László TÓTH, Nóra SZŰCS Szabolcs SZÁVAI

2nd Hungarian-Ukrainian Joint Conference on SAFETY-RELIABILITY AND RISK OF ENGINEERING PLANTS AND COMPONENTS September 19-21, 2007. Kyiv

László TÓTH, László TÓTH,

Nóra SZŰCSNóra SZŰCS

Szabolcs SZÁVAISzabolcs SZÁVAI

Handbook of the Crack Propagation Handbook of the Crack Propagation sensitivity Indexsensitivity Index


The Basic Terms of The Basic Terms of Technical-Economic Life Technical-Economic Life

Safety Safety

ReliabilityReliability

RiskRisk

CostsCosts

Level of


At a given technical level !!


Where We come from? What We Are? Where we are going?

Paul GAUGUIN, 1897 (Boston, Museum of Fine Arts)


The Driving Forces of The Driving Forces of DevelopmentDevelopment


0

500

1000

1500

2000

2500

3000

3500

Mill

ion

oper

atio

n/se

cond

s

1978 1982 1985 1989 1993 1995 1997 1998 1999 2000 2001 2002 2006


NDE BNDE Backgroundackground

19501950 20020066


Crack Propagation Sensitivity IndexConcept

K,J,G

Crack Size

Crack Growth Resistance

CPSI

Safety Factor

UNIT

K-a

dK/da


Crack size

Component 1 Component 2

KIc

Str

ess

Inte

nsi

ty F

acto

rRequired NDE reliability


• loading conditions,

• flaw location,

• flaw geometry

CPSI= f

K=.f(a,geometry)

CPSI=dK/da= .{[f(a,geometry)]/da} CPSI


EExamplexample 1 1

pRK F a

t

2

3 4 5

1 0.072449 0.64856

0.2327 0.038154 0.0023478

F

a

Rt

CYLINDER UNDER INTERNAL PRESSURE WITH AXIAL CRACK

Through-Thickness Crack


Derivate Derivate FFunctionsunctions

,

1

2

dK dF pR pRa F

da da t t a

dF d

da da

2 3 40.072449 1.29712 0.6981 0.152616 0.011739

1d

da Rt


EExamplexample 2 2

4

11 4

c a

aat

K Ka cc

2 2

a 2 20.97 0.5i a i

a i i

R R R a tK F a

R R R t R

SPHERICAL SHELL UNDER INTERNAL PRESSURE WITH CRACK

Embedded Elliptical Crack (Centred)


2

pR

t

2 4

1 2 3

a aM M M

t tF

Q

1.65

1 1.464a

Qc

1 1M 2 3

2

0.05

0.11

Mac

3 3

2

0.29

0.23

Mac


Derivate Derivate FFunctionsunctions

2 2a

2 2

2 2

2 2

0.97 0.5

1 10.97 0.5 0.97

2 4

i a i

a i i

i a i i

a i i i

dK R R RdF a ta

da da R R R t R

R R R Ra t tF F aR a R R t R R Rat

3 4 4

244 44

4 42 1

4 1 4 14 1

121 4

c aa

a a aa

a aaa t tctc ccdK dK at

Kada da c acc


2 4 2 4331 2

2 3 1 2 32 4

12 4

2

dMdM dM a a a a a a dQM M Q M M M

da da t t da t t t t dadF

da Q Q

0.65

1.652.4156

dQ a

da c

1 0dM

da

223

32

2

0.075

0.11

dM a

daa

cc

323

32

2

0.435

0.23

dM a

daa

cc


More illustrationMore illustration




The derivate functions are ready yet:The derivate functions are ready yet:• For 74 cases including:

• Plates• Pipes and Cylinders• Spherical sells and Spheres• Round bars and bolts• Component with hole

• The software for calculating the CPSI=dK/da for 12 cases including:

• Plates• Pipes and Cylinders


CONCLUSIONSCONCLUSIONSThe integrity of the structures can be evaluated at a given technical level

The CPSI concept is the only tool to link the safety requirement of a structure and the NDE requirements

Introducing the CPSI concept a COST EFFECTIVE NDE can be achieved

Collection of the K-solutions, i.e the K vs. crack geometry (size) in a handbook

Preparation of their derivative functions


Further Further TTasksasksPreparation of more derivative function

Preparation of a guideline for the given type of component (tubes, vessels, turbine blades, etc)

Optimization of NDE (method, personnel, equipment, etc.)


Zoltán Bay (1900 - 1992)

• He measured the distance between the Earth and the Moon using micro-wave technology (1946), Radar Astronomy

• Re-definition of the unit of the distance, meter (1965-1983)


Thank you for your kind attention

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László TÓTH, Nóra SZŰCS Szabolcs SZÁVAI