Airframe Digital Twin - DDSim: A Multiscale Damage …...DDSim: A Multiscale Damage and Durability Simulation Strategy Digital Twin Workshop NASA Langley Research Center John Emery,

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


Fatigue is Inherently Multiscale and Stochastic!

~1m


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!.



g! = Go

#gs ! g!

gs ! go

$ %

"

2&&&S!

ij S"ij

&&&&&""

&& ,




gs = gso

&&&&"

"s

&&&&#

,


slip systems,

" =Nss%

!=1

|"!| .






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


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!.



g! = Go

#gs ! g!

gs ! go

$ %

"

2&&&S!

ij S"ij

&&&&&""

&& ,




gs = gso

&&&&"

"s

&&&&#

,


slip systems,

" =Nss%

!=1

|"!| .






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!.



g! = Go

#gs ! g!

gs ! go

$ %

"

2&&&S!

ij S"ij

&&&&&""

&& ,




gs = gso

&&&&"

"s

&&&&#

,


slip systems,

" =Nss%

!=1

|"!| .






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.


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:


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)


How to map:

Stress à Life prediction?

DDSim Level I

Stress field contour plot: Rib-stiffened element

A

B


How to map:

Stress à Life prediction?

Stress field contour plot: x-section A,

Rib-stiffened element

DDSim Level I


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


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


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


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)



Level I Life prediction contour plot (x-section B slide 13)

DDSim Level II




DDSim Level II




Automatically inserted, grown and remeshed crack, step 8

DDSim Level II

Initial crack, 0.38 mm




Automatically inserted, grown and remeshed crack, step 8

DDSim Level II

~(6 mm)

Initial crack, 0.38 mm


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)


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


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


♦ 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


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

Documents

Airframe Digital Twin - DDSim: A Multiscale Damage …...DDSim: A Multiscale Damage and Durability Simulation Strategy Digital Twin Workshop NASA Langley Research Center John Emery,