February 2004 Mullite/Alumina Mixtures for Use as Porous Matrices in Oride Fiber Composites Aging time 0h.2h e 言 L 0.1 Alumina content.×A(%) Aging time, t(h) 1.02 Fig 3. Effects of aging time on Youngs modulus and toughne (b mullite. Power law fits of the experimental data yield exponents 90M/10A 0.03 and 0.28= 0.03 for modulus and toughness, respectively 100M with those predicted for surface diffusion controlled sintering BOM/20A 0.143ando.286 ≥o6. where r is sintering time. I, is a reference time and n is a constant both Ig and n depend on the transport mechanism. Sintering Alumina 70M/0A models yield values of n=3 for vapor transport, n= 5 for lattice diffusion, and n=7 for surface diffusion 094 In turn, for monosized spherical particles with small junctions 60M/40A scales linearly with junction radius in accordance with / segregate (a/R < I, the Youngs modulus of a bonded particle ag 0.92 Aging time, t(h) E Fig. 2. (a) Effects of composition and aging time on compact porosity. where Ep and v are the Youngs modulus and Poisson's ratio of the The data for O h and 2 h are virtually identical to one another and ar particles: z is the particle coordination number (-6 for random indistinguishable on the graph. (b) Results in (a), normalized by the initial packing): D is the relative packing density: E is a numerical (green) porosity at the same composition. The solid line for alumina in the parameter: and g(v) is given by inset was obtained by dilatometry. the symbols are based on the Archimedes measurements, and all other lines are simply curve fits through g()=(1= For values of v in the range0≤v≤0.25.8(v)=1±0.004the dependence on v is extremely small and is subsequently neglected Both the modulus and the toughness of the mullite comp This result, with E=I was derived by Walton, using Hertzian bly with aging g time, by a factor of -3-4(Fig 3). contact mechanics to describe junction stiffness and assuming a These property changes indicate sintering at the particle junctions, uniform aggregate strain. A more rigorous model that accounts for but the absence of porosity change implies a mechanism that does finite junction size and multiparticle interactions yields results in the domain of small junctions(a/R s 0.3)that are consistent with include transport of matter from surface sources via either surface Eq (5)when E is taken to be -076(simulation of modulus has diffusion, lattice diffusion, or vapor transport. The dominant been performed for two limiting cases: assuming that the torsional mechanical measurements in the manner described in the follow- of results are fit well by Eq. (5). using 5=0.65 and 0.88, Ing section. respectively. The average of these, E=0. 76 is used in the present SEM observations of the fracture surfaces reveal only a small work). Combining Eqs. (4)and (5) and taking g(v)= I yields the number of well-defined broken junctions(Figs. 4(a) and (b)), time-dependence of the modulus These are somewhat more prevalent after the longest agi because of the increase in junction size. The small number g time Junctions indicates that fracture normally occurs"cleanl r of such E nly"without E=0.76127 (7) appreciable crack meandering, suggesting a low fracture energy. It also precludes direct measurement of junction size. The relationship between toughness and junction radius for a bonded particle nte has been obtnined herical simulations of fracture, using a technique based on the discrete When the junction radius, a, is much smaller than the partic le element method(DEM). Details of the method and its implemen radius,R, junction growth owing to sintering follows a power law tation are presented elsewhere. Briefly, a computer-simulated of the form: 3. 1-4 sintering algorithm is used to generate a random three-dimensional array of spherical particles with a prescribed junction radius. The simulated aggregates consist of1000 particles. A crack is defined by a plane separating particles that have had the junction