ersan Üstündag iowa state university danse: engineering diffraction
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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