Reducing Uncertainty:
Reflections on Establishing
Life Limits
2014 ASTM JoDean Morrow Lecture
on 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
Integrity  Service  Excellence
Air Force Research Laboratory
Wright-Patterson Air Force Base, OH 45433
1AFRL/RXC, 2Universal
3University
Technology Corporation
of Dayton Research Institute, 4UES, Inc.., 5Special Metals Corp.
Approved
for
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No.88-ABW-2013-0906
88ABW-2015-0198
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forpublic
publicrelease:
release: Case
1
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)
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
Mike Dent
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2
Outline
Life management of high performance turbine engines
– Today and tomorrow
Alloys explored:
Ti-10V-2Fe-3Al
Ti-6Al-2Sn-4Zr-6Mo ()
Fatigue variability and uncertainty
Ti-6Al-2Sn-4Zr-6Mo (L-)
– Examples
Ti-6Al-2Sn-4Zr-2Mo ()
• Ti-6Al-2Sn-4Zr-6Mo ()
Ti-6Al-4V
• IN100
Gamma TiAl
Waspaloy (Wrought)
Future opportunities
IN100 (P/M: fine grain)
– Life management & design
IN100 (P/M: coarse grain)
– Verification & validation
René-88 DT (P/M)
– Optimize Performance, Safety, Reliability,
IN718 (Wrought)
Maintainability, Affordability, Utilization
Ni Single Crystal 1484
Al 7075-T651
Acknowledgements:
Al-Cu-Mg-Ag alloy
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)
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3
Outline
Life management of high performance turbine engines
– Today and tomorrow
Alloys explored:
Ti-10V-2Fe-3Al
Ti-6Al-2Sn-4Zr-6Mo ()
Fatigue variability and uncertainty
Ti-6Al-2Sn-4Zr-6Mo (L-)
– Examples
Ti-6Al-2Sn-4Zr-2Mo ()
• Ti-6Al-2Sn-4Zr-6Mo ()
Ti-6Al-4V
• IN100
Gamma TiAl
Waspaloy (Wrought)
Future opportunities
IN100 (P/M: fine grain)
– Life management & design
IN100 (P/M: coarse grain)
– Verification & validation
René-88 DT (P/M)
– Optimize Performance, Safety, Reliability,
IN718 (Wrought)
Maintainability, Affordability, Utilization
Ni Single Crystal 1484
Al 7075-T651
Acknowledgements:
Al-Cu-Mg-Ag alloy
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)
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4
Design Certification Methodology to Assure
Integrity Throughout the Life Cycle
Usage (e.g. Stress)
Propulsion System Integrity Program (PSIP) - MIL-STD-3024
Untapped
Performance
Mean
Max Safe
Life
Typical

log Life (e.g. Cycles or TACs)
• 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
“Safe Life” has been standard
practice for engine rotors
for over 50 years.
……………………..
Used to compensate for
uncertainty/lack of knowledge
For Official Use Only (FOUO)
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5
Traditional Life Prediction Process
Stress-life (S-N) Fatigue Tests –
All conditions
Fit S-N data with Multi-Condition
Regression
• Data-Driven
99.9%
B50/B.1 = Scatter Factor
(material + condition + model)
• Distribution w.r.t.
mean behavior
50%
• Potentially
Condition 1
untapped
performance
0.1%
Condition 2
B.1
B50
Actual/Predicted Lifetime (A/P)
Condition n
Fleet Scale-up B0.1 Lifetime
Component Scale-up
• Needs generation
of new database
for new material
or microstructure
• Difficult to
incorporate
effects of
residual stress,
mission,
microstructure,
etc.
B0.1
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Propulsion System Integrity Program
Life-Cycle Design Philosophy (PSIP; MIL-STD-3024)
Low-Cycle-Fatigue Design Criteria
(safe life)
Based on statistical lower bound
1 in 1000 components predicted to
initiate a 0.8 mm crack
Deterministic
1 or 2 safety inspections during
service life
•
•
aC
Mean
Typical
Lower Bound

Crack Length
Usage (e.g. Stress)
•
•
Damage-Tolerant Design Criteria
(fracture mechanics)
a*
ai
log Life (e.g. Cycles or TACs)
Cycles (or Equivalent)
Both design criteria are met at all critical locations on a component
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Move Engine Lifing from
Safe-Life Approach to Retirement For Cause
LCF Initiation Distribution
Traditional “Safe-Life”
Retirement Approach
Manage to -3 Lower Bound
-3
0
Before 1980s
RFC program
10000
20000
30000
40000
Life (Time or Cycles)
50000
-3
60000
70000
Number of Parts
0
10000
10000
Traditional “Safe-Life”
Retirement Approach
Manage to -3 Lower Bound
20000
30000
40000
50000
60000
70000
B0.1 = 8000 TAC
LCF Initiation Distribution
-3
0
After 1980s
RFC program
Life (Time or Cycles)
B0.1 = 4000 TAC
Retire all components
when 1 in 1000 is
predicted to fail
Retire all components
when 1 in 1000 is
predicted to fail
Economic/Risk Limit = Definition of Retirement for Cause
After ERLE
program
Traditional “Safe-Life”
Retirement Approach
Manage to -3 Lower Bound
20000
30000
40000
Life (Time or Cycles)
B0.1 = 12000 TAC
50000
60000
70000
0
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
Number of Parts
Retire all components
when 1 in 1000 is
predicted to fail
Number of Parts
LCF Initiation Distribution
Penetrate the LCF Distribution
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8
Prognosis will Enable Transformation
in Asset Management
Dr. Leo Christodoulou
Yes  Service
Failure physics,
damage evolution,
predictive models
Prognosis
Database:
Mission History,
Maintenance, Life Extension,
and Design
Failure Occurrences
Usage (Duty Cycles)
State Awareness
Interrogation
“Book Life” Today
“Book Life”
Tomorrow
Reduce and
Manage
Uncertainty
NO  Retire
Prognosis Translates Knowledge and Information Richness to Physical Capability
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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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Opportunity: Physics-Based Description
of Fatigue Variability
Traditional (Empirical) Description
Physics-Based Description of Fatigue Variability
Fatigue variability described as deviation
from the expected mean-behavior
Fatigue variability described as separation of the mean
and the life-limiting behavior
Overall mean behavior
Mean behavior
Distribution in the lifelimiting mechanism
(crack-growth controlled)
Variability described w.r.t.
the overall mean behavior
max
max
Variability in the meandominating response
Nf (Cycles)
POF = 0.1%
life limit
(Book life)
Life-limit based
on the uncertainty
in the worst-case
mechanism
Large degree of
uncertainty associated
with life prediction
Failure Occurrence
Failure Occurrence
Nf (Cycles)
POF = 0.1%
life limit
Usage (Duty cycles)
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Crack growth
related peak
(life-limiting
mechanism)
Mean-lifetime
dominating peak
Total
variability
Duty cycles
11
N. E. Frost, K. J. Marsh, and L. P. Pook
"Metal fatigue, 1974." Oxford University Press, Oxford.
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Life-limiting Fatigue
Total Fatigue Life = NTotal
Small-Crack
Crack Initiation 0? Growth
Long-Crack
Growth
NTotal
?
?
?
Ni
NP,small
NP,long
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.
For Official Use Only (FOUO)
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13
Outline
Life management of high performance turbine engines
– Today and tomorrow
Alloys explored:
Ti-10V-2Fe-3Al
Ti-6Al-2Sn-4Zr-6Mo ()
Fatigue variability and uncertainty
Ti-6Al-2Sn-4Zr-6Mo (L-)
– Examples
Ti-6Al-2Sn-4Zr-2Mo ()
• Ti-6Al-2Sn-4Zr-6Mo ()
Ti-6Al-4V
• IN100
Gamma TiAl
Waspaloy (Wrought)
Future opportunities
IN100 (P/M: fine grain)
– Life management & design
IN100 (P/M: coarse grain)
– Verification & validation
René-88 DT (P/M)
– Optimize Performance, Safety, Reliability,
IN718 (Wrought)
Maintainability, Affordability, Utilization
Ni Single Crystal 1484
Al 7075-T651
Acknowledgements:
Al-Cu-Mg-Ag alloy
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)
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14
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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Confidence Bounds
on B0.1 Lifetime -- All Data
99.99
Probability of failure (%)
99.9

max
= 820 MPa
99
95
90
80
70
50
30
20
10
5
1
All data points
721 cycles
95% confidence
intervals
.1
.01
100
3
10
4
10
10
5
10
6
10
7
8
10
9
10
Lifetime, N (Cycles)
f
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Bimodal Model
99.9

Probability of failure (%)
max
99
95
90
80
70
= 820 MPa
f t ( N )  pl f l ( N )  (1  pl ) f m ( N )
50
30
20
10
5
1
Data
Bimodal fit
Lower bound
Upper bound
4565 cycles
.1
100
10
3
4
10
5
10
10
6
10
7
10
8
9
10
N (Cycles)
f
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Confidence Bounds on B0.1 Lifetime
Limiting Condition of pl → 1
99.99
Probability of failure (%)
99.9

max
= 820 MPa
99
95
90
80
70
50
30
20
10
5
1
f t ( N )  pl f l ( N )  (1  pl ) f m ( N )
pl  1
Life-limiting
distribution
5660 cycles
95% confidence
intervals
.1
.01
100
10
3
4
10
5
10
10
6
10
7
10
8
9
10
Lifetime, N (Cycles)
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
Probability of Occurence (%)
Effect of Stress Level on Mean vs. Life-Limiting Behavior
99
Meandominating
behavior
95
90
80
70
50
1040 MPa
925 MPa
900 MPa
860 MPa
820 MPa
700 MPa
650 MPa
600 MPa
550 MPa
30
20
10
5
1 4
10
Life-limiting
behavior
5
10
6
10
7
10
10
8
10
9
10
10
Cycles to Failure
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Bimodal Fatigue Behavior
Ti-6Al-2Sn-4Zr-6Mo; RT
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99
95
90
ys= 1140 MPa
80
70
50
1040 MPa
925 MPa
900 MPa
860 MPa
820 MPa
700 MPa
650 MPa
600 MPa
550 MPa
30
20
10
5
1 4
10
5
10
6
10
10
7
10
8
10
9
10
10
Cycles to Failure
Failure Occurrence
Probability of Occurence (%)
Probability of Occurrence of LifeLimiting Failures
Probability of Life-Limiting Failures
Crack-growth-controlled
B0.1
density (Critical
lifetimes
heterogeneity level) Mean-dominating
density (Smaller
heterogeneity scales)
Empirically-derived
density
Duty cycles
Stress (MPa)
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Alternate Life-Prediction Approach
99.99
behavior separate with decreasing 
and respond differently to operating
variables.
• Life Prediction based on variability
in the worst‐case mechanism.
Probability of Failure (%)
• The Mean and the worst‐case
All points
Type I
Type II
99.9
99

max
95
90
80
70
= 860 MPa
Type I
50
30
20
10
5
Type II
Reduction in
uncertainty
1
.1
when compared to the traditional
approach.
• Improved reliability of design life.
10
4
1 in 1000
Life limits
10
5
Cycles to Failure, N
Variability in
crack growth
6
10
7
10
f
Variability in crack
Initiation + growth
Failure Occurrence
• Significant reduction in uncertainty
.01
1000
Duty cycles
FOR OFFICIAL USE ONLY
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Alternate Life-Prediction Approach
99.99
behavior separate with decreasing 
and respond differently to operating
variables.
• Life Prediction based on variability
in the worst‐case mechanism.
Probability of Failure (%)
• The Mean and the worst‐case
All points
Type I
Type II
Simulated, Type I
99.9
99
95
90
80
70

max
= 860 MPa
Type I
50
30
20
10
5
Type II
Reduction in
uncertainty
1
.1
when compared to the traditional
approach.
• Improved reliability of design life.
10
4
1 in 1000
Life limits
10
5
Cycles to Failure, N
Variability in
crack growth
6
10
7
10
f
Variability in crack
Initiation + growth
Failure Occurrence
• Significant reduction in uncertainty
.01
1000
Duty cycles
FOR OFFICIAL USE ONLY
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Mechanism-Based Probabilistic
Prediction of Limiting Life
Crack Initiation Size
Predicted Life-Limiting Distribution
35
99.99
 area
p
99.9
Crcak nucleation area
Probability of Failure (%)
Occurrence frequency
30
25
20
15
10
5
0
0
20
40
60
80
100 120 140 160
2
 area; Crack nucleation area (m )
180

max
99
95
90
80
70
50
30
20
10
5
10
-4
10
-5
10
-6
Experimental
.1
Life-limiting
population
.01
4
10
10
da/dN (m/cycle)
Long crack
10
10
-8
10
-9
da
 f (K )
dN
max
af
-10

Ti-6-2-4-6
= 860 MPa
max
R = 0.05
 = 20 Hz
T = 23°C
-11
10
-12
1
6
10
10
7
f
10
10
5
N (Cycles)
Small cracks
(
= 860 MPa)
Power-law fits
-7
Experimental
(Life limiting)
Predicted
(Life limiting)
1
p
Small-Crack Growth Variability
= 860 MPa
10
K (MPa-m )
1/2
Np 

a  ai
da
f (K )
• Prediction of limiting life of Ti6Al-2Sn-4Zr-6Mo
• Monte Carlo simulation based on
microstructural features and
small-crack growth
100
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Confidence Bounds on B0.1 Lifetime
Limiting Condition of pl → 1
99.99
Probability of failure (%)
99.9

max
= 820 MPa
99
95
90
80
70
50
30
20
10
5
1
f t ( N )  pl f l ( N )  (1  pl ) f m ( N )
pl  1
Life-limiting
distribution
5660 cycles
95% confidence
intervals
.1
.01
100
10
3
4
10
5
10
10
6
10
7
10
8
9
10
Lifetime, N (Cycles)
f
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Crack-Growth-Controlled Failures
99.99
Probability of Failure (%)
99.9

max
= 820 MPa
99
95
90
80
70
50
30
20
10
5
B0.1
lifetime
Predicted life-limiting
distribution
1
Crack-growthcontrolled failures
.1
.01
100
1000
10
4
10
5
10
6
7
10
8
10
10
9
Lifetime, N (Cycles)
f
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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?
An Integrated Design Criterion
B0.1 Lifetime
Predicted Distribution in a vs. N
820 MPa
Limiting Damage
Tolerance Curve
Cycles
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Life-Limiting Failure
IPF map
N1
N1
N2
F1
F1
F1
N2
Faceted p
Loading axis
Crackinitiation
facet
Basal plane
trace
Specimen
tilt = 30°
• max = 860 MPa; Nf = 49,893 cycles
• Facet inclination = 31°
Methods:
• Quantitative tilt microscopy using MEXTM
• FIB sectioning through crack-initiation facet (in some cases)
• EBSD analysis of the crack-initiation region
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Summary of Mean vs. Life-Limiting Configurations
Surface-Initiated Mechanisms
Faceted grains
Resolved along the
loading axis
Facet inclination w.r.t. the loading axis (°)
Facet inclination
Resolved along the
facet normal
50
45
40
35
Neighboring grains
30
Life-limiting
25
4
10
Mean-dominating
5
10
6
10
7
10
Lifetime (Cycles)
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Probability of occurrence
Hypothesis: Hierarchy of Fatigue
Deformation Heterogeneities
Basal plane
Inclination
≤ 30
,
p
soft
Heterogeneity level
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Microstructure-Based Prediction of Life-Limiting
Fatigue Mechanisms in Ti-6-2-4-6
Using the Hierarchy Model of Heterogeneity levels
Microstructure
Model
0.0
1.0
0.5
0.0
1
• CP-FEM
• Definition of
method1
• Statistically
representative
volume element
• Smaller than labscale specimen
heterogeneity
parameter
distribution
heterogeneity
parameter
1C.
2R.
, str, etc.
0
• Model the
• Ellipsoid packing
1.0
3
2
Deformation parameter
model2
0.5
P(Life-limiting failure)
Fatigue
Model
Probability of occurrence
Compute Fatigue
Heterogeneity
Parameter
Hierarchy
Model
Probability of lifelimiting mechanism
• Simulate fatigue
specimens (lab
scale) using the
hierarchy model
• Spatial distribution
given by the Poisson
point process
• Interrogate for lifelimiting criterion
P. Przybyla and D . L. McDowell, International Journal of Plasticity, 2010
A. Brockman, et al.
Approved for public release: Case No. 88-ABW-2013-0906
Approved for public release: Case No. 88ABW-2015-0198
34
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
Approved for public release: Case No. 88-ABW-2013-0906
Approved for public release: Case No. 88ABW-2015-0198
35
Outline
Life management of high performance turbine engines
– Today and tomorrow
Alloys explored:
Ti-10V-2Fe-3Al
Ti-6Al-2Sn-4Zr-6Mo ()
Fatigue variability and uncertainty
Ti-6Al-2Sn-4Zr-6Mo (L-)
– Examples
Ti-6Al-2Sn-4Zr-2Mo ()
• Ti-6Al-2Sn-4Zr-6Mo ()
Ti-6Al-4V
• IN100
Gamma TiAl
Waspaloy (Wrought)
Future opportunities
IN100 (P/M: fine grain)
– Life management & design
IN100 (P/M: coarse grain)
– Verification & validation
René-88 DT (P/M)
– Optimize Performance, Safety, Reliability,
IN718 (Wrought)
Maintainability, Affordability, Utilization
Ni Single Crystal 1484
Al 7075-T651
Acknowledgements:
Al-Cu-Mg-Ag alloy
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)
Approved for public release: Case No. 88ABW-2015-0198
36
Model-Based Fatigue Life-Limits
Mean-Based → Life-Limiting-Mechanism-Based
Model-Based
Probability of Life-Limiting
Mechanism (Ni = 1)
Probability of Life-Limiting Mechanism
Crack-growth
lifetime distribution
Model- (life-limiting distribution)
based
B0.1
Mean-dominating
P(Life-limiting
mechanism)
max = 1150 MPa; Nf = 2,210
Critical microstructural
neighborhood for Ni = 1
Mechanistic
Understanding
distribution
Volume
da/dN
Model of LifeLimiting Distribution
PDF
Data-based
approach
Small
cracks
•
•
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.
Probability
Crack Initiation Size
•
Distribution in Life-Limiting Mechanism
Life-limiting
distributions
K
B0.1
Nf (Life-Limiting)
Approved for public release: Case No. 88ABW-2015-0198
37
Mechanism Mapping for Kt = 1
w.r.t. Stress Level
Fine Grain IN100 (650°C)
Coarse Grain IN100 (650°C)
1150
1250
Subsurf. NMP
Surf. pore
1100
Mean lifetime
Surface
NMP
(MPa)
1150
IN100
650°C
1050
max
1100


Surface NMP
Subsurface NMP
Surface pore
Subsurface pore
Surf. NMP
max
(MPa)
Surface
1200 pore
1050
1000
1000
950
100
Subsurface NMP
1000
4
10
10
N (Cycles)
5
10
6
7
10
950
100
1000
f
max = 1150 MPa; Nf = 2,210
Surface NMP
Surface pore
4
10
10
N (Cycles)
5
10
6
10
7
f
Subsurface NMP
Surface pore
Approved for public release: Case No. 88ABW-2015-0198
Subsurface NMP
38
Incorporation of Crack-Initiation
Mechanism in Life Prediction
Experimental Observations of Mechanism Variations
Non-metallic
Particle (NMP)
Mean lifetime
Mixed
mode
(MPa)
1200

Plate
300
1150
50
40
30
20
10
0
0
IN100
650°C
1100
Step 1
max
Surface
pore
Simulation of Crack-Initiating Features
1250
1050
200
100
Pore
100
Specimens
200
1000
max = 1150 MPa; Nf = 2,210
Surface NMP
950
100
Step 2
1000
4
10
10
N (Cycles)
5
10
f
Subsurface NMP
Transgranular
20 m
0
40 m
Transgranular
6
7
10
99.999
99.99
99.9
99
95
90
80
70
50
30
20
10
5
1
.1
.01
.001
100
Probability of Failure (%)
10 m
300
1100 MPa Data
1000
4
5
10
10
Cycles to Failure, N
10
6
f
Model Prediction and Validation
• 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
For Official Use Only
Forrelease:
OfficialCase
Use No.
Only
Approved for public
88ABW-2015-0198
39
Model-Based Fatigue Limits
Non-metallic
particle
Pores
P-life-limiting
Feature volume
0.1
0.01
Lab-scale
specimen
Interrogate
simulated
specimens for
microstructural
condition
representing
Ni =1
1
l
Simulated
Plate Lab-scale
specimen Component
feature volume
Probability of finding a condition leading
to life-limiting mechanism, P
Probability of Occurrence of Life-Limiting Mechanism
0.001
0.0001
0.01
0.1
1
10
100
3
Surface layer volume (mm )
• 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
For Official Use Only
Approved for public release: Case No. 88ABW-2015-0198
40
Model-Based Fatigue Life Limits
Smooth Geometry
Life-limiting distribution
99.99
1
P-life-limiting
538°C, Subsurface initiation
99.9
566°C, Subsurface initiation
max = 1000 MPa
T = 538°C
Lab-scale
specimen
0.01
0.001
Feature volume
0.1
Probability of Failure (%)
l
Probability of finding a condition leading
to life-limiting mechanism, P
Probability of occurrence of life-limiting mechanism
0.1
1
593°C, Subsurface initiation
95
90
80
70
50
30
20
10
5
593°C, Surface initiation
1
621°C, Subsurface initiation
650°C, Subsurface initiation
677°C, Subsurface initiation
593°C, predicted lifelimiting distribution
max = 1000 MPa
.1
0.0001
0.01
99
10
100
.01
100
4
1000
5
10
10
10
6
Cycles to Failure, N
3
Surface layer volume (mm )
f
max = 1150 MPa; Nf = 2,210
Life-limiting mechanism:
Surface NMP Initiation
• 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
Courtesy of John Leugers, AFRL/RW
Public Release #88ABW‐2012‐2266
20 m
Approved for public release: Case No. 88ABW-2015-0198
41
Mechanism-Based Prediction of LifeLimiting Distribution
Predictions
Inputs
NMP crack-initiation
size distribution
Probability of Failure (%)
7
99.99
99.9
Fine Grain
6
Frequency
Coarse Grain
5
4
3
2
1
.1
.01
100
95
11
0
12
5
14
0
15
5
17
0
Initiation Size (m)
Variability in small-crack
growth rate
10
-2
650°C; 0.33 Hz; R = 0.05
-3
da/dN (mm/cycle)
10
-4
10
-5
Long cracks (No dwell)
Small cracks, pore crack
initiation (1150 MPa)
-6
10
Small crack, NMP crack
initiation (1150 MPa)
-7
10
4
6
8 10
1/2
K (MPa-m )
30
50
70
99.99
99.9
Probability of Failure (%)
80
65
50
35
20
0
10
1150 MPa
99
95
90
80
70
50
30
20
10
5
1
Predicted life-limiting
distribution
1000
4
10
10
Cycles to Failure, N
5
10
6
f
1100 MPa
99
95
90
80
70
50
30
20
10
5
1
.1
.01
100
Predicted
life-limiting
distribution
1000
4
10
10
Cycles to Failure, N
5
10
6
f
Approved for public release: Case No. 88ABW-2015-0198
42
Comparison to Data-Based Method
Predictions
Inputs
NMP crack-initiation
size distribution
Probability of Failure (%)
7
99.99
99.9
Fine Grain
6
Frequency
Coarse Grain
5
4
3
2
1
95
11
0
12
5
14
0
15
5
17
0
Variability in small-crack
growth rate
10
-2
650°C; 0.33 Hz; R = 0.05
-3
da/dN (mm/cycle)
10
-4
10
-5
Long cracks (No dwell)
Small cracks, pore crack
initiation (1150 MPa)
-6
Small crack, NMP crack
initiation (1150 MPa)
-7
10
4
6
8 10
1/2
K (MPa-m )
30
50
70
99.99
99.9
Probability of Failure (%)
80
65
50
35
20
Initiation Size (m)
10
Overconservative
.1
.01
100
0
10
1150 MPa
99
95
90
80
70
50
30
20
10
5
1
1150 MPa
(10 random tests)
Predicted life-limiting
distribution
1000
4
5
10
10
Cycles to Failure, N
10
6
f
1100 MPa
99
95
90
80
70
50
30
20
10
5
1
.1
.01
100
Anticonservative
1100 MPa
(15 tests)
Predicted
life-limiting
distribution
1000
4
10
10
Cycles to Failure, N
5
6
10
f
Approved for public release: Case No. 88ABW-2015-0198
43
Mechanism-Based Prediction of LifeLimiting Distribution
Predictions
Inputs
NMP crack-initiation
size distribution
Probability of Failure (%)
7
99.99
99.9
Fine Grain
6
Frequency
Coarse Grain
5
4
3
2
1
.1
.01
100
95
11
0
12
5
14
0
15
5
17
0
Initiation Size (m)
Variability in small-crack
growth rate
10
-2
650°C; 0.33 Hz; R = 0.05
-3
da/dN (mm/cycle)
10
-4
10
-5
Long cracks (No dwell)
Small cracks, pore crack
initiation (1150 MPa)
-6
10
Small crack, NMP crack
initiation (1150 MPa)
-7
10
4
6
8 10
1/2
K (MPa-m )
30
50
70
99.99
99.9
Probability of Failure (%)
80
65
50
35
20
0
10
1150 MPa
99
95
90
80
70
50
30
20
10
5
1
1150 MPa, Experiment
Life-limiting points
Predicted life-limiting
distribution
1000
4
10
10
Cycles to Failure, N
5
6
10
f
1100 MPa
99
95
90
80
70
50
30
20
10
5
1
.1
.01
100
1100MPa,
20 tests
Predicted
life-limiting
distribution
1000
4
5
10
10
Cycles to Failure, N
6
10
f
Approved for public release: Case No. 88ABW-2015-0198
44
Understanding Crack Growth at
Fracture Critical Locations
Machining, shot peening, glass-bead peening, blend repair => surface residual stresses
Shot Peening
Benefit
5.0
IN100 (cg): 650°C
0.333 Hz, R = 0.05
Kt,net = 1.8
Crack Length (mm)
4.0
net = 680.6 MPa
3.0
LSG, bore
LSG, face
SP = 6A, bore
SP = 6A, face
2.0
1.0
0.0
0
3000
6000
9000
12000
Total Cycle Count, N
• Notched specimens simulate fracture-critical features of components
– Simulate crack growth under stress gradients (notches)
– Simulate crack growth with shot peened residual stresses
DISTRIBUTION C: Distribution authorized to US Government agencies and their contractors (Critical Technology), XX October 2013.
Other requests
for this document
shallrelease:
be referredCase
to AirNo.
Force88ABW-2015-0198
Research Laboratory, AFRL/RXCM.
Approved
for public
45
Model-Based Fatigue Life Limits
Benefit of Surface Residual Stress
Residual Stress MPa
200
æ
-200 æ
æ
æ æ
æ
æ
æ
æ
æ
æ
æ
æææ
æ
-600 æ
æ ææ
æ
æ
æ
-800
æ
æ
-400 æ
ææ
æ
-1000
0.0
æ
æ
ææ
ææ
Measured shotpeen RS profiles
0.2
0.3
Distance mm
0.1
æ
æ æ
ææ
0.4
0.5
3.5x10 4
Benefit
of RS
99
95
90
80
70
50
30
20
10
5
1
650°C
900 MPa
B0.1
Without SP
residual stress
.1
.01
1000
Without RS
With SP RS
3x10 4
B0.1 Lifetime (Cycles)
Probability of Failure (%)
99.99
99.9
æ
æ æ
æ
æ æ
ææ æ
æ æ
æ
æ
ææ
0
With SP
residual stress
4
10
10
5
10
6
With shotpeen RS
2.5x10 4
2x10
4
1.5x10
4
900 MPa
1x10 4
5x10 3
0
300
Without RS
350
Cycles to Failure, N
400
450 500 550
Temperature (°C)
600
650
700
f
• Benefit of shot-peen residual stress can be readily
incorporated in the proposed model-based life limits
Courtesy of John Leugers, AFRL/RW
Public Release #88ABW‐2012‐2266
Approved for public release: Case No. 88ABW-2015-0198
46
Applicability to Notched Geometries
-MotivationNotch Locations are
often Life Limiting
• Air Hole
• Bolt hole
• Tang
• Snap Fillet
• …

Point Solution @ 650°C
for Kt = 1.89
99.999
Kt = 1.89
99.99
T= 650˚C; f=0.33 Hz; R=0.05
99.9
99
95
90
Percent
Elastic‐Plastic Notch Analysis
80
70
50
30
20
10
5
800 MPa
900 MPa
1
Prediction
800 MPa
900 MPa
.1
.01
.001
10
3
Mechanical
Specimen
10
4
10
5
10
6
Cycles to Failure
All lifing methods have to predict notch life
For Official Use Only
Approved for public release: Case No. 88ABW-2015-0198
47
Model-Based Fatigue Life-Limits
Process for Components
Stress Analysis
K solution for fracturecritical features
K
Component
Feature 1
Feature 2
Bolt hole
a
Surface RS
Microstructure
Mission
Fillet
•
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
B0.1 limit
Life-limiting
distribution
Nf (life-limiting)
For Official Use Only
Approved for public release: Case No. 88ABW-2015-0198
P(Life-limiting
mechanism)
•
Probability
Model-based B0.1
Model-based probability of lifelimiting mechanism (Ni = 1)
Volume
48
Outline
Life management of high performance turbine engines
– Today and tomorrow
Alloys explored:
Ti-10V-2Fe-3Al
Ti-6Al-2Sn-4Zr-6Mo ()
Fatigue variability and uncertainty
Ti-6Al-2Sn-4Zr-6Mo (L-)
– Examples
Ti-6Al-2Sn-4Zr-2Mo ()
• Ti-6Al-2Sn-4Zr-6Mo ()
Ti-6Al-4V
• IN100
Gamma TiAl
Waspaloy (Wrought)
Future opportunities
IN100 (P/M: fine grain)
– Life management & design
IN100 (P/M: coarse grain)
– Verification & validation
René-88 DT (P/M)
– Optimize Performance, Safety, Reliability,
IN718 (Wrought)
Maintainability, Affordability, Utilization
Ni Single Crystal 1484
Al 7075-T651
Acknowledgements:
Al-Cu-Mg-Ag alloy
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)
Approved for public release: Case No. 88ABW-2015-0198
49
Model-Based Life-limits:
Deconstruct Uncertainty to Capture Benefits
Surface
Residual Stresses
Microstructural Hierarchies
Surface NMP
max = 1150 MPa; Nf = 2,210
Surface pore
5.0
Transgranular
IN100 (cg): 650°C
0.333 Hz, R = 0.05
Kt = 1.8, net = 680.6 MPa
Subsurface NMP
Crack Length (mm)
4.0
Mixed mode
Crystallographic
Notch Analysis
LSG, bore
LSG, face
SP = 6A, bore
SP = 6A, face
3.0
2.0
1.0
0.0
0
3000
6000
9000
12000
Total Cycle Count, N
Model‐based life limit
Transgranular
Mission Usage
% Max Stress
100
Simulate lifetime
3D Effects,
etc.
80
60
40
20
0
Time
For Official Use Only
Approved for public release: Case No. 88ABW-2015-0198
50
Multi-scale Physics and Mechanics
of Materials Fatigue Life Limits
Mechanisms
Simulations
0.0
1.0
0.5
0.0
0.5
1.0
3
2
1
0
What controls life-limit uncertainty?
For Official Use Only
Approved for public release: Case No. 88ABW-2015-0198
51
Integrated Computational
Materials Engineering (ICME) for Life
Macro-scale
• Fatigue crack development
and growth from a life-limiting location
in a component
• Detecting “large” cracks
10,000 m
Crack
origin
Meso-scale
Top-down approach
– determine the
physics of fatigue
damage and lifetime
variability
• 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
Probabilistic lifeprediction on the
component-scale by
integrating lab-scale
information
Slip traces
Approved for public release: Case No. 88ABW-2015-0198
mechanisms
promoting
crack initiation
52
Model-based Life-limit Approach
Implications -- Based on Predicted Risk
Reliability
• Deconstruct Uncertainty
• Microstructure-based lifing
Maintainability
• Integrated life cycle
• Optimize for maintainability
Affordability
• Much less testing
• NDE: Tailored POD
Sustainment of
Legacy Engines
• Understand & reduce
life-cycle uncertainty
Digital material lifecycle and design
• Optimize for full life
Life-cycle Design
• Materials / microstructures
• Components / features
Verification & Validation
• Probabilistic risk
• Validation material science
Manufacturing
• Optimized processes
• Digital Thread life-cycle data
For Official Use Only (FOUO)
Approved for public release: Case No. 88ABW-2015-0198
New Engines
• Minimize life-cycle
uncertainty
53
Related Publications
•
•
•
•
•
•
•
•
•
•
•
•
S. K. Jha, C. J. Szczepanski, R. John, and J. M. Larsen, “Demonstration of a Method for Predicting the Probability of LifeLimiting 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-6Al2Sn-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-MgAg 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. 40974112, 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.
Approved for public release: Case No. 88ABW-2015-0198
54
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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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-2Sn4Zr-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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