Opening Area, function of Critical Pressure

and Material Properties within a pressurised Pipein uniaxial stress state


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( )212

3

2

1

2. gtE

gRhvhauCQ

ydactual

+=

Derived Equation for flow leakage through a

longitudinal crack function of Pressure, MaterialProperties, Pipe geometry and Fluid Properties

within a pressurised Pipe in uniaxial stress state


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Effect of Pressure on Leakage flow due to

expansion of the Crack


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LOSS ESTIMATION

6.185 l/s at 17 bar

534384 l/day

R 2404728/day

R 72141840/month


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DISCUSSION

Effect of the opening is more important the

longer the crack is

Buckling mode of the crack in plate issimilar to the Bulging mode of a

longitudinal crack in pressurised pipe


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SUMMARY

Material around the crack bulges out

Increase of the leak area due pressure

Leakage exponents are considerably

larger than 0.5 and increase as the crack

area expands.


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ACKNOWLEDGEMENTS

This project research wishes to gratefully

acknowledge the financial support fromRand Water.


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THANK YOU

c pipe material behaviour didier ilunga only]

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