Reducing Uncertainty: Reflections on Establishing Life Limits 2014 - - PowerPoint PPT Presentation

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Integrity  Service  Excellence

Reducing Uncertainty: Reflections on Establishing Life Limits

2014 ASTM JoDean Morrow Lecture

• n Fatigue of Materials

New Orleans, LA 11 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 Laboratory Wright-Patterson Air Force Base, OH 45433

1AFRL/RXC, 2Universal Technology Corporation 3University of Dayton Research Institute, 4UES, Inc.., 5Special Metals Corp.

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In-house and Collaborative Team

Government

Mike Caton

• Lt. Chris Fetty

Pat Golden

• Lt. Sigfried Herring

Jay Jira Reji John Jim Larsen Siamack Mazdiyasni Ryan Morrissey Andy Rosenberger Mike Shepard Chris Szczepanski

• Lt. Steve Visalli

On-site Contractor (UDRI)

Bob Brockman Marc Huelsman Dennis Buchanan David Johnson Kezhong Li John Porter Herb Stumph Pete Phillips

On-site Contractor (GDIT)

Mike Dent

Universal Technology Corp. (UTC)

Sushant Jha

Universal Energy Systems (UES)

Vikas Sinha

University of Texas at San Antonio

Harry Millwater

University of Michigan

Wayne Jones Tresa Pollock Christ Torbet

Ohio State University

Alison Polasik Hamish Fraser Mike Mills Jim Williams

Statistical Engineering Inc.

Chuck Annis, Jr., P.E. Independent Consultant Tom Cruse

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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/HQ AFOSR -- 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-4V Gamma TiAl Waspaloy (Wrought) IN100 (P/M: fine grain) IN100 (P/M: coarse grain) René-88 DT (P/M) IN718 (Wrought) Ni Single Crystal 1484 Al 7075-T651 Al-Cu-Mg-Ag alloy

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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/HQ AFOSR -- 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-4V Gamma TiAl Waspaloy (Wrought) IN100 (P/M: fine grain) IN100 (P/M: coarse grain) René-88 DT (P/M) IN718 (Wrought) Ni Single Crystal 1484 Al 7075-T651 Al-Cu-Mg-Ag alloy

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For 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 for uncertainty/lack of knowledge log Life (e.g. Cycles or TACs) Usage (e.g. Stress)

Typical Mean  Max Safe Life

• Design and certify all components

are within this “safe” zone.

• All components are “not safe” if
• ne in 1000 is predicted to initiate a

crack Untapped Performance

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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-up Fleet Scale-up B0.1 Lifetime

B0.1

• Data-Driven
• Distribution w.r.t.

mean behavior

• Potentially

untapped performance

• Needs generation
• f new database

for new material

• r microstructure
• Difficult to

incorporate effects of residual stress, mission, microstructure, etc.

Condition 1 Condition 2

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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) Usage (e.g. Stress)

Typical Mean Lower Bound 

Cycles (or Equivalent) Crack Length a

i

a

C

a

*

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

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Move Engine Lifing from Safe-Life Approach to Retirement For Cause

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10000 20000 30000 40000 50000 60000 70000 Number of Parts Life (Time or Cycles)

LCF Initiation Distribution

• 3

Retire all components when 1 in 1000 is predicted to fail

B0.1 = 4000 TAC

Traditional “Safe-Life” Retirement Approach Manage to -3 Lower Bound

Before 1980s RFC program

10000 20000 30000 40000 50000 60000 70000 Number of Parts Life (Time or Cycles)

LCF Initiation Distribution

• 3

Retire all components when 1 in 1000 is predicted to fail

B0.1 = 8000 TAC

Traditional “Safe-Life” Retirement Approach Manage to -3 Lower Bound

After 1980s RFC program

10000 20000 30000 40000 50000 60000 70000 Number of Parts Life (Time or Cycles)

LCF Initiation Distribution

• 3

Retire all components when 1 in 1000 is predicted to fail

B0.1 = 12000 TAC

Traditional “Safe-Life” Retirement Approach Manage to -3 Lower Bound

After ERLE program

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000 24000 26000 28000 30000 32000 34000 36000 38000 40000 42000 44000 46000 48000 50000 52000 54000 56000 58000 60000 62000 64000 66000 68000 70000 Life (Time or Cycles)

Economic/Risk Limit = Definition of Retirement for Cause

Penetrate the LCF Distribution

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Yes  Service NO  Retire

Usage (Duty Cycles) Failure Occurrences

“Book Life” Today

Prognosis will Enable Transformation in Asset Management

Database: Mission History, Maintenance, Life Extension, and Design

Prognosis

Failure physics, damage evolution, predictive models State Awareness Interrogation Prognosis Translates Knowledge and Information Richness to Physical Capability

Reduce and Manage Uncertainty

“Book Life” Today “Book Life” Tomorrow

• Dr. Leo Christodoulou

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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

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Large degree of uncertainty associated with life prediction Failure Occurrence Usage (Duty cycles)

POF = 0.1% life limit (Book life)

Failure Occurrence Duty cycles

POF = 0.1% life limit Life-limit based

• n the uncertainty

in the worst-case mechanism Crack growth related peak (life-limiting mechanism) Mean-lifetime dominating peak Total variability

Traditional (Empirical) Description

Fatigue variability described as deviation from the expected mean-behavior

Physics-Based Description of Fatigue Variability

Fatigue 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 Description

• f Fatigue Variability

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• N. E. Frost, K. J. Marsh, and L. P. Pook

"Metal fatigue, 1974." Oxford University Press, Oxford.

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For Official Use Only (FOUO)

Life-limiting Fatigue

Small-Crack Growth Crack 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 Understanding Life-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?

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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/HQ AFOSR -- 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-4V Gamma TiAl Waspaloy (Wrought) IN100 (P/M: fine grain) IN100 (P/M: coarse grain) René-88 DT (P/M) IN718 (Wrought) Ni Single Crystal 1484 Al 7075-T651 Al-Cu-Mg-Ag alloy

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

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Lifetime Distribution

Ti-6-2-4-6, RT, R = 0.05,  = 20 Hz and 20 kHz

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100 103 104 105 106 107 108 109 .01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99 All data points

Lifetime, Nf (Cycles) Probability of failure (%)

95% confidence intervals max = 820 MPa

Confidence Bounds

• n B0.1 Lifetime -- All Data

721 cycles

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100 10

3

10

4

10

5

10

6

10

7

10

8

10

9

.1 1 5 10 20 30 50 70 80 90 95 99 99.9

Data Bimodal fit Lower bound Upper bound

Nf (Cycles) Probability of failure (%)

max = 820 MPa

Bimodal Model

) ( ) 1 ( ) ( ) ( N f p N f p N f

m l l l t

  

4565 cycles

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100 103 104 105 106 107 108 109 .01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99 Life-limiting distribution

Lifetime, Nf (Cycles) Probability of failure (%)

95% confidence intervals 

max = 820 MPa

Confidence Bounds on B0.1 Lifetime Limiting Condition of pl → 1

5660 cycles

1 ) ( ) 1 ( ) ( ) (    

l m l l l t

p N f p N f p N f

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Lifetime Distribution

Ti-6-2-4-6, RT, R = 0.05,  = 20 Hz and 20 kHz

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CDF Space

Effect of Stress Level on Mean vs. Life-Limiting Behavior

104 105 106 107 108 109 1010 1 5 10 20 30 50 70 80 90 95 99

1040 MPa 925 MPa 900 MPa 860 MPa 820 MPa 700 MPa 650 MPa 600 MPa 550 MPa

Cycles to Failure Probability of Occurence (%)

Life-limiting behavior Mean- dominating behavior

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

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Probability of Life-Limiting Failures

ys= 1140 MPa Stress (MPa) Probability of Occurrence of Life- Limiting Failures

104 105 106 107 108 109 1010 1 5 10 20 30 50 70 80 90 95 99

1040 MPa 925 MPa 900 MPa 860 MPa 820 MPa 700 MPa 650 MPa 600 MPa 550 MPa

Cycles to Failure Probability of Occurence (%)

Failure Occurrence Duty cycles

B0.1 lifetimes Crack-growth-controlled density (Critical heterogeneity level) Mean-dominating density (Smaller heterogeneity scales) Empirically-derived density

Failure Occurrence Duty cycles

B0.1 lifetimes Crack-growth-controlled density (Critical heterogeneity level) Mean-dominating density (Smaller heterogeneity scales) Empirically-derived density

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FOR OFFICIAL USE ONLY

Alternate Life-Prediction Approach

• The Mean and the worst‐case

behavior separate with decreasing  and respond differently to operating variables.

• Life Prediction based on variability

in the worst‐case mechanism.

• Significant reduction in uncertainty

when compared to the traditional approach.

• Improved reliability of design life.

1 in 1000 Life limits Failure Occurrence Duty cycles

Variability in crack growth Variability in crack Initiation + growth

1000 10

10

10

10

.01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99

All points Type I Type II

Cycles to Failure, Nf Probability of Failure (%)

Type I Type II 

Reduction in uncertainty

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FOR OFFICIAL USE ONLY

Alternate Life-Prediction Approach

• The Mean and the worst‐case

behavior separate with decreasing  and respond differently to operating variables.

• Life Prediction based on variability

in the worst‐case mechanism.

• Significant reduction in uncertainty

when compared to the traditional approach.

• Improved reliability of design life.

1 in 1000 Life limits Failure Occurrence Duty cycles

Variability in crack growth Variability in crack Initiation + growth

1000 10

10

10

10

.01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99

All points Type I Type II Simulated, Type I

Cycles to Failure, Nf Probability of Failure (%)

Type I Type II 

Reduction in uncertainty

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10

10

10

10

.01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99

Experimental Experimental (Life limiting) Predicted (Life limiting) Nf (Cycles) Probability of Failure (%) max = 860 MPa

Life-limiting population

5 10 15 20 25 30 35 20 40 60 80 100 120 140 160 180 

Crcak nucleation area Occurrence frequency 

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

) ( K f dN da  





 

f i

a a a p

K f da N ) (

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/dN (m/cycle) K (MPa-m1/2)

Ti-6-2-4-6 

R = 0.05  = 20 Hz T = 23°C Power-law fits

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100 103 104 105 106 107 108 109 .01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99 Life-limiting distribution

Lifetime, Nf (Cycles) Probability of failure (%)

95% confidence intervals 

max = 820 MPa

Confidence Bounds on B0.1 Lifetime Limiting Condition of pl → 1

5660 cycles

1 ) ( ) 1 ( ) ( ) (    

l m l l l t

p N f p N f p N f

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100 1000 104 105 106 107 108 109 .01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99 Predicted life-limiting distribution Crack-growth- controlled failures

Lifetime, Nf (Cycles) Probability of Failure (%)



max = 820 MPa

Crack-Growth-Controlled Failures

B0.1 lifetime

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

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

Predicted Distribution in a vs. N 820 MPa

An Integrated Design Criterion

B0.1 Lifetime Limiting Damage Tolerance Curve

Cycles

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Loading axis

F1 N2 F1 F1 N1 N2 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

Specimen tilt = 30°

Crack- initiation facet Faceted p

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

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Summary of Mean vs. Life-Limiting Configurations Surface-Initiated Mechanisms

25 30 35 40 45 50 104 105 106 107 Life-limiting Mean-dominating

Facet inclination w.r.t. the loading axis (°) Lifetime (Cycles)

Neighboring grains Faceted grains

Resolved along the loading axis Resolved along the facet normal Facet inclination

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soft

, p

Basal plane Inclination ≤ 30

Hypothesis: Hierarchy of Fatigue Deformation Heterogeneities

Probability of occurrence Heterogeneity level

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Probability of occurrence Deformation parameter

Microstructure-Based Prediction of Life-Limiting Fatigue Mechanisms in Ti-6-2-4-6 Using the Hierarchy Model of Heterogeneity levels

P(Life-limiting failure) , str, etc.

Microstructure Model Microstructure Model Compute Fatigue Heterogeneity Parameter Compute Fatigue Heterogeneity Parameter Hierarchy Model Hierarchy Model Fatigue Model Fatigue Model

• 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 mechanism Probability of life- limiting mechanism

• 1C. P. Przybyla and D . L. McDowell, International Journal of Plasticity, 2010
• 2R. A. Brockman, et al.

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Summary Ti-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

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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/HQ AFOSR -- 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-4V Gamma TiAl Waspaloy (Wrought) IN100 (P/M: fine grain) IN100 (P/M: coarse grain) René-88 DT (P/M) IN718 (Wrought) Ni Single Crystal 1484 Al 7075-T651 Al-Cu-Mg-Ag alloy

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Model-Based Fatigue Life-Limits

Mean-Based → Life-Limiting-Mechanism-Based

Mechanistic Understanding

Model- based B0.1 Crack-growth lifetime distribution (life-limiting distribution) Mean-dominating distribution Data-based approach

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

Life-limiting distributions

Distribution in Life-Limiting Mechanism Model 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.

Critical microstructural neighborhood for Ni = 1 PDF Crack Initiation Size da/dN K Small cracks Probability Nf (Life-Limiting) B0.1 P(Life-limiting mechanism) Volume

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Mechanism Mapping for Kt = 1

w.r.t. Stress Level

950 1000 1050 1100 1150 1200 1250 100 1000 104 105 106 107

• Surf. NMP
• Subsurf. NMP
• Surf. pore

Mean lifetime

max (MPa) Nf (Cycles) IN100 650°C

Surface NMP Subsurface NMP Surface pore

Surface NMP Subsurface NMP Surface pore

Fine Grain IN100 (650°C)

950 1000 1050 1100 1150 100 1000 104 105 106 107 Surface NMP Subsurface NMP Surface pore Subsurface pore max (MPa) Nf (Cycles)

Coarse Grain IN100 (650°C)

Surface pore Subsurface NMP

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For Official Use Only

100 1000 104 105 106 .001 .01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99 99.999 Cycles to Failure, Nf Probability of Failure (%)

1100 MPa Data

Model Prediction and Validation

950 1000 1050 1100 1150 1200 1250 100 1000 104 105 106 107

max (MPa) Nf (Cycles) IN100 650°C

max = 1150 MPa; Nf = 2,210

Surface NMP

Transgranular

20 m

Subsurface NMP

Transgranular

40 m

Surface pore

Mixed mode

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

Specimens Pore Non-metallic Particle (NMP) Plate

Step 1 Step 2

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Model-Based Fatigue Limits

Probability 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 particle Pores

Simulated Plate Component feature volume Lab-scale specimen

Interrogate simulated specimens for microstructural condition representing Ni =1

0.0001 0.001 0.01 0.1 1 0.01 0.1 1 10 100 P-life-limiting

Probability of finding a condition leading to life-limiting mechanism, Pl Surface layer volume (mm3) Lab-scale specimen Feature volume

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

100 1000 10

10

10

.01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99

538°C, Subsurface initiation 566°C, Subsurface initiation 593°C, Subsurface initiation 621°C, Subsurface initiation 650°C, Subsurface initiation 677°C, Subsurface initiation 593°C, predicted life- limiting distribution

Cycles to Failure, Nf Probability of Failure (%)

593°C, Surface initiation

Model-Based Fatigue Life Limits Smooth Geometry

0.0001 0.001 0.01 0.1 1 0.01 0.1 1 10 100 P-life-limiting

Probability of finding a condition leading to life-limiting mechanism, Pl Surface layer volume (mm3) Lab-scale specimen

Probability of occurrence of life-limiting mechanism

max = 1150 MPa; Nf = 2,210

Life-limiting mechanism: Surface NMP Initiation 20 m

Life-limiting distribution

max = 1000 MPa max = 1000 MPa T = 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
• f the predicted probability of occurrence and the

life-limiting distribution

Feature volume

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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/dN (mm/cycle) K (MPa-m1/2) 650°C; 0.33 Hz; R = 0.05 1 2 3 4 5 6 7 2 3 5 5 6 5 8 9 5 1 1 1 2 5 1 4 1 5 5 1 7

Initiation Size (m) Frequency

NMP crack-initiation size distribution Variability in small-crack growth rate

Inputs Predictions

100 1000 104 105 106 .01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99 Predicted life-limiting distribution Cycles to Failure, Nf Probability of Failure (%) 100 1000 104 105 106 .01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99 Predicted life-limiting distribution Cycles to Failure, Nf Probability of Failure (%)

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1150 MPa 1100 MPa

10-7 10-6 10-5 10-4 10-3 10-2 4 6 8 10 30 50 70

da/dN (mm/cycle) K (MPa-m1/2) 650°C; 0.33 Hz; R = 0.05 1 2 3 4 5 6 7 2 3 5 5 6 5 8 9 5 1 1 1 2 5 1 4 1 5 5 1 7

Initiation Size (m) Frequency

NMP crack-initiation size distribution Variability in small-crack growth rate

Inputs Predictions

Comparison to Data-Based Method

Over- conservative Anti- conservative

100 1000 104 105 106 .01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99 1150 MPa (10 random tests) Predicted life-limiting distribution Cycles to Failure, Nf Probability of Failure (%) 100 1000 104 105 106 .01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99 1100 MPa (15 tests) Predicted life-limiting distribution Cycles to Failure, Nf Probability of Failure (%)

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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/dN (mm/cycle) K (MPa-m1/2) 650°C; 0.33 Hz; R = 0.05 1 2 3 4 5 6 7 2 3 5 5 6 5 8 9 5 1 1 1 2 5 1 4 1 5 5 1 7

Initiation Size (m) Frequency

NMP crack-initiation size distribution Variability in small-crack growth rate

Inputs Predictions

100 1000 104 105 106 .01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99 1150 MPa, Experiment Life-limiting points Predicted life-limiting distribution Cycles to Failure, Nf Probability of Failure (%) 100 1000 104 105 106 .01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99 1100MPa, 20 tests Predicted life-limiting distribution Cycles to Failure, Nf Probability of Failure (%)

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DISTRIBUTION 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 at Fracture 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 3000 6000 9000 12000 LSG, bore LSG, face SP = 6A, bore SP = 6A, face Crack Length (mm) Total Cycle Count, N IN100 (cg): 650°C 0.333 Hz, R = 0.05 Kt,net = 1.8

net = 680.6 MPa

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

46

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

Model-Based Fatigue Life Limits Benefit of Surface Residual Stress

æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ ææ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ

0.0 0.1 0.2 0.3 0.4 0.5

• 1000
• 800
• 600
• 400
• 200

200 Distance mm ResidualStressMPa

1000 104 105 106 .01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99

Without SP residual stress With SP residual stress

Cycles to Failure, Nf Probability of Failure (%)

650°C 900 MPa

B0.1 Benefit

• f RS

5x103 1x104 1.5x10

4

2x10

4

2.5x104 3x104 3.5x104 300 350 400 450 500 550 600 650 700 Without RS With SP RS B0.1 Lifetime (Cycles) 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

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For Official Use Only

Applicability to Notched Geometries

• Motivation-

Notch Locations are

• ften Life Limiting
• Air Hole
• Bolt hole
• Tang
• Snap Fillet
• …

Point Solution @ 650°C for Kt = 1.89

103 104 105 106

.001 .01 .1 1 5 10 20 30 50 70 80 90 95 99 99.9 99.99 99.999

Kt = 1.89

800 MPa 900 MPa 800 MPa 900 MPa

Cycles to Failure Percent

Prediction

T= 650˚C; f=0.33 Hz; R=0.05



All lifing methods have to predict notch life

Elastic‐Plastic Notch Analysis

Mechanical Specimen

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For Official Use Only

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 distribution B0.1 limit

Nf (life-limiting) Probability

Feature 1 Feature 2

P(Life-limiting mechanism) Volume

Model-based B0.1

Surface RS Microstructure Mission

• 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

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49

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/HQ AFOSR -- 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-4V Gamma TiAl Waspaloy (Wrought) IN100 (P/M: fine grain) IN100 (P/M: coarse grain) René-88 DT (P/M) IN718 (Wrought) Ni Single Crystal 1484 Al 7075-T651 Al-Cu-Mg-Ag alloy

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

50

For Official Use Only

Mission Usage

Model-Based Life-limits:

Deconstruct Uncertainty to Capture Benefits

Notch Analysis 3D Effects, etc. Simulate lifetime Surface Residual Stresses

Microstructural Hierarchies

Transgranular

Surface NMP Transgranular Surface pore Mixed mode Subsurface NMP Crystallographic

Model‐based life limit

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For Official Use Only

Multi-scale Physics and Mechanics

• f Materials Fatigue Life Limits

What controls life-limit uncertainty?

Mechanisms Simulations

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Top-down approach – determine the physics of fatigue damage and lifetime variability

Integrated Computational Materials 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

mechanisms promoting crack initiation

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

10,000 m Slip traces Crack

• rigin

Macro-scale

• Fatigue crack development

and growth from a life-limiting location in a component

• Detecting “large” cracks

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

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 Approach

Implications -- 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

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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 fatigue

failures 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 facets

in 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.

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55

Related Publications

• 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.

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56

Related Publications

• 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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