Post on 01-Jan-2016
A Study of Crack Formation and its Effective Internal Surface A Study of Crack Formation and its Effective Internal Surface Area using Area using
X-ray Micro-Tomography (XMT) X-ray Micro-Tomography (XMT)
University of Johannesburg
Energy Postgraduate Conference 2013
Introduction X-ray Microtomography (also referred to as micro CT) is a
radiographic imaging technique that can produce 3D images of
a material's internal structure at a spatial resolution < 1μm
(Landis et al. 2010).
Fractal techniques have been used extensively to characterize
crack formation via details of the crack surface roughness.
•They represent defects in solid materials
• To find convenient scale invariant ways for their characterisation
• Phase reactions occur at the fluid-material interface
• The larger the effective area of interaction the faster the reaction
rate
Why cracks are important to
study
Intuitive definition of dimensionConsider a geometric object F, with measure (F)
F (F) (F)
Line segment Length 21 = 2
Rectangle Area 22 = 4
Parallelepiped Volume 23 = 8
s dim F = (F) r= 1/s resolution
FsF loglogdim
sFF loglogdim
rFF 1loglogdim
If F is scaled by a factor of 2 say, how does the measure scale?
Von Koch Curve (Self-similar Construct)
1 D line segmentDivide into 3 units (s=1/3 unit )
New patterns generated, N= 4
Repeat the recipe for each new straight line segmentRepeat on new smaller scale
We have a theoretical algorithm that creates a self-similar structure – – the Von Koch curve. . It has fractal geometry - a
mixture of 1 D and 2D charracters.
Dimension of the Von Koch
CurveScale (compass setting) Length
nS 31 nL 341/3(1/3)2
(1/3)3
4/3(4/3)2
(4/3)3
sn 13
ns 1log3 34loglog 33 nL
sL 1log34loglog 333 2619.0
3log
34log
3
4log
10
103
Compass dimension (Dcom )
Dfrac = 1 + Dcom =1.2619
Determining the Df of Fracture
Cracks
Crack surface
Section to surface
Fractal character
At large and small distance scales relationship may break down
S = scale
L = Length
SL
PenumbraNo penumbra, sharp focus with magnification, M, increasing as df increases:
Microfocus X-ray Geometry
Micro-focus X-ray technology uses micrometer sized source to produce sharp image projections at micrometer scale resolution
ds df s
f
d
dM 1
Source Sample Detector
Preliminary results
Compass dimension(Dcom ) Dcom=0.45
Dfrac = 1 + Dcom
= 1.45
Log/Log plot for the crack of the coal sample