Modeling study of effects of temperature profiling on CVI processing of woven graphite preforms with dimethyldichlorosil
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There is currently considerable interest in producing high temperature capability graphitic materials by first weaving graphite fiber tows (yarns) into a "preform" structure, followed by densification via cracking of precursor compounds such as dimethyldichlorosilane within the pores (macro and micro) at high temperature. The model described in this paper addresses this densification process, treating diffusion of gaseous species both within the macropores (spaces between the tows) and the micropores (spaces between individual fibers in the tows) and finite kinetics associated with the cracking of the precursor gas (treated parametrically). The resulting model is used to examine the effects of temperature distributions through cylindrical preforms on ultimate densification distribution. As might be expected (and as observed experimentally), uniform temperature through the preform leads to premature full densification of the pore structure at the periphery of the cylinder (blocking further densification in the interior), leading to severe porosity in the interior regions. Effects of externally imposed nonuniform temperature profiles (possibly via microwave heating) in alleviating this problem are examined, and it is shown that proper profiling can lead to nearly complete uniform densification throughout the preform.
I. ANALYSIS OF DIFFUSION AND REACTION WITHIN A SINGLE TOW The first part of this model development consisted of an analysis of diffusion and reaction of dimethyldichlorosilane (DDS) to deposit silicon carbide (and possibly carbon as well) within the micropores between individual fibers in a cylindrical tow, given gas composition at the periphery of the tow, total pressure, and temperature distribution from the center to the outer radius of the tow. A tow architecture consisting of evenly spaced fibers in a cubic array (three mutually orthogonal directions) was used as an approximation for calculation of initial pore surface area per unit volume and "effective" initial pore diameter, and for relating porosity to the individual fiber diameter and spacing between centerlines of adjacent parallel fibers. The geometrical equations developed for these calculations are: 4
= 4(1 -
Sj)/Df
(1)
•^pore,/
= (37r/4)(Df/L)2 D pore.equiv = Dfe,/{\ - £/),
(2)
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J
= 4850Dpore(r/M/),
(4)
where Dkj is the Knudsen diffusivity of species J (cm 2 / s), Opore is the equivalent pore diameter (DpOre,equiv)> T is the local temperature (K), and M, is the molecular weight of the diffusing species (gm/gm-mol). The effective diffusivity within the porous structure may in turn be related to this Knudsen diffusivity by multiplication by the porosity and division by the pore tortuosity parameter, T, leading to:
(3)
where A porej/ is the initial pore surface area per unit volume (cm""1), L is the spacing between centerlines of adjacent parallel fibers (cm), £/ is the initial porosity, Df a) Present
is the initial fiber diameter (cm),
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