A Study of Crack Formation and its Effective Internal Surface Area using Xray MicroTomography...

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A Study of Crack Formation and its Effective Internal Surface Area using Xray MicroTomography (XMT)University of JohannesburgEnergy Postgraduate Conference 2013

IntroductionXray 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 < 1m (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 fluidmaterial interface The larger the effective area of interaction the faster the reaction rateWhy cracks are important to study

Intuitive definition of dimension
Consider a geometric object F, with measure (F)
s dim F = (F)r= 1/s resolutionIf F is scaled by a factor of 2 say, how does the measure scale?
F(F) (F)
Line segmentLength21 = 2RectangleArea22 = 4ParallelepipedVolume23 = 8

Von Koch Curve (Selfsimilar Construct)Divide into 3 units (s=1/3 unit )New patterns generated, N= 4Repeat the recipe for each new straight line segmentRepeat on new smaller scaleWe have a theoretical algorithm that creates a selfsimilar structure the Von Koch curve. It has fractal geometry  a mixture of 1 D and 2D characters.

Dimension of the Von Koch CurveScale (compass setting)Length1/3(1/3)2(1/3)34/3(4/3)2(4/3)3Compass dimension (Dcom )Dfrac = 1 + Dcom =1.2619

Determining the Df of FractureCracksCrack surfaceSection to surfaceFractal characterAt large and small distance scales relationship may break down

Acquisition and ReconstructionTomographic reconstruction

PenumbraNo penumbra, sharp focus with magnification, M, increasing as df increases:Microfocus Xray GeometryMicrofocus Xray technology uses micrometer sized source to produce sharp image projections at micrometer scale resolution dsdfSourceSampleDetector

Preliminary results
Compass dimension(Dcom ) Dcom=0.45 Dfrac = 1 + Dcom = 1.45
Log/Log plot for the crack of the coal sample

ConclusionsInherent crack surface geometry will be revealed over many orders of magnitude and analysed for fractal nature CT measures with fundamental fractal nature will be identifiedBest presentation and interpretation of data forthcoming from fractal measures will be sought
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