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

laurent.babout@p.lodz.pl, 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