7th National Turbine Engine HCF Conference

Role of Crack Size and Microstructure in Influencing Role of Crack Size and Microstructure in Influencing

Mixed-Mode High Cycle Fatigue Thresholds in Ti-6Al-4VMixed-Mode High Cycle Fatigue Thresholds in Ti-6Al-4V

R.K. Nalla, J.P. Campbell and R.O. Ritchie

Department of Materials Science and Engineering, University of California, Berkeley, CA 94720

May 15, 2002

Work supported by the U.S. Air Force Office of Scientific Research under Grant No. F49620-96-1-0418 under the auspices of the Multidisciplinary University Research Initiative (MURI) on High Cycle Fatigue to the University of California.

MotivationMotivation

• High Cycle Fatigue (HCF) has been identified as the single biggest cause of failures in military turbine engines. Such failures result in costly engine damage/loss and related down-time, in addition to loss of human life

• A successful “solution” would save ~$2 billion over the next 20 years

• A “damage-tolerant approach” may offer an alternative over the combination of Goodman Diagram/ “Safe Life” (S/N) based approach used now

• The basis of the MURI has been to seek a physical understanding behind the development of such a damage- tolerant approach

time

0 < R < 1

HCF/LCF Interactions

Foreign Object Damage

Fretting at Dovetail/Fir Tree Attachment

time

kt

residual

time

Edge of contact

Center of Contact

time

{

• High Cycle Fatigue (HCF)

• Low Cycle Fatigue (LCF)

• Foreign Object Damage (FOD)

• Fretting

Why Study Multiaxial Fatigue?Why Study Multiaxial Fatigue?

• Common in turbine engines - e.g., in association with fretting in the dovetail/disk contact region

• High frequencies involved (1-2 kHz) may necessitate a threshold-based methodology incorporating mode-mixity effects

• Presence of shear loading known to dramatically reduce mode I threshold (John et al, in: Mixed-Mode Crack Behavior, ASTM STP 1359, 1999)

• No information on HCF mixed-mode thresholds for small cracks

• Multiaxial fatigue research goes back to only 1969 (Iida and Kobayashi, J. Bas. Eng., 1969), while fatigue research goes back well over a century (Albert, Archive für Minerlogie, Geognosie, Bergbau und Hüttenkunde, 1838)

• Only two studies on Ti-6Al-4V in the archival literature - by Pustejovsky (Eng. Fract. Mech., 1979) and Gao et al (Multiaxial Fatigue, ASTM STP 853, 1985)

Problem Statement and ObjectiveProblem Statement and Objective

• Very little data have been reported on the role of mode-mixity in influencing fatigue thresholds in Ti-6Al-4V alloys

• Similarly, little information is available on how microstructure can affect such mixed-mode thresholds

• There is no information on the role of crack size on mixed-mode thresholds in any material

• Hence, our objective is to:

- compare the mixed-mode HCF threshold behavior for two microstructures in Ti-6Al-4V with widely differing micro-

structural dimensions, i.e., bimodal (STOA) and lamellar

- characterize the effect of mode-mixity and load ratio on mixed-mode thresholds for cracks with widely

differing dimensions, i.e., large (>4 mm) and short (~200 m) through-thickness cracks and small (<50 m) surface cracks

Material & Microstructures InvestigatedMaterial & Microstructures Investigated

Yield Strength Ultimate Tensile Reduction Fracture Toughness (MPa) Strength (MPa) in Area (%) KIc (MPam)

A: 930 978 45 64

B: 975 1055 10 100

Ti Al V Fe O N H

Bal. 6.29 4.17 0.19 0.19 0.013 0.0041

Uniaxial Tensile Properties

Alloy Composition (wt%)

bimodal (STOA) structure 64% primary grain size ~ 20 m lath spacing ~ 1-2 m

-annealed lamellar structureprior- grain size ~ 1 mm colony size ~ 500 m, lath spacing ~ 1-2 m

A

B

Small Fatigue CracksSmall Fatigue Cracks

Ritchie and Lankford, Mater. Sci. Eng. A, 1986

Small cracks

Short cracks from notches

Large cracks

Mode I large crack threshold

Cracks that can be considered “small”:

Large, Short and Small Fatigue CracksLarge, Short and Small Fatigue Cracks

Ritchie and Lankford, Mater. Sci. Eng., 1986

• Large in all dimensions

• Small in one dimension

• Reduced crack-tip shielding

• Small in all dimensions

• Reduced crack-tip shielding

• Biased microstructural sampling

Asymmetric Four-Point Bend SpecimenAsymmetric Four-Point Bend Specimen

• The offset s, from the load-line is used to control the degree of mode-mixity, KII /KI, and hence the phase angle, = tan-1 (KII /KI)

• Range of mixities studied: KII/KI from 0 to 7.1; from 0 to 82

• Linear-elastic stress-intensity solutions from He and Hutchinson, J. Appl. Mech., 2000:

KI =

w

aFa

w

MI

26

KII =

w

aF

wa

wa

w

QII2/1

2/3

)/1(

)/(

w

M M

Large Crack ThresholdsLarge Crack Thresholds

0 1 2 3 4 5 6 7 8M O D E I STR ESS-INTEN SITY R ANG E AT TH RESH O LD

K I,TH (M Pam )

0

2

4

6

8

10

12

MO

DE

II S

TR

ES

S-I

NT

EN

SIT

Y R

AN

GE

AT

TH

RE

SH

OLD

KII

,TH (

MP

am

)

0

2

4

6

8

10

KII,

TH (

ksi i

n)

0 1 2 3 4 5 6 7K I,TH (ksiin)

Bimodal Ti-6Al-4V25oC, Air

Growth

No Growth

=26o

=62o

=82o

R=0.1R=0.5R=0.8

Lamellar Ti-6Al-4V25oC, Air

0 1 2 3 4 5 6 7 8M O D E I STR ESS-INTEN SITY R ANG E AT TH RESH O LD

K I,TH (M Pam )

0

2

4

6

8

10

12

MO

DE

II S

TR

ES

S-I

NT

EN

SIT

Y R

AN

GE

AT

TH

RE

SH

OLD

KII,

TH (

MP

am

)

0 1 2 3 4 5 6 7K I,TH (ksiin )

0

2

4

6

8

10

KII,

TH (

ksi i

n)

Growth

No Growth

=26o

=62o

=82o

R=0.1R=0.5R=0.8

• Lamellar microstructure shows superior resistance, especially at low phase angles

• Load ratio, R, and mode mixity, can reduce KI significantly for both microstructures

Nalla, Campbell & Ritchie, Fat. Fract. Eng. Mater. Struct., 2002

Single Parameter CharacterizationSingle Parameter Characterization

• Lamellar microstructure shows superior resistance, especially at low phase angles

• ThresholdGTH measured in pure mode I can be considered as “worst-case”

Nalla, Campbell & Ritchie, Fat. Fract. Eng. Mater. Struct., 2002

G = (KI2 + KII

2)/E′

0 10 20 30 40 50 60 70 80 90PH ASE AN G LE, (o )

0

200

400

600

800

1000

TH

RE

SH

OLD

ST

RA

IN E

NE

RG

Y R

ELE

AS

E

RA

TE

RA

NG

E,

GT

H (

J/m

2 )

M ode I M ode II

R=0.1

R=0.5

R=0.8

8

9

10

0

3

5

6

7

11

TH

RE

SH

OLD

EQ

UIV

ALE

NT

ST

RE

SS

-IN

TE

NS

ITY

R

AN

GE

, K

eq,T

H (

MP

am

)

Lamellar Ti-6Al-4V25oC, Air

0 10 20 30 40 50 60 70 80 90PHASE ANG LE, (o )

0

200

400

600

800

1000

TH

RE

SH

OLD

ST

RA

IN E

NE

RG

Y R

ELE

AS

E

RA

TE

RA

NG

E,

GT

H (

J/m

2 )

M ode I M ode II

R=0.1

R=0.5

R=0.85

6

8

9

10

0

3

7

11

TH

RE

SH

OLD

EQ

UIV

ALE

NT

ST

RE

SS

-IN

TE

NS

ITY

R

AN

GE

, K

eq,T

H (

MP

am

)90

Bimodal Ti-6Al-4V25oC, Air

Large Fatigue Crack ProfilesLarge Fatigue Crack Profiles

Campbell & Ritchie, Metall. Mater. Trans. A, 2001

• Observed crack paths follow a path of maximum tangential stress (MTS), i.e., one of KII = 0, for the bimodal microstructure

• For the coarser-grained lamellar microstructure, significant deviations were observed from MTS predictions – the role of microstructure becomes critical, especially in the precrack wake

Mode I applied = 26°

exp

~39°

(a)

400 m

MTS =60.8°

Mode I applied = 62°

exp

~ 37°

(b)

200 m

a

Mode I applied = 26o

MTS = 39.7o

exp ~ 39o

Mode I applied = 62o

MTS = 60.8o

exp ~ 37o

Correction for Crack-tip ShieldingCorrection for Crack-tip Shielding

Campbell & Ritchie, Eng. Fract. Mech., 2000

• Mode I shielding, in the form of crack closure, determined from the compliance curve for the opening displacements from the first deviation from linearity on unloading: KI,eff = KI,max – Kcl

• Mode II shielding, in the form of asperity rubbing and interlock, determined in an analogous fashion from the compliance curve for shear displacements: KII,eff

= KII,maxtip - KII,min

tip

Shielding Corrected ThresholdsShielding Corrected Thresholds

Nalla, M.S. Thesis, U.C. Berkeley, 2001

Lamellar Ti-6Al-4V25oC, Air R=0.1

R=0.5

R=0.8

Shielding-CorrectedLarge Crack data

R=0.1

R=0.5

R=0.8

(b) 0 10 20 30 40 50 60 70 80 90PH ASE AN G LE, (o )

0

200

400

600

800

1000

TH

RE

SH

OLD

ST

RA

IN E

NE

RG

Y R

ELE

AS

E

RA

TE

RA

NG

E,

GT

H (

J/m

2 )

M ode I M ode II

0

3

5

6

7

8

9

10

11

TH

RE

SH

OLD

EQ

UIV

ALE

NT

ST

RE

SS

-IN

TE

NS

ITY

R

AN

GE

, K

eq,T

H (

MP

am

)

Bimodal Ti-6Al-4V25oC, Air

R=0.1

R=0.5

R=0.8

R=0.1

R=0.5

R=0.8

Shielding-CorrectedLarge Crack data

0 10 20 30 40 50 60 70 80 90PH ASE AN G LE, (o )

0

200

400

600

800

1000

TH

RE

SH

OLD

ST

RA

IN E

NE

RG

Y R

ELE

AS

E

RA

TE

RA

NG

E,

GT

H (

J/m

2 )

M ode I M ode II

8

0

3

5

6

7

9

10

11

TH

RE

SH

OLD

EQ

UIV

ALE

NT

ST

RE

SS

-IN

TE

NS

ITY

R

AN

GE

, K

eq,T

H (

MP

am

)

• Effects of mode-mixity, load ratio and microstructure markedly reduced after taking account of crack-tip shielding from mode I closure and mode II crack-surface interference

Short-Crack ThresholdsShort-Crack Thresholds

0 10 20 30 40 50 60 70 80 90PH ASE AN G LE, (o )

0

200

400

600

800

1000

TH

RE

SH

OLD

ST

RA

IN E

NE

RG

Y R

ELE

AS

ER

AT

E R

AN

GE

, G

TH (

J/m

2 )

M O D E I M O D E II

Bimodal Ti-6Al-4V25oC, Air

R=0.1

R=0.5

R=0.8

R=0.1

R=0.5

R=0.8Shielding-Corrected Large Crack Scatter band

Small Crack

Short Crack

8

0

3

5

6

7

9

10

11

TH

RE

SH

OLD

EQ

UIV

ALE

NT

ST

RE

SS

-IN

TE

NS

ITY

R

AN

GE

, K

eq,T

H (

MP

am

)0 10 20 30 40 50 60 70 80 90

PH ASE AN G LE, (o )

0

200

400

600

800

1000

TH

RE

SH

OLD

ST

RA

IN E

NE

RG

Y R

ELE

AS

ER

AT

E R

AN

GE

, G

TH (

J/m

2 )

M O D E I M O D E II

Lamellar Ti-6Al-4V25oC, Air

R=0.1

R=0.5

R=0.8

Shielding-Corrected Large Crack Scatter band

R=0.1

R=0.5

R=0.8

Short Crack0

3

5

6

7

8

9

10

11

TH

RE

SH

OLD

EQ

UIV

ALE

NT

ST

RE

SS

-IN

TE

NS

ITY

R

AN

GE

, K

eq,T

H (

MP

am

)

Nalla, Campbell & Ritchie, Fat. Fract. Eng. Mater. Struct., 2002

• The role of crack-tip shielding is evident from the substantially lower thresholds

• The technique for estimating the mixed-mode shielding by Campbell et al gives reasonable, though slightly overestimated, values for the thresholds

Definition of the Mixed-Mode ThresholdDefinition of the Mixed-Mode Threshold

• G calculation based on precrack

where

k1 = aII() KI + aI2() KII k2 = a2I() KI + a22() KII

b << aa

KII

KI

b

k2

k1

G = (KI2 + KII

2)/E′

Geff = (kI2 + kII

2)/E′

• G calculation based on infinitesimal kink

direction of subsequent propagation

where

k1 = KI k2 = KII

a

KII

KI

k2

k1

Nalla, Campbell & Ritchie, Int. J. Fatigue, 2002

Mode I applied = 26°

exp

~39°

(a)

400 m

MTS =60.8°

Mode I applied = 62°

exp

~ 37°

(b)

200 m

a

Nalla, Campbell & Ritchie, Int. J. Fatigue, 2002

Definition of the Mixed-Mode ThresholdDefinition of the Mixed-Mode Threshold

• In general, the trend is to reduce the computed values of Keq,TH somewhat, except at very high phase angles

• At = 26o, however, the large crack Keq,TH threshold is reduced by as much as 40%; this translates into a reduction in threshold Keq,TH values by between 1 and 2 MPam

• Effects are far less significant for short cracks

Bimodal Ti-6Al-4V25oC, Air

R = 0.1

R = 0.5

R = 0.8

Large Crack Data

0

200

400

600

800

1000

1200

Bimodal Ti-6Al-4V25oC, Air

Short Crack Data

R = 0.1

R = 0.5

R = 0.8

Large Crack DataR = 0.8

TH

RE

SH

OL

D E

QU

IVA

LE

NT

ST

RE

SS

-IN

TE

NS

ITY

RA

NG

E,

Ke

q,T

H (

MP

am

)

0 10 20 30 40 50 60 70 80 90

PHASE ANGLE, (o)

0

200

400

600

800

1000

1200

Mode I Mode II

8

0

3

5

6

7

9

10

11

0

12

8

0

3

5

6

7

9

10

11

0

12

PHASE ANGLE, (o)

TH

RE

SH

OL

D S

TR

AIN

EN

ER

GY

RE

LE

AS

E R

AT

E,

GT

H (

J/m

2 )

Small Crack Thresholds in Mode ISmall Crack Thresholds in Mode I

Nalla et al, Metall. Mater. Trans. A, 2002

• Optical micrograph showing a typical initiation site for the bimodal microstructure - Initiation predominantly occurs in the primary- grains.

• SEM image of crack initiation and early growth along planar slip bands leading to facet type fracture surface - EBSD analysis of fractured -grains 1 to 3 revealed near-basal orientation of the fracture plane.

10-11

10-10

10-9

10-8

10-7

10-6

10-5

Ti-6Al-4VAir, RT

Cra

ckG

row

thR

ate,

(m/c

ycle

)d

da/

N

Stress Intensity Range, (MPa m )K 1/2

5 10 20 50 100 200 500 1000 (450.0 MPa)

Surface Crack Length ( m)2c

20 50 100 200 500 1000 2000 (202.5 MPa)

Z

0.6 1 2 4 6 8 10 20 40

Bi-m Lam300 m/s250 m/s200 m/s

Large Cracks C(T)

Bi-modalLamellar

R = 0.1

FOD Cracks, = 0.1R = 202.5 - 450 MPa

1/2

R = 0.91 - 0.95Constant-K =max36.5 MPa m

(a)

BimodalLamellar

Bim. Lam.

25oC, Air

10 m

(Courtesy: Dr. J.O. Peters)

123

11

12

22

Mixed-Mode Small-Crack TestingMixed-Mode Small-Crack Testing

wide bend bar specimen

Nalla, Campbell & Ritchie, Fatigue Fract. Eng. Mater. Struct., 2002

small “inclined-crack” specimen

KI – Newman & Raju, Eng. Fract. Mech., 1981

KII – He & Hutchinson,

Eng. Fract. Mech., 2000

• the tensile loading component, 22 induces the mode I contribution

• the shear loading component, 12 induces the mode II and mode III components

• the in-plane component, 11 makes no contribution.

KI = (t + Hb) Q

a F

,,,b

c

c

a

t

a

KII = 12 a

Inclined Semi-Elliptical Surface CrackInclined Semi-Elliptical Surface Crack

Nalla, Campbell & Ritchie, Fatigue Fract. Eng. Mater. Struct., 2002

• A typical crack path taken by a microstructurally-small crack under mixed-mode loading (R = 0.1, ~ 28o, G ~ 20 J/m2, angle of inclination ~ 50o)

• Strong influence of local microstructure near the crack tip is evident on the crack path

initial precrack

subsequent crack growth

5 m

~ 50o

Mixed-Mode Small-Crack ThresholdsMixed-Mode Small-Crack Thresholds

Nalla, Campbell & Ritchie, Fatigue Fract. Eng. Mater. Struct., 2002

0 10 20 30 40 50 60 70 80 90PH ASE AN G LE, (o )

0

50

100

150

200

250

300

350

TH

RE

SH

OLD

ST

RA

IN E

NE

RG

Y R

ELE

AS

ER

AT

E R

AN

GE

, G

TH (

J/m

2 )

M O D E I M O D E II

Bimodal Ti-6Al-4V25oC, Air

Shielding-Corrected Large Crack Scatter band

Large CrackR=0.8

ShortCrack

Small Crack 2

0

3

4

5

6

TH

RE

SH

OLD

EQ

UIV

ALE

NT

ST

RE

SS

-IN

TE

NS

ITY

R

AN

GE

, K

eq,T

H (

MP

am

)

• Thresholds for small cracks (<50 m) are significantly lower than for large (>4 mm) and short (~200 m) cracks, especially under shear-dominant loading

• Large reductions in KEQ,TH (up to ~7 times) and GTH (up to ~50 times) with respect to large cracks seen for microstructurally-small cracks

ConclusionsConclusions

• Marked effect of mode-mixity and load ratio on mixed-mode fatigue

thresholds for large (> 4 mm) through-thickness cracks

• Thresholds GTH values measured in pure Mode I represent a “worst-case”

condition

• Lamellar structure generally exhibited higher large-crack thresholds

• Thresholds for short (~200 m) through-thickness cracks were considerably lower and were relatively insensitive to load ratio, mode-mixity and microstructure. This was attributed to a reduced role of crack-tip shielding

• Thresholds for microstructurally-small (< 50 m) surface cracks in the

bimodal microstructure were similarly insensitive to load ratio and mode-

mixity, and were substantially lower than those for large cracks. This was

related to limited crack-tip shielding and biased microstructural sampling

associated with the small cracks.