3D quantification
of trans- and inter-lamellar
fatigue crack in Ti alloy
L. Babout1, L. Jopek1, M. Preuss2
1Institute of Applied Computer Science, Lodz University of
Technology, Poland2School of Materials, University of Manchester, UK
[email protected], http://lbabout.iis.p.lodz.pl
Outline
• Introduction
• Experimental set-up
• Image processing steps
• Results
• Conclusion
Introduction (1/4)
• Myriads of applications of Ti alloy
• Different complex microstructures
• Need to understand short fatigue
crack-microstructure interaction
• X-ray microtomography: technique of
choice for mechanistic studies of
crack propagation
Introduction (2/4)
• Lamellar microstructure of (α+β) Ti alloy
• X-ray CT +EBSD study[1] shown crack
propagation influenced by
– β-gb misorientation
– α-lamellae/colonies favorably oriented for <a>
basal slip and <a> prismatic slip
[1] Birosca et al. Acta Mater., 2009, 57: 5834-5847
Introduction (3/4)
• α plates growth in the β phase Burgers
relationship: (100)β || (0002)α and [1-11]β || [11-20]α
α plates (1-100)
(0002)
TL crack
IL crack
Introduction(4/4)
• What about proportion of trans-/inter-
lamellar cracking?
X-ray μCT / in situ fatigue
Image processing:
crack segmentation
α-lamellar/colony segmentation
(β-gb segmentation)
Local orientation calculation
Experimental set-up• ME1230 (ID19 ESRF, back to 2006!)
– X-ray μCT: 0.7μm, 40 keV, phase contrast
– fatigue: 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
Image processing: α-colony
segmentation
• Existing method: local orientation map
based on image gradient (eigenvector
calculation)[1,2]
• Our method: directional filter bank (DFB)
using special structuring element
sensitive to surface-like objects[3]
[1] D. Jeulin, M. Moreaud, Im. Anal. Stereol., 2008, 27: 183-192.
[2] N. Vanderesse et al., Scripta Mater., 2008,58: 512-515.
[3] L. Babout, L. Jopek, M. Janaszewski, In 13th IAPR International Conference on Machine Vision
Applications. Kyoto. 2013.
CHG filter(1/2)
• Complementary of HourGlass
– tunable (default: r=5, θ=22.5°)
– Epanechnikov profile
– Default: 13 directions in <100>,<110> and
<111> directions
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
CHG filter (2/2)
• Lamellar classification (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
yz
Image processing: β-gb
segmentation
• Challenging task
– local similarity of
α-layer/α-lamellae
– phase contrast “leaks”
• Multiple step
approach
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 shift smoothing[1]
• Does not fully solve
the problem
[1] Comaniciu et al., IEEE Trans.Pattern Anal.Mach.Intell., 2002, 17: 790-799.
NC>2950
Step 2: hole closing correction
Manual
segmentation
• Undersegmentation of β-gb leaves holes
• Can be filled using
Hole Closing Algorithm[1,2]
• Successfully used for
IGSCC in stainless steel[3]
[1] Z. Aktouf et al., Pattern Recogn. Lett., 2002, 23: 523-531.
[2] M. Janaszewski, et al., Pattern Recogn. Lett., 2011, 32: 2231-2238.
[3] L. Babout et al., Scripta Mater., 2011, 65: 131-134.
20 μm
crack
bridge
Step 3: CHG filtering +topological
criterion• Numerous surface-like defects can be distinguished from
β-gb using CHG-DFB
• Size criterion and topological
criterion helps at removing
them
– based on topological numbers
– usually defects have more border
pts than 2D junction pts
i
s
t
h
m
u
s
Defect
After CHG-DFB
Image processing: crack
segmentation and image registration
• 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
Results (1/4)• 2 samples – 2 scenarios (notch position)
• Crack orientation w.r.t. fatigue loading (z-axis)
– CHG classification + 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°
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
Results (2/4)
• Cracks crossing colonies of ≠ orientations
– sA: crack1 not deflected by numerous colonies
– sB: strong deflection 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
Results (3/4)• Angle between crack and lamellar orientation
– lamellar orientation: 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
Results (4/4)• Trans-lamellar cracking predominant
– ~60% larger than 70°
– colonies favorably oriented for basal <a> slip
• Non negligible
inter-lamellar
– 10-20%
– prismatic <a> slip
• Samples show
similar trends
• Comfort Birosca
et al. EBSD observations
Conclusions
First 3D quantitative analysis of cracking type in
lamellar Ti Alloy using well-suited image
processing strategy
Short fatigue crack propagation strongly driven
by the crystallographic nature of the colonies
when favorably oriented (i.e. basal/prismatic slip)
Possible future work
Test method on Birosca et al. tomography data
DCT (above β transus) + IP + known variants 3D
crystallographic orientation of α phase
Microstructure Faithful Modeling
Acknowledgements
• Polish National Research Centre (grant no:
6522/B/T02/2011/40)
• ME1230 team
– J.Y Buffiere (Quezac support )
– M. Karadge
– F. Garcia-Pastor
