Ersan Üstündag

Iowa State University

DANSE:

Engineering Diffraction

Engineering Diffraction: Scope

Main objective: Predict lifetime and performance Needed:

– Accurate in-situ constitutive laws: = f()– Measurement of service conditions: residual and internal stress

Typical engineering studies:– Deformation studies– Residual stress mapping– Texture analysis– Phase transformations

Challenges:– Small strains (~0.1%)– Quick and accurate setup– Efficient experiment design and

execution– Realistic pattern simulation– Real time data analysis– Realistic error propagation– Comparison to mechanics

models– Microstructure simulation

Incidenth1k1l1

Scatteredh1k1l1 Incident

h2k2l2

Scatteredh2k2l2

Incident Neutron Beam

+90° DetectorBank

-90° DetectorBank

Q Q

Compression axisBragg’s law: = 2dsin

100

0

hkl

hkl

hkl

hklhklelhkl d

d

d

dd

Engineering Diffraction: Typical Experiment

Eng. Diffractometers:

SMARTS (LANSCE)

ENGIN X (ISIS)

VULCAN (SNS)

Engineering Diffraction: Vision for DANSE

Objectives:– Enable new science (& enhance the value of EngND output)– Utilize beam time more efficiently– Help enlarge user community

Approach:– Experiment planning and setup: (Task 7.1)

» Experiment design» Optimum sample handling (SScanSS)» Error analysis

– Mechanics modeling (FEA, SCM): (Task 7.2)» Multiscale (continuum to mesoscale)» Constitutive laws: = f()

– Experiment simulation: (Task 7.3)» Instrument simulation (pyre-mcstas)» Microstructure simulation (forward / inverse analysis)

Impact:– Re-definition of diffraction stress analysis– Easy transfer to synchrotron XRD

Use Case: Engineering Diffraction

User

Reduce

()

I(TOF)

NeXus file

ABAQUS

<include>

<include>

pyre-mcstas<include>

Activity Diagram: FEA (Finite Element Analysis)

SNS Laptop Linux cluster

Archive NeXus

Rietveld

a1(P), a2(P)

1c, 2c

ABAQUS

E1, Y1, E2, Y2

1(a1), 2(a2)

(P)

Compare (fmin) & Optimize (E1,Y1…)

1(1), 2(2)

Example: BMG-W fiber composite

Residual stresses

Compression loading at SMARTS

Experiments on 20% to 80% volume fraction of W

Unit cell finite element model

GSAS output for average elastic strain in W in the longitudinal direction

Reference: B. Clausen et al., Scripta Mater. 49 (2003) p. 123

BMG W-BMG composite

20% W/BMG 80% W/BMG

Activity Diagram: FEA (Finite Element Analysis)

1c, 2c

ABAQUS

E1, Y1, E2, Y2

1(a1), 2(a2)

(P)

Compare & Optimize

1(1), 2(2)

experimental data

Power-law

leastsq

<include>

Voce<include>

fmin

<include><include>

Easy utilization of various software components

Constitutive Laws for W

o

n

oo

ooo

for

for

σo

σ

εo ε

n=∞

n=1n=4 σ1

σo

σ

εo ε

θ1

θ0

Power-law Voce

00 1 1

1

( ) 1 exp

Constitutive Laws for W

Voce plasticity more suitable

Unrealistic power-law coefficient (~47)

Unequal weighting of data

-2250

-2000

-1750

-1500

-1250

-1000

-750

-500

-250

0

-0.4 -0.2 0 0.2 0.4

W lattice strain (%)

Ap

plie

d c

om

po

site

str

ess

(MP

a)

Diffraction data

Voce

Power-law

Optimization Results: FEA

Comparison of Optimization Algorithms

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0 100 200 300 400 500 600 700

ABAQUS calls

Re

sid

ua

l (R

wp

)Least Square

Fmin

Fmin Powell

48 min

5 hr 44 min

15 hr 30 min

Also studied:• Stability of algorithms• Effects of initial values -> neural network algorithms

Optimization Results: FEA

Comparison of W Constitutive Laws

0

500

1000

1500

2000

2500

0 0.5 1 1.5 2 2.5 3 3.5 4

Total Strain (%)

vo

n M

ise

s S

tre

ss

(M

Pa

)

W fiber (as-received)

W fiber (in-situ by manual analysis)

W fiber (in-situ by leastsq analysis)

y = 1300 MPa

y = 1140 MPa

Use Case: Engineering Diffraction

User

Reduce

()

I(TOF)

NeXus file

EPSC

<include>

<include>

pyre-mcstas<include>

c c

HEM

• Self-consistent modeling (SCM)

• Estimate of lattice strain (hkl dependent)

• Study of deformation mechanisms

002

200

1

2

002

200

1

2

002

200

3

4

002

200

3

4

103301

5 6

103301

5 6

ScatteringVector

Incident beamIncident beam DetectorDetector

Post ProcessMainProcess

Pre Process

SCM Code Flow

appEpsc.py

collectData.pysetParameters.py

readModelOutput.py

readExpOutput.py

parameters.py

interpolateFunction.py

Set parameters EPSC RunInput Files

getDataModule.py

inputGenerate.py plotEngine.py

textureInput.py

materialsInput.py

processInput.py

diffractionInput.py

Output Files Set data

runEpsc.py

Plot

Optimization Process Optimizer

Pre Process

ExpData

+ smooth(): float

EpscOutput

+ interpolate(): float

Data+ s, e total

+ s, e hkl

+ collect(): array

EpscBlackBox- P: Parameters

- main(): epsc1 ~11.out

DataControl

+ select(): boolean+ weigh(): array

ParameterControl

+ select(): boolean+ set() : float

Optimizer

+ interrupt()

OptController

EpscInput

+ collect(): file

PlotController

+ plot()

+ select(): boolean+ set() : float

Post Process

Optimization Process

Main Process

Analysis Methods

-0.0025

-0.002

-0.0015

-0.001

-0.0005

0

-200 -150 -100 -50 0

Applied Stress (MPa)

Lat

tice

Str

ain

rsca c strain

regular Rietveld c strain

single peak 002

Elastic

Mechanical Loading of BaTiO3

M. Motahari et al. 2006

• Time-of-flight neutron diffraction data from ISIS

• Complete diffraction patterns in one setting

• Simultaneous measurement of two strain directions

Different data analysis approaches:

Single peak fitting: natural candidate; but some peaks vanish as the corresponding domain is depleted

Rietveld: crystallographic model fit to all peaks; but results are ambiguous

Constrained Rietveld: multi-peak fitting, but accounting for strain anisotropy (rsca); most promising

Incident Neutron Beam

+90° DetectorBank

-90° DetectorBank

Q Q

Compression axis

Strain Anisotropy Analysis

Desirable to perform multi-peak fitting (e.g. via Rietveld analysis) to improve counting statistics.

Question: How to account for strain anisotropy (hkl-dependent) due to elastic constants and inelastic deformation (e.g., domain switching)?

Current approach for cubic crystals (in GSAS):

is called ‘rsca’ and is a refined parameter for some peak profiles.

Works reasonably well in the elastic regime, but not beyond.

Need to develop a rigorous approach to allow multi-peak fitting with peak weighting and peak shift dictated by mechanics modeling.

2222222222 )/()( lkhhllkkhAhkl

cAnisotropi

hkl

Isotropic

hkl

hklhklhkl A

d

dd

0

0

cAnisotropi

hkl

Isotropichkl

ASSSSE )2/(2144121111

Out

put V

ecto

rTar

get V

ecto

r

Inpu

t V

ecto

r 2

3

n

11

1

m

2

p

X1

X2

X3

Xn

O1

Op

T1

Tp

Error

Activation process to transport

input vector into the network

i

kj

Wij

Qjk

Backpropagation of error toupdate weights and biases

Neural Network Analysis

Schematic Representation

H. Ceylan et al.

Constitutive Laws for W and BMG

o

n

oo

ooo

for

for

σo

σ

εo ε

n=∞

n=1n=4 σ1

σo

σ

εo ε

θ1

θ0

Power-law Voce

00 1 1

1

( ) 1 exp

WBMG

Input parameters: (σ0)BMG, nBMG, (σ0)W, (σ1)W, (θ0)W, (θ1)W and T

Neural Network Analysis

Approach

L. Li et al.

•1200 runs of ABAQUS with random input parameters

•Training of ANN algorithms with 1100 datasets

•Use of 100 datasets as test case

•Use of experimental data for inverse analysis:

Prediction of ‘optimum’ values of input parameters

400

500

600

700

800

900

1,000

400 500 600 700 800 900 1,000

Given

Art

ifici

al N

eura

l Net

wor

k Pr

edic

tion

Average Absolute Error = 0.21%

(σ1)W

• Successful training of ANN

• Strong influence for this parameter

Neural Network Analysis

Sensitivity Studies

L. Li et al.

• Strong influence by parameters: (σ0)BMG, (σ0)W, (σ1)W and (θ0)W

• Weak/no influence by parameters: nBMG, (θ1)W and T

-0.5

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Applied Stress (MPa)

W L

atti

ce

Str

ain

(%

)

Series1

Series2

Series3

Series4

Series5

Effect of W sigma1 parameter-0.5

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0 500 1000 1500 2000

Applied Stress (MPa)W

Lat

tice

Str

ain

(%

)

Series1

Series2

Series3

Series4

Series5

Effect of BMG n parameter

Neural Network Analysis

Result

L. Li et al.

• Use of experimental data for inverse analysis

• Prediction of ‘optimum’ values of all 7 input parameters

• Previous analyses optimized only 3 parameters

W Consittutive Laws

0

500

1000

1500

2000

2500

0 1 2 3 4

Total Strain (%)

vo

n M

ise

s S

tre

ss

(M

Pa

)W (as-received)

W (in-situ by manual anal.)

W (in-situ by leastsq)

W (in-situ by ANN)

Engineering Diffraction: Microstructure

Si single crystals (0.7 and 20 mm thick)

SMARTS data

Double peaks due to dynamical diffraction

(a)

Sample

Incident beam

45°

(2)

Detectors

ts

A

B

C

1500 mm A'

B'

C'

1.33 1.34 1.35 1.36 1.37 1.380.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.00

0.01

0.02

0.03

0.04

0.05

Nor

mal

ized

inte

nsity

(a.

u.)

d spacing (Angstrom)

Thick Si

Thin Si

Engineering Diffraction: Microstructure

Si single crystal (20 mm thick)

ENGIN-X depth scan

Data originates from surface layers

45°

Incident beam

Sample

Shield

Shield

Sampling volume

2 90°

Detectors

(b)

0.6 0.8 1.0 1.2 1.4 1.6 1.8

Inte

nsity

(a.

u.)

d spacing (Angstrom)

+0.16 mm (edge) -1.84 mm -3.84 mm -5.84 mm -7.84 mm -9.84 mm (center) -11.84 mm -13.84 mm -15.84 mm -17.84 mm -19.84 mm (edge)

Depth

E. Ustundag et al., Appl. Phys. Lett. (2006), in print

Critical question: Transition between a single crystal and polycrystal?

Engineering Diffraction: Team

E. Üstündag‡, S. Y. Lee, S. M. Motahari (ISU)

X. L. Wang‡ (SNS) - VULCAN

C. Noyan‡, L. Li (Columbia) – microstructure

M. Daymond‡ (Queens U., ISIS) – ENGIN X, SCM

L. Edwards‡ and J. James (Open U., U.K.) - SScanSS

C. Aydiner, B. Clausen‡, D. Brown, M. Bourke (LANSCE) - SMARTS

J. Richardson‡ (IPNS)

P. Dawson (Cornell) – 3-D FEA

H. Ceylan (ISU) - optimization

‡ Member of EngND Executive Committee