Journal of the American Ceramic Society-Parthasarathy and Kerans Vol. 80. No 8 Progressive roughness h=20nm:2d-=0.3m 8 Progressive rough h=2nm:2d=0.3m 可6 Constant roughness 10 Constant Roughness Model (Smooth same clamping stress) 00.]0.20.3040.506呀O 00.l020.3040.50.6 Debond Length(mm) Debond Length(mm) 40 Pros Progressive roughne Roughness h=20nm:2d=1.5 园30 h=20 nm: 2d=0.6 um 0 E 10 Constant Roughness Model. 10 Constant Roughness 0 0 00.【0.20.3040.50.6 0010.20.304050.6 Debond Length(mm) Debond length(mm) (d) Fig. 4. For the Nicalon/SiC system, the progressive roughne redicts the average T value(see text for definition) to be higher than that predicted by a constant roughness model(Fig 4(a)). Lowering the hess amplitude, h, only diminishes the difference, not the trend(Fig. 4(b). However, as the roughness period is increased, the trend is reversed(Figs. 4(c)and(d).(See text for implications on seating drop during push-back ( Interaction with Other Parameters doubling the fiber strength from I GPa to 2 GPa increases the debond length by a factor of-4, whereas doubling h from 0.01 Because several different constituent and composite proper- mm to 0.02 mm causes an increase in the debond length by a ties can affect debond length, it is important to know how the factor of only -2 influences from other factors compare with that from rough- Fiber diameters can vary significantly ness. To estimate the relative effects of parameters other than Nicalon-fiber diameter can vary by a factor of 2. The fiber 30m由mr订mbd1hea到 ignificant effect on the Is u varies as the ratio of roughness amplitude to fiber radius. This volume fraction of the fiber. interface toughness interfacial could be one source of the wide variation in measured inter- friction coefficient, and fiber radius. Of these factors, only fiber facial properties. Now, when the fiber diameter varies, it is strength and fiber radius had effects that were significant, com- possible that roughness either scales with fiber size, because of pared to the effect of roughness amplitude; the effects of these processing artifacts, or is independent of fiber size, equal to two parameters are presented and discussed below coating thickness, for example. If the roughness is independent The strength of Nicalon fiber has been measured and re- of fiber diameter, then the misfit stress also will vary by a ported to be in a range of 2-2.5 GPa In processed composites, factor of 2 amongst different fibers. The conse the strengths of the fiber can be lower because of processing substantial, as illustrated in Fig. &(a). The effect of fibe effects. In one study, 6 the strength was estimated from fracture is far more than that of the roughness amplitude. He mirrors on fibers in a composite to be -1. 7 GPa. Depending on when the roughness amplitude and period scale with the processing cycle, the strength can probably vary in the radius, then there is no significant effect(Fig. 8(b)) range of 1-2 GPa. In addition, there also is potential fiber From Fig. 8, it is clear that a distribution of fiber diameters strength degradation from environmental exposure. Figure 7 an cause a distribution in debond lengths and, thus, pullout shows the effect of varying the fiber strength over the range of lengths in a composite, provided that the roughness paramete 1-2 GPa, as a function of the roughness amplitude. generally do not scale with the fiber diameter. The work of Benoit er a/ 39 speaking, there is a fairly strong effect of fiber stress through experimentally explored the above-mentioned effect in the out the range of roughnesses. For example, at h=0.02 mm Nicalon/MAS-L system. Their results are shown, plotted with(3) Interaction with Other Parameters Because several different constituent and composite proper￾ties can affect debond length, it is important to know how the influences from other factors compare with that from rough￾ness. To estimate the relative effects of parameters other than roughness, the debond lengths were calculated as a function of roughness amplitude for different values of fiber strength, Pois￾son’s ratio of the fiber (which is usually not well known), volume fraction of the fiber, interface toughness, interfacial friction coefficient, and fiber radius. Of these factors, only fiber strength and fiber radius had effects that were significant, com￾pared to the effect of roughness amplitude; the effects of these two parameters are presented and discussed below. The strength of Nicalon fiber has been measured and re￾ported to be in a range of 2–2.5 GPa. In processed composites, the strengths of the fiber can be lower because of processing effects. In one study,36 the strength was estimated from fracture mirrors on fibers in a composite to be ∼1.7 GPa. Depending on the processing cycle, the strength can probably vary in the range of 1–2 GPa. In addition, there also is potential fiber strength degradation from environmental exposure. Figure 7 shows the effect of varying the fiber strength over the range of 1–2 GPa, as a function of the roughness amplitude. Generally speaking, there is a fairly strong effect of fiber stress through￾out the range of roughnesses. For example, at h 0.02 mm, doubling the fiber strength from 1 GPa to 2 GPa increases the debond length by a factor of ∼4, whereas doubling h from 0.01 mm to 0.02 mm causes an increase in the debond length by a factor of only ∼2. Fiber diameters can vary significantly; for example, the Nicalon-fiber diameter can vary by a factor of 2. The fiber radius may be expected to have a significant effect on the debond length, because the roughness-induced misfit stress varies as the ratio of roughness amplitude to fiber radius. This could be one source of the wide variation in measured inter￾facial properties. Now, when the fiber diameter varies, it is possible that roughness either scales with fiber size, because of processing artifacts, or is independent of fiber size, equal to coating thickness, for example. If the roughness is independent of fiber diameter, then the misfit stress also will vary by a factor of 2 amongst different fibers. The consequences can be substantial, as illustrated in Fig. 8(a). The effect of fiber radius is far more than that of the roughness amplitude. However, when the roughness amplitude and period scale with the fiber radius, then there is no significant effect (Fig. 8(b)). From Fig. 8, it is clear that a distribution of fiber diameters can cause a distribution in debond lengths and, thus, pullout lengths in a composite, provided that the roughness parameters do not scale with the fiber diameter. The work of Benoit et al.39 experimentally explored the above-mentioned effect in the Nicalon/MAS-L system. Their results are shown, plotted with Fig. 4. For the Nicalon/SiC system, the progressive roughness model predicts the average
value (see text for definition) to be higher than that predicted by a constant roughness model (Fig. 4(a)). Lowering the roughness amplitude, h, only diminishes the difference, not the trend (Fig. 4(b)). However, as the roughness period is increased, the trend is reversed (Figs. 4(c) and (d)). (See text for implications on seating drop during push-back tests.) 2048 Journal of the American Ceramic Society—Parthasarathy and Kerans Vol. 80, No. 8