Fatigue life prediction of small notched TI-6AL-4V based...

IHI000001-003 Copyright © 2009 IHI Corporation All Rights Reserved.

Fatigue life prediction of small notched TI-6AL-4V based on the theory of critical distance

25th ICAF Symposium – Rotterdam, 27-29 May 2009

Yoichi Yamashita, Masakazu Shinozaki, Hiroshi Kuroki and Yusuke Ueda

( IHI Corporation

), Japan

1IHI000001-003 Copyright © 2009 IHI Corporation All Rights Reserved. 25th ICAF Symposium

Contents

1 Background and objective2 Experiment 3 Application of

conventional theory of critical distance (TCD)4 SEM observation5 Appropriate method

for determination of critical distance stress6 Minimum fatigue strength of small notched Ti-647 Discussion of residual stress effects on FOD-HCF8 Conclusions

Ref: Nicholas(2004), 10th National Turbine Engine HCF Conference New Orleans


Background• FOD may result in “nick”, “dent” and “scratch” at the leading edges of airfoils which in turn, reduce the fatigue strength of the material.

• FOD-induced HCF is one of the significant themes in fatigue problems of aero-engine component.

• Small notch effects on fatigue strength should be taken into account.

Scratch

Nick Dent


Objective•To investigate the method for fatigue life prediction of small notched Ti-64 specimens using the theory of the critical distance (TCD)

•To construct the appropriate method to evaluate fatigue life of Ti-64 with various notch radii and notch depths from the relationships between the critical distance stress and fatigue crack initiation life

fan balde small FOD damageFOD damage at leading edge of airfoil


Experiment

C V Al Ti N Fe O H0.002 4.16 6.3 bal. 0.004 0.16 0.2 0.0053

σY0 σuts εf ψ E(MPa) (MPa) (%) (%) (GPa)935 1006 18.4 44.5 110

Chemical composition of Ti-64 (mass %).

Mechanical properties of Ti-64.

Bimodal microstructure of Ti-64 (STOA)

R60

10

Φ15

Φ7.

5

Small notch

110

R60

10

Φ15

Φ7.

5

Small notch

110

d

45°

ρ d

45°

ρ

Circumferential notch


Experiment

Notch depth, d (mm) Notch root radius, ρ (mm) Note0 ∞ Smooth specimen

0.1 0.05 Notch specimen0.3 0.05 Notch specimen0.5 0.05 Notch specimen0.3 0.2 Notch specimen

Fatigue test conditions (0-tension, R=0).

d

45°

ρ d

45°

ρ

101 102 103 104 105 106 107 1080

200

400

600

800

1000

1200

R = 0

RunoutTi- 6Al- 4V, R.T.Round bar tensile fatigue specimen

d=0.3, ρ=0.2

d=0.5, ρ=0.05

d=0.3, ρ=0.05

d=0.1, ρ=0.05

Smooth

Str

ess

ran

ge, Δ

σ (M

Pa)

Number of cycles to failure, Nf (cycles)

R60

10

Φ15

Φ7.

5

Small notch

110

R60

10

Φ15

Φ7.

5

Small notch

110

Δσ Δσ


Maximum peak stress approach

ρx

y

oF

dσyy

σpeak,max

ρx

y

oF

dσyy

σpeak,max

Fatigue life prediction based on maximum peak stress approach givesinaccurate results for the notch fatigue life of various notch root radii.

101 102 103 104 105 106 1070

500

1000

1500

2000

2500

3000

3500

ρ=0.2mm

ρ=0.05mm

d=0.1, ρ=0.05 d=0.3, ρ=0.05 d=0.5, ρ=0.05 d=0.3, ρ=0.2

Ti- 6Al- 4V, R.T., R=0

Max

imum

peak

str

ess

, σ

peak

,max

(M

Pa)



Stress distributions inward from notch root

Comparison at the same life of Nf=1.0×105 cycles

Maximum peak stress at notch root and the stress gradient have to be taken into account in fatigue life prediction for small notched specimens.

0

500

1000

1500

2000

2500

0 0.02 0.04 0.06 0.08 0.1

Distance from notch root, x (mm)

Axi

al s

tress

, σ

yy(x

) (M

Pa)

d=0.1mm, ρ=0.05mmd=0.3mm, ρ=0.05mmd=0.5mm, ρ=0.05mm

Stress distribution at maximum loading

of Nf=105 cycles Ti- 6Al- 4V, R.T.

d=0.3mm, ρ=0.2mm

ρx

y

oF

dσyy

σpeak,max

ρx

y

oF

dσyy

σpeak,max


Application of conventional TCD

Line method

Conventional TCD was proposed by :

Neuber: (1958) [4], Peterson: (1959) [5]

Tanaka: Int. J. of Fract. (1983) [13]

Taylor: Eng. Fract. Mech. (2008) [6-8]

mm032.02LM == LL

20

th )(1σΔ

Δπ

KL =

MPa5380 =σΔmMPa86.3th =KΔ

NASA / NASGLO

The most simple approach conventionally determines the distance inward from the notch root to the location at which the average stress range of the notched specimen is equal to the stress range of smooth specimens at the same fatigue life.

Notch

Linear-Elastic Stress Distribution

⊿σ0

⊿σyy

LLM

00

yyLM

LM)(1 σΔσΔ =∫

Ldxx

L

xLine method


Application of conventional TCD

Line method

LLM =2L of the line method of determination of the critical distances are much smaller than the critical distances as the distance inward from the notch root to the location at which the stress range required for a fatigue failure life is equal to the stress range required for the same fatigue failure life for smooth specimens.

The critical distances for ρ=0.2mm are larger than those for ρ=0.05mm.

Notch

Linear-Elastic StressDistribution

⊿σ0

⊿σyy

LLM

00

yyLM

LM)(1 σΔσΔ =∫

Ldxx

L

x

104 105 106 1070.0

0.1

0.2

0.3

0.4

2L=0.032mm

d=0.3mm, ρ=0.2mm

d=0.1, ρ=0.05 d=0.3, ρ=0.05 d=0.5, ρ=0.05

Ti- 6Al- 4V, R.T., R = 0Small notched specimen

Critical

dis

tance, L

LM (m

m)


The conventional TCD approach may not give an appropriate unified value, when the notch tip radius of the notched specimens is different from each other.


Fatigue crack initiation site→quasi-cleavage, crystallographic facets at origin, no inclusionThe facets : α phase (A. Nozue [17], H. Oguma [18], O. Jin [19]),

approximately semi-circle, equal to average αphase size

SEM observation

Smooth specimen of Nf=5.67×104


SEM observation

Smooth specimen of Nf=3.86×104

The determination procedure of the critical distance calculatedfrom ⊿K equation of semi-circle crack is appropriate for the forged Ti-64.


103 104 105 106 107 1080

200

400

600

800

1000

1200

Smooth specimenR = 0

RunoutTi- 6Al- 4V, R.T.Round bar tensile fatigue specimen

Str

ess

ran

ge, Δ

σ (M

Pa)


Smooth specimen sub-crack

The volume effects of fatigue fracture process zone extend throughout the gauge length of 10mm.

Difference in volume effects between the notched and smooth specimenThis is the evidence that the approach in determination of the critical

distance, as the distance inward from the notch root to the location at which the stress range is equal to the stress range of smooth specimens, does not give an appropriate unified value.


Appropriate critical distance stress

ρx

y

oF

dσyy

ρx

y

oF

dσyy

aK πσΔΔ =∵

aK πσΔπΔ ⋅⋅= )/2(1.1215∵

200 )/th()/1( σΔΔπ Ka ⋅=

Critical distance stress : Average stress in fatigue fracture process zone

y

a0 a0

σyy

R0

x

y

a0 a0

σyy

R0

x

∫ ⋅−⋅∫ ⋅−⋅⋅=00

00

00yyCD )(2)(2)(

aadxxRdxxRx ππσσ

Method (1) : K eq. of through crack in infinite plate (0.016mm)

Method (2) : K eq. of semi-circle surface crack (0.032mm)200 ))21215.1/(th()/1( σΔΔππ ××⋅⋅= Ka

Notch


⊿σCD

⊿σyy

a0

CD0

yy0

0

)(1 σσ Δ=Δ∫a

dxxa

xNotch


⊿σCD

⊿σyy

a0

CD0

yy0

0

)(1 σσ Δ=Δ∫a

dxxa

x


103 104 105 106 1070

500

1000

1500

2000

2500

3000

Ti- 6Al- 4V, R.T., R=0Round bar tensile fatigue specimen

C

ritical

dis

tance s

tress

, σ

CD (M

Pa)

Crack initiation life, Ni (cycles)

103 104 105 106 1070

500

1000

1500

2000

2500

3000


Critical

dis

tance s

tress

, σ

CD (M

Pa)



Method (1) a0 = 0.016 mm

Method (2) a0 = 0.032 mm

(3) a0 = 0.064mm = 0.032×2 mm

Best correlationfor all fatigue test data

20 ))21215.1/(th()/1(0 σΔΔππ ××⋅⋅= Ka

200 )/th()/1( σΔΔπ Ka ⋅=

◆d=0.1mm, ρ=0.05mm

■d=0.3mm, ρ=0.05mm

▲d=0.5mm, ρ=0.05mm

●d=0.5mm, ρ=0.2mmd

45°

ρ d

45°

ρ

103 104 105 106 1070

500

1000

1500

2000

2500

3000


Critical

dis

tance s

tress

, σ

CD (M

Pa)



103 104 105 106 1070

500

1000

1500

2000

2500

3000


C

ritical

dis

tance s

tress

, σ

CD (M

Pa)



20 ))21215.1/(th()/1(0 σΔΔππ ××⋅⋅= Ka

◆d=0.1mm, ρ=0.05mm

■d=0.3mm, ρ=0.05mm

▲d=0.5mm, ρ=0.05mm

●d=0.5mm, ρ=0.2mm

d

45°

ρ d

45°

ρ

There exists the good correlation between critical distance stress and crack initiation life of small notched specimen if the critical distance, a0, is determined with 107 cycle ⊿σ0, and ⊿Kth using the K equation of semi-circle surface crack.


Min. fatigue strength : Effects of small notch root radius

Minimum notch fatigue strength existsfor each notch depth of d=0.1, 0.3 and 0.5mm.

Very small notch root radius of ρ=0.001-0.01mm gives the constant critical distance stress at the same fatigue initiation life.

0

100

200

300

400

500

600

0.001 0.01 0.1 1Notch root radius, ρ (mm)

Critica

l di

stan

ce s

tress

, σ

CD

(MPa)

Ti- 6Al- 4V, R.T.

Nominal stress in notch section,σn = 100 MPa

d=0.5mm

d=0.3mm

d=0.1mm


Min. fatigue strength of small notched Ti-64

■

: minimum fatigue

reduction

curve(ρ=0.001mm) can be determined

by

the appropriate critical

distance

stress

Δσw

: 107 notch fatigue strength

Δσ0

: 107 smooth specimen fatigue strength

The design engineer can determine the minimum fatigue strength of the airfoils with nicks, dents and scratches in fatigue strength design of the airfoils.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6

Notch depth, d (mm)

Non-

dim

ens

iona

l　fa

tigu

e st

reng

th,

Δσ

w/Δ

σ0

Ti- 6Al- 4V, R.T.

ρ=0.05mm

Minimum notch fatigue strength (ρ=0.001mm)


Example residual stress simulation due to FOD

Example of FOD simulationRef. The Research and Technology Organisation (RTO) of NATO, RTO technical report, TR- AVT-094 (2007) 78-84.


Discussion : Residual stress effects on FOD induced HCF

Residual stress effects may be needed to take into account to evaluatethe FOD-induced HCF.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6

Notch depth, d (mm)

Non-d

imen

sional

fat

igue

stre

ngt

h, Δ

σw/Δ

σ0

ρ=0.05mm

minimum notch fatigue strength (ρ=0.001mm)

Effects of residual stressintroduced by FOD ?

?


Conclusions

There exists the good correlation between critical distance stress and crack initiation life when the critical distance, a0, was determined with plain fatigue limit, ⊿σ0, and ⊿Kthusing the K equation of semi-circle surface crack.

The critical distance approach is powerful engineering tool to determine the small notched minimum fatigue strength under a required fatigue life in design if it is appropriately applied.

Small notched fatigue strength

based on the appropriate TCD for Ti-64


Thank Youfor Attention.

25th ICAF Symposium – Rotterdam, 27-29 May 2009

ACKNOWLEDGEMENTS

This study is conducted under the contract with New Energy and Industrial Technology Development Organization (NEDO) as a part of "aircraft and space industry innovation program" and "energy innovation program" of Ministry of Economy, Trade and Industry (METI).

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