fracture mechanic

Download fracture mechanic

Post on 24-Nov-2014

104 views

Category:

Documents

1 download

Embed Size (px)

TRANSCRIPT

FITNET BASIC TRAINING PACKAGE

F. Gutirrez-Solana (UC) S. Cicero (UC) J.A. lvarez (UC) R. Lacalle (UC) F. Gutirrez-Solana (UC) J.A. lvarez (UC)W P 6: TRAINING & EDUCATION F. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

S. Cicero (UC)

FITNET consortium AUTHORS: F. Gutirrez-Solana (UC)S. Cicero (UC) J.A. lvarez (UC) R. Lacalle (UC)F. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

W P 6: TRAINING & EDUCATION

G1RT-CT-2001-05071

CONTENTSI. TRAINING PACKAGE ON FRACTUREA- BASIC CONCEPTS B- INTRODUCTION TO ASSESSMENT PROCEDURES FOR CRACKED COMPONENTS C- PROCEDURE APPLICATION (FITNET) D- EXAMPLES

56 40 63 139

II.

TRAINING PACKAGE ON FATIGUEA- BASIC CONCEPTS B- INTRODUCTION TO FATIGUE ASSESSMENT PROCEDURES C- PROCEDURE APPLICATION (FITNET) D- EXAMPLES

183184 253 266 316

W P 6: TRAINING & EDUCATION

F. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

G1RT-CT-2001-05071

CONTENTSIII. TRAINING PACKAGE ON CREEPA- BASIC CONCEPTS B- INTRODUCTION TO ASSESSMENT PROCEDURES FOR CRACKED COMPONENTS AT HIGH TEMPERATURES C- PROCEDURE APPLICATION (FITNET) D- EXAMPLES 374 388 426

337338

IV.

TRAINING PACKAGE ON ENVIRONMENT EFFECTSA- BASIC CONCEPTS B- INTRODUCTION TO ASSESSMENT PROCEDURES FOR CRACKED COMPONENTS C- PROCEDURE APPLICATION (FITNET) D- EXAMPLES

471472 487 495 521

W P 6: TRAINING & EDUCATION

F. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

G1RT-CT-2001-05071

I. TRAINING PACKAGE ON FRACTURE

W P 6: TRAINING & EDUCATION

F. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

5

G1RT-CT-2001-05071

A. BASIC CONCEPTS

W P 6: TRAINING & EDUCATION

F. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

6

G1RT-CT-2001-05071

FRACTURE BEHAVIOURINTRODUCTIONThe final fracture of structural components is associated with the presence of macro or microstructural defects that affect the stress state due to the loading conditions. Fracture occurs when this state reaches at local level a critical condition.component

Material + Geometry

and defects + loading

Vs.

Toughness

Stress state (local)

Vs.

Critical local condition to fracture

W P 6: TRAINING & EDUCATION

F. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

7

G1RT-CT-2001-05071

FRACTURE BEHAVIOURINTRODUCTIONProcessing Crack (defect): produced by Cracking processes Operation damagecomponentMaterial + Geometry and defects + loading Vs. Vs. Toughness

Stress state (local)

Critical local condition to fracture

Fracture analysis

FRACTURE MECHANICSF. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

W P 6: TRAINING & EDUCATION

8

G1RT-CT-2001-05071

FRACTURE BEHAVIOURINTRODUCTIONFracture Mechanics aCrack growth

a0Critical loading evolution Safety

tFRACTURE classic design use

a

C design. use

Crack growthF. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

a (t)9

W P 6: TRAINING & EDUCATION

G1RT-CT-2001-05071

FRACTURE BEHAVIOURINTRODUCTIONFracture ModesF F: Loading forces a: crack advance n: crack plane normal a n n a

F n F // n F F // a F a

MODE I TensileW P 6: TRAINING & EDUCATION

MODE II Shear

MODE III TorsionF. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

10

G1RT-CT-2001-05071

FRACTURE CRITERIAStress state in a crack frontStress concentration factor, Kt

Stress concentration

Stress

X X

W P 6: TRAINING & EDUCATION

F. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

Stress concentration factor, Kt

Stress concentration factor, Kt

FRACTURE BEHAVIOUR

11

G1RT-CT-2001-05071

FRACTURE BEHAVIOURFRACTURE CRITERIALocal stress and strain states in a crack front (Irwin)Semiinfinite plate, uniform stress (MODE I) xy Y y x z X

STRESSESPlane solutionx = y = xy =

a 2r

3 cos 1 sen sen 2 2 2

a 3 cos 1 + sen sen 2r 2 2 2 a 3 cos 2 sen 2 cos 2 2r

ijI =

a I f ( ) 2 r ij

Plane stress (PSS)z = 0

Plane strain (PSN)z = (x + y)

DISPLACEMENTSu = 3 ar (1 + ) (2 1)cos 2 cos 2 2E 2

r

a

3 ar (1+ )(2 + 1)sen 2 sen 2 2E 2 3 = = 3 4 (PSS) 1+ (PSN) v=w= E

W P 6: TRAINING & EDUCATION F. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

(

x

+ y dz

)

12

G1RT-CT-2001-05071

FRACTURE BEHAVIOURFRACTURE CRITERIA Stress state in a crack front. Stress Intensity Factor

xy Y

y x z

r X

1 a I f ijI () = f ij () = a 2r 2r 1 Iij = K I f ijI () Position 2rI ij

Stress Intensity Factor

a

K I = aKI defines the stress state in the crack frontF. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

W P 6: TRAINING & EDUCATION

13

G1RT-CT-2001-05071

FRACTURE BEHAVIOURFRACTURE CRITERIA Stress state in a crack front Stress Intensity FactorFor any component (geometry + defects)a

K I = f a orf: geometric factor

f g(a)

For other modes analogously ...W P 6: TRAINING & EDUCATION

K II = f II g(a)F. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

14

G1RT-CT-2001-05071

FRACTURE BEHAVIOURFRACTURE CRITERIA Stress fracture criterionIf If KI ij (local) ij (local) = ij (critical) KI = KIC Local fracture criterion Sress fracture criterion

If fracture critical conditions (KIC) only depend on material KIc (Fracture Toughness) Stress Fracture Criterion KI = KIc15

W P 6: TRAINING & EDUCATION

F. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

G1RT-CT-2001-05071

FRACTURE BEHAVIOURFRACTURE CRITERIA Stress fracture criterion c (ao) ao ao 4ao

KI = KIc Fracture occurs with c (a)

c (4ao) =

c (ao)2

Another observation:

strain

The compliance of the component increases with the length of the defects. Compliance: Indicates the length of the defects.W P 6: TRAINING & EDUCATION F. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

16

G1RT-CT-2001-05071

FRACTURE BEHAVIOURFRACTURE CRITERIA Energetic fracture criterion (Griffith)Comparison between the energy that is released in crack extension and the energy that is necesary to generate new surfaces because of that extension.

d(U) dE da daunitary thickness

Crack grows (Fracture)

d(U) dE = 2 Bda Bda

: surface energy of the material (Energy per unit of generated surface)W P 6: TRAINING & EDUCATION F. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

17

G1RT-CT-2001-05071

FRACTURE BEHAVIOURFRACTURE CRITERIA Energetic fracture criterion (Griffith)As a geometry function Semiinfinite plate

f (, a, E ) 2

2 a Gc G= EG = GcFracture criterion

G: Energy release rate Gc: Fracture Toughness Where:

K I2 G= E

=1 (Plane stress) = (1 2 ) (Plane strain)

Gc= 2 in very brittle materials >> 2 in materials with plasticity before fractureW P 6: TRAINING & EDUCATION F. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

18

G1RT-CT-2001-05071

FRACTURE BEHAVIOURFRACTURE TOUGHNESS Fracture Toughness CharacterisationA) Standardised specimens

B) Fatigue precracked specimens : a (a as initial crack length)W P 6: TRAINING & EDUCATION F. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

19

G1RT-CT-2001-05071

FRACTURE BEHAVIOURFRACTURE TOUGHNESS Fracture Toughness CharacterisationC) Mechanical Testing PQ (Load on Fracture initiation) KQ = f (PQ, a, geometry)Pmax Pmax

Pmax

P Q KQ = 1 B W2

f a W

for CTs

a measured on fracture surface KQ = KIc (toughness), if some normalised conditions are fulfilledW P 6: TRAINING & EDUCATION F. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

20

G1RT-CT-2001-05071

FRACTURE BEHAVIOURFRACTURE TOUGHNESS Fracture Toughness Characterisation6

Fatigue crack profile

a

Load (kN)

4

Fracture mechanisms

2

UCQ-1230 0 1 2 3 COD (mm) 4 5 6

50 mF. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

W P 6: TRAINING & EDUCATION

21

G1RT-CT-2001-05071

FRACTURE BEHAVIOURFRACTURE TOUGHNESS Thickness effectKc Ic Tensin plana PLANE STRESS Fracture at 45 with respect to the Rotura formando 45 con el plano original crack plane original de fisura

45

X TENSION PLANA PLANE STRESSDeformacin plana PLANE STRAIN

Y

crack Fisura

Z

Z

Z = 0

+

Effect of Plastic Zone

K Ic

Fracture in plano de Rotura en crack planefisura Labios a 45 en extremos

Bmin

Espesor (B) Thickness (B)X Z Y

B min

2 K Ic (P.Strain ) = 2.5 2 Y

PLANE STRAIN DEFORMACION PLANAF. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

W P 6: TRAINING & EDUCATION

22

G1RT-CT-2001-05071

FRACTURE BEHAVIOURFRACTURE TOUGHNESS Effect of temperature and loading rateaTOUGHNESSSTATIC TEST INCREASING LOADING RATE IMPACT

TEMPERATURE

b

c

K IcTOUGHNESS

K IcSTATIC

K IdDYNAMIC

TEMPERATUREF. GUTIRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE

LOADING RATE

W P 6: TRAINING & EDUCATION

23

G1RT-CT-2001-05071

FRACTURE BEHAVIOURMATERIAL TOUGHNES