Generation of random microstructure in fiber reinforced composites and its comparison with carbon/carbon composite test samples through statistical analysis

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ABSTRACT

The elastic properties are important parameters for design of components using carbon/carbon composites. These elastic properties are required to be estimated with acceptable level of accuracy. These elastic properties are normally determined numerically. Estimation of elastic properties using numerical methods require accurate representation of microstructure of fibres in composite materials. Fibre arrangement is an important factor in the microstructure that shall be agree closely to the real composites. One of the method to compare the fibre arrangements in composites is through use of spatial statistics. In the present work the fibre arrangement in unidirectional composites is generated with volume fraction of 0.52–0.58 using an algorithm based on random removal of fibres. The fibre arrangements in carbon/carbon composite test samples are taken from microscopy images of unidirectional carbon/carbon composite, with same volume fraction of fibres. The simulated fibre arrangements are compared with carbon/carbon composites samples using statistical descriptors. The statistical descriptors are chosen from the spatial statistics. All the statistical descriptors show close agreement between the real and simulated microstructures.

KEYWORDS:

• Carbon/carbon composites
• spatial statistics
• statistical analysis
• distance analysis artefacts

Disclosure statement

No potential conflict of interest was reported by the author(s).

Nomenclature

V^f = Volume Fraction of fiber

d(ran)=Mean random distance

A = Area of the sample

N = No of fibers

NNI = Nearest Neighbor Index

d(NN) = Nearest neighbor distance

d_ij= distance between neighboring points

SE_{d(ran) =} standard error of average random distance

d(ran) = Average random distance

d (${\mathrm{K}}_{\mathrm{r}\mathrm{a}\mathrm{n}})=$ Average random Distance to nearest neighbor

K(h) = Ripley’s K function

Kp(h) = Ripley’s K function for complete spatial randomness

g(h) = Pair distribution function

CSR = Complete spatial randomness