Characterization technics in fracture mechanicsincluding

K1c test, J1c test and da/dN-K curve measurement

1

Jianqiang Chenjchen.map@gmail.com

Safety factor and damage tolerance design

Conventional turbine runner design

approach: max <

YS or

UTS

Fracture mechanics damage

tolerance approach: K < K1c, af < ac

[ALSTOM HYDRO]

Fracture toughness K1c and fatigue crack growth rates da/dN-K should be known. 2

CT specimen(compact tension)

( )( )

2 2 3 3 4 4

3/ 21/ 2

(2 a w) 0.886 4.64a w 13.32a w 14.72a w 5.6a wPKBW 1 a w

+ + + =

B = 0.5W In general

Fracture toughness K1c test (ASTM E399)

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USERText BoxK=f() est fonction du stress P et une caracteristique du defaut (B ou a ou W)

Fatigue pre-cracking is often used to obtain a sharp crack with small plastic deformation;

Chevron notch is necessary to initiate a straight crack;

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Fatigue pre-cracking (ASTM E399)

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5Crack mouth opening displacement

Load

CMOD

PQ

( )WafWB

PQ /KQ =

(c)

USERText BoxCrack Mouth Opening Displacement

Small scale yielding and plane strain conditions:

YS

Q

YS

Q0

K2.5B and

2

K2.5a

6

If not, increase specimen thickness B () or fatigue pre-cracking length a0 ()

KQ = K1c ?

7KQ = K1c ?

Even the two previous conditions are met, the recording of force-displacment

curve could include some non-linarity for two reasons:

plasticity near the crack tip;

beginning of stable crack extension.

if Pmax/PQ < 1.10 and the two previous conditions are met, then KQ = K1C

8Material studied CA6NM steel

K1c testing - small scale plasticity and plane strain condition

a = initialcracklength

B = specimenthickness

a, B 258 mm !, if a/W = 0.5, W= 516 mm !!

2

K2.5Bet 2

K2.5aYS

1c

YS

1c

C Mn Si S P Cr Ni Mo

CA6NM 0.03 0.57 0.37 0.02 0.02 12.68 4.03 0.67

Chemical composition of the tested material CA6NM (wt. %)

E (GPa) YS (MPa) UTS (MPa) A (%)

CA6NM 207 763 837 27.0

Tensile properties of the tested material

Fracture toughness

K1c test is not appropriate for CA6NM steel

The Rices J Integral Going back to Griffith ?

=S

dSx

uTwdyJ with = ijijdw

crack

[Rice, J Appl Mech 35, p.379, 1968]

9

)1( 2=EJK

)1( 22

vE

KGJ ==(plan strain)

Linear Elastic Fracture Mechanics (LEFM)

Stress singularity near a crack tip

o(r1/2) is higher order stress terms

)o(r)f(r 2

K 1/2ij +=

S

S

r

ax

K-controlled zone

Small-scale yielding

)m(MPa aY K =

10

Going back to Griffith ?

)f(r 2

Kij =

Elastic-Plastic Fracture Mechanics (EPFM)

Generalisation of the approach with the HRR field near a crack tip

)(frI

J ij

1)1/(n

nyyij

+

=

S

S

a

J-controlled zone

Large Scale Yielding

J represents the elastic-plastic stress fields intensity near a crack tip

As fo K and Kc, when J reaches a criticalvalue Jc, the crack will propagate stably

n

yyy

+=Ramberg-Osgood

[Hutchinson, J Mech Phys Solids 16, p.13, 1968] [Rice & Rosengren, J Mech Phys Solids 16, p.1, 1968] 11

Hutchinson + Rice & Rosengren

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Measure of J at begining of a R-curve (initiation of crack extension) Test on SENB and CT specimens; W= 2 inch and B= 1 inch usually; B can be reduced to 0.25 W; Modified geometry for that the extensometer can measure the load-

line displacement (work)

Fracture toughness J1c test (ASTM E1820)

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Procedure: Fatigue pre-cracking of n specimens (n5) to the same a0 Stop the tests at different af Marking of final crack length

Break the specimen

Measurement of af Fitting of J-a curve

JQ = (BL)(J-a)

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Multi-specimen method

P-v curve J-a curve

Long and expensive

Procedure:

Fatigue precracking of one specimen,

Ductile tearing of specimen with partial unloading to get the elastic compliance,

After the final unloading, heat tinting to measure a0 and af , and break the

specimen,

Results analysis.

P-v curve J-a curve

Single-specimen method

0.0 0.5 1.0 1.5 2.0 2.5 3.00

5

10

15

20

25

30

35

40

45

L

o

a

d

(

k

N

)

Load line displacement (mm)0.0 0.5 1.0 1.5 2.0 2.5 3.0

0

100

200

300

400

500

600

700

data points regression line

J

(

k

J

/

m

2

)

crack extension - a (mm)

1/C

Load-unload slope compliance crack length a

Plastic area under P-v curve + elastic part J integral

0.0 0.5 1.0 1.5 2.0 2.5 3.00

100

200

300

400

500

600

700

J

(

k

J

/

m

2

)

crack extension - a (mm)

J0.2

0,2mm offset line

14

)(1E

KJ 22

el =

)a(WBA

J0n

plpl

=

plel JJJ +=

Force

Load-line displacement

15

Calculation of J and a

Apl

depends on specimens geometry

[ ]5432 677.650355.464106.335u-11.242u4.06319u-1.000196 / uuWai ++=a= ai -a0

Calculation of J

Calculation of a

For the candidate JQ value is a valid measurement of J1c, several conditions should be met, including:

B and W-a0 > 10 JQ/Y Straightness of a0 et af, a - aavg < 0.05B a (marking) - a (predicted) < 15%

e.g. CA6NM steel, K1c = 245 MPa ,YS = 763 MPa, UTS =837 MPa

B 3.31 mm ! 16

J-a curve and validation

Initial procedure 12.7 mm thick smooth CT specimen

Problems :

Significant lateral contraction is observed.

There are nearly no crack growth at the side surfaces of the specimen while the crack

front at the center advanced by more than 2 mm.

KJ1c measured = 452MPa !!! (valid test, K1c = 245 MPa ).

10 mm

crack extension direction

Fracture surfaceSpecimen

2 mm

17

New procedure 12.7 mm thick side-grooved CT specimen

Fracture surface

The crack tunneling is less pronounced by the introduction of side-grooves.

The crack still grows faster at the center of the specimen compared to the side surfaces.

The test is not valid according to ASTM E1820 (straightness of af).

crack extension direction

BN = 0.8 B

2 mm

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12.7 mm smooth specimen

Side-grooves effect

Smooth specimen: invalid test KJ1c = 452 MPa !!!

Side-grooved specimen: invalid test K1c = 241 MPa .

12.7 mm side-grooved specimen

10 mm 10 mm

19

New procedure 25.4 mm thick side-grooved CT specimen

crack propagation direction

Fracture surfaceBN = 0.8 B

The crack extension front is nearly straight, the specimen is in plane strain condition

(little lateral contraction).

The test is valid according to ASTM E1820.

5 mm

20

J-a curve

0.0 0.5 1.0 1.5 2.0 2.5 3.00

100

200

300

400

500

600

700

B = 0.5 inch B = 1.0 inch

J

(

k

J

/

m

2

)

crack extension - a (mm)

0.2 mm offset line

Thickness effect 12.7 mm vs 25.4 mm

Similar fracture initiation toughness J0.2

values can be obtained on both thin and thick

specimens even though the test done on thin specimen was not valid according to ASTM

standard E1820.

The tearing modulus dJ/da is much higher for thin specimens than thick specimens.

thickness

(mm)

J0.2(kJ/m2)

KJIc(MPa )

dJ/da

(MPa)

12.7 256 241 215

25.4 266 245 128

Measured values

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12.7 mm thick specimen 25.4 mm thick specimencrack propagation direction

5 mm 5 mm

Thickness effect 12.7 mm vs. 25.4 mm

J1c 12.7 mm: significant crack front curvature and lateral contraction.

J1c 25.4 mm: straight crack extension front and little lateral contraction

However, the measured fracture initiation toughness J0.2

values are approximately

equal.

22

fatigue

precracking

Microscopic fracture surface SEM observation

transgranular

fracture

intergranular

fracture

500 m

stable crack extension

dimple ductile

fracture surface50 m

23

Fracture mechanism in ductile material

d

=

23

exp21

RdR

VM

H

=

Growing crack in a ductile material1Stage 1: Void nucleation

Stage 2: Void growth

Stage 3: Void coalescence

where, R: current void radius, and stress triaxiality

For the stage 2: Rice and Tracey2 established the following law:

1[Gullerud et al., Eng Fract Mech 66, p.65, 2000] 2[Rice & Tracey., J Mech Phys Solids 17, p.201, 1969]

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FEM model

Mesh of CT specimen

12.7 mm thick smooth specimen

12.7 mm thick side-grooved specimen

Voce nonlinear isotropic hardening law:

where, R0, Q, b, material constants,

p, accumulated plastic strain

CA6NM: YS = 763 MPa, R0 = 2665 MPa,

Q = 42.7 MPa, b = 3000

quarter of specimen: 41599 nodes, 22940 elements

(20-node elements + 10-node elements)

[ ])exp(10 ppYSeq bQR ++=

25

FEM Results

-0.50 -0.25 0.00 0.25 0.500.0

0.5

1.0

1.5

2.0

12.7 mm thick smooth specimen 12.7 mm thick side-grooved specimen 25.4 mm thick side-grooved specimen

S

t

r

e

s

s

t

r

i

a

x

i

a

l

i

t

y

(

)

Normalized distance to midsection (Z/B)

Variation of stress triaxiality across

the specimen thickness

-0.50 -0.25 0.00 0.25 0.500.000

0.005

0.010

0.015 12.7 mm smooth specimen 12.7 mm side-grooved specimen 25.4 mm side-grooved specimen

P

l

a

s

t

i

c

s

t

r

a

i

n

i

n

t

h

i

c

k

n

e

s

s

d

i

r

e

c

t

i

o

n

(

Z

)

Normalized distance to midsection (Z/B)

Variation of plastic strain across the

specimen thickness

For 12.7 mm thick smooth specimen, the stress triaxiality falls rapidly for |Z/B| >

0.25.

For 25.4 mm thick side-grooved specimen, the plane strain condition is maintained

over the entire specimen thickness.

26

Main differences between K1c and J1c tests

K1c J1c

Concept Linear Elastic Fracture Mechanics

(LEFM)

Elastic-Plastic Fracture Mechanics

(EPFM)

Loading condition Small-Scale Yielding

(Elastic)

Large-Scale Yielding

(Elasto-Plastic)

Extensometers poistion

(CT specimen)

Crack Mouth Load-Line

Testing Procedure P-v curve KQ K1C P-v curve J-a curve JQ J1C

Application field Brittle materials

(high strength & low toughness)

Ductile materials

(low strength & high toughness)

27

Charpy test

ASTM E23: Standard test methods for notched bar impact testing of metallic materials

28

Charpy test on Titanics steel

Can we estimate fracture toughness K1c from Charpy test ?

=

2051 YSYSYS

c CVNK

Rolfe-Novak-Barsom correlation:

29

Titanics steel at 0oC

Actual A36 steel at 0oC Energy absorbed as function of temperature

Fatigue crack growth da/dN - K curve

[Paris et al. The Trend in Engineering 13, p.9-14, 1961]30

Measure of da/dN-K curve Test on CT and MT specimens; W= 2 inch and B= 0.5 inch usually; B can be reduced to 0.05 W; Modified geometry for that a longer ligament can be used for crack

growth measurement

Fatigue crack growth rates measurement (ASTM E647)

31

( )( )

2 2 3 3 4 4

3/ 21/ 2

(2 a w) 0.886 4.64a w 13.32a w 14.72a w 5.6a wPKBW 1 a w

+ + + =

da/dN K curve

Where to start the measurement (test) ?32

start of test

K decreases

until the threshold

K increases

end of test

da/dN K test

33

2max,

1

=

YSmy

Kr

pi

2

, 21

=

YScy

Kr

pi

(Monotonic)

(Cyclic)

108.01 >

= mm

dadK

KC

K decreasing phase K-gradient limit (ASTM E647)

Monotonic and cyclic plastic zones

34

K decreasing at R = 0.1 and R = 0.7

[Bui-Quoc T. et al. Final report of project CDT P3768, 2009]35

da/dN-K curve of CA6NM steel at R = 0.1 and R = 0.7

[Bui-Quoc T. et al. Final report of project CDT P3768, 2009]36

Main fatigue crack closure mechanisms in metals

(a) Plasticity-induced closure

(b) Roughness-induced crack closure

(c) Oxide-induced closure

(d)Closure induced by a viscous fluid

(e) Phase transformation-induced closure

[Suresh & Ritchie, Int metall Rev 29, p.445, 1984]37

vv

LoadP-v curve P-v curve

Pv

=

compliance of

opening crack

Pv ='v

Fatigue crack closure measurement

opeff KKK = max

Effective stress intensity range keff :

38

( )meffKCdN

da =

Pariss equation:

[Trudel A. et al. Int J Fatigue 66, p. 39-46, 2014]

Master curve

39

Thank you for your attention!

Questions ?

40

Relation entre G et K

-Dplacement impos

-plaque dpaisseur unitaire

-Contrainte plane

La propagation de la fissure de a a+ se traduit par une dcroissance de lnergie lastique: dU= - G On peut retourner ltat initial en refermant la fissure avec les forces qui agissaient entre a et a+ . Lnergie G est gale au travail de ces forces de fermeture :

2I I

I I I0

K K1 8 xG K dx d 'o : G2 E 2 E2 x

= = pipi

22 I

IKG (1 ) en dformation planeE

=