Mecaniquede la rupture

D. P. Miannay

Ingenieur ECPDocteur es-Sciences Physiques

Ingenieur a 1'Institut de Protection et de Surete NucleaireCommissariat a l'Energie Atomique

I

• lea editionsi

ck physique

I 7 avenue du HoggarI Zone Industrielle de Courtabosuf,I B.P. 112

F-91944 Les Ulis Cedex A, France

FRACTURE MECHANICSfrom D. P. Miannay, Ingcnicur ECP, Doctcur cs-Scicnccs Physiques, lngcnicur a 1' I P S N.

This book entitled <\ Fracture Mechanics », the first one of the monograph « Materiologie » isgeared to design engineers, material engineeers, non destructive inspectors and safety experts. Theresearcher will find as well interesting guidances for his work. The professor will extract some basicfundamental parts for his teaching.

This book covers fracture mechanics in isotropic homogeneous continuum. Only themonotonic static loading is considered.

This book intended to be a reference with the current state of the art gives the fundamental ofthe issues under concern and avoids the developments too complicated or not yet mastered for notmaking reading cumbersome. A non exhaustive bibliography with the more relevant references in thefield is provided and can be used for further developments.

The subject matter is organized as going from a easy to a more complicated level and thusfollows the chronological evolution in the field. Similarly the microscopic scale is considered beforethe macroscopic scale, the physical understanding of phenomena linked to the experimentalobservation of the material preceded the understanding of the macroscopic behaviour of structures.In this latter fied the relatively recent contribution of finite element computations with some analogywith the experimental observation is determining. However more sensitive analysis is not skipped.

Some exercices are proposed. They are aimed at underlining important points or giving moreinsight into the developments.In French.

MECANIQUE DE LA RUPTUREpar D. P. Miannay, Jngcnieur E C P , Doctcur es-Scicnccs Physiques, Ingenieur a I' 1 P S N.

Cet ouvragc intitule : « Mecanique de la Rupture », le premier dc la monographic Materiolocjt: s'adresse aux ingenieursdu bureau deludes, de la science des maleriaux, du controle non deslructifct de I'expertise do la surele des structures. Lechcrcheur trouvera egalement des elements interessants pour guider ses recherches. Le professcur pourra extraire certaines partiespour ensdgncr.

Get ouvrage traile de la meeanique de la rupture dans des milieux homogenes ct isotropes. Seul le chargement monotoneet statique est considerc.

Get ouvragc qui se veut ctrc un texte de reference prenant en comple les demiers acquis foumit les elements dc base dela mecaniquc de la rupture et cherchc a eviter les developpements trop complets ou non encore maitrises pour ne pas alourdir lalecture. Une bibliographic non exhaustive correspondant aux sujets introduils est disponible el peut ainsi etre mise a profit pourlies developpements complementaires.

L'ouvrage est organise dc fa^on a aller du plus simple au plus complique et suit ainsi naturcllement le developpemenlchronologiquc dc cettc discipline. Dans l'ordre egalement l'echelle microscopique est considerec avant l'echelle macroscopique, carla comprehension physique des phenomenes liec a l'observation experimentale du maleriau a precede la comprehension ducomportement macroscopique des structures. Dans ce deniier domaine l'apport relativement recent des calculs aux elements finisqui s'apparentenl a I'observation experimentale est determinant. L'analyse plus delicate n'est cependant pas oabliee

Des cxercices sont proposes. Us sont destines a souligner des points importants ou a expliciter des devcloppemcnts.

Les Editions de Physique, 7 avenue du Hoggar - B P 112 - F 91944 Les Ulis Ccdex A.juin 1995.

TABLE DES MATIERES

CONTENTS

Contents.Table des maticrcs.

Foreword.Avant-propos.

Symbols.Symbolcs.

1.Microscopic aspects of fracture. Cohesive stress.1.- Aspect microscopiquc dc In rupture. Contminlc dc cohesion.

2.- Linear elastic behaviour of flaws. Purely elastic treatment.2.-Traitenient elxstiquc lineaire des discontinuities. Traitement purcnicnt clrtsliquc.

2.1. The notch- Stress and strain concentrations.2.1. L'entaille- Concentrations dc conlraintc ct dc deformation.

2.1.1.- Stress and strain fields.2.1.1- Champs dc contraintc ct de deformation

2.1.2.- Energy aspect.2.1.2.- Aspect encrgetique.

2.1.3.- Failure criteria.2.1.3.- Critercs dc rupture.

2.2.- The crack. Stress intensity factors.2.2.- La lissuro Factcurs d'intensitc dc contraintc.

2.2.1.- General representation of a crack.2.2.1.- Representation generate d'une fissure.

2.2.2.- Stress and strain fields around a crack.2.2.2.- Champs dc contraintc ct dc deformation an voisinage d'une fissure.

2.2.3.-Energy aspect.2.2.3.- Aspect energe'tique.

2.2.4.- Fracture criteria.2.2.4.- Critcres de rupture.

2.3.- The tridimensional crack.2.3.- La fissure tridimcnsionnclle.

3.- Linear elastic treatment of flaws. Plasticity correction.3.- Traitcntcnt elastique lincairc des discontinuites. Correction dc plasticitc.

3.1.- Model of small scale yielding for a notch.3 . 1 - Modele de plasticitc confincc pour unecnUiille.

3.2.- Model of small scale yielding for a crack.3.2.- Modeles dc plasticitc confinee pour unc fissure.

3.2.1.- First model: plastic zone's correction of IRWIN.3.2.1.- Premier modele : correction dc zone plastiquc cflRWIN.

3.2.2- Second model: The strip yield model or model of DUGDALE-BARENBLATT.3.2.2- Second modclc : modelc de la Iwndc plastifiee ou modele dc DUGDALE-BARENRLATT.

3.2.3.- Third model: elastoplastic treatment of mode III.3.2.3.- Troisictne modclc : trailemcnt elastoplastique du mode III.

3.2.4.- Fourth model: model of BILBY, COTTRELL, SWINDEN.3.2.4.- Qualriemc modelc : modele dc BILBY, COTTRELL, SWINDEN.

3.2.5.- Fifth model: model of the notch with a circular root of TETELMAN.3.2.5.- Cinquieme modelc : modelc de I'cntaille a fond circulaire de TETELMAN.

3.3.- Implications of these models in fracture.3.3.- Implications de ces modcles pour la rupture.

3.3.1.- Fracture criteria3.3.1.- Criteres de rupture.

3.3.2.- Fracture Assessment Diagram - Two criteria method or R6 rule.3.3.2.- Diagramme d'cvaluation de la rupture-Methodtf des deux criteres ou me'thode U6.

3.3.3.- Specimens for toughness measurement.3.3.3- Eprouvetles de mesure dc la lenacitc.

4.- Linear elastic treatment of fracture. The risk of brittle fracture.4.- Traitenicnt clastiquc lineaire dc la rupture. Lc risque dc rupture brutalc.

4.1.- The toughness.4.1 - Latcnacite

4.1.1.- The crack growth resistance curves.4.1.1.- Lcs courbes dc resistance a U propagation.

4.1.2.- The plane stress correction.4.1.2.- La correction de contrainte plane.

4.1.3.- The statistical nature of toughness.4.1.3.- Lc caracterc statistique dc la tenacite.

4.2.- The flaw.4.2.- Lc defaut.

4.2.1.- The nature of flaws.4.2.1 -1JI nature des dclauts.

4.2.1.- The Non Destructive Inspection.4.2.1.- I-e controle non destructif.

4.3.- The mechanical loading.4.3.- Lcs sollicitations mecaniques.

4.4.- Application examples : the pressure vessels.4.4.- Excmple d'application : les capacites sous pression.

4.4.1.- Material selection with regard to Non Destructive Inspection.4.4.1.- Selection d'un matcriau en t'onction du controle non destructif.

4.4.2.- Concept of proof testing.4.4.2 - Concept du cycle d'epreuvc.

4.4.3.- Concept of leak before break.4.4.3.- Concept de la tiiite avant rupture.

4.4.4.- The risk of brittle fracture.4.4.4.- Lc risque de rupture brutalc.

5.- Microscopical aspect of fracture. Cleavage and ductile rupture.5.- Aspect microscopiquc dc la rupture. Clivage ct rupture ductile.

5.1.- Background of dislocation theory.5.1.- Rappel sur la theorie des dislocations.

5.2.- Experimental methods of analysis.5.2.- Mclhodes expcrimentales d'analyse.

5.2.1- Bend testing of edge notched specimens.5.2.1- Essais de flexion d'eprouvettcs entaillees latcralcmcnt.

5.2.2.- Tension testing of axisymetric notched specimens.5.2.2.- Essais de traction d'eprouvettes axisymctriqucs cnuu'Ilees.

5.3.- Cleavage fracture.5.3.- Rupture de clivage.

5.3.1.- Elementary mechanisms.5.3.1.- Mecanismes elementaires.

5.3.2.- Statistical treatment.5.3.2.- Trailement stalistiquc.

5.4.- Intergranular fracture.S.4.- Rupture intcrgranulaire.

5.5.-Ductile rupture.5.5.- Rupture ductile.

5.5.1.-Elementary mechanisms.5.5.1.- Mecanismes elementaires.

5.5.2.- Continuum damage mechanics.5.5.2.- Mccaniquc des milieux dommageables.

5.6.- The brittle ductile transition with plain and notched specimens.5.: i-i transitionfragile ductile avec les eprouvettes lissesel cnluillees.

5.6.1.-.The brittle ductile transition grain size.5.6.1.-. La transition fragile ductile en taillcde grain.

5.6.2.- The britttle ductile transition temperature.5.6.2.- La transition fragile ductile en temperature.

6.- Plastic treatment of discontinuities. Fully plastic treatment and large deformationcorrection.(>.- Truitcinent plastiquc dcs discontiniiite.s. TraitenienI purcment plastique et correction do grandrs deformations.

6.1.- Rigid-purely plastic material. The limit load.6.1 - Materiau rigide-parfaitcment plastiquc. Le chargement liniite.

6.1.1- The limit load.6.1.1 - Le chargenient limite.

6.1.2.- The deformation field.6.1.2.-1/: champ dc deformation.

6.1.3.- The threedimensional configuration.6.1.3- Lc cas tridimensionncl

6.2.- Strain hardening plastic material. The contour integral.6.2- Matcriau plastiquc avcc consolidation, L'integralc de contour

6.2.1.- The contour integrals.6.2.1.- Les integrates do contour.

6.2.2.- The special case of the HOLLOMON material.6.2.2.- Cas parliculier du materiau d'HOLLOMON.

6.2.3.- Case of a material with a non analytical deformation law. The AINSWORTHapproach.1.2.3.- Cas d'un maleriau avec unc loi dc deformation non analyliquc. L'approche d'AINSWORTI 1.

6.3.- The threedimensional problem.6.3.- I.e problcmc tridimensionnel.

6.3.1.- Definition of J and determination.methods.6.3.1.- Definition de J ct methodes de determination.

6.3.2.-J solutions.6.3.2.- Expressions de J.

6.4.- Crack extension.6.4.- Extension dc fissure.

7.- Plastic treatment of discontinuities. Elastic-plastic treatment.7.- Trailenicnt plastiquc dcs discontinuitcs. Traitentcnt clasto-plastiquc.

7.1.- General description of stress and strain fields.7.1.- Expression generalc des champs dc contrainte et de deformation.

7.2.- The small scale yielding and the fields described by Q.7.2.- La plaslicile confuiee limitee ct les champs decrits par Q.

7.2.1.- Properties of the J contour integral.7.2.1.- Proprietcs dc 1'integralc dc contour J.

7.2.2.- Description of stress and strain fields.7.2.2.- Description des champs dc contrainte et dc deformation.

7.3.- Cracked bodies with finite width.7.3.- Corps fissures de largeur finie.

7.4.- The loading parameters.7.4.- Les parametres de chargement.

7.4.1.- J determination and estimation.7.4.1.- Determination ct estimation de J.

7.4.2.- Q estimation.7.4.2.- Estimation de Q.

7.5.- The threedimensional problem.7.5.- Lc problemc tridimensionnel.

7.6.- The quasi static propagation.7.6- La propagation quasi-siatiquc.

7.6.1.- Case of an elastic-purely plastic material and of small defonnations.7.6.1.- Cas du matcriau clastiquc-parfailement plastiquc cl des pctitcs deformations.

7.6.2.- Case of an elastic plastic material and of small defonnations.7.6.2- Cas du maicnau claslo plastiquc et des pomes deformations

7.7.- Modeling implications for fracture.7.7 - Implication dc ces modclcs pour la rupture.

7.7.1.- Fracture criteria.7.7.1 - Critcrcs de rupture.

7.7.2.- Specimens for toughness measurement.7.7.2.- EprouvcUes dc mesurc de la tenacite

8.- Elastoplastic treatment of discontinuities. The risk of fracture.8.- Traiteiuent elasto-plastique des discontinuites. IA' risque dc rupture.

8.1.- Toughness : relationship between microscopic and macroscopic aspects.8.1.- La tenacity : relation cntrc aspect microscopique ct aspect macroscopiquc.

8.1.1- Fully brittle behaviour.8.1.1 - Comportement totalement fragile.

8.1.2.- Fully ductile behaviour.8.1.2.- ComportcmcTit tolalcmenl ductile.

8.1.3.- Ductile then brittle behaviour.8.1.3.-Comportement ductile puis fragile.

8.1.4.- The brittle ductile transition.8.1.4.- La transition fragile ductile.

8.2.- Practical applications.8.2- Applications pratiques.

8.2.1.- The safety factor for brittle fracture.8.2.1 - Lc facteur de suretc pour la rupture fragile.

8.2.2.- The stability of J controlled propagation.8.2.2.- La stabilite de la propagation controlee par J.

8.2.3.- Threedimensional effect.8.2.3.- Effct tridimensionncl.

AppendicesAnnexes.

Solutions of exercicesSolutions d'exerciccs.

Dominique Moinereau1, Gilles Rousselier1

CLEAVAGE FRACTURE OF LARGE SCALE CLADDED MOCK-UPSCONTAINING AN UNDERCLAD CRACK. ANALYSES BY THE LOCALAPPROACH OF CLEAVAGE FRACTURE.

REFERENCE : Moinereau D., Rousselier G., "Cleavage Fracture of Large ScaleCladded Mock-ups Containing an Underclad Crack. Analyses by the LocalApproach of Cleavage Fracture", Fatigue and Fracture Mechanics : 27ih Volume, ASTMSTP, R. Piascik, J. Newman, R.P. Gangloff, and N. Dowiing, Eds., .American Society forTesting and Materials, Philadelphia.

ABSTRACT : Electricite de France has conducted a large program including experiments onlarge size cladded specimens and their interpretations to evaluate different methods of fractureanalysis used in French safety studies regarding the risk of fast fracture in reactor pressurevessels. Four specimens made of ferritic steel A50S C13 with stainless steel cladding containingsmall artificial underclad defects are loaded in four-point bending. Experiments are conducted atvery low temperature to obtain crack instability by cleavage fracture. In each case, the crackinstability' is obtained by cleavage fracture in base metal, without crack arrest.The tests are interpreted using the local approach of cleavage fracture (WeibuL! model) by two-dimensional finite element computations. The identification of the WeibuU model parameters onaxisymmetricaJ notched specimens is described in a first pan. Tne probability of failure is thenevaluated in each test using different meshes. The results show an important effect of the size ofthe elements at the crack tip on the probability of failure. Those effects are confirmed on a CTspecimen. In a third part, the shallow flaw effect is discussed with the Weibull model.

KEY WORDS : fracture mechanics, fracture toughness, local approach, cladding, cleavage,structural integrity', shallow flaw, subclad flaw

Weibull stress GW (MPa) CT specimen(a / W = 0.55)

4 PB specimen(a / V/'= 0.55)

4 PB specimen(a / W = 0.2)

4 PB specimen(a / W = 0.05)

4 PB cladded specimena / W = 0.05

cladded mock-ups DSR4, DSR1, DD2(0.033 < a / W < 0.042)

Stress intensity factor Kj (MPa_Tn ' )

Fig. S—Notched tensile specimen used to identify Weibull model parameters.

21fl - 10 R - 2

|1S-.-0.05 i 10--0.05

00

. m = 27, ou = 2657 (20 specimens)

. m = 24, Gu = 2696 (40 specimens)

5000 kN ramof test machine

Mock-up

A508 C13ferritic steel

120 mm 500 mm _ _ 45Q m Cladding

\S0

Fig. 9—Probability of failure versus load curve for DSR4 mock-up. aj\

1.0

§ ^ o.ed =< n.u. oLL 0 .6 -O m

3>• a^ " d

J 0,4 -

0 J 2 -

DSR4size of elements at crack tip 50 urncritical load : 640 kN

m=24, su=2696

200 400 600 BOO 1000

LOAD (kN)

E L S E V I E R N' . : : ; ; . - Er.j:.-.sjr:.-.j ar.c D J J I J . I i f : { ! « - ) 11 - -5

First spinning cylinder \st analysis using a local approachto fracture

C. Eriprei, G. Rousselier•leant* de rrcr.ee (EOF). Service Re'-ae't-s \:iclhire: ?: fr;-.T"?»>i-j fR\'FI Lei Rer.rr-:e-e' P 3 f "J.'O '.'d':V w £.P:T r

Abstract

In recent years, several experimental pr02ramrr.es or. larse-scaie specimens have been organized to evaluate th;capabilities of the fracture mechanics concepts employed in structural intesricv assessment of pressurized wate:reactor pressure vessels. During the first spinning cylinder test, a geometry effect was revealed experimentally showingthe difficulties of transferring toughness data from small-scale to large-scale specimens. An original analysis of thistest, by means of a local approach to fracture, is presented in this paper. Both compact tension specimen and spinningcylinder fracture behaviour were computed using a continuum damaae mechanics model developed a: EDF Weconfirmee by numerical analysis that the cylinder's resistance to ductile tearins was considerably larger than insmall-scale fracture mechanics specimen tests, about 50'/i The final crack s rou th predicted by the model was closeto the experimental value. Discrepancies in J R curves seemed to be due to an erfec; of stress triaxiahty and plasticzone evolution. The geometry effect inducing differences in resistance to ductile tearing of the material involved in thespecimens can be investigated and explained using a local approach to fracture methodology.

and DesignE L S E V I E R Nuclear Ens-njj-inj ?..-: Design 152 (199-:) I — 10 = = = =

Prediction of the first spinning cylinder test usingcontinuum damage mechanics

D.P.G. Lidbury", A.H. Sherry2, B.A. Bilbyb, I.C. Howard b, Z.H. Lib, C. Eripret -"* ABA Technology. Reactor Services. Risley. V/arrir.^ton. Cheshire. I'.'AJ 6AT. UK

s SIR/US. University of Sheffield. Department of Mechanical and Process Engineering. Sheffield. SI 3JD. UK' Electncu- de France. Department MTC. Les Renardieres. SPl. 77250 Mom-siir-Loui^. Frc.r.ce

Abstract

For many years large-scale experiments have been performed world-wide to validate aspects of fracture mechanicsmethodology. Special emphasis has been given to correlations between small- and large-scale specimen behaviour inquantifying the structural behaviour of pressure vessels, pipina and closures. Within this context, the first threespinning cylinder tests, performed by AEA Technology at its Risley Laboratory, addressed the phenomenon of stablecrack growth by ductile tearing in contained yield and conditions simulating pressurized thermal shock loading in aPWR reactor pressure vessel. A notable feature of the test data was that the effective resistance to crack growth, asmeasured in terms of the J R-curve, was appreciably greater than that anticipated from small-scale testing, both atinitiation and after small amounts (a few millimetres) of tearing. In the present paper, two independent finite elementanalyses of the first-spinning cylinder test (SC 1) are presented and compared. Both involved application of theRousselier ductile damage theory in an attempt to understand better the transferabtlity of test data from smallspecimens to structural validation tests. In each instance, the parameters associated with the theory's constitutiveequation were calibrated in terms of data from notched-tensile and (or) fracture mechanics tests, metallographicobservations and (or) chemical composition. The evolution of ductile damage local to the crack tip during SC I wasthereby calculated and, together with a crack gro^u criterion based on the maximisation of opening-mode stress.used as the basis for predicting cylinder R-curves (angular velocity vs. An. J integral vs. Art). Except in the initiationregion, the results show the Rousselier model to be capable of predicting correctly the enhancement of tearingtoughness of the cylinder relative to that of conventional test specimens, given an appropriate choice of finite elemenicell size in the region representing the crack tip. As such, they represent a positive step towards achieving the goal toestablish continuum damage mechanics as a reliable predictive engineering tool.

ao r

0 i 0.5 '.2

Dlt placement, mm

1.5

*: 0.3 h

-> 0.2 "

0 0.5

CT S*35n-ra. S o . : : * "j—5—Cel S'is • 0 5TV-. j

1.5 2 2.5 3

.ia, mm

ao

70

60

= =0

•3 4 0

i"" 30

20

10

i l

uI*- . . . 1 . . . 1

• • • ' i-

\ '-

—=—Cel l SH9 * O.25rv-i

-.

-_

t . . . I . , . -

0.-! 0.5 1.2

Displacement, mm

1.5

0.5

O.-s

- C 3

->' 0 .2

t i • i i

\

. . . i . . . . i . . i . • '

-

-

—=—Call sue * 0 2Srrv^

. . . t . . . . i . . . . i . . . .

0 0.5 1 1.5 2 2.5 3 3.5

3a, mm

80

70

SO

; iO :

30

20

10

0

; " 1 ' ' ' 1

f f

•i

-,

a— Call si29 . 0.125mm •i

. 1 . . . I . . . •

0.4 0.8 1.2 1.6

Dl«plac«m«nt, mm

Fig. 6. Predicted and experimental load vs. displacement curvesfor the AEIO notched tensile specimen. From Bilby (1992).

0.5

O.i

" - 0.3

0.2

o.r -CT:B-3smm:SG-JCr.-C«ll sija - 0.125mm

. I • • • ' ' • ' • 'I

0 0.5 1 1.5 2 2.5 3 3.5 4

Aa, mm

Fis. 7. Predicted and experimental J R-curves for 35 mm ihickside srooved compact specimens. From Bilby (1992).

the authors of thatpaper calibrated Eq. (3) in terms of c, with refer-ence to the J R-curve data for 35 mm thick sidegrooved compact specimens presented in Laceyand Leckenby (19S9). The test temperature was290 =C, corresponding to the temperature at whichSC 1 was carried out. A value of c, = 350 MPawith / 0 = / v = 6.07 x IO-J and L = 550 nm gavethe best overall prediction of this data, Fig. 5.

In Bilby (1992), values of c, for a temperatureof 290 :C were determined (D = 2^/3) to be 443,516 and 571 MPa for 1 = 500, 250 and 125 urnrespectively. These values represent a compromiseresulting from predicted curves "tuned" to fitnot only AEIO, AE4 and AE2 notched tensileresults ' but also the results from 35 mm thick sidegrooved compact specimens, Figs. 6 and 7.

13C0-n

S i o : c e o t n : 1C7 m m

Fig. 1. Cylinder geometr> for firs; spinn;.".; cylinder c.\penment.

0 5

. s " " ^ " 'r H= :

= Measure:• Measu'*-

—Z— Pr*CiCtic

n-ninemnentn

S:aSta

cnon

Slaton

123

0 i : '— :

0 0.5 1 1.5 2 2.5 3 3.5 JCrack growtn, mm

Fig. S. Predicted and experimental J R-curves for the first

spinning cylinder lest. From Eripret and Rousselier (1991).

0 5

0 5

0.-

0.3

0 2

0.1

0

;

9 MeasuM«45U

Ct» S

Ceil S

i '-*^*^

z ^

f»m«rt S:at'O«r-men: Stationrcmcnl Stationz« • 0 125mm

, ; . . 0 SOOmc

-

-

1 .23

0 5 1 1.5 2 2.5Crack growth, m m

3.5

Fia. 9. Predicted and experimental J R-curves for the firs;spinning cylinder test. From Bilby (1992).

DIE METHODE DE5 "LOCAL APPROACH OF FRACTURE" UND IHRE ANWENDUNG

AUF EIN THERMOSCHOCKEXPERIMENT

THE METHOD OF "LOCAL APPROACH OF FRACTURE" AND

ITS APPLICATION TO A THERMAL SHOCK EXPERIMENT

M. Sethmont, G. Rousselisr, EDF, Moret sur Loing/Frankreich

K. Kussmaul, A. Sauter, A. Jovanovic, MPA 5tuttgart

14 th MPA-5eminar, October 6 and 7, 1988

ABSTRACT

The pressurized thermal shock experiment NKS-3, of MPA Stuttgart (a large,

cracked, hollow cylinder exposed to sudden cooling in presence of mechanical

loads), is analyzed by means of a local approach of ductile fracture based on

Rousselier damage model. This model can be calibrated by simple tests on

cylindrical notched tension specimens. The crack growth is calculated from the

stresses and the damage variable computed by a finite element program. The

experimental and numerical results are in a good agreement. In parallel, a

development of the model in the frame of ABACUS finite element program has been

described, using the Gurson formulation of the plastic potential wich is very

similar to the Rousselier formulation.

1 - INTRODUCTION

Generally, fracture mechanics material data are generated from small

laboratory test specimens subjected to monotonically increasing single load.

These data are used in fracture mechanics criteria for safety assessment of

flawed structures. The transferring of fracture mechanics data to industrial

components may be questionable, especially if complex situations are involved :

thermo-mechanical loadings, historical effects (warm prestress), residual

stresses, heterogeneous materials, etc...

Thermal shoc'<330°C - 20°C

Pressure 30 MPs

Flaw

200 mm •

Axial load 100 MN

Figure 2 - Large scale hollow cylinder ofpressurized thermal shockexperiment.

Figure 3 — Cylindrical notched tensilespecimen.

Load IkN)°0

80

70

60

50

40

30

20

10

o

. . Experiment/

Numerical curve NKS-3steel, 200°C. fo = 5.10~4,o, = 415 MPa, l c = 0.4 mm

•

-

0 0.2 0.4 0.6 0.8 1 1.2

Diametral contraction (mm)

Figure 4 — Load-displacement curve ofa notched tensile specimen(NKS-3 steel).

400Temperature (°C)

300 . - '

200

t = 0 min

ment

Numerical curves

Crack tip

200 300 400

Radius (mm)

Figure 7 — Temperature in the thicknessof the test vessel.

1 C -7

2000

Figure 9 — Stable crack growth(damaged zone in grey,(3 > 4) after the thermalshock.

Figure 11 — Longitudinal stress at thecrack tip (the symbolscorrespond to the locationsof f ig.9).

!*^~~\ trn

30 mm 70 10 "C

Time

3 1 N/mm ]

ifJL

i j

V! 3:.» = 13

-STM blunting

oihtl lints/ !

/ !

/i ; _/1 — • - " i

3 «/mm / i|

2 ]

stablt crock giowlri 3,5 mm

mm 5

Figure 13 — J-based crack driving force and crack resistance curve (220^0in PTS experiment NKS 3.

e TO.Q

E

• \

1

0

i

1 2

i,

\

* ;

^"^^

. . . . . .

A

( <o

)

si

1.VJ

W\

r -

2 * i 9 ? a t

ersjnifergntid position, h

* ,

A! V\

W 11 S

I N K s~3i

^ crock «»len»oo (3.5 mm)

<

cv«rog« irtrt;d

crock doptn SZ5mm

uitro sonic crack Oeptft meosurement

& - Cfti*- t«3t

^TXtogrcp^Tic crock deotn mecssunemeni

• - oft«* Mat

Figure 14 — Crack extension measured on the fracture surface in PTS experiment NKS 3.

August 1995

THE SURVEILLANC^PROGRAMME

THE 900 MWe SERIES

D. MIANNAY

m ira.1

&v/etY>

FIGURE 3

6

JTu£- QXL Ltruap

/ . /coe-ux

E F |

o o j

i

__L

l-'i* O Or:,

ESTIMATION FORMULA FOR THE NIL DUCTILITY TEMPERATURE SHIFT

0_=286°C

DAS FORMULA :

BASE METAL

ART (68 J) =[9.51 + 280.91 (Cu - 0,08) + 19.64 (Ni - 0.7) - 1949.12 (Cu - 0.08)(Ni - 0.7) + 592.05 P] I-'07

a = 12.6

WELD METAL

ART (68 J) =[5.66 + 261.17 (Cu - 0,08) + 2.86 (Ni - 0.7) + 571.60 (Cu - 0.08)(Ni - 0.7) + 657.59 P] F°~

a = 12.2

-0 35

FIM FORMULA :

ART (68 J) = [l7.3 + 1537 (P - 0.008) + 238 (Cu - 0.08) + 191 Ni: *Cu] F(

a = 10

FIS FORMULA :

ART (68 J) = 8 + [24 + 1537 (P - 0.008) + 238 (Cu - 0.08) + 191 Ni2*CuJF° 35

- D

CP 0

dT exp

oo

x0)

1 2 3 4 5

F, 10A19 n/cmA2

Cu

surv

eilla

nce

- *

£ -

0I

* *

Cu

rece

ptio

n

o O

CP 0

is 01i u

! Z

ni reception

Ni coulee

I o ;

<uuC OS

ni surveillance

Ni reception

P s

urve

illan

ceP

rece

ptio

n

O

CP 0

60

t/fCO

20

dT das

• • •

20 40 60

dT exp, °C80 100

CP 1 - CP 2

dT exp

oo

c£X0)f-•a

BO706050 •

40 •

3020 •

10 •

• • A *

*

1 2 3 4 5 6

F, 10A19 n/cmA2

dT exp

oodx

ir —"

!

I,

ri ••

*

Bn: -

*

—

n

i

—i

|

0 1 1 10

F, 10M9 n/cmA2

O

reacteur (MB, S)

Tfinal

Fiuence, 10A19 n/cmA2

CP 1 - CP 2

1

co1

cu reception

4 •

ow cos

cu coulee

008 0.1

cu surveillance

4>un

eill

Ain

M

U

U . I

on*

O.D:

D

« 1 -

4 4

I .4 «

*

*

ni reception

Ia.

i

4 * * ft

* • •

ni coulee

ooi ow oul

cu reception

ni surveillance

lanc

ei

surv

eil

0 1!

or

oe:

06

015

3 i

* t

4 4

4 4

•J4

* 4 ft » 44 ft 44 ft 4 4

' ! : : *4 44

36 Cti 01 Oli 3S

ni reception

P reception

OP1*

cO Q0<

pti

O ooc;

»- owe

a0OC4

arc;

4

4 4

ft 4 4 4

4 4ft ft

ft 4

4

COCi J C " . O&B 0C1 Of-12 CO'J " 3 ' Q

P coulee

P surveillance

CP 1 - CP 2

dtdas

o

20 40 60 80 100

60

Oo

20

dTfim

•

• •

»

»

20 40 60 60 100

dT exp, °C

BO

60

o<n 40

•4—

20

dTfis

«»

•

* •

•

•

4

0 20 40 60 80 100

dT exp, °C