Orynyak I.V., Borodii M.V. , Batura A . S

Orynyak I.V., Borodii M.V., Batura A.S.

Orynyak I.V., Borodii M.V., Batura A.S.

IPS NASUIPS NASU

Pisarenko’ Institute for Problems of Strength , Kyiv, Ukraine National Academy of Sciences of Ukraine

Pisarenko’ Institute for Problems of Strength , Kyiv, Ukraine National Academy of Sciences of Ukraine

SOFTWARE FOR ASSESSMENT OF BRITTLE FRACTURE OF THE NPP REACTOR PRESSURE VESSEL USING THE FRACTURE MECHANICS METHODOLOGY

SOFTWARE FOR ASSESSMENT OF BRITTLE FRACTURE OF THE NPP REACTOR PRESSURE VESSEL USING THE FRACTURE MECHANICS METHODOLOGY

IPS NASUIPS NASU Software “REACTOR”Software “REACTOR”

• Residual life is calculated Residual life is calculated deterministically and deterministically and probabilistically (MASTER probabilistically (MASTER CURVE approach) for CURVE approach) for various points of crack frontvarious points of crack front

• Residual life is calculated Residual life is calculated deterministically and deterministically and probabilistically (MASTER probabilistically (MASTER CURVE approach) for CURVE approach) for various points of crack frontvarious points of crack front

• This program is intended This program is intended for calculation of reactor for calculation of reactor pressure vessel residual life pressure vessel residual life and safety margin with and safety margin with respect to brittle fracturerespect to brittle fracture.

• This program is intended This program is intended for calculation of reactor for calculation of reactor pressure vessel residual life pressure vessel residual life and safety margin with and safety margin with respect to brittle fracturerespect to brittle fracture.

IPS NASUIPS NASU Software advantagesSoftware advantages

• The sizes of stress and temperature fields' aren't bounded• Number of time moments is bounded only by the

computer memory size • Cladding is taken into account • Welding seam and heat-affected area are taken into

account • Deterioration is taken into account not only as shift of

the material fracture toughness function but also as its inclination

• Original feature of the software is using of the author variant of the weight function method. It allows to set loading on the crack surface in the form of table.

• The sizes of stress and temperature fields' aren't bounded• Number of time moments is bounded only by the

computer memory size • Cladding is taken into account • Welding seam and heat-affected area are taken into

account • Deterioration is taken into account not only as shift of

the material fracture toughness function but also as its inclination

• Original feature of the software is using of the author variant of the weight function method. It allows to set loading on the crack surface in the form of table.

IPS NASUIPS NASU Report sectionsReport sections

Theoretical background and verification of the SIF calculation methods.

Kinetics of the crack growth by fatigue or stress-corrosion mechanism.

Software description and residual life calculation of the NPP pressure vessel using fracture mechanics methods

Theoretical background and verification of the SIF calculation methods.

Kinetics of the crack growth by fatigue or stress-corrosion mechanism.

Software description and residual life calculation of the NPP pressure vessel using fracture mechanics methods

IPS NASUIPS NASU1. SIF calculation by Point Weight

Function Method1. SIF calculation by Point Weight

Function Method

Q’- point on the front; - value SIF; -weight function;

- loading; - crack surface; Q – load application point

Q’- point on the front; - value SIF; -weight function;

- loading; - crack surface; Q – load application point

'QK

)(' QW

QQ

)(Qq S

)(

'' )()(S

QQQ dSQqQWK

Q’

x

!!! The contribution in SIF 1/800 area nearby Q’ point correspondent to 1/4 value of SIF

We search weight function in the form

- asymptotic WF (elliptic crack in infinite body)

- correction coefficient, basic solution is used

We search weight function in the form

- asymptotic WF (elliptic crack in infinite body)

- correction coefficient, basic solution is used

Rr

DWW AQQQQ

1)(1''

'QQW

AQQ

W '

)(D

1

2'

2'

21

2

24

1

')(

)(1)(2

QQQQ

AQQ

l

dl

R

raW

IPS NASUIPS NASU

IPS NASUIPS NASUUsing our Point Weight Function Method

in engineering applications Using our Point Weight Function Method

in engineering applications 1. Software for fracture design of the complex turbine engine

component (Southwest Research Institute, San Antonio, USA, 2004)

1. Software for fracture design of the complex turbine engine component (Southwest Research Institute, San Antonio, USA, 2004)

Our approach is used

completely

IPS NASUIPS NASUUsing our Point Weight Function Method

in engineering applications Using our Point Weight Function Method

in engineering applications 2. Modeling of elliptical crack in a infinite body and in a

pressured cylinder by a hybrid weight function approach (France, Int. J. Pressure Vessel and Piping. 2005)

2. Modeling of elliptical crack in a infinite body and in a pressured cylinder by a hybrid weight function approach (France, Int. J. Pressure Vessel and Piping. 2005)

Our approach to take for a

basis

SIF along crack front (angle), homogeneous loadingSIF along crack front (angle), homogeneous loading

IPS NASUIPS NASUCheck of the PWFM accuracy for

semi-elliptic cracks

Check of the PWFM accuracy for semi-elliptic cracks

a/l=0.2 (a/t=0.8)

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

2

0 20 40 60 80 100

Angle, degree

Tension by the PWFM Tension by Raju-Newman

Bending by the PWFM Banding by Raju-Newman

a/l=0.4 (a/t=0.8)

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

0 20 40 60 80 100

Angle, degree


Bending by the PWFM Bending by Raju-Newman

0

90

IPS NASUIPS NASU

a/l=0.6 (a/t=0.8)

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 20 40 60 80 100

Angle, degree



a/l=1.0 (a/t=0.8)

-0,2

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

0 20 40 60 80 100

Angle, degree

Tension by the PWFM Tension by Raju-Newmen


a/l=2.0 (a/t=0.8)

-0,2

0

0,2

0,4

0,6

0,8

1

0 20 40 60 80 100

Angle, degree



IPS NASUIPS NASU

IPS NASUIPS NASU

Homogeneous loading

1

1,2

1,4

1,6

1,8

2

0 0,2 0,4 0,6 0,8 1 1,2

a/l

90 degree by the PWFM 90 degree by Murakami


Linear loading

0,2

0,4

0,6

0,8

1

1,2

1,4

0 0,2 0,4 0,6 0,8 1 1,2

a/l



Dependence SIF from ratio a/lDependence SIF from ratio a/l

IPS NASUIPS NASU

Quadratic loading

0

0,2

0,4

0,6

0,8

1

1,2

0 0,2 0,4 0,6 0,8 1 1,2

a/l



Cubic loading

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 0,2 0,4 0,6 0,8 1 1,2

a/l



Dependence SIF from ratio a/lDependence SIF from ratio a/l

),( RKfdN

dlI

1),( CRKfdN

daI )/()(

if ,

if ,

)(

32

2

12

1

2

HafKfdt

da

KKv

KC

KKv

Kfdt

dl

I

upTHI

n

lowTHI

I

1. Fatigue

2. Stress-corrosion

IPS NASUIPS NASU2. Kinetics of the crack growth by fatigue or

stress-corrosion mechanism2. Kinetics of the crack growth by fatigue or

stress-corrosion mechanism

upTH

lowTH KK ,

IPS NASUIPS NASU

TdaTkdaaaa CFCF

TdlTkdllll CFCF

where C1, C2 , v1 , v2 , - material constants

t, - time, N – loading cycles, H – wall thicknessT – unit time, k – number of cycles in unit of time

where C1, C2 , v1 , v2 , - material constants

t, - time, N – loading cycles, H – wall thicknessT – unit time, k – number of cycles in unit of time

Complex damageComplex damage

IPS NASUIPS NASUUsing stable form crack growthUsing stable form crack growth

nIKAl

af

dl

da

fc

fc

dldldl

dadada

0 2 4 6 8 10 12 14 16 0.0

0.5

1.0

1.5

2.0

00 / la

2

0.666

0.2

0.1

Stable form

a/L,

a, мм

Input Data

1) Stress field for time1) Stress field for time it

Table arbitrary sizeTable arbitrary size

IPS NASUIPS NASU3. Residual Life calculation of the NPP

pressure vessel using fracture mechanics methods

3. Residual Life calculation of the NPP pressure vessel using fracture mechanics

methods

IPS NASUIPS NASU

2) Temperature field for time2) Temperature field for time0t it

Input Data

Table arbitrary sizeTable arbitrary size

a) Axial with weld seama) Axial with weld seam

IPS NASUIPS NASU

Input Data

weld seamheat-affected zonebase materialcladdingcrack

weld seamheat-affected zonebase materialcladdingcrack

base materialcladdingcrack

base materialcladdingcrack

b) circumferentialb) circumferential

3) Crack types3) Crack types

)f(TAKcI

IPS NASUIPS NASU

4) The basic material characteristics4) The basic material characteristics

1. Arctangents 1. Arctangents 0arctan2 TTBAK

cI

2. Exponent2. Exponent

0exp TTBAKcI

Common shape of the crack growth resistance function is

for user function A takes from coordinates of first point

Common shape of the crack growth resistance function is

for user function A takes from coordinates of first point

3. User (pointed) function3. User (pointed) function

IPS NASUIPS NASU

1. Shift1. Shift

TTAKcI

f

2. Shift + Inclination2. Shift + Inclination

TT

TTTAK

cI

1

1f

A

ICK

T

T

A

ICK

T

T

5) Shift and inclination conceptions 5) Shift and inclination conceptions

nn

FF YTF

ffAAT

exp

0

00

IPS NASUIPS NASU

a)Analytical forma)Analytical form

b)Table formb)Table form

6) Dependence of shift on radiation6) Dependence of shift on radiation

IPS NASUIPS NASU Results

Scenario – Break of the Steam Generator Collector WWER-1000 operated at full powerScenario – Break of the Steam Generator Collector WWER-1000 operated at full power

It is given : - stress field, - temperature field,

= 1000, 2000, 2800, 3000, 3160, 3600, 4000 sec - time points

It is given : - stress field, - temperature field,

= 1000, 2000, 2800, 3000, 3160, 3600, 4000 sec - time points

Axial crack. Half-length l - 40 мм., depth a - 50 мм.

Axial crack. Half-length l - 40 мм., depth a - 50 мм.

ii tT

it

ii t

IPS NASUIPS NASU

a) Dependences of the calculated and critical SIF from temperature for time = 3000 sec

a) Dependences of the calculated and critical SIF from temperature for time = 3000 sec

SIF for base material --//-- for welding seam

Critical SIF for base material --//-- for welding seam

--//-- for heat-affected area

SIF for base material --//-- for welding seam

Critical SIF for base material --//-- for welding seam


it

IPS NASUIPS NASU

history for base material --//-- for welding seam critical SIF for base material --//-- for welding seam


history for base material --//-- for welding seam critical SIF for base material --//-- for welding seam


b) History of the dependences calculated SIF from temperature for some points and all times intervals and

critical SIF

b) History of the dependences calculated SIF from temperature for some points and all times intervals and

critical SIF

T

IPS NASUIPS NASU

fields for chosen history pointsminimal marginmargin for time points

fields for chosen history pointsminimal marginmargin for time points

c) Table of the calculated temperature margin

for all points of crack front and time points

c) Table of the calculated temperature margin

for all points of crack front and time points

T

T

calculated temperature marginshift of the temperature by user table

shift of the temperature by analytical model

calculated temperature marginshift of the temperature by user table

shift of the temperature by analytical model

IPS NASUIPS NASUd) Figure of the calculated margind) Figure of the calculated margin

IPS NASUIPS NASU

New geometry for axial crackNew geometry for axial crack

Calculated temperature marginCalculated temperature margin

Half length l - 60мм Depth a - 40 ммHalf length l - 60мм Depth a - 40 мм

Results for other crack geometries

New geometry for axial crackNew geometry for axial crack


IPS NASUIPS NASU

Calculated temperature marginCalculated temperature margin


New geometry for circumferential crackNew geometry for circumferential crack

IPS NASUIPS NASU

calculated temperature margincalculated temperature margin

IPS NASUIPS NASU

1. Failure probability calculation for structural element 1. Failure probability calculation for structural element

bIi

f KTK

KK

B

BP i

imin0

min

0exp1

2. Failure probability calculation for crack2. Failure probability calculation for crack

N

iiff PP

1, )1(1

3. Calculation parameters 3. Calculation parameters

))(019,0exp(7731 00 xTTTK

4. In addition4. In addition

Кmin , K0(Т), В0, b - arbitrarily

Pf = 63,2% Кmin = 20 В0 = 25 мм b = 4

Implementation MASTER CURVE Conception

Implementation MASTER CURVE Conception

For time T =0 failure probability equal 1.07*10-05For time T =0 failure probability equal 1.07*10-05

IPS NASUIPS NASU

Time point t4 = 3000 sec - the most dangerous time step

Axial crack half length l - 40 мм., depth a - 50 мм.

Time point t4 = 3000 sec - the most dangerous time step

Axial crack half length l - 40 мм., depth a - 50 мм.

50

60

70

80

90

100

110

0 20 40 60 80 100 120 140 160 180

Angle, degree

K1

SIF dependences on angleSIF dependences on angle

Result for main scenario

Dependences of logarithm probability on TDependences of logarithm probability on T

IPS NASUIPS NASU

ln(Pf) from deltaT

-14

-12

-10

-8

-6

-4

-2

0

0 50 100 150 200

deltaT

ln(P

f)

IPS NASUIPS NASUProbability density for T = 50Probability density for T = 50

IPS NASUIPS NASU CONCLUSIONCONCLUSION

1. Efficient method of stress intensity factor (SIF)calculation is developed.

2. The computer software which reflected all modern requirements for brittle strength analysis of Reactor Pressure Vessel is created.

3. The program application were demonstrated by prediction residual life and temperature margins under modeling of the incident scenario.

1. Efficient method of stress intensity factor (SIF)calculation is developed.

2. The computer software which reflected all modern requirements for brittle strength analysis of Reactor Pressure Vessel is created.

3. The program application were demonstrated by prediction residual life and temperature margins under modeling of the incident scenario.

Documents

Orynyak I.V., Borodii M.V. , Batura A . S