Kic Ctod시험법[1]

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1Yong-Hak Huh, [email protected],Center for Environment & Safety Measurement

(Fracture Toughness Testing)

KIC & CTOD

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KIC

CTOD

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WWII Tanker failure Rocket Case failure

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Alaska MD-80 crash (1999)

death 88 people

Challenger (1986)

Excessive wearon stabilizer

jackscrew

Failure an O-ring

seal(polymer)

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The strength of an engineering structure

is reduced by crack growth in service

Highest Stress Expected

Typical Stress in Service

Design Stress

Time or Load Cycles

Stress

Failure Stress

Failure

can occur

No Failure Failure

will occur

Typical Range of Stress

Time or Load Cycles

CrackSize

Cracks can grow

during the life of acomponent

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Notches act as stress concentrators.

stressapplied

stressmaximum

21

max

max

=

=

+=

ba

Stress

Distance2b

2a

(Stress concentration) : using the Inglis ellipse

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Criteria : Critical Work of Fracture (Gc)

Critical Stress Intensity Factor (Kc).

Critical Crack Tip Opening Displacement (c).

Critical J-Integral (Jc).

(stable)

(unstable)

(Fracture criteria)

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: ( plastic deformation)

(stressconcentration)

(Yield Stress)

(Stress)

Distance

(Fracture criteria)

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All the fracture criteria are related to the intrinsic toughness of

the material.

Fracture before Yield (very small plasticity).

Fracture before Yield (significant plasticity). Yield before Fracture (large plasticity).

Different fracture criteria are needed to cope with cracked

structures:

(Fracture criteria)

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(LEFM: Linear Elastic Fracture Mechanics)

(

) LEFM

Crit ical Work of Fracture (Gc).

Critical Stress Intensity Factor (Kc)

(Fracture toughness)

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Critical work of Fracture

For a crack to propagate:

It must be energetically favourable, and

there must be a mechanism for crack propagation.

Energy is required to create fracture surfaces.

This energy is provided by the release of elastic strain energy due to

crack growth.

Thermodynamics and the Griffi th Equation.

2a

2a

Elastic strain

energy released

by crack

Thickness = tModulus = E

Surface energy

per unit area =

22

at

E

Ue

=

Elastic Strain Energy

ss atU 4=Surface Energy

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The total energy of the system is a function of crack length.

Critical work of Fracture :Griff ith Eq.

22

atE

Ue

=

Elastic Strain Energy

Strain Energy

Energy,

U

Crack Length, a

Total

EnergyU = Us-Ue

ss atU 4=Surface Energy

Surface Energy

Critical Crack Length

dU/da=0

STABLE UNSTABLE

At the critical crack lengt

EadadU s2

20 ==

a

E sf

2=

The Griffi th Equation

critical stress to propagate a

crack of length 2a

es UUU =Total Energy

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The Fracture Toughness, Gc.

Gc is the energy required to propagate the crack

(surface energy s, plastic work p etc).

Gc includes all the work done in the fracture

process zone.

aEGc

f = pscG += 2

ps

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, K,

:

Stress Intensity Factor

a= Y

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Stress Intensity Factor: Effect of Specimen Geometry

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Fracture Toughness, Gc.

Fracture Toughness, Kc.

aEGc

f =

aK fc =

E.g. for the Griffith Crack

cc EGK = FOR ALL CRACK SHAPESKc is easier to use in engineering

Equivalence of Gc and Kc

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The fracture toughnessdepends on specimen

thickness.

This is due to constraintand the crack tip plasticzone size

1

thickness

Mea

suredToughness,

Kc

K1c

PLANE

STRAIN

PLANE

STRESS

Fracture Toughness : Effect of thickness

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The plastic zone

size depends onconstraint Crack

Plastic Zone (Size ry)

Plane StressPlane StrainPlane Stress

Plane Strain

2

2

1

y

y

Kr

2

6

1

y

y

Kr

Constraint reduces the

volume of the plastic zone

Fracture Toughness : Plane strain & Plane Stress

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The plane strain toughness, K1c, is the lowest value.

It is a conservative measure of the toughness.

Thick structures may be less tough than thin structures.

K1c is usually used in engineering design

PLANE STRAIN : Thickness ~ 50 x plastic zone

PLANE STRESS : Thickness ~ plastic zone

Fracture Toughness : Plane Strain Fracture Toughness, KIC

-

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Tough Materials.

LEFM is often not valid for tough materials.

2

y

1c

K5.2a-WB,a,

W B

a

For valid LEFM K1c measurement

-

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General Yielding Fracture Mechanics.

Methods are needed to measure the toughness of tough materials usingsmall test specimens.

The small test specimen may yield before fracture.

The same material in a large structure may fracture before yielding.

Crack Tip Opening Displacement.

J-Integral.

-

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Crack Tip Opening Displacement (c)

The local conditions of stress and strain at the crack tip which

cause fracture are the same for small test specimens and large

structures. These are described by the crack tip opening displacement

(c or CTOD)

Force

Distance

Force

Distance

LARGE PlasticZone

Plastic

ZoneSMALL

-

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Equivalence of c and Gc. c is measured during the toughness test.

Stress

Distance

Plastic Zone

a

c

y

Virtual Work W to extend crack by distance a: aGW c=

Virtual Work to open

crack by distance cagainst stress y:

aW yc =

E

KG ccyc

2

==

PLANE STRESS (no constraint)

(c affected by thickness)

-

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The J-Integral.

The J-Integral is a measure of the work done (elastic and

plastic) for crack growth.

Force

Distance

W=Gc

Distance

Force

W=Jc

ELASTIC ELASTIC-PLASTIC

a1

a1

a2

a2

Crack Length

a1 < a2

-

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The J-Integral

The J-integral is affected by size in the same way as Gc and Kc

J-Integral measured in small test specimens.

Specimen size ~20x smaller than LEFM

J-integral calculated in yielding cracked structures using finite

element models.

The J-integral characterises the crack tip strain necessary forcrack propagation.

-

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Summary: Criteria for Fracture

The fracture toughness (Gc, dc, Kc, Jc) describes the resistanceto crack propagation.

The measured toughness depends on constraint.

Specimen size and thickness.

Plane stress and plane strain.

All these toughness parameters are related

to the crack tip deformation required for

fracture

The lowest toughness is in PLANE STRAIN.

G1c, K1c, J1c, 1c. Minimum specimen size for measurement.

Valid measurement in smaller

specimens for J1c and 1c . The actual toughness of a cracked engineering structure

depends on constraint.

-

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KIC

CTOD

- StandardStandard

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StandardStandard

ASTMASTM BSBS

E 1820E 1820

E 1737E 1737

E 1290E 1290E 813E 813

E 399E 399

BS 5762BS 5762 BS 5447BS 5447

BS 7448BS 7448

BS 7448 1991) : Fracture Mechanics toughness Tests

ASTM E 1820 2001) : Standard Test Method for Measurement of

Fracture Toughness

-

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KIC Testing

(ASTM)

: ASTM E399 -> E1820()

ISO 12737 :Metallic material-Determination of

plane-strain fracture toughness

-

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ASTM E399 : Standard Test Method for Plane-Strain

Fracture Toughness of Metallic Material

Scope :

1.6mm KIC .

Summary of Method

: Plane Strain Fracture Toughness KIC

2 % -

LEFM

KIC .

-

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Clip gage displacement, Vg

Load,

P

A A'

(A)

PmaxPS=PQ

0.95

0

Vg

P

Vg

P

P

Autographic X-Y Recorder

-

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Compact Specimen

K

Q

= (P

Q

/BW

1/2

) f(a/W)

Bend Specimen

K

Q

= (P

Q

S/BW

3/2

) f(a/W)

B : Specimen Thickness

W : Specimen Width

a : Crack Length

S : Distance Between Centers of Rolls

-

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start

, P

Q

P

max

/P

Q

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Number of Test : 3

Dimension Measurement :

B, W 0.025mm 0.1%

Alignment

Bend specimen

1) Support Roll 1% 2) Span nominal length 0.5%

3) Roll 1%

4) Roll 2

Compact Tension Specimen

1) Upper Rod Lower Rod : 0.76 mm

-

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Loading Rate : Stress Intensity Factor

0.55 - 2.75MPa m1/2/sec

30,000 - 150,000 psi in1/2/min

Ex) W/B = 2, B = 2 in

Loading Rate : 0.34 - 1.7 kN/s

4,500 - 22,500 lbf/min

Clip-on Gage Installation :

Knife Edge Screw gage Screw

-

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Test Record

* Load sensing transducer Displacement gage Output

autographic plot.

* Plot : 0.7 - 1.5

* Load .

* Test Record PQ1% .

Calculation and Interpretation :

95% Secant Line PQ .

-

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Fatigue Crack Length & Requirement

* Crack Length : KQ 3( 1/4, 2/4, 3/4)

0.5% .

* Fatigue Crack Front Requirement1) ai - aj0.1 aav2) For Chevron Notch Starter

a(s1, s2) - aav0.1 aava(s1) - a(s2)0.1aav

3) For Straight-Through Starter Notch

amin - M(Notch Length) 1.3mm

a(s1, s2) - aav0.15 aava(s1) - a(s2)0.1aav

4) Crack Plane 10

-

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Pmax/PQ 1.10 : KQ is valid (A)

Pmax/PQ >1.10 : KQ is invalid

B, a > 2.5 (KQ/sYS)2 (B)

(A), (B) 1.5 .

-

Typical force displacement records

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Typical force-displacement records

Displacement, V

Force,

F

Typ

eI

Typ

eII

Typ

eIII

0 00

FmaxFmax

A AA

F5=F

Q Fmax=FQF5

FQ

-

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C B A

KIC18 tests

23 tests

2.5

1 2 3 4 5 6

60

80

100

120

Kc(

ksiin)

B

=(Kc/Y)2

1 ksi in = 3.54 kgf/mm3/2

-

S i di i f lidS i di i f lid

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2008-04-252008-04-25 41Yong-Hak Huh, [email protected],Center for Environment & Safety Measurement

Minimum RecommendedThickness and Crack Length

YS

/E in

YS

/E in

0.0050 To 0.0057

0.0057 To 0.0062

0.0062 To 0.0065

0.0065 To 0.0068

0.0068 To 0.0071

3

2 1/2

2

1 3/4

1 1/2

0.0071 To 0.0075

0.0075 To 0.0080

0.0080 To 0.0085

0.0085 To 0.0100

0.0100 or greater

1 1/4

1

3/4

1/2

1/4

Minimum RecommendedThickness and Crack Length

Specimen dimensions necessary for a valid

determination of KIC

Specimen dimensions necessary for a valid

determination of KIC

-

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(B) (C)

(A)

(Plane Strain)

B

t

Plane Stress State

Plane Strain State

-

()

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24

6

8

10

60

80

100

120

2.5

a

(Kc/Y)2

1 ksi in = 3.54 kgf/mm3/2

Kc(ksiin)

()

a

(Kc/Y)2> 2.5

-

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Fatigue Cracking Machine

Fatigue Cycle & Fatigue Force

Load Accuracy : 1

Testing Machine

Force signal & Gage Disp. Output X-Y Recorder

Load Accuracy : 1

Clevis & Pin for Compact Specimen

Bend Test Fixture : Support Roll

Knife Edge : .

-

Alternative C(T) Specimen DesignsAlternative C(T) Specimen Designs

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C(T) Specimen for pin of

0.24W(+0.000W/-0.005W)diameterC(T) Specimen for pin of

0.1875W(+0.000W/-0.001W)diameter

0.5W

2H=1.2W

+ 0.01W

-

0.5W

2H=1.2W

+ 0.01W-

W+0.005W-

0.355W

0.375W

W+0.005W-

0.25W DIA.0.188W DIA.

Alternative C(T) Specimen DesignsAlternative C(T) Specimen Designs

-

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.( 0.375in )

0.24W + 0.000W/- 0.005W .Y1379MPa 0.3W + 0.005W/-0.000W. 0.288W +0.000W/-0.005W .

A , 0.002in .

0.25W0.005W

0.26W

0.5

W

0.6W

0.25W

0.5W 0.005W

0.5W 0.015W

R 1.270.254

0.3W0.005W

0.025W

0.025WR 2.54

D

D

1.2

5D

0.25W

A

)

-

Fatig e P e c acking

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Fatigue Pre-cracking

Pre-crack : .

Crack Length (Crack Starter Notch + Fatigue Crack) : 0.45-0.55 W

Fatigue Crack : 0.025 W 1.3 mm

: -1 < (

/

) < 0.1

Cycle Number : 104 -106

Specimen SizeNotch Preparation

Stress Intensity Factor Level

- Fatigue Pre-cracking

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Pre-cracking : Kmax < 0.8 KQ

Pre-cracking (2.5 % of Crack)

Kf (max)/ E 0.00032 mm1/2

Kf (max) 0.6 KQ

Kf (max) K f(min) 0.9 Kf (max)

Crack Initiation

Sharp Notch Tip

Statically Preloading : Compressive

Negative Fatigue Load Ratio

Crack :

, 180.

-

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a

f

a

30

1.5mmW/10

120

a

1

a

2

a

3

120

)

a

f

a

30

1.5mmW/10

a

1

a

2

a

3

)

Notch RadiusStraight-Across Notch : 0.08mmChevron Notch : 0.25 mm

-

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KIC

CTOD

-

COD (Crack Opening Displacement)

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Crack Tip

.

BS 5762 (1979) :

Crack Opening Displacement(COD) Testing ASTM E 1290 (1989) :

Crack-Tip Opening Displacement(CTOD) Fracture

Toughness Measurement

Crack tip r

0ys~

0y~

r*p

Plastic zone size

x

y

CODv

(Dugdale model)

COD (Crack Opening Displacement)

-

Definition of CTODDefinition of CTOD

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Crack tip

r

0ys~

0y~

r*p

Plastic zone size

Dugdale model

x

y

CODv

Plastic zone

The displacement of the surfaces of a crack normal to theoriginal (undeformed) crack plane at the tip of the fatigue

precrack (mm).

-

( ) ( )

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1122

3

: COD

: CTOD

-

Notch Profile During BendingNotch Profile During Bending

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W

r(W-a)

(W-a)

a

c

Knife Edge to

Support Clip Gage

Apparent Center

of Rotation

Angle of Bend

O

Z

(Measured With Clip Gage)

CTOD

CMD

a r(W-a)

CTOD = { COD)r W-a)}/{a+r W-a)}

COD

Z

Notch Profile During BendingNotch Profile During Bending

-

Various physical definitions of CTOD

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Various physical definitions of CTOD

Original crack Deformed crack

b) More realistic shapea) Early idealisation

d) Tengent CTOD e) CTOD at original crack tip

position (Dawes)

c) Elastic plastic interface

plastic zone

f) CTOD at position subtending @90

at crack tip (Rice)

-

Flowchart for CTOD Testing

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g

CTOD

CTOD

()

YES

NO

-

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C(T) Specimen Designs


0.24W(+0.000W/-).005W)diameter


0.1875W(+0.000W/-.001W)diameter

0.5W

2H=1.2W+ 0.01W-

0.5W

2H=1.2W+ 0.01W-

W+0.005W-

0.355W 0.375W

W+0.005W-

0.25W DIA. 0.188W DIA.

-

Proportional SE(B) Specimens

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p ( ) p

W 0.005W

TEST SPECIMENa

2.25W 2.25W

B

B=W/2 0.010W

W 0.005W

TEST SPECIMENa

2.25W 2.25W

W 0.01W

-

(Rectangular Section),

(Square Section),

: Dimensions and Tolerances

-

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Notch Width N

= 0.065Wmax(if W is over 25mm)

1.5mm max (if W is less than or equal to 25mm)

@ 60

M

a

N

-

Crack Plane Orientation Code for Rectangular Section

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Crack Plane Orientation Code for Rectangular Section

T-S

T-L

L-T

S-L

S-T

L-S

S

L

ROLLING DIRECTION

EXTRUSION DIRECTION

AXIS OF FORGING

LENGTH

LONGITUDINAL

THICKNESS

SHORT TRANSVERSE

WIDTH

LONG TRANSVERSE

-

SE(B) Test Fixture Design

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S ( ) g

S=4W 0.02W

W

W

TEST SPECIMEN

DISPLACEMENT GAGE

TEST FIXTURE

-

Clevis for CT Specimen

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0.25W0.005W

0.26W

0.5W

0.6W

0.25W

0.5W 0.005W

0.5W 0.015W

R 1.270.254

0.3W0.005W

0.025W

0.025W

R 2.54

D

D

1.25D

0.25W

.

( 0.375in

)

: 0.24W+0.000W

-0.005W

Y 1379MPa

-: 0.3W + 0.005W

-0.000W.

- : 0.288W+0.000W-0.005W

A , 0.002in .

A

p

-

Displacement Measuring Devices

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70

60

110

T1

T2

C1C2

p g

0.030

0.025

0.021

0.019

0.006

0.004R 90 701

1.625

1.620

0.3750.373

0.188

0.186

0.188

0.186

0.020

0.010R

-

Displacement Measuring Devices

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N

0.06

0.050.25

0.20

4560

90

.

0.07

0.06

0.023in

0.125

0.100

C

=

.

2C+

W/2

p g

: Knife Edge

Notch Width N

= 0.065Wmax(if W is over 25mm)

1.5mm max (if W is less than or equal to 25mm)

-

Fatigue precrack

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Fatigue precrack

6 7 8 91 2 3 4 5

B

W

Machined notch

Fatigue crack

Slow crack growth

Post-test f racture

Post-test f racture

initiating saw cut

Fracture test piece face

Load for fatigue precracking < Pf

Pf = 0.5(Bb0Y/S) for SE(B) specimen

Pf = 0.4Bb0

2Y/(2W+a

0) for CT specimen

Fatigue precrack length : Notch tip1.25mm.

Main problems during fatigue precracking

1). Crack tip bowing2). Effects of residual stress

3). Crack tip location

-


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Crack tip bowing

Notch tip

stress field :

.

6 7 8 91 2 3 4 5

B

W

Machined notchFatigue crack

Post-test fracture

Post-test fracture

initiating saw cut


-


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Shape of crack Propagation

Effects of residual stress

Multipass weld specimen : -

-

Singlepass weld specimen : -

-

1% Strain (Dawes) : Notch

Fatigue

precrack

Notch

Fatigue

precrack

Notch

Fatigue

precrack

Notch


-


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Crack tip location

COD toughness .

(, HAZ, )-

-

COD Testing

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up to Pfstress intensity factor : 0.55 ~ 2.75 MPam1/2 /s

(30000 ~ 150000 psi in 1/2 /min)

crosshead or clip gage displacement control

-

Type of Load Versus Clip Gage

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Type of Load Versus Clip Gage

Displacement Records

Vp Vp Vp

Vp

Vp

Vp

Vp

Vp

Load, P

Clip gage displacement, v g

Pc

Vc

Pc

Vi

Pi

Pu

Vc

VuVi

Vu

Vm

Vi

Pu

Pm

Pi Pi

Pop-inPop-

in

(a) (b)(c) (d) (e)

(a), (b)

: cr itical CTOD

c

(c),(d),(e)

: u, m

-

Analysis of Experimental Data

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Max. pop-in crack extension > 0.04b0- calculate c, u

Analysis of Experimental Data

Calculation of c, u, m

= K2(1-2)/2YS E +rp(W-a0)p/[rp(w-a0)+a0+z]

K=YP/[BW1/2]

Qualifying CTOD values

- difference between the max. and min. of all 9 crack length < 0.1a0- fatigue crack front

: not closer to the machined notch than the lesser of 0.025W or 1.3mm

- plane of the fatigue crack surface

: not exceed an angle of 10o from the plane of the notch

- crack front : not multi-planar or branched

-

Autographic test plot

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Autographic test plot

Clip gauge displacement Vg

Load P

Maximum load

12345

6 7 8 91 2 3 4 5

B

W

Machined notch

Fatigue crack

Slow crack growth

Post-test fracture

Post-test fracture

initiating saw cut


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CTOD vs Crack Extension

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0.2mmoffset

0.15mm

offset

0.5mm

offset1mm

offset

1.5mm

offset

i

m

R-curve

= 0.4221(0.2972+ a )p0.5971

ap

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COD vs slow crack growth (R-curve)

Slow crack growth a

Initiation

COD

1

2

3

4

5

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R = Pfmin/ Pfmax < 0.1

Kf

< 0.63ys

B

0.45 < a/W < 0.55

ai - aj < 0.05W ( i, j = 1,2,3)

amax - amin < 0.1W

amin - M > 0.025W or 1.25 mm

1/2

Documents

Kic Ctod시험법[1]