DDSim: A Multiscale Damage and
Durability Simulation Strategy Digital Twin Workshop
NASA Langley Research Center
John Emery, Sandia National Laboratories Prof. Tony Ingraffea, Cornell University
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company,for the United States Department of Energy’s National Nuclear Security Administration
under contract DE-AC04-94AL85000."
2 DDSim: A Damage and Durability Simulator
Outline for the Talk
Goal: Improved prognosis / diagnosis ♦ Motivation & broad overview
• Why do we need a new fatigue life prediction tool? ♦ The probabilistic, hierarchical, multiscale approach ♦ DDSim Level I – Reduced-order filter
• Approach • Results & Performance
♦ Level II – Automated crack propagation • Approach • Results
♦ Level III – Multiscale simulation (Dr. Hochhalter) • In brief
♦ Conclusions
3 DDSim: A Damage and Durability Simulator
Fatigue is Inherently Multiscale and Stochastic!
~1m
4 DDSim: A Damage and Durability Simulator
DDSim
Finite element model of structure including boundary/environmental conditions
Best available physics-based damage models
Random input
Time to failure, N
Probabilistic life prediction w/
confidence bounds
The Challenge
PΤ
~100 µm
Material system & pertinent microstructural statistics
stress tensor as
!! =!
eC S"
: P!.
3.1 Precipitation Hardening
In the case of precipitation hardening, the hardness values g! evolve according to the following rule
g! = Go
#gs ! g!
gs ! go
$ %
"
2&&&S!
ij S"ij
&&&&&""
&& ,
where Go is a hardening rate parameter, go is the initial hardness, gs is the saturation hardness, and S is
the symmetric part of the Schmid tensor.
The saturation hardness is given by
gs = gso
&&&&"
"s
&&&&#
,
where # is a material parameter, gso is the initial saturation hardness, and " is the total slip rate over all
slip systems,
" =Nss%
!=1
|"!| .
Note that setting # to zero results in a fixed value for the saturation hardness, gs = gso .
The precipitation hardening law was chosen to give strong self hardening, which results from the Orowan
looping mechanism observed in this materrial.
3.1.1 Backward Euler scheme for precipitation hardening
In the case of precipitation hardening, the hardness along slip system $ is updated in the UpdateState()routine with a backward Euler scheme,
g!n+1 = g!
n + !t g!n+1
g!n+1 = g!
n + !t Go
'gsn+1 ! g!
n+1
gsn+1 ! go
(%
"
2&&&S!
ij S"ij
&&&&&&""
n+1
&&&
4
stress tensor as
!! =!
eC S"
: P!.
3.1 Precipitation Hardening
In the case of precipitation hardening, the hardness values g! evolve according to the following rule
g! = Go
#gs ! g!
gs ! go
$ %
"
2&&&S!
ij S"ij
&&&&&""
&& ,
where Go is a hardening rate parameter, go is the initial hardness, gs is the saturation hardness, and S is
the symmetric part of the Schmid tensor.
The saturation hardness is given by
gs = gso
&&&&"
"s
&&&&#
,
where # is a material parameter, gso is the initial saturation hardness, and " is the total slip rate over all
slip systems,
" =Nss%
!=1
|"!| .
Note that setting # to zero results in a fixed value for the saturation hardness, gs = gso .
The precipitation hardening law was chosen to give strong self hardening, which results from the Orowan
looping mechanism observed in this materrial.
3.1.1 Backward Euler scheme for precipitation hardening
In the case of precipitation hardening, the hardness along slip system $ is updated in the UpdateState()routine with a backward Euler scheme,
g!n+1 = g!
n + !t g!n+1
g!n+1 = g!
n + !t Go
'gsn+1 ! g!
n+1
gsn+1 ! go
(%
"
2&&&S!
ij S"ij
&&&&&&""
n+1
&&&
4
5 DDSim: A Damage and Durability Simulator
DDSim
Finite element model of structure including boundary/environmental conditions
Best available physics-based damage models
Random input
Time to failure, N
Probabilistic life prediction w/
confidence bounds
The Challenge
PΤ
~100 µm
Material system & pertinent microstructural statistics
stress tensor as
!! =!
eC S"
: P!.
3.1 Precipitation Hardening
In the case of precipitation hardening, the hardness values g! evolve according to the following rule
g! = Go
#gs ! g!
gs ! go
$ %
"
2&&&S!
ij S"ij
&&&&&""
&& ,
where Go is a hardening rate parameter, go is the initial hardness, gs is the saturation hardness, and S is
the symmetric part of the Schmid tensor.
The saturation hardness is given by
gs = gso
&&&&"
"s
&&&&#
,
where # is a material parameter, gso is the initial saturation hardness, and " is the total slip rate over all
slip systems,
" =Nss%
!=1
|"!| .
Note that setting # to zero results in a fixed value for the saturation hardness, gs = gso .
The precipitation hardening law was chosen to give strong self hardening, which results from the Orowan
looping mechanism observed in this materrial.
3.1.1 Backward Euler scheme for precipitation hardening
In the case of precipitation hardening, the hardness along slip system $ is updated in the UpdateState()routine with a backward Euler scheme,
g!n+1 = g!
n + !t g!n+1
g!n+1 = g!
n + !t Go
'gsn+1 ! g!
n+1
gsn+1 ! go
(%
"
2&&&S!
ij S"ij
&&&&&&""
n+1
&&&
4
stress tensor as
!! =!
eC S"
: P!.
3.1 Precipitation Hardening
In the case of precipitation hardening, the hardness values g! evolve according to the following rule
g! = Go
#gs ! g!
gs ! go
$ %
"
2&&&S!
ij S"ij
&&&&&""
&& ,
where Go is a hardening rate parameter, go is the initial hardness, gs is the saturation hardness, and S is
the symmetric part of the Schmid tensor.
The saturation hardness is given by
gs = gso
&&&&"
"s
&&&&#
,
where # is a material parameter, gso is the initial saturation hardness, and " is the total slip rate over all
slip systems,
" =Nss%
!=1
|"!| .
Note that setting # to zero results in a fixed value for the saturation hardness, gs = gso .
The precipitation hardening law was chosen to give strong self hardening, which results from the Orowan
looping mechanism observed in this materrial.
3.1.1 Backward Euler scheme for precipitation hardening
In the case of precipitation hardening, the hardness along slip system $ is updated in the UpdateState()routine with a backward Euler scheme,
g!n+1 = g!
n + !t g!n+1
g!n+1 = g!
n + !t Go
'gsn+1 ! g!
n+1
gsn+1 ! go
(%
"
2&&&S!
ij S"ij
&&&&&&""
n+1
&&&
4
Plan for ever evolving technologies: faster computers, better experimental techniques, more efficient numerical approaches, etc., etc.
6 DDSim: A Damage and Durability Simulator
A Hierarchical Approach
♦ Level I: A fast, analytical, reduced-order filter to determine life-limiting hot-spots in complex structures and approximate Ntotal
♦ Level II: Traditional continuum fracture mechanics, FRANC3D, to compute the life of the structure consumed by growth of microstructurally Large cracks (NMLC)
♦ Level III: Multiscale simulation to compute the life of the structure consumed by incubation, nucleation and propagation of microstructurally small cracks (NMSC)
♦ Level IV: (plan for evolving technologies)
Take full advantage of “what we do now” and develop better numerical methods / physical models
Assuming: Ntotal = NMLC + NMSC A multiscale approach with 3 hierarchical levels:
7 DDSim: A Damage and Durability Simulator
A Brief Excursion – Common Interests
weld data
0.5 1 1.5 2 2.5x 108
0100200
E1
2 4 6x 105
0500
E2
1 2 3x 105
0500
E3
200 400 6000
100200
S1
100 200 3000
100200
S2
20 40 600
10002000
S3
200 400 600 8000
100200
K1
200 400 600 8000
100200
K2
50 100 150 200010002000
K3
0.1 0.2 0.30
100
M1
0.025 0.050
1000
M2
0.1 0.2 0.30
100200
M3
0.5 1 1.5 2 2.5x 108
0100200
E1
2 4 6x 105
0500
E2
1 2 3x 105
0500
E3
200 400 6000
100200
S1
100 200 3000
100200
S2
20 40 600
10002000
S3
200 400 600 8000
100200
K1
200 400 600 8000
100200
K2
50 100 150 200010002000
K3
0.1 0.2 0.30
100
M1
0.025 0.050
1000
M2
0.1 0.2 0.30
100200
M3
many detailed FE models of component
response of laser welds
Op5miza5on for cons5tu5ve
parameters with coarse FE models of component
detailed FE models of system
cons5tu5ve parameters Probability
of Failure
Hierarchical approach for duc5le failure of laser welds – Level I
*SROM *SROM
0.5 1 1.5 2 2.5x 108
0100200
E1
2 4 6x 105
0500
E2
1 2 3x 105
0500
E3
200 400 6000
100200
S1
100 200 3000
100200
S2
20 40 600
10002000
S3
200 400 600 8000
100200
K1
200 400 600 8000
100200
K2
50 100 150 200010002000
K3
0.1 0.2 0.30
100
M1
0.025 0.050
1000
M2
0.1 0.2 0.30
100200
M3
0.5 1 1.5 2 2.5x 108
0100200
E1
2 4 6x 105
0500
E2
1 2 3x 105
0500
E3
200 400 6000
100200
S1
100 200 3000
100200
S2
20 40 600
10002000
S3
200 400 600 8000
100200
K1
200 400 600 8000
100200
K2
50 100 150 200010002000
K3
0.1 0.2 0.30
100
M1
0.025 0.050
1000
M2
0.1 0.2 0.30
100200
M3
0.5 1 1.5 2 2.5x 108
0100200
E1
2 4 6x 105
0500
E2
1 2 3x 105
0500
E3
200 400 6000
100200
S1
100 200 3000
100200
S2
20 40 600
10002000
S3
200 400 600 8000
100200
K1
200 400 600 8000
100200
K2
50 100 150 200010002000
K3
0.1 0.2 0.30
100
M1
0.025 0.050
1000
M2
0.1 0.2 0.30
100200
M3
0.5 1 1.5 2 2.5x 108
0100200
E1
2 4 6x 105
0500
E2
1 2 3x 105
0500
E3
200 400 6000
100200
S1
100 200 3000
100200
S2
20 40 600
10002000
S3
200 400 600 8000
100200
K1
200 400 600 8000
100200
K2
50 100 150 200010002000
K3
0.1 0.2 0.30
100
M1
0.025 0.050
1000
M2
0.1 0.2 0.30
100200
M3
• Simulation of joining (mechanically fastened, bonded, welded, etc.) technology • Combining data from variable-fidelity models • Large-scale computation of full-scale models (time dependent solution of many DOF models) • Simulation of response and damage to complex environments (severe thermal, acoustic,
corrosive, embrittlement) and loading, (e.g., hypersonic) requires multi-physics modeling • Modeling of corrosion (stress and chemical state) • Limited results from experiments – interpolation/extrapolation • Multi-site, multi-component, system-level failure mechanisms • Damage evolution models starting from low length scales • Verification and validation all length and time scales (full large-scale and local) and loading
environments • Robust digital representation of microstructure (see p. 5 Roadmap)
8 DDSim: A Damage and Durability Simulator
How to map:
Stress à Life prediction?
DDSim Level I
Stress field contour plot: Rib-stiffened element
A
B
9 DDSim: A Damage and Durability Simulator
How to map:
Stress à Life prediction?
Stress field contour plot: x-section A,
Rib-stiffened element
DDSim Level I
10 DDSim: A Damage and Durability Simulator
Life prediction contour plot
on original FE Mesh (63,974 surface nodes, average ai=4µm)
• Analytical solutions & field data from undamaged FEM used to estimate service life limited by damage at a large number of possible origins (each mesh node).
• These damage origins do NOT become part of the geometrical model in Level I.
• These damage origins do NOT interact with each other.
• These simplifications readily allow parallel processing.
• Initial flaw size from statistical distribution (eg. particle x-sectional area).
DDSim Level I
11 DDSim: A Damage and Durability Simulator
Life prediction contour plot
on original FE Mesh (63,974 surface nodes, average ai=4µm)
Key Ideas for Level I: High Volume, High Automation, Probabilistic, &
Conservative First Order Analysis
• Analytical solutions & field data from undamaged FEM used to estimate service life limited by damage at a large number of possible origins (each mesh node).
• These damage origins do NOT become part of the geometrical model in Level I.
• These damage origins do NOT interact with each other.
• These simplifications readily allow parallel processing.
• Initial flaw size from statistical distribution (eg. particle x-sectional area).
DDSim Level I
12 DDSim: A Damage and Durability Simulator
Level I is a low-fidelity, multiscale, probabilistic prediction
Reliability, P(N>n) Density of Particle Diameter, µm
Particle radius randomly selected from a list of observed particles ∑
∑==
>=>=
m
ii
ii
nodesm
iii
qBBqaP
aPanNPnNP
;)(
)()|()( #
qi = # broken particles at node i
Under fatigue spectrum: 63,974 FE nodes (i.e. initial flaw locations); 10,000 samples of initial flaw size (w/ particle filter); 20,802 - 99,999 cycles min & max computed life; ~20 min on 170 dual 3.6 GHz processors w/ 4GB RAM
13 DDSim: A Damage and Durability Simulator
Fully 3D crack growth simulation at “hot spots”: • Explicit representation of crack surface in FE model geometry • Automatically inserted at “hot spots” determined by Level I analysis
DDSim Level II
~(6 mm)
14 DDSim: A Damage and Durability Simulator
Fully 3D crack growth simulation at “hot spots”: • Explicit representation of crack surface in FE model geometry • Automatically inserted at “hot spots” determined by Level I analysis
Level I Life prediction contour plot (x-section B slide 13)
DDSim Level II
15 DDSim: A Damage and Durability Simulator
Fully 3D crack growth simulation at “hot spots”: • Explicit representation of crack surface in FE model geometry • Automatically inserted at “hot spots” determined by Level I analysis
Level I Life prediction contour plot (x-section B slide 13)
DDSim Level II
16 DDSim: A Damage and Durability Simulator
Fully 3D crack growth simulation at “hot spots”: • Explicit representation of crack surface in FE model geometry • Automatically inserted at “hot spots” determined by Level I analysis
Level I Life prediction contour plot (x-section B slide 13)
Automatically inserted, grown and remeshed crack, step 8
DDSim Level II
Initial crack, 0.38 mm
17 DDSim: A Damage and Durability Simulator
Fully 3D crack growth simulation at “hot spots”: • Explicit representation of crack surface in FE model geometry • Automatically inserted at “hot spots” determined by Level I analysis
Level I Life prediction contour plot (x-section B slide 13)
Automatically inserted, grown and remeshed crack, step 8
DDSim Level II
~(6 mm)
Initial crack, 0.38 mm
18 DDSim: A Damage and Durability Simulator
Level II Results
a
b
0 1 2 3 4 5 6 7
2000
4000
6000
8000
10000
12000
14000point apoint bmid-‐point
Crack length, (mm)
N, (
load
cyc
les)
NMLC = 9025
Low fidelity NMLC = 803 cycles
High fidelity NMLC = 9025 cycles
~(plate thickness)
19 DDSim: A Damage and Durability Simulator
Level II Conditional Reliability at Hot-spot
NMLC
Level I Level II
Our example is a deterministic calculation, but is not limited to such, e.g. if statistical data were available for parameters in the crack growth equation
20 DDSim: A Damage and Durability Simulator
Level III - Concurrent multiscale w/ L2 coupling
With a first-order, probabilistic prediction completed, focus on the “hot spots” to increase the accuracy of the NMSC prediction using:
• Concurrent multiscale (there are other methods)
• Representative digital microstructure • Best available physics • High performance parallel computing
High resolution meso-scale model
Level I Life contour plot from initial prediction
21 DDSim: A Damage and Durability Simulator
♦ DDSim Level I provides a high volume, highly automated, probabilistic, and conservative life prediction (Ntotal) for real structures & locates areas of high interest for the Level II & III simulations
♦ Level II uses the current best-practice fracture mechanics life predictions methodologies for high fidelity NMLC
♦ The Level III multiscale simulation will incorporate state-of-the-art microstructural models and best-available physics to account for microstructural stochasticity resulting in a high fidelity estimate of NMSC
♦ DDSim, as a multiscale system, will provide microstructurally educated reliability predictions for real structures
Conclusions
Our assumption was: Ntotal = NMLC + NMSC
22 DDSim: A Damage and Durability Simulator
Acknowledgments
Essential Contributors: ♦ Dr. Bruce Carter, Fracture Analysis Consultants ♦ Dr. Gerd Heber, Oxford University ♦ Dr. Jacob Hochhalter, NASA LaRC ♦ Dr. John Papazian, Northrop Grumman ♦ Dr. Wash Wawrzynek, Fracture Analysis Consultants ♦ The Cornell Fracture Group
Financial support: ♦ NASA’s Constellation University Institutes Project
• NCC3-994, Dr. Claudia Meyer ♦ DARPA Structural Integrity Prognosis System Program:
• HR0011-04-C-0003, Dr. Leo Christodoulou ♦ Sandia National Laboratories