Ersan Üstündag

Iowa State University

Engineering Diffraction:

Update and Future Plans

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

Incident Neutron Beam

+90° DetectorBank

-90° DetectorBank

Q Q

Compression axis

Engineering Diffraction: Typical Experiment

Proposed Applications

1. Experiment Design and Simulation

• Instrument simulation

• Optimization of parameters

• Microstructure simulation

2. Mechanics modeling I: finite element analysis (FEA)

3. Mechanics modeling II: self-consistent modeling (SCM)

4. Data analysis

Efforts underway in all of these tasks

Experiment Design and Simulation

Instrument simulation

– McStas

– Machine studies (SMARTS, ENGIN X)

Optimization of parameters

– Sample setup and alignment (SScanSS)

– Parametric studies (e.g., neural network analysis)

Microstructure simulation

– Defining the sample kernel for experiment simulation

– Full forward simulation of experiment

ISIS: SScanSS Software

• Implemented on ENGIN X

• Ideal for efficient sample setup

• Controlled by IDL scripts

• Generates a computer image of sample

• Creates and executes a measurement plan

• Performs GSAS analysis

• Creates 2-D data/result plots

J. James et al.

Experiment Design and Simulation

Instrument characterization (machine studies)

SMARTS

1.340 1.350 1.360 1.370 1.380

0.000

0.004

0.008

0.012

0.016

0.020

0.024

0.028

0.032

0.036

-0.010

0.000

0.010

0.020

0.030

0.040

0.050

0.060

I norm (62) I norm (63) I norm (64)N

orm

aliz

ed

inte

nsi

ty (

de

tect

ors

)

d spacing (A)

Bank 1

Si 004theta = -44.700

No

rma

lize

d in

ten

sity

(B

an

k 1

)

22000 24000 26000 28000 30000

0

2

4

6

8

10

12

14

Inte

nsity

(a.

u.)

Time-of-flight (TOF), microseconds

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

Depth Scan

ENGIN-X

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°

D(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)

Critical question: Transition between a single crystal and polycrystal?

Object Oriented Finite Element Analysis

A. Reid (NIST)

• Modeling of real microstructure

• Will be employed in DANSE for microstructure modeling

• Needs to become 3-D and validated

Three Grain Model Description

xy

z

5 μm 5 μm

1 μm

0.1 μm

x-dim

[111] [001] [111]

Unixaxial Tension:

σapplied = 100, 200 & 300 MPa (along x)

x-dim varies:5 μm, 3 μm, 1 μm, 0.8 μm, 0.6 μm

Cu parametersC111

11 = 220.3 GPa, C11112 = 104.1 GPa, C111

44 = 40.8 GPa

C00111 = 168.4 GPa, C001

12 = 121.4 GPa, C00144 = 75.4 GPa

I.C. Noyan et al.

Microstructure Simulation

Results from FE Model (300 MPa)

Using COMSOL Multiphysics, we obtain the out of plane strain along center line in central grain.

xy

z

5 μm 5 μm

1 μm

0.1 μm

3 μm

Interaction strain we are interested in measuring.

Bulk Strain Values

I.C. Noyan et al.

Using kinematic diffraction theory, we simulate a rocking curve diffraction pattern.

Total peak shift of ~0.05o from any one edge.

Kinematic X-Ray Modeling

~0.05o

Individual Peaks

I.C. Noyan et al.

Peak Fitting Analysis

Fitting the diffraction peak with multiple Gaussians, it is possible to determine the peak position and breadth at each step of the summation.

A FWHM value does not necessarily predict a unique strain distribution in a specimen.

I.C. Noyan et al.

•How to determine strain profiles from peak position and shape?

•What happens in the inelastic regime?

Mechanics Modeling

Finite element analysis (FEA)

– ABAQUS

– Optimization of material parameters

Self-consistent modeling (SCM)

– EPSC code from LANL

– Optimization of material parameters

Mechanics Modeling: 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)

ABAQUS CALL

call services call services

Framework

Optimizer

Visualizer

Preprocessor

Main processor

Postprocessor

Use Case Diagram for FEA Application

FEA (Finite Element Analysis)

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 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 DT

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 DT

• Rigorous experiment planning to optimize data collection

-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 L

atti

ce S

trai

n (

%) Series1

Series2

Series3

Series4

Series5

Effect of W σ1 parameter-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0 500 1000 1500 2000 2500

Applied Stress (MPa)W

Lat

tice

Str

ain

(%

)

Series1

Series2

Series3

Series4

Series5

Effect of W θ0 parameter

Important region

-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

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)

FEA (Finite Element Analysis)

Custom (standard) geometries as templates

API release planned for 2007

Mechanics Modeling: Self-Consistent Model

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

• In collaboration with C. Tome (LANL)

• Parallel modularization of EPSC, VPSC codes and DANSE implementation

Data Analysis

Peak fitting

– Rietveld (full-pattern) analysis GSAS, DiffLab

– Single peak fitting

Integration of mechanics models to peak fitting

– Strain anisotropy analysis

Texture analysis and visualization (MAUD)

Real-time data analysis

Analysis Methods

-0.0025

-0.002

-0.0015

-0.001

-0.0005

0

-200 -150 -100 -50 0

Applied Stress (MPa)

Lat

tice

Str

ainrsca c strain

regular Rietveld c strain

single peak 002

Elastic

Data Analysis: 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.

Needed: rigorous 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/(21

44121111

Integration of crystallographic and mechanics models

Anisotropic Strain Analysis in Rietveld

a

c

cos isotropichkl

2 2 4 2 23 11 3 33 3 3 13 44

1(1 ) (1 )(2 )

hkl

l S l S l l S SE

)1()1( 23

233

432

2231 llllisotropichkl

30

35

40

45

50

55

60

0 10 20 30 40 50 60 70 80 90 100

phi angle (degrees)

Eh

kl

Ehkl

up to cos(phi)^1

up to cos(phi)^2

up to cos(phi)^3

16

18

20

22

24

26

28

30

0 20 40 60 80 100

phi angle (degrees)

1/E

hkl

1/Ehkl

1 parameter

2 parameters

3 parameter

Engineering Diffraction: Team

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

X. L. Wang‡ (SNS) - VULCAN

C. Noyan‡, L. Li, A. Ying (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