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A Study of Crack Formation and its Effective A Study of Crack Formation and its Effective Internal Surface Area using Internal Surface Area using X-ray Micro-Tomography (XMT) X-ray Micro-Tomography (XMT) University of Johannesburg Energy Postgraduate Conference 2013
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• A Study of Crack Formation and its Effective Internal Surface Area using X-ray Micro-Tomography (XMT)University of JohannesburgEnergy Postgraduate Conference 2013

• IntroductionX-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 < 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 fluid-material 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 (Self-similar 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 self-similar 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 X-ray GeometryMicro-focus X-ray 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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