2014 ASTM JoDean Morrow Lecture on Fatigue of … JoDean Morrow Presentation... · New Orleans, LA 11 November 2014 ... John Porter Herb Stumph Pete Phillips ... Multi-Scale Structural

1Approved for public release: Case No. 88-ABW-2013-0906

Integrity Service Excellence

Reducing Uncertainty: Reflections on Establishing

Life Limits

2014 ASTM JoDean Morrow Lecture on Fatigue of Materials

New Orleans, LA11 November 2014

J.M. Larsen1, S.K. Jha2, M.J. Caton1,R. John1, A.H. Rosenberger1, D.J. Buchanan3,C.J. Szczepanski5, W.J. Porter3, A.L. Hutson3,

P.J. Golden1, J.R. Jira1, S. Mazdiyasni1, V. Sinha4

Air Force Research LaboratoryWright-Patterson Air Force Base, OH 45433

1AFRL/RXC, 2Universal Technology Corporation3University of Dayton Research Institute, 4UES, Inc.., 5Special Metals Corp.

Approved for public release: Case No. 88ABW-2015-0198

2

In-house and Collaborative Team

GovernmentMike CatonLt. Chris FettyPat GoldenLt. Sigfried HerringJay JiraReji JohnJim LarsenSiamack MazdiyasniRyan MorrisseyAndy RosenbergerMike ShepardChris Szczepanski Lt. Steve Visalli

On-site Contractor (UDRI)Bob BrockmanMarc HuelsmanDennis BuchananDavid JohnsonKezhong LiJohn PorterHerb StumphPete Phillips

On-site Contractor (GDIT)Mike Dent

Universal Technology Corp. (UTC)Sushant Jha

Universal Energy Systems (UES)Vikas Sinha

University of Texas at San AntonioHarry Millwater

University of MichiganWayne JonesTresa PollockChrist Torbet

Ohio State UniversityAlison PolasikHamish FraserMike MillsJim Williams

Statistical Engineering Inc.Chuck Annis, Jr., P.E.

Independent ConsultantTom Cruse


3

Life management of high performance turbine engines– Today and tomorrow

Fatigue variability and uncertainty– Examples

• Ti-6Al-2Sn-4Zr-6Mo ()• IN100

Future opportunities– Life management & design– Verification & validation– Optimize Performance, Safety, Reliability,

Maintainability, Affordability, Utilization

Acknowledgements:AFRL/RX & AFRL/HQAFOSR -- Multi-Scale Structural Mechanics and Prognosis (Dr. David Stargel)AFOSR -- Structural Mechanics (Dr. Victor Giurgiutiu)DARPA/DSO – Engine System Prognosis (Dr. Leo Christodoulou)

Outline

Alloys explored:Ti-10V-2Fe-3Al

Ti-6Al-2Sn-4Zr-6Mo ()Ti-6Al-2Sn-4Zr-6Mo (L-)Ti-6Al-2Sn-4Zr-2Mo ()

Ti-6Al-4VGamma TiAl

Waspaloy (Wrought)IN100 (P/M: fine grain)

IN100 (P/M: coarse grain)René-88 DT (P/M)IN718 (Wrought)

Ni Single Crystal 1484Al 7075-T651

Al-Cu-Mg-Ag alloy


4







Outline



Ti-6Al-4VGamma TiAl




Al-Cu-Mg-Ag alloy


5For Official Use Only (FOUO)

Design Certification Methodology to Assure Integrity Throughout the Life Cycle

Propulsion System Integrity Program (PSIP) - MIL-STD-3024

“Safe Life” has been standard practice for engine rotors

for over 50 years. ……………………..

Used to compensate foruncertainty/lack of knowledge

log Life (e.g. Cycles or TACs)

Usa

ge (e

.g. S

tres

s)

TypicalMean

Max Safe Life

• Design and certify all components are within this “safe” zone.• All components are “not safe” if one in 1000 is predicted to initiate a crack

Untapped Performance


6

Traditional Life Prediction Process

Stress-life (S-N) Fatigue Tests –All conditions

Condition n

Fit S-N data with Multi-Condition Regression

Actual/Predicted Lifetime (A/P) B.1 B50

50%

99.9%

0.1%

B50/B.1 = Scatter Factor(material + condition + model)

Component Scale-upFleet Scale-up B0.1 Lifetime

B0.1

• Data-Driven

• Distribution w.r.t. mean behavior

• Potentially untapped performance

• Needs generation of new database for new material or microstructure

• Difficult to incorporate effects of residual stress, mission, microstructure, etc.

Condition 1

Condition 2



Low-Cycle-Fatigue Design Criteria (safe life)

• Based on statistical lower bound• 1 in 1000 components predicted to

initiate a 0.8 mm crack

Damage-Tolerant Design Criteria(fracture mechanics)

• Deterministic• 1 or 2 safety inspections during

service life

Both design criteria are met at all critical locations on a component

log Life (e.g. Cycles or TACs)

Usa

ge (e

.g. S

tres

s)

TypicalMean

Lower Bound

Cycles (or Equivalent)

Cra

ck L

engt

hai

aC

a*

Propulsion System Integrity ProgramLife-Cycle Design Philosophy (PSIP; MIL-STD-3024)


Move Engine Lifing fromSafe-Life Approach to Retirement For Cause

8

0 10000 20000 30000 40000 50000 60000 70000

Num

ber o

f Par

ts

Life (Time or Cycles)

LCF Initiation Distribution

-3

Retire all componentswhen 1 in 1000 ispredicted to fail

B0.1 = 4000 TAC

Traditional “Safe-Life” Retirement ApproachManage to -3 Lower Bound

Before 1980s RFC program

0 10000 20000 30000 40000 50000 60000 70000

Num

ber o

f Par

ts



-3


B0.1 = 8000 TAC


After 1980s RFC program

0 10000 20000 30000 40000 50000 60000 70000

Num

ber o

f Par

ts



-3


B0.1 = 12000 TAC


After ERLE program

020

0040

0060

0080

0010

000

1200

014

000

1600

018

000

2000

022

000

2400

026

000

2800

030

000

3200

034

000

3600

038

000

4000

042

000

4400

046

000

4800

050

000

5200

054

000

5600

058

000

6000

062

000

6400

066

000

6800

070

000


Economic/Risk Limit = Definition of Retirement for Cause

Penetrate the LCF DistributionApproved for public release: Case No. 88ABW-2015-0198

9

Yes Service

NO Retire

Usage (D

uty Cycles)

Failure Occurrences“Book Life” Today

Prognosis will Enable Transformationin Asset Management

Database:Mission History,

Maintenance, Life Extension, and Design

Prognosis

Failure physics, damage evolution,predictive models

Stat

e Aw

aren

ess

Interrogation

Prognosis Translates Knowledge and Information Richness to Physical Capability

Reduce andManage

Uncertainty

“Book Life” Today

“Book Life”Tomorrow

Dr. Leo Christodoulou



Background•Current design and life management of turbine engine materials– Extensive fatigue testing required to produce large databases– Statistically-based life limits by extrapolation from the mean behavior

•Next-generation design and life management– Design Target Risk:

• DoD: < 5*10-8 failures/engine flight hour• FAA: < 1*10-9 failures/flight

– Safety, reliability, affordability– Reduced life-cycle cost– Reduction in uncertainty in materials life-cycle prediction– Reduce requirements for materials testing

•Overarching science and technology initiatives– DoD Engineered Resilient Systems– Materials Genome Initiative (MGI)– Integrated Computational Materials Engineering (ICME)– Big Data


11

Large degree ofuncertainty associatedwith life prediction

Failu

re O

ccur

renc

e

Usage (Duty cycles)

POF = 0.1%life limit(Book life)

Failu

re O

ccur

renc

e

Duty cycles

POF = 0.1%life limit

Life-limit based on the uncertaintyin the worst-case mechanism

Crack growthrelated peak(life-limitingmechanism)

Mean-lifetimedominating peak

Total variability

Traditional (Empirical) DescriptionFatigue variability described as deviation from the expected mean-behavior

Physics-Based Description of Fatigue VariabilityFatigue variability described as separation of the mean and the life-limiting behavior

Mean behavior

Variability described w.r.t. the overall mean behavior

Nf (Cycles)

max

Overall mean behavior

Distribution in the life-limiting mechanism(crack-growth controlled)

max

Nf (Cycles)

Variability in the mean-dominating response

Opportunity: Physics-Based Descriptionof Fatigue Variability



N. E. Frost, K. J. Marsh, and L. P. Pook"Metal fatigue, 1974." Oxford University Press, Oxford.


13For Official Use Only (FOUO)

Life-limiting Fatigue

Small-Crack GrowthCrack Initiation

Long-Crack Growth

Ni

? ? ?NP,small NP,long NTotal

Total Fatigue Life = NTotal

Ni NP,small NP,long

NTotal

Low-Cycle-Fatigue Life Limits: A New UnderstandingLife-limiting low-cycle-fatigue life is governed by the growth of a dominant crack from an initial crack size defined by the microstructural features & mechanisms that control crack formation.

0?


14







Outline



Ti-6Al-4VGamma TiAl




Al-Cu-Mg-Ag alloy



Ti-6Al-2Sn-4Zr-6Mo (Ti-6-2-4-6)



Lifetime DistributionTi-6-2-4-6, RT, R = 0.05, = 20 Hz and 20 kHz



100 103 104 105 106 107 108 109.01

.1

1

51020305070809095

99

99.9

99.99

All data points

Lifetime, Nf (Cycles)

Pro

babi

lity

of fa

ilure

(%

)

95% confidence intervals

max

= 820 MPa

Confidence Boundson B0.1 Lifetime -- All Data

721 cycles



100 103 104 105 106 107 108 109

.1

1

51020305070809095

99

99.9

DataBimodal fitLower boundUpper bound

Nf (Cycles)

Pro

babi

lity

of fa

ilure

(%

)

max

= 820 MPa

Bimodal Model

)()1()()( NfpNfpNf mlllt

4565 cycles



100 103 104 105 106 107 108 109.01

.1

1

51020305070809095

99

99.9

99.99

Life-limiting distribution


Prob

abilit

y of

failu

re (

%)


max

= 820 MPa

Confidence Bounds on B0.1 LifetimeLimiting Condition of pl → 1

5660 cycles

1)()1()()(

l

mlllt

pNfpNfpNf



Lifetime DistributionTi-6-2-4-6, RT, R = 0.05, = 20 Hz and 20 kHz



CDF SpaceEffect of Stress Level on Mean vs. Life-Limiting Behavior

104 105 106 107 108 109 10101

5102030

50

70809095

99

1040 MPa925 MPa900 MPa860 MPa820 MPa700 MPa650 MPa600 MPa550 MPa

Cycles to Failure

Prob

abili

ty o

f Occ

uren

ce (%

)

Life-limiting behavior

Mean-dominating behavior



Bimodal Fatigue BehaviorTi-6Al-2Sn-4Zr-6Mo; RT



Probability of Life-Limiting Failures

ys= 1140 MPa

Stress (MPa)

Prob

abili

ty o

f Occ

urre

nce

of L

ife-

Lim

iting

Fai

lure

s

104 105 106 107 108 109 10101

5102030

50

70809095

99

1040 MPa925 MPa900 MPa860 MPa820 MPa700 MPa650 MPa600 MPa550 MPa

Cycles to Failure

Prob

abili

ty o

f Occ

uren

ce (%

)

Failu

re O

ccur

renc

e

Duty cycles

B0.1 lifetimes

Crack-growth-controlled density (Critical heterogeneity level) Mean-dominating

density (Smaller heterogeneity scales)

Empirically-derived density

Failu

re O

ccur

renc

e

Duty cycles

B0.1 lifetimes

Crack-growth-controlled density (Critical heterogeneity level) Mean-dominating

density (Smaller heterogeneity scales)

Empirically-derived density


24FOR OFFICIAL USE ONLY

Alternate Life-Prediction Approach

• The Mean and the worst‐case behavior separate with decreasing and respond differently to operatingvariables.

• Life Prediction based on variabilityin the worst‐case mechanism.

• Significant reduction in uncertaintywhen compared to the traditionalapproach.

• Improved reliability of design life.

1 in 1000Life limits

Failu

re Occurrence

Duty cycles

Variability incrack growth Variability in crack

Initiation + growth

1000 104 105 106 107.01

.1

1

51020305070809095

99

99.9

99.99All pointsType IType II

Cycles to Failure, Nf

Pro

babi

lity

of F

ailu

re (

%)

Type I

Type II

max

= 860 MPa

Reduction inuncertainty


25FOR OFFICIAL USE ONLY

Alternate Life-Prediction Approach

• The Mean and the worst‐case behavior separate with decreasing and respond differently to operatingvariables.

• Life Prediction based on variabilityin the worst‐case mechanism.

• Significant reduction in uncertaintywhen compared to the traditionalapproach.

• Improved reliability of design life.

1 in 1000Life limits

Failu

re Occurrence

Duty cycles

Variability incrack growth Variability in crack

Initiation + growth

1000 104 105 106 107.01

.1

1

51020305070809095

99

99.9

99.99All pointsType IType IISimulated, Type I


Pro

babi

lity

of F

ailu

re (

%)

Type I

Type II

max

= 860 MPa

Reduction inuncertainty



104 105 106 107.01

.1

1

51020305070809095

99

99.9

99.99

ExperimentalExperimental (Life limiting)Predicted (Life limiting)

Nf (Cycles)

Pro

babi

lity

of F

ailu

re (

%)

max

= 860 MPa

Life-limitingpopulation

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120 140 160 180

p area

Crcak nucleation area

Occ

urre

nce

frequ

ency

p area; Crack nucleation area (m2)

Crack Initiation Size

Small-Crack Growth Variability

Predicted Life-Limiting Distribution

• Prediction of limiting life of Ti-6Al-2Sn-4Zr-6Mo

• Monte Carlo simulation based on microstructural features and small-crack growth

Mechanism-Based Probabilistic Prediction of Limiting Life

)( KfdNda

f

i

a

aap Kf

daN)(

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

1 10 100

Long crack

Small cracks(

max = 860 MPa)

da/d

N (

m/c

ycle

)

K (MPa-m1/2)

Ti-6-2-4-6

max = 860 MPa

R = 0.05 = 20 HzT = 23°C

Power-law fits



100 103 104 105 106 107 108 109.01

.1

1

51020305070809095

99

99.9

99.99



Prob

abilit

y of

failu

re (

%)


max

= 820 MPa

Confidence Bounds on B0.1 LifetimeLimiting Condition of pl → 1

5660 cycles

1)()1()()(

l

mlllt

pNfpNfpNf



100 1000 104 105 106 107 108 109.01

.1

1

51020305070809095

99

99.9

99.99

Predicted life-limitingdistribution

Crack-growth- controlled failures


Prob

abilit

y of

Fai

lure

(%

)

max

= 820 MPa

Crack-Growth-Controlled Failures

B0.1 lifetime



Bimodal Fatigue BehaviorTi-6Al-2Sn-4Zr-6Mo; RT



How Can this Understanding Affect the Life-Cycle Design Philosophy?

Predicted Distribution in a vs. N820 MPa

An Integrated Design CriterionB0.1 Lifetime

Limiting DamageTolerance Curve

Cycles



Loading axis

F1

N2

F1

F1

N1N2

N1

Methods:• Quantitative tilt microscopy using MEXTM

• FIB sectioning through crack-initiation facet (in some cases)• EBSD analysis of the crack-initiation region

Basal plane trace

IPF map

Life-Limiting Failure

Specimentilt = 30°

Crack-initiationfacet

Faceted p

• max = 860 MPa; Nf = 49,893 cycles • Facet inclination = 31°



Summary of Mean vs. Life-Limiting ConfigurationsSurface-Initiated Mechanisms

25

30

35

40

45

50

104 105 106 107

Life-limiting

Mean-dominatingFace

t inc

linat

ion

w.r.

t. th

e lo

adin

g ax

is (

°)

Lifetime (Cycles)

Neighboring grains

Faceted grainsResolved along the

loading axisResolved along the

facet normalFacet inclination



soft

, p

Basal plane Inclination ≤ 30

Hypothesis: Hierarchy of Fatigue Deformation Heterogeneities

Prob

abili

ty o

f occ

urre

nce

Heterogeneity level



0.0

0.5

1.00.0

0.51.0

0

1

2

3

Prob

abili

ty o

f occ

urre

nce

Deformation parameter

Microstructure-Based Prediction of Life-Limiting Fatigue Mechanisms in Ti-6-2-4-6

Using the Hierarchy Model of Heterogeneity levels

P(Li

fe-li

miti

ng fa

ilure

)

, str, etc.MicrostructureModel

MicrostructureModel

Compute Fatigue Heterogeneity

Parameter

Compute Fatigue Heterogeneity

Parameter

Hierarchy Model

Hierarchy Model

FatigueModel

FatigueModel

• Ellipsoid packing method1

• Statistically representative volume element• Smaller than lab-scale specimen

• CP-FEM model2• Definition of heterogeneity parameter

• Model the heterogeneity parameter distribution

• Simulate fatigue specimens (lab scale) using the hierarchy model• Spatial distribution given by the Poisson point process• Interrogate for life-limiting criterion

Probability of life-limiting mechanismProbability of life-

limiting mechanism

1C. P. Przybyla and D . L. McDowell, International Journal of Plasticity, 20102R. A. Brockman, et al.



SummaryTi-6-2-4-6

• Study fundamental drivers of fatigue lifetime distribution – Stresses and lifetimes representative of engine rotors designs

• Total fatigue lifetime (NT) :NT = Ni + NSC + NLC

– Ni is the dominant term only in the mean lifetime as the stress level is decreased

– Ni approaches 0 cycles for the life-limiting failures

• The minimum lifetime was spent almost completely in the growth of a crack that began on the microstructural scale

• How can one preclude the rare conditions that lead to Ni 0?– Microstructure, surface treatments (e.g., residual stresses), etc.– Need to quantify the probability of life-limiting failure (Ni 0)

• Suggests alternative interpretation for integrated life-cycle design and management of turbine-engine rotor materials and components


36







Outline



Ti-6Al-4VGamma TiAl




Al-Cu-Mg-Ag alloy


37

Model-Based Fatigue Life-LimitsMean-Based → Life-Limiting-Mechanism-Based

Mechanistic Understanding

Model-based B0.1

Crack-growth lifetime distribution(life-limiting distribution)

Mean-dominatingdistribution

Data-basedapproach

Model-Based Probability of Life-Limiting

Mechanism (Ni = 1) Probability of Life-Limiting Mechanism

Life-limitingdistributions

Distribution in Life-Limiting MechanismModel of Life-Limiting Distribution

• Life-limiting trend is different from the mean-behavior trend

• Model-based predictions focus on the life-limiting behavior

• Method also enables incorporation of new material, microstructure, residual stress, mission, etc.

max = 1150 MPa; Nf = 2,210Critical microstructural neighborhood for Ni = 1

PDF

Crack Initiation Size

da/d

N

K

Small cracks

Prob

abili

ty

Nf (Life-Limiting)

B0.1

P(Li

fe-li

miti

ng

mec

hani

sm)

Volume


38

Mechanism Mapping for Kt = 1w.r.t. Stress Level

950

1000

1050

1100

1150

1200

1250

100 1000 104 105 106 107

Surf. NMPSubsurf. NMPSurf. poreMean lifetime

max

(M

Pa)

Nf (Cycles)

IN100650°C

Surface NMP

Subsurface NMP

Surface pore

max = 1150 MPa; Nf = 2,210Surface NMP Subsurface NMPSurface pore

Fine Grain IN100 (650°C)

950

1000

1050

1100

1150

100 1000 104 105 106 107

Surface NMPSubsurface NMPSurface poreSubsurface pore

max

(M

Pa)

Nf (Cycles)

Coarse Grain IN100 (650°C)

Surface pore Subsurface NMP


39For Official Use Only

100 1000 104 105 106.001.01

.115

102030507080909599

99.999.99

99.999


Prob

abili

ty o

f Fai

lure

(%

)

1100 MPa Data

Model Prediction and Validation

950

1000

1050

1100

1150

1200

1250

100 1000 104 105 106 107

Mean lifetime

max

(M

Pa)

Nf (Cycles)

IN100650°C

max = 1150 MPa; Nf = 2,210Surface NMP

Transgranular

20 m

Subsurface NMP

Transgranular40 m

Surface pore

Mixedmode

10 m

Experimental Observations of Mechanism Variations

Incorporation of Crack-Initiation Mechanism in Life Prediction

For Official Use Only

• There are competing mechanisms for crack-initiation• Incorporating these mechanisms in life prediction models can lead to lower uncertainty and better

utilization of residual useful life

Simulation of Crack-Initiating Features

0

100

200

3000

100

200

300

01020304050

0

100

200

300

SpecimensPore

Non-metallic Particle (NMP)

Plate

Step 1

Step 2



Model-Based Fatigue LimitsProbability of Occurrence of Life-Limiting Mechanism

• Model-based probability of occurrence of life-limiting mechanism (Ni = 1)

• Volumetric effect on the probability of occurrence enables scale-up to component feature volumes

Non-metallic particlePores

SimulatedPlate

Componentfeature volume

Lab-scale specimen

Interrogate simulated specimens for microstructuralcondition representing Ni =1

0.0001

0.001

0.01

0.1

1

0.01 0.1 1 10 100

P-life-limiting

Prob

abili

ty o

f fin

ding

a c

ondi

tion

lead

ing

to li

fe-li

miti

ng m

echa

nism

, Pl

Surface layer volume (mm3)

Lab-

scal

esp

ecim

en

Feat

ure

volu

me


41Courtesy of John Leugers, AFRL/RW Public Release #88ABW‐2012‐2266

100 1000 104 105 106.01

.1

1

51020305070809095

99

99.9

99.99538°C, Subsurface initiation

566°C, Subsurface initiation593°C, Subsurface initiation

621°C, Subsurface initiation650°C, Subsurface initiation677°C, Subsurface initiation593°C, predicted life-limiting distribution


Pro

babi

lity

of F

ailu

re (

%)

593°C, Surface initiation

Model-Based Fatigue Life LimitsSmooth Geometry

0.0001

0.001

0.01

0.1

1

0.01 0.1 1 10 100

P-life-limiting

Prob

abili

ty o

f fin

ding

a c

ondi

tion

lead

ing

to li

fe-li

miti

ng m

echa

nism

, Pl

Surface layer volume (mm3)

Lab-

scal

esp

ecim

en

Probability of occurrence of life-limiting mechanism

max = 1150 MPa; Nf = 2,210Life-limiting mechanism:Surface NMP Initiation

20 m


max = 1000 MPa

max = 1000 MPaT = 538°C

• Life-limiting mechanism ≡ Crack initiation from surface NMP

• 1 out of 76 specimens failed by surface NMP at 1000 MPa (T = 538 – 677°C)

• Reasonable agreement between data and predictions of the predicted probability of occurrence and the life-limiting distribution

Feat

ure

volu

me


42

Mechanism-Based Prediction of Life-Limiting Distribution

1150 MPa

1100 MPa

10-7

10-6

10-5

10-4

10-3

10-2

4 6 8 10 30 50 70

Long cracks (No dwell)

Small cracks, pore crack initiation (1150 MPa)

Small crack, NMP crackinitiation (1150 MPa)

da/d

N (

mm

/cyc

le)

K (MPa-m1/2)

650°C; 0.33 Hz; R = 0.05

0

1

2

3

4

5

6

7

20 35 50 65 80 95 110

125

140

155

170

Initiation Size (m)

Freq

uenc

y

Fine GrainCoarse Grain

NMP crack-initiation size distribution

Variability in small-crack growth rate

Inputs Predictions

100 1000 104 105 106.01.115

102030507080909599

99.999.99

Predicted life-limitingdistribution


Pro

babi

lity

of F

ailu

re (

%)

100 1000 104 105 106.01

.115

102030507080909599

99.999.99

Predictedlife-limitingdistribution


Pro

babi

lity

of F

ailu

re (

%)


43

1150 MPa

1100 MPa

10-7

10-6

10-5

10-4

10-3

10-2

4 6 8 10 30 50 70




da/d

N (

mm

/cyc

le)

K (MPa-m1/2)

650°C; 0.33 Hz; R = 0.05

0

1

2

3

4

5

6

7

20 35 50 65 80 95 110

125

140

155

170

Initiation Size (m)

Freq

uenc

y




Inputs Predictions

Comparison to Data-Based Method

Over-conservative

Anti-conservative

100 1000 104 105 106.01.115

102030507080909599

99.999.99

1150 MPa(10 random tests)Predicted life-limitingdistribution


Pro

babi

lity

of F

ailu

re (

%)

100 1000 104 105 106.01

.115

102030507080909599

99.999.99

1100 MPa(15 tests)Predicted life-limitingdistribution


Pro

babi

lity

of F

ailu

re (

%)


44

Mechanism-Based Prediction of Life-Limiting Distribution

1150 MPa

1100 MPa

10-7

10-6

10-5

10-4

10-3

10-2

4 6 8 10 30 50 70




da/d

N (

mm

/cyc

le)

K (MPa-m1/2)

650°C; 0.33 Hz; R = 0.05

0

1

2

3

4

5

6

7

20 35 50 65 80 95 110

125

140

155

170

Initiation Size (m)

Freq

uenc

y




Inputs Predictions

100 1000 104 105 106.01.115

102030507080909599

99.999.99

1150 MPa, ExperimentLife-limiting pointsPredicted life-limitingdistribution


Pro

babi

lity

of F

ailu

re (

%)

100 1000 104 105 106.01.115

102030507080909599

99.999.99

1100MPa,20 testsPredictedlife-limitingdistribution


Pro

babi

lity

of F

ailu

re (

%)


45DISTRIBUTION C: Distribution authorized to US Government agencies and their contractors (Critical Technology), XX October 2013.

Other requests for this document shall be referred to Air Force Research Laboratory, AFRL/RXCM.

Understanding Crack Growth atFracture Critical Locations

Machining, shot peening, glass-bead peening, blend repair => surface residual stresses

• Notched specimens simulate fracture-critical features of components– Simulate crack growth under stress gradients (notches)– Simulate crack growth with shot peened residual stresses

0.0

1.0

2.0

3.0

4.0

5.0

0 3000 6000 9000 12000

LSG, boreLSG, faceSP = 6A, boreSP = 6A, face

Cra

ck L

engt

h (m

m)

Total Cycle Count, N

IN100 (cg): 650°C0.333 Hz, R = 0.05Kt,net = 1.8net = 680.6 MPa

Shot PeeningBenefit


46Courtesy of John Leugers, AFRL/RW Public Release #88ABW‐2012‐2266

Model-Based Fatigue Life LimitsBenefit of Surface Residual Stress

ææææææ

æææææææææææ

æææ

æ

ææ

æææ

æ

ææææ

æ

æ

æææ

æ

æ

ææ

ææ

æææææ

æææææææ æ ææææ

0.0 0.1 0.2 0.3 0.4 0.5-1000

-800

-600

-400

-200

0

200

Distance mm

Resid

ualS

tress

MPa

1000 104 105 106.01

.115

102030507080909599

99.999.99

Without SPresidual stress

With SPresidual stress


Pro

babi

lity

of F

ailu

re (

%)

650°C900 MPa

B0.1

Benefit of RS

0

5x103

1x104

1.5x104

2x104

2.5x104

3x104

3.5x104

300 350 400 450 500 550 600 650 700

Without RSWith SP RS

B0.

1 Li

fetim

e (C

ycle

s)

Temperature (°C)

With shot-peen RS

Without RS

900 MPa

Measured shot-peen RS profiles

• Benefit of shot-peen residual stress can be readily incorporated in the proposed model-based life limits



Applicability to Notched Geometries-Motivation-

Notch Locations are often Life Limiting • Air Hole• Bolt hole• Tang• Snap Fillet• …

Point Solution @ 650°Cfor Kt = 1.89

103 104 105 106.001

.01

.1

1

5102030

50

70809095

99

99.9

99.99

99.999Kt = 1.89

800 MPa900 MPa

800 MPa900 MPa

Cycles to FailurePe

rcen

t

Prediction

T= 650˚C; f=0.33 Hz; R=0.05

All lifing methods have to predict notch life

Elastic‐Plastic Notch Analysis

MechanicalSpecimen



Model-Based Fatigue Life-Limits Process for Components

Bolt hole

Fillet

Model-based probability of life-limiting mechanism (Ni = 1)

K solution for fracture-critical features

Component Stress Analysis

K

a

Life-limiting distributionB0.1 limit

Nf (life-limiting)

Prob

abili

ty

Feature 1

Feature 2

P(Li

fe-li

miti

ng

mec

hani

sm)

Volume

Model-based B0.1

Surface RSMicrostructureMission

• Model-based B0.1 method can be scaled up to a component or feature

• Variables such surface RS, microstructure, and mission are inputs to the model


49







Outline



Ti-6Al-4VGamma TiAl




Al-Cu-Mg-Ag alloy



Mission Usage

0

20

40

60

80

100

Time

% M

ax S

tres

sModel-Based Life-limits:

Deconstruct Uncertainty to Capture Benefits

Notch Analysis

3D Effects,etc.

Simulate lifetime

SurfaceResidual Stresses

0.0

1.0

2.0

3.0

4.0

5.0

0 3000 6000 9000 12000

LSG, boreLSG, faceSP = 6A, boreSP = 6A, face

Cra

ck L

engt

h (m

m)

Total Cycle Count, N

IN100 (cg): 650°C0.333 Hz, R = 0.05Kt = 1.8, net = 680.6 MPa

Microstructural Hierarchies

Transgranular

max = 1150 MPa; Nf = 2,210Surface NMP

Transgranular

Surface pore

Mixed mode

Subsurface NMP Crystallographic

Model‐based life limit



0.0

0.5

1.00.0

0.51.0

0

1

2

3

Multi-scale Physics and Mechanicsof Materials Fatigue Life Limits

What controls life-limit uncertainty?

Mechanisms Simulations


52

Top-down approach – determine the

physics of fatigue damage and lifetime

variability

Integrated ComputationalMaterials Engineering (ICME) for Life

Meso-scale• Fracture modes, small-crack growth, fracture

morphology, and local neighborhood• Characterizing smaller flaws

Micro-scale• Crack-initiating

microstructural arrangements and mechanisms

• NDE of microstructure features

Nano-scale• Slip

mechanismspromoting crack initiation

Probabilistic life-prediction on the component-scale by integrating lab-scale information

10,000 m

Slip traces

Crackorigin

Macro-scale• Fatigue crack development

and growth from a life-limiting locationin a component

• Detecting “large” cracks


For Official Use Only (FOUO)

New Engines• Minimize life-cycle

uncertainty

Digital material life-cycle and design• Optimize for full life

53

Reliability• Deconstruct Uncertainty• Microstructure-based lifing

Affordability• Much less testing• NDE: Tailored POD

Maintainability• Integrated life cycle• Optimize for maintainability

Manufacturing• Optimized processes• Digital Thread life-cycle data

Model-based Life-limit ApproachImplications -- Based on Predicted Risk

Verification & Validation• Probabilistic risk• Validation material science

Life-cycle Design• Materials / microstructures• Components / features

Sustainment of Legacy Engines• Understand & reduce

life-cycle uncertainty


54

Related Publications

• S. K. Jha, C. J. Szczepanski, R. John, and J. M. Larsen, “Demonstration of a Method for Predicting the Probability of Life-Limiting Fatigue Failures,” to be submitted, Engineering Fracture Mechanics

• S. K. Jha, C. J. Szczepanski, R. John, and J. M. Larsen, “Deformation heterogeneities and their role in life limiting fatiguefailures in a two-phase titanium alloy,” Acta Materialia, Vol. 82, pp. 378-395, 2015.

• A. L. Hutson, S. K. Jha, W. J. Porter, and J. M. Larsen, “Activation of life-limiting fatigue damage mechanisms in Ti-6Al-2Sn-4Zr-6Mo,” International Journal of Fatigue, Vol. 66, pp. 1-10, 2014.

• S. K. Jha, R. John, and J. M. Larsen, “Incorporating small fatigue crack growth in probabilistic life prediction: Effect of stress ratio in Ti-6Al-2Sn-4Zr-6Mo,” International Journal of Fatigue, Vol. 51, pp. 83-95, 2013.

• J. M. Larsen, S. K. Jha, C. J. Szczepanski, M. J. Caton, R. John, A. H. Rosenberger, D. J. Buchanan, P. J. Golden, and J. R. Jira, “Reducing uncertainty in fatigue life limits of turbine engine alloys,” International Journal of Fatigue, Vol. 57, pp. 103-112, 2013.

• C. J. Szczepanski, S. K. Jha, P. A. Shade, R. Wheeler, and J. M. Larsen, “Demonstration of an in situ microscale fatigue testing technique on a titanium alloy,” International Journal of Fatigue, Vol. 57, pp. 131-139, 2013.

• C. J. Szczepanski, P. A. Shade, M. A. Groeber, J. M. Larsen, S. K. Jha, and R. Wheeler, “Development of a microscale fatigue testing technique,” Advanced Materials and Processes, Vol. 171, pp. 18-21, 2013.

• M. E. Burba, M. J. Caton, S. K. Jha, and C. J. Szczepanski, “Effect of aging treatment on fatigue behavior of an Al-Cu-Mg-Ag alloy,” Metallurgical and Materials Transactions A, Vol. 44, pp. 4954-4967, 2013.

• S. K. Jha, C. J. Szczepanski, P. J. Golden, W. J. Porter, III, and R. John, “Characterization of fatigue crack initiation facetsin relation to lifetime variability in Ti-6Al-4V,” International Journal of Fatigue, Vol. 42, pp. 248-257, 2012.

• C. J. Szczepanski, S. K. Jha, J. M. Larsen, and J. W. Jones, “The role of local microstructure on small fatigue crack propagation in an a+b titanium alloy, Ti-6Al-2Sn-4Zr-6Mo,” Metallurgical and Materials Transactions A, Vol. 43, pp. 4097-4112, 2012.

• A. H. Rosenberger, D. J. Buchanan, D. A. Ward, and S. K. Jha, “The variability of fatigue in notched bars of IN100,” Superalloys 2012, pp. 143-148, 2012.

• S. K. Jha, C. J. Szczepanski, C. P. Przybyla, and J. M. Larsen, “The hierarchy of fatigue mechanisms in the long-lifetime regime,” VHCF-5, pp. 505-512, 2011.


55


• C. J. Szczepanski, S. K. Jha, J. M. Larsen, and J. W. Jones, “The role of microstructure on sequential stages of the very high cycle fatigue behavior of an a+b titanium alloy, Ti-6Al-2Sn-4Zr-6Mo,” VHCF-5, pp. 225-230, 2011.

• M. J. Caton and S. K. Jha, “Small fatigue crack growth and failure mode transitions in a Ni-base superalloy at elevated temperature,” International Journal of Fatigue, Vol. 32, pp. 1461-1472, 2010.

• R. John, D. J. Buchanan, M. J. Caton, and S. K. Jha, “Stability of shot peen residual stresses in IN100 subjected to creep and fatigue loading,” Procedia Engineering, Vol. 2., pp. 1887-1893, 2010.

• S. K. Jha, R. John, and J. M. Larsen, “Nominal vs local shot-peening effects on fatigue lifetime in Ti-6Al-2Sn-4Zr-6Mo,” Metallurgical and Materials Transactions A, Vol. 40, pp. 2675-2684, 2009.

• R. John, D. J. Buchanan, S. K. Jha, and J. M. Larsen, “Stability of shot-peen residual stresses in an a+b titanium alloy,” Scripta Materialia, Vol. 61, pp. 343-346, 2009.

• S. K. Jha, H. R. Millwater, and J. M. Larsen, “Probabilistic sensitivity analysis in life prediction of an a + b titanium alloy,” Fatigue and Fracture of Engineering Materials and Structures, Vol. 32, pp. 493-504, 2009.

• S. K. Jha, J. M. Larsen, and A. H. Rosenberger, “Towards a physics-based description of fatigue variability behavior in probabilistic life prediction,” Engineering Fracture Mechanics, Vol. 76, pp. 681-694, 2009.

• C. J. Szczepanski, S. K. Jha, J. M. Larsen, and J. W. Jones, “Microstructural influences on very-high-cycle fatigue-crack initiation inTi-6246,” Metallurgical and Materials Transactions A, Vol. 39, pp. 2841-2851, 2008.

• S. K. Jha, M. J. Caton, and J. M. Larsen, “Mean vs. life-limiting fatigue behavior of a nickel-based superalloy,” Superalloys-2008, pp. 565-572, 2008.

• W. J. Porter III, K. Li, M. J. Caton, S. K. Jha, B. B. Bartha, and J. M. Larsen, “Microstructural conditions contributing to fatigue variability in P/M nickel-base superalloys,” Superalloys-2008, pp. 541-548, 2008.

• S. K. Jha, M. J. Caton, and J. M. Larsen, “A new paradigm of fatigue variability behavior and implications for life predictions,” Materials Science and Engineering A, Vol. 468, pp. 23-32, 2007.

• S. K. Jha and J. M. Larsen, “Random heterogeneity scale and probabilistic description of the long-lifetime regime of fatigue,” VHCF-4, pp. 385-396, 2007.


56


• C. J. Szczepanski, S. K. Jha, J. M. Larsen, and J. W. Jones, “The role of microstructure on the fatigue lifetime variability in an a+b titanium alloy, Ti-6Al-2Sn-4Zr-6Mo,” VHCF-4, pp. 37-44, 2007.

• S. K. Jha, J. M. Larsen, and A. H. Rosenberger, “The role of competing mechanisms in the fatigue-life variability of a titanium and gamma-TiAl alloy,” JOM, Vol. 57, pp. 50-54, 2005.

• S. K. Jha, M. J. Caton, J. M. Larsen, A. H. Rosenberger, K. Li, and W. J. Porter, “Superimposing mechanisms and their effect on the variability in fatigue lives of a nickel-based superalloy,” Materials Damage Prognosis, TMS, pp. 343-350, 2005.

• S. K. Jha, J. M. Larsen, and A. H. Rosenberger, “The role of competing mechanisms in fatigue life variability of a nearly fully-lamellar g-TiAl based alloy,” Acta Materialia, Vol. 53, pp. 1293-1304, 2005.

• K. S. Ravi Chandran and S. K. Jha, “Duality of the S-N fatigue curve caused by competing failure modes in a titanium alloy and the role of Poisson defect statistics,” Acta Materialia, Vol. 53, pp. 1867-1881, 2005.

• C. Annis, J. M. Larsen, A. H. Rosenberger, S. K. Jha, and D. H. Annis, “RFTh, a random fatigue threshold probability density for Ti6246,” Materials Damage Prognosis, TMS, pp. 151-156, 2005.

• C. J. Szczepanski, A. Shyam, S. K. Jha, J. M. Larsen, C. J. Torbet, S. J. Johnson, and J. W. Jones, “Characterization of the role of microstructure on the fatigue life of Ti-6Al-2Sn-4Zr-6Mo using ultrasonic fatigue,” Materials Damage Prognosis, TMS, pp. 315-320, 2005.

• S. K. Jha, J. M. Larsen, and A. H. Rosenberger, “The role of fatigue variability in life prediction of an a+b titanium alloy,” Materials Damage Prognosis, TMS, pp. 1955-1960, 2005.

• S. K. Jha, J. M. Larsen, A. H. Rosenberger, and G. A. Hartman, “Mechanism-based variability in fatigue life of Ti-6Al-2Sn-4Zr-6Mo,” Journal of ASTM International, Vol. 1, 2004.

• M. J. Caton, S. K. Jha, A. H. Rosenberger, and J. M. Larsen, “Divergence of mechanisms and the effect on the fatigue life variability of Rene’88DT,” Superalloys-2004, pp. 305-312, 2004.

• S. K. Jha, J. M. Larsen, A. H. Rosenberger, and G. A. Hartman, “Dual fatigue failure modes in Ti-6Al-2Sn-4Zr-6Mo and consequences on probabilistic life prediction,” Scripta Materialia, Vol. 48, pp. 1637-1642, 2003.

• S. K. Jha and K. S. Ravi Chandran, “An unusual fatigue phenomenon: duality of the S-N fatigue curve in the b titanium alloy Ti-10V-2Fe-3Al,” Scripta Materialia, Vol. 48, pp. 1207-1212, 2003.


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