The document reviews challenges related to automated characterization of microstructures from X-ray microtomography images of engineering materials. It presents case studies on characterizing intergranular stress corrosion cracking in stainless steel wires and extracting bridge ligaments along cracks. Advanced 3D image processing techniques like minimal surface segmentation and hole closing algorithms are demonstrated to extract crack surfaces and bridge ligaments from the microtomography data in a quantitative way. The study aims to increase awareness in the materials community of such computational approaches for automated and quantitative analysis of complex microstructures from 3D imaging.

1. Review
of
challenges
related
to
automated
X-­‐
ray
microtomography
image
characteriza:on
of
engineering
materials
L.
Babout1,
P.J.
Withers2
1Ins:tute
of
Applied
Computer
Science,
Lodz
Univ.
Technology,
Poland
2Henry
Moseley
X-­‐ray
Imaging
Facility,
School
of
Materials,
University
of
Manchester,
UK
Warsaw,
Poland,
September
20
–
24,
2015

2. Agenda
• Introduc:on
– General
context
– Advanced
3D
image
processing
– Mo:va:on
• Case
studies
– Extrac:ng
bridge
ligaments
along
IGSCC
in
stainless
steel
– Correla:ng
fa:gue
crack
propaga:on
with
lamellar
microstructure
in
(α+β)
Ti
alloy
– Structure
characteriza,on
of
GFRP
– Towards
local
characteriza:on
of
structural
changes
in
auxe:c
polyurethane
foam
during
deforma:on
• Concluding
remarks
2

3. 3
3
Introduc:on:
general
context
• Materials
route:
from
fabrica:on
to
modelling
Fabrica:on
Heat
treatment
Assembling
Tests/Service
Modeling
and
op:misa:on
Microstructural
characterisa.on
Effects
of
degrada:on
processes
on
proper:es
/
microstructural
changes
Degrada.on
process:
succession
of
steps
generated
by
an
exposure
to
an
external
environment
which
causes
prejudice
to
a
structure
by
weakening
one
or
more
key
proper.es.

4. 4
4
Introduc:on:
general
context
• Numerous
ways
to
image
microstructure
– Different
scales,
local/global
– Possibility
to
combine
with
in
situ
tests
– Imaging
techniques,
spanning
almost
the
alphabet
www.hexapolis.com
E.H.
Lehmann
et
al.
2010
G.C.
Yin
et
al.
2006
W.
Ludwig
et
al.
2010
P.
Cloetens
et
al.
2000
N.
Limodin
et
al.
2010

5. • Characteriza:on:
qualita:ve
è
quan:ta:ve
• Informa:on
extrac:on
– “sofware
engineering”
approach
– “computer
science”
approach
• Time
vs.
accuracy
dilemma…
Introduc:on:
general
context
:me
accuracy
SE
CS
“…The
α-­‐Al
dendri:c
structure
was
segmented
by
hand
into
sub-­‐volumes
of
350
×
220
×
200
voxels
(…)
to
i m p r o v e
t h e
q u a l i t y
o f
t h e
reconstructed
slices.”
Ar,cle
published
in
Acta
Mater.
(2012)
5
Manual
coun:ng
L.
Babout
et
al.
2001,
2004

6. Introduc:on:
advanced
IP
Digital/discrete
topology
Graph-­‐based
IP
Non
linear
filtering
in
spa.al/frequency
domain
f ⊗g
ω1
ω2
ω3
-(π,π,π)
(π,π,π)
!
Texture
analysis/PaHern
recogni.on
6

7. Introduc:on:
mo:va:on
• Two
scien:fic
communi:es
with
common
interest
• …but
with
limited
interac:on
• Raise
the
awareness
of
the
MS&E
community
on
exis:ng
advanced
IP
approaches
7
1mm
MS&E
I
have
tremendous
data
but
don’t
know
how
to
analyze
them!
CS
I
have
tremendous
IP
algo.
but
don’t
have
real
data
to
test
it!

8. 8
Case
study
#1:
IGSCC
in
stainless
steel
Detector
302
stainless
steel
wire
(Φ0.4mm)
X-­‐ray
Source
Tensile
machine
Cell
with
corrosive
solu:on
(K2S4O6
–
pH
2)
•
SR:
0.7
μm,
E=30
keV,
1500
projec:ons,
distance
sample-­‐detector:
4
cm
•
Sample
coupled
to
counter
electrodes
(Al
/
Pt)
to
stop/start
corrosion
ac:vity
•
Tensile
load:
up
to
100
MPa
(10-­‐15
MPa
during
tomography
observa:ons)
• Experimental
set-­‐up:
ID19
beamline
(ESRF)
L.
Babout
et
al.
2006

9. 9
Case
study
#1:
IGSCC
in
stainless
steel
40
µm
Scan
1
Scan
2
40 µm
L.
Babout
et
al.
2006
• 2D
images
reveal
evolu:on
of
bridge
ligaments
along
crack
over
:me
• What
about
visualisa:on
of
bridges
in
3D?
Scan
3
40 µm

10. • How
can
we
segment
the
crack?
• One
way
is
by
using
the
Minimal
Surface
by
Maximum
Flow
method
10
Case
study
#1:
IGSCC
in
stainless
steel
∂P
∂τ
= −∇⋅F
∂F
∂τ
= −∇P
F ≤ g
B.
Appleton
and
H.
Talbot
2006
S
E S⎡⎣ ⎤⎦ = g S( )ds
S
∫
∀x ∈Smin
: Fmax
x( )= g x( )N x( )
A.
Kornev
et
al.
2010

11. • Now,
the
IGSCC
reveals
the
presence
of
holes,
corresponding
to
bridge
ligaments
in
the
sample
• Problema:c:
bridges
do
not
correspond
to
standard
features
(not
subsets
of
the
3D
space)
• Hole
closing
algorithm
can
extract
them
for
you!
11
Case
study
#1:
IGSCC
in
stainless
steel

12. 12
Case
study
#1:
IGSCC
in
stainless
steel
• Hole
filling
algorithm
– Based
on
approach
by
Atkouf
et
al.
– thinning
approach
which
is
based
on
discrete
geometry
no:ons
such
as
topological
numbers
and
topological
preserva:on
– Method:
• Generate
cuboid
Y
which
contains
object
X
• Voxels
p
of
YX
with
special
topological
number
are
sequen:ally
removed
from
the
furthest
to
the
closest
of
X
un:l
2D-­‐isthmuses
which
fill
the
holes
in
the
object
remain
(HCA)
• Filling
of
the
local
volume
of
the
hole
which
approximate
the
local
thickness
of
the
object
X
(HFA)
M.
Janaszewski
et
al.
2010
Z.
Aktouf
et
al.
2002

13. 13
Case
study
#1:
IGSCC
in
stainless
steel
Superposi:on
on
fracture
surface
together
with
crack:
history
of
IGSCC
HCA
for
bridge
segmenta:on
Bridge
A
Bridge
B
Bridge
C
θ
(°)
62
86
83
Scan
#2
541
μm2
-­‐
382
μm2
Scan
#3
282
μm2
770
μm2
161
μm2
Scan
#4
106
μm2
443
μm2
-­‐
L.
Babout
et
al.
2011
20 µm
crack
bridge
θ

14. Case
study
#2:
fa:gue
crack
in
Ti
alloy
• Lamellar
microstructure
of
(α+β)
Ti
alloy
• Complex
microstructure
/
Need
to
understand
short
fa:gue
crack-­‐microstructure
interac:on
• X-­‐ray
CT
+EBSD
study
shown
crack
propaga:on
influenced
by
– β-­‐gb
misorienta:on
– α-­‐lamellae/colonies
favorably
oriented
for
<a>
basal
slip
and
<a>
prisma:c
slip
14
S.
Birosca
et
al.
2009

15. Case
study
#2:
fa:gue
crack
in
Ti
alloy
• α
plates
growth
in
the
β
phase
Burgers
rela:onship:
(100)β
||
(0002)α
and
[1-­‐11]β
||
[11-­‐20]α
• What
about
propor:on
of
trans-­‐/inter-­‐lamellar
cracking?
Ø X-­‐ray
μCT
/
in
situ
fa:gue
Ø Image
processing:
crack
segmenta:on
/
α-­‐lamellar/colony
segmenta:on
/
(β-­‐gb
segmenta:on)
α
plates
(1-­‐100)
(0002)
TL
crack
IL
crack
15

16. Case
study
#2:
fa:gue
crack
in
Ti
alloy
• Experimental
set-­‐up
• ME1230
(ID19
ESRF)
– X-­‐ray
μCT:
0.7μm,
40
keV,
phase
contrast
– fa:gue:
50
Hz,
0.5σ0.2,
R=0.1
• 2
samples
of
Ti-­‐6246
with
notch
notch
β-­‐gb
α-­‐colony
β
grain
1
β
grain
2
crack1
crack2
27
kcycles
16

17. Case
study
#2:
fa:gue
crack
in
Ti
alloy
• Image
processing:
α-­‐lamellae/colony
segmenta.on
• direc:onal
filter
bank
(DFB)
using
special
structuring
element
sensi:ve
to
surface-­‐like
objects
• Complementary
of
HourGlass
(CHG)
filter
bank
– tunable
(default:
r=5,
θ=22.5°)
– Epanechnikov
profile
– Default:
13
direc:ons
in
<100>,<110>
and
<111>
direc:ons
θ
n
r
[1
0
0]
[0
1
0]
[0
0
1]
[-­‐1
1
1]
[1
1
1]
[1
-­‐1
1]
[1
1
-­‐1]
[1
0
-­‐1]
[1
0
1]
[1
1
0]
[1
-­‐1
0]
[0
1
1]
[
0
1
-­‐1]
y
x
z
17
L.
Babout
et
al.
2013a

18. Case
study
#2:
fa:gue
crack
in
Ti
alloy
• Lamellar
classifica:on
(largest
response
to
DFB)
[1 1 1]
[1 1 0]
[1 1 -1]
[1 0 1]
[1 0 0]
[1 0 -1]
[1 -1 1]
[1 -1 0]
[-1 1 1]
[0 1 1]
[0 1 0]
[0 1 -1]
[0 0 1]
x
y
z
18

19. Image
processing:
β-­‐gb
segmenta.on
• Challenging
task
– local
similarity
of
α-­‐layer/α-­‐lamellae
– phase
contrast
“leaks”
• Mul:ple
step
approach
19
Case
study
#2:
fa:gue
crack
in
Ti
alloy
L.
Babout
et
al.
2013b

20. • Step
1:
Edge
preserving
smoothing
• Goal:
vanish
as
much
as
α-­‐lamellae
as
possible
while
keeping
sharp
β-­‐gb
• Possible
methods:
– non
linear
diffusion
filtering
(used
in
Amira)
– Mean
shif
smoothing
• Step
2:
Segmenta.on
+
hole
closing
correc.on
• Undersegmenta:on
of
β-­‐gb
leaves
holes
• Can
be
filled
using
HCA
20
Case
study
#2:
fa:gue
crack
in
Ti
alloy
D.
Comaniciu
and
P.
Meer,
2002
Manual
segmenta:on

21. • Step
3:
CHG
filtering
+topological
criterion
• Numerous
surface-­‐like
defects
can
be
dis:nguished
from
β-­‐gb
using
CHG-­‐DFB
• Size
criterion
and
topological
criterion
helps
at
removing
them
– based
on
topological
numbers
– usually
defects
have
more
border
points
than
2D
junc,on
points
isthmus
junc:on
border
Defect
Afer
CHG-­‐DFB
21
Case
study
#2:
fa:gue
crack
in
Ti
alloy

22. • Step
4:
crack
segmenta.on
and
image
registra.on
• Crack
segmented
from
tomo.
image
at
t1
…
• …
Superimposed
with
microstructural
features
from
tomo.
image
at
t0
x
y
z
[1
1
1]
[1
1
0]
[1
1
-­‐1]
[1
0
1]
[1
0
0]
[1
0
-­‐1]
[1
-­‐1
1]
[1
-­‐1
0]
[-­‐1
1
1]
[0
1
1]
[0
1
0]
[0
1
-­‐1]
[0
0
1]
crack
notch
β-­‐gb
22
Case
study
#2:
fa:gue
crack
in
Ti
alloy
L.
Babout
et
al.
2014

23. • Quan.fica.on:
crack
vs.
microstructural
features
• 2
samples
–
2
scenarios
(notch
posi:on)
• Crack
orienta:on
w.r.t.
fa:gue
loading
(z-­‐axis)
– CHG
classifica:on
+
MV=max{λi}i=1,2,3V
Sample
A
30°-40°
20°-30°
10°-20°
0°-10°
80°-90°
70°-80°
60°-70°
50°-60°
40°-50°
50 µm
x
y
z
crack #2
crack #1
Sample
B
30°-40°
20°-30°
10°-20°
0°-10°
80°-90°
70°-80°
60°-70°
50°-60°
40°-50°
z
x
y
β-gb1
β-gb2
β-gb3
23
Case
study
#2:
fa:gue
crack
in
Ti
alloy

24. • Cracks
crossing
colonies
of
≠
orienta:ons
– sA:
crack1
not
deflected
by
numerous
colonies
– sB:
strong
deflec:on
in
same
colony
([001])
near
notch
x
y
z
[1 1 1]
[1 1 0]
[1 1 -1]
[1 0 1]
[1 0 0]
[1 0 -1]
[1 -1 1]
[1 -1 0]
[-1 1 1]
[0 1 1]
[0 1 0]
[0 1 -1]
[0 0 1]
[0 1 -1]
[-1 1 1]
[1 1 1]
[1 1 -1]
[1 -1 1]
x
y
z
[0 1 1]
[0 0 1]
[0 1 1]
β-gb1
β-gb2
β-gb3
24
Case
study
#2:
fa:gue
crack
in
Ti
alloy

25. • Angle
between
crack
and
lamellar
orienta:on
– lamellar
orienta:on:
3D
gradient
map
+
MV=max{λi}i=1,2,3V
– inter-­‐
lamellar:
angle
<
30°
x
y
z
80°-90°
70°-80°
60°-70°
50°-60°
40°-50°
30°-40°
0°-30°
x
y
z
β-gb1
β-gb2
β-gb3
25
Case
study
#2:
fa:gue
crack
in
Ti
alloy

26. • Trans-­‐lamellar
cracking
predominant
– ~60%
larger
than
70°
– colonies
favorably
oriented
for
basal
<a>
slip
• Non
negligible
inter-­‐lamellar
– 10-­‐20%
– prisma,c
<a>
slip
• The
2
samples
show
similar
trends
• Complete
Birosca
et
al.
EBSD
observa:ons
26
Case
study
#2:
fa:gue
crack
in
Ti
alloy

27. • Problem
with
image
processing:
always
space
for
improvement
• Recent
approach
combining
orienta:on
histogram
and
watershed-­‐based
segmenta:on
• Inspired
by
Jeulin
and
Moreaud’s
approach
• Step
1:
local
orienta.on
maps
using
PCA
(Arnoldi
method)
–
Hadamard
product
27
Vx
Vy
Vz
D.
Jeulin
and
M.
Moreaud.
2008
X
Y
Z
Another
angle
to
approach
direc:onal
textured
image
segmenta:on

28. • Step
2:
cartesian
(x,y,z)-­‐to-­‐polar
(θ,ϕ)
coordinate
conversion
+
2D
histogram
• Vθ=atan(Vy/Vx)
ϵ
[-­‐90
90]
• Vϕ=acos(Vz)
ϵ
[0
180]
28
Segmenta:on
of
α-­‐colonies
in
Ti
alloy
Vϕ
Vθ
0
180
90
-­‐90
90
0
X
Y
Z
Vϕ
Vθ

29. • Step
3:
histogram
par..oning
using
grayscale
watershed
with
markers
watershed
par::oning
(afer
image
mirroring)
0
H2
12
labelled
regions
in
H2P
29
Segmenta:on
of
α-­‐colonies
in
Ti
alloy
M.
Couprie
and
G.
Bertrand.
1997
F.
Meyer
1994

30. 30
Segmenta:on
of
α-­‐colonies
in
Ti
alloy
• Step
4:
segmenta.on
∀p ∈I,SI
p( )= H2PI
Vϕ
p( ),Vθ
p( )( )
Visible
improvement
over
CHG!
Is
it
worth
it?
CHG-­‐based
segmenta:on

31. • May
be
not
if
we
look
at
the
recent
breakthrough
in
Near
field
High
Energy
X-­‐ray
diffrac.on
microscopy
@
APS
…
• New
way
to
image
polycrystalline/polyphase
materials
from
R.
Suter’s
team
(Carnegie
Mellon
Univ.)
• Recently
applied
to
fully
lamellar
Ti-­‐6Al-­‐4V
31
E.
Wielewski
et
al.
2015
α
colonies
Recovered
primary
β
grains

32. • …However,
may
be
useful
for
other
types
of
materials
with
direc.onal
microstructure
• Example:
GFRP
– wef
and
binder
yarn:
90°
to
each
other
– similar
approach
to
lamellar
segmenta:on
32
J.
Stein
et
al.
2014
H2
H2P
3D
gradient
map
+
MV=min{λi}i=1,2,3V

33. 33
• GFRP
segmenta.on
• Possibility
to
separate
groups
of
wefs
• Segmenta:on
preŒy
sa:sfying
for
a
first
go

34. 34
Case
study
#3:
characteriza:on
of
auxe:c
polyurethane
foam
• Problema:c:
– Auxe:c
:nega:ve
Poisson
ra:o.
So
tendency
to
expand
/
contract
laterally
when
stretched
/
compressed
– How
this
process
occurs
locally
(at
the
level
of
the
joints/ribs)
in
APF?
Joint
rota:on?
Ribs
straightening,
stretching
and
twis:ng?
• Primary
objec:ves
– Scan
polyurethane
foam
samples
(classic/auxe:c)
@
HMXIF
for
different
tension
loading
– Extract
joints
/
ribs
from
curvilinear
skeleton
of
foam
– Look
at
local
geometrical
characteris:cs
and
see
how
they
evolve
over
deforma,on
,me

35. 35
• Comparison
auxe.c
/
conven.onal
foam
• Auxe:c
presents
bent
ribs
while
conven:onal
foam
has
cells
with
polygonal
shape
• Usually
cells
consist
of
4-­‐6
joints
• Curvilinear
skeleton
helps
in
quan:fying
microstructural
features
such
as
rib
length,
curvature,
joint-­‐to-­‐joint
distance
Classical
foam
Auxe:c
foam
Case
study
#3:
characteriza:on
of
APF

36. 36
• How
to
quan.fy
microstructure?
• Best
way
is
to
use
graph
theory:
joint
ó
node,
ribósegment,
cellócycle
• Extract
each
feature
from
ul:mate
curvilinear
skeleton
(Amira)
Node 1
Node 2
d
l
α1
α2
α1
α2 α3
α4
L1
L2
L3
L4
Node
characterisa:on
Cycle
characterisa:on
Case
study
#3:
characteriza:on
of
APF

37. 37
Cycle
characteriza:on
• Problem:
which
R+T
combina:on
needed
for
cycle
to
recover
polygonal
shape?
α1
α2 α3
α4
L1
L2
L3
L4
L1
L2
L3
L4
α1 α4
α2 α3
•
Need
to
quan:fy
if
conserva:on
of
angle
for
polygon
s:ll
true
for
auxe:c
structure
(error
es:ma:on)
( ) 1802
1
×−≡∑
=
N
N
i
iα
•
Also
the
level
of
cycle
distor:on
related
to
auxicity
can
be
easily
evaluated
from
rib
length-­‐to-­‐joint
distance
ra:o
Df
=
1
N
li
dii=1
N
∑
Case
study
#3:
characteriza:on
of
APF
• Parameters
can
be
visually
checked
locally
using
hole
closing
algorithm

38. Normal
foam
[0-­‐1[
[1-­‐2[
[2-­‐5[
[5-­‐10[
[10-­‐20[
[20-­‐50[
• Polygon
rule
verified
in
the
very
large
majority
(error
<
2%)
• Skeletoniza:on
and
tangent
es:ma:on
adequate
38
Case
study
#3:
characteriza:on
of
APF

39. Auxe:c
foam
[0-­‐1[
[1-­‐2[
[2-­‐5[
[5-­‐10[
[10-­‐20[
[20-­‐50[
39
Case
study
#3:
characteriza:on
of
APF
• More
than
200
cycles
analyzed
• ~55%
of
cycles
for
which
error
>2%
!

40. How
to
interpret
this?
• Correla:on
between
structure
deforma:on
and
loss
of
polygon
rule
during
conversion
(compression/hea:ng)
process
?
• Or
is
it
simply
a
problem
in
the
tangent
descriptor
as
rib
distorted?
Skeletoniza:on?
40
Case
study
#3:
characteriza:on
of
APF

41. Concluding
remarks
• Three
cases
studies
to
show
the
need
of
advanced
IP
for
materials
characteriza:on…
• …But
not
an
easy
task
• Not
yet
a
centralized
plaŽorm
informing
how
to
find
his
way
through
the
myriads
of
IP
approaches
– Commercialized
sofware:
Avizo,
Simpleware,
Aphelion,
VGStudio
Max,
Matlab…
– Free
sofware:
ImageJ
and
co.
(good
lis:ng
@
nic.med.harvard.edu)
– Plugins/libraries:
• Java:
ImageJ
(hŒp://imagejdocu.tudor.lu/)
• C:
PINK:
library
from
ESIEE
(univ.
Paris-­‐Est)
• C++:
VTK,
ITK,
DGTal
• Matlab:
Matlab
File
exchange
• Python:
scikit-­‐image
• Stronger
coopera:on
between
materials
and
computer
scien:sts
is
an
evidence!
41

42. Acknowledgements
• ESRF-­‐ID19:
E.
Boller,
P.
Cloetens
• IGSCC
– T.
J.
Marrow
(Univ.
Oxford)
– D.
Engelberg
(Univ.
Manchester)
– J.-­‐Y.
Buffiere
(INSA-­‐Lyon)
– M.
Janaszewski
(Lodz
Univ.
of
Technology)
– M.
Couprie
(ESIEE,
Univ.
Paris-­‐Est)
• Ti
alloy
– M.
Preuss
(Univ.
Manchester)
– S.
Birosca
(Swansea
University)
– J.-­‐Y.
Buffiere
(INSA-­‐Lyon)
– L.
Jopek,
R.
Al
Darwich,
M.
Janaszewski
(Lodz
Univ.
of
Technology)
42

43. Acknowledgements
43
• GFRP
– P.M.
Mummery
(Univ.
Manchester)
• Polyurethane
foams
– S.A.
McDonald
(Univ.
Manchester)
• SPECIAL
THANK
TO
P.J.
WITHERS