Physically-Based Modeling in State-Awareness Monitoring Strategies
David L. McDowell1,2
Regents’ Professor and Carter N. Paden, Jr. Distinguished Chair in Metals Processing
Director, MPRL1School of Materials Science and Engineering
2GWW School of Mechanical EngineeringGeorgia Institute of Technology, Atlanta, GA 30332
February 19, 2008
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Background
• DARPA AIM program (2001-2003, GEAC) – Development of hierarchical multiscale microstructure sensitive crystal plasticity models for Ni-base superalloys to support objectives of modeling strength and fatigue resistance (PI)
• ONR/DARPA Prognosis program (2004-2007, PWA) – Microstructure-sensitive macroscale models for component level design, informed by crystal plasticity calculations for Ni-base and Ti alloys (PI)
Shearing
Looping
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Related Technoliges
• ONR MURI on Integrated Diagnostics (1995-2000) GT, NWU, U. Minn
• NSF Center for Computational Materials Design (PSU-GT I/UCRC)
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Elements of Next Generation State-Awareness
• Characterization and “fingerprinting” of as-processed materials and components (including secondary processing)
• Modeling of material damage level/state
• Strategy for fusion of sensor-model-decision framework that integrates NDE with systems strategies to define the current state and project future state of the system.
Paraphrased from comments of Thomas A Cruse, DARPA/DSO Consultant, on Prognosis – A Vision for 2030
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
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Damage State Interrogation
Prognosis System
Life Estimate Models
Uncertain Prognosis Results /
Prediction
Model Uncertainty
Noise, Uncertain Sensor Data
• How should the damage state analysis process be configured? Which models should be employed
for diagnosis? How do we account for process
history and initial conditions?
• Sensors? Number, locations and types Nonunique relation to material state What is uncertainty of representing
state? What is state? Affected by
conception of failure mode – system related coupled
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
System-Level (Fleet) Decision Support
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Damage State InterrogationRemaining Life Models
Decisions
Uncertain Prognosis Results /
Prediction
Model Uncertainty
Noise, Uncertain Sensor Data
• How should the prognosis results be used for real-time decisions? Appropriately setting the operating
conditions Redesigning critical parts
• System-level Prognosis based on part-level prognosis data
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Triad of Technologies Embedded in Decision Support Framework
methods for in situ interrogation of state
coupled state-awareness and life models
physically-based models
Treatment of uncertainty is paramountProbabilistic micromechanics approachesRobust decision-support framework
• Feasibility studies• Justifying impact of prognosis
Premise: This is a system and couplings contribute to uncertainty
Decision-support framework
Materials design for prognosis requirements
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
System-Based, Concurrent Product and Materials Design
Part
Continuum
Microscale
Molecular
Quantum
Goal-Oriented Design Methods
Cause/Effect Analysis Methods
MaterialSelection
New areaNew area
Design methods are availableDesign methods are available
High Degree of UncertaintyHigh Degree of Uncertainty
Structure
Properties
Performance
Goals/means (in
ductive)
Cause and effect (d
eductive)
Processing
Structure
Properties
Performance
Goals/means (in
ductive)
Cause and effect (d
eductive)
Processing
Limitation in Limitation in Inverse Inverse problemproblem
G.B. Olson, Science, 29 Aug., 1997, Vol. 277
System
Assembly
Top-down design requirements can include design for damage tolerance and probability of detection
CCMD – GT/PSU
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Classification of Uncertainty based on Isukapalli’s Definition (Isukapalli, et al., 1998)
• Natural Uncertainty (system variability) Parameterizable: Errors associated with process history, operating
conditions, etc. (noise and control factors) Unparameterizable: random microstructure; randomness of initial conditions
of microstructure state
• Model Parameter Uncertainty (parameter uncertainty) Incomplete knowledge of model parameters due to insufficient or inaccurate
data; material and interrogation scheme
• Model Structural Uncertainty (model uncertainty ) Uncertain structure of a model due to insufficient knowledge (approximations
and simplifications) about a system; NDE interrogation algorithms; definition of what constitutes “state” is a substantial one.
• Propagated Uncertainty in a Process Chain (process uncertainty) Propagation of natural and model uncertainty through a chain of models
(e.g., multiscale materials; sequence of hot spots, etc.)
Uncertainty as a Driver in Hierarchical, Multilevel Decision Framework
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Balancing System Uncertainty• Undue emphasis on accuracy and/or fidelity of material structure-
property models may be unwarranted if uncertainty of distribution of initial conditions, residual stresses, secondary processing, etc. is prominent
• Models aimed at producing probabilistic/stochastic information are desirable extreme value prognosis (both hot spots and rogue flaws)
• Multiple models with different potential mechanisms may be preferable to single, complex model for supporting decisions regarding range of remaining system life
• Balanced investment in more comprehensive characterization, monitoring and damage state modeling is warranted
• State-awareness sampling and material modeling are strongly coupled, and assessment of coupling effects should be evaluated at the systems level.
Uncertainty as a Driver in Hierarchical, Multilevel Decision Framework
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Microstructure-Sensitive Fatigue Analysis
Controlling microstructure features for crack formation and early growth
Numerical analyses for representative loading cases
Physically Based Crystal Plasticity Models
a[010]
r a3 = a/78 [7 3 5 0]
b2
b1
Cross-slip onto {112}
{211} planes
-ra3 3ra3
-ra3
a3 a3
a/3[1120] a3=
Variation ofMicrostructure
Variation ofFatigue Life
Fatigue indicator parameters
Nonlocal Coffin-Manson relation
2Nf
1e+3 1e+4 1e+5 1e+6
/ re
f
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
' '(2 )cFS f fP N
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Crack Initiation Life Distribution - Polycrystals
a y0.5
Distribution of the fraction of cracks as a function of the crack initiation life, Rε=-1,
T=650C.
a y0.8
a y0.5
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
P
t
P
B
HHot
H - AE, EC
B - AE, UL, DSR
Spot
RogueFlaw
ONR MURI on Integrated Diagnostics (CBM) (1995-00)
GT, NWU, U. Minn.
McDowell, Saxena, Qu, Jacobs, Neu, Johnson,Jarzynski
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Ti-6Al-4V
Hamm (1998)
0.0001
0.001
0.01
0.1
1
1 10 100 1000a (m)
da/d
N (
m/c
ycle
)ExperimentWang modelEnhanced Wang
Smax = 405 MPa
R = 0
Kt = 3.2
0.00001
0.0001
0.001
0.01
0.1
1
1 10 100 1000a (m)
da/d
N (
m/c
ycle
)
ExperimentWang modelEnhanced Wang
Smax = 277 MPa R = .4Kt = 3.62
0.0001
0.001
0.01
0.1
1
1 10 100 1000a (m)
da/d
N (
m/c
ycle
)
ExperimentWang modelEnhanced Wang
Smax = 305 MPaR = .4Kt = 3.62
Microstructurally Small Fatigue Crack Growth
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Neu and Papp
Microstructurally Small Fatigue Crack Growth
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Test System Configuration
1
4
3
2
Transducer output
Compact PZT AE sensor
AE Waveform Acquisition Fracture
Wave Analysis
Digital Wave Signal Conditioning Module
Preamplifier
Monitoring crack to length of 1 mm (SAW)and up to 3 mm (AE)
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Needs: Physically Based Models
• Identifying and modeling sources of damage and/or degradation, linking physics-based models to engineering models that have utility in prognosis• Computational micromechanics to model variability of microstructurally small crack behavior (formation, propagation)• Effects of load history on evolving damage state and interpretation of sensor signals• Predicting variability of mechanical properties (strength, ductility, fatigue resistance) to stochastic microstructure, initial conditions, environmental exposure, etc.• Nonlinear acoustics or other means of interpreting material state prior to formation of cracks.• Accounting for process history effects on residual stresses, initial damage and defect density, etc. that affect future evolution in prognosis
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
ONR D3D Tool Suite
New Material System
Primary Deformation processing
Thermo-Chemo-Mechanical Processing
Surface treatment (e.g. shot or shock
peening)
Microstructure and Inclusion distribution
information
Apply fatigue analysis algorithms
Depth (m)
50 100 150 200 250 300 350
0.0
2.0e-5
4.0e-5
6.0e-5
8.0e-5
1.0e-4
1.2e-4
Case ACase B
Depth (m)
Dri
vin
g f
orc
e
HIPping, altering inclusion orientation,
inclusion modification
S
N
Explore surface vs. subsurface nucleation
Modify process route
Improved fatigue Improved fatigue performance performance
Extreme value
statistics
With QuesTek, LLC
The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
System Level Needs – State Awareness
• Material modeling should not be done in a “vacuum” apart from systems level considerations.
• Methodologies for fingerprinting materials and initial conditions on material state and relation to sensor thresholds/signals• Coupling of models with interrogation schemes via probabilistic, decision-based framework for state awareness• Methods for quantifying level of uncertainty and quantifying propagation of uncertainty (microstructure, model, etc.) in prognosis systems• Shifting the balance of sensing and modeling state via new materials may require materials design
Questions?