August 1997 Predicted Effects of Interfacial Roughness on the Behavior of Selected Ceramic Composites SCSG/Glass- Single fiber Pushout SCSG/ RBSN. Single Fiber Pushout onstant Roughness Model Constant roughness conStant Toughness.inditEd stress) 6 Smooth Fiber(n4 RcHEhness Debond Lcngth (mm) 0 (a) Maximum Load (N) Fig. 5. For large-fiber-diameter systems, such as(a)SCS6/glass and(b)SCS6-RBSN, the progressive roughness model that the average value will change as the debond increases from that of a smooth fiber with no roughness to that predicted by a roughness model Fig. 5(b), experimental evidenc idge et al.3 on SCS/RBSN) for such an effect of debond length(or load on the measured average T value is shown for comp or these systems, the smooth transition is such that a pronounced seating drop is predicted for specimen of thicknesses up to at least 5 mm, in contrast with the small-fiber-diameter Nicalon/SiC system(Fig. 4), where the seating drop is not predicted for reasonable choice of roughness parameters. These are consistent with experimental findings(see text) the progressive roughness model predictions, in Fig. 9. Al- mm(0. 2-0.3 mm is typical), then the fiber stress at a debond though the correlation is not definitive, the trend favors the length of 0. 3 mm from the plot gives the peak fiber stress in the constant roughness amplitude model pushout test. If this peak stress is used to calculate a constant T value, it will yield a value of 40 MPa. However, this value will vary with the specimen thickness, as shown in Fig. 10(a) (4 Constant-T Approximation If one uses this T value to predict the debond length in a The obvious advantages of simplifying assumptions has led multifiber pullout test(composite fracture), one obtains debond to the development and use of the constant- approximation. lengths that are far from the real value, as shown in Fig. 10(c); Although this has been helpful as a simple approximation, its note that Fig. 10(c)represents a plot of debond length versus accuracy has always been in doubt. The validity of this ap- bridging fiber stress. A similar problem occurs for a frictionally and using it to predict the debond length during mults st lading fiber that is completely debonded, as shown in Fig proximation has been examined by studying the consequence f measuring a constant T value from a single-fiber pushout tes o(b); however, the range of T that is obtained is much na ullout, as in a composite. Figure 10(a) shows the debond The values of T in Fig. 10(c)are those that would be obtained est(Nicalon/SiC), calculated using the progressive roughness cured at the corresponding point on the curve. Because matrix del. If the specimen thickness during a pushout test is 0.3 cracking usually occurs at small strains (0.05%0.01%), the T Nicalon/Sic 1.2 04;:1 日 ′btm (6 2505007501000 50010015002000 Fiber Stress(MPa) Fiber stress (MPa) ig. 6. Calculated roughness on debond in a Nicalon/SiC composite, plotted as a function of fiber stress. At low fiber stresses(Fig. 6( has slid, relative to the x, by distances less than the period of roughness, as in region Il(Fig. 2) At higher stresses, a of the plot is observed, corresponding to the initiation of region Ill ( Fig. 2). At high stresses( Fig. 6(b), most of the fiber is that roughness decreases the debond length significantlythe progressive roughness model predictions, in Fig. 9. Al￾though the correlation is not definitive, the trend favors the constant roughness amplitude model. (4) Constant-
Approximation The obvious advantages of simplifying assumptions has led to the development and use of the constant-
approximation. Although this has been helpful as a simple approximation, its accuracy has always been in doubt. The validity of this ap￾proximation has been examined by studying the consequence of measuring a constant
value from a single-fiber pushout test and using it to predict the debond length during multifiber pullout, as in a composite. Figure 10(a) shows the debond length as a function of the fiber stress during a fiber pushout test (Nicalon/SiC), calculated using the progressive roughness model. If the specimen thickness during a pushout test is 0.3 mm (0.2–0.3 mm is typical), then the fiber stress at a debond length of 0.3 mm from the plot gives the peak fiber stress in the pushout test. If this peak stress is used to calculate a constant
value, it will yield a value of 40 MPa. However, this value will vary with the specimen thickness, as shown in Fig. 10(a). If one uses this
value to predict the debond length in a multifiber pullout test (composite fracture), one obtains debond lengths that are far from the real value, as shown in Fig. 10(c); note that Fig. 10(c) represents a plot of debond length versus bridging fiber stress. A similar problem occurs for a frictionally sliding fiber that is completely debonded, as shown in Fig. 10(b); however, the range of
that is obtained is much nar￾rower. The values of
in Fig. 10(c) are those that would be obtained from matrix crack spacing if the cracking were to have oc￾curred at the corresponding point on the curve. Because matrix cracking usually occurs at small strains (0.05%–0.01%), the
Fig. 6. Calculated effect of the interfacial roughness on debond lengths in a Nicalon/SiC composite, plotted as a function of fiber stress. At low fiber stresses (Fig. 6(a)), much of the fiber has slid, relative to the matrix, by distances less than the period of roughness, as in region II (Fig. 2). At higher stresses, a transition in the slope of the plot is observed, corresponding to the initiation of region III (Fig. 2). At high stresses (Fig. 6(b)), most of the fiber is in region III. It is clear that roughness decreases the debond length significantly. Fig. 5. For large-fiber-diameter systems, such as (a) SCS6/glass and (b) SCS6-RBSN, the progressive roughness model predicts that the average
value will change as the debond length increases from that of a smooth fiber with no roughness to that predicted by a constant roughness model. In Fig. 5(b), experimental evidence (Eldridge et al.38 on SCS6/RBSN) for such an effect of debond length (or load on the fiber) on the measured average
value is shown for comparison. For these systems, the smooth transition is such that a pronounced seating drop is predicted for specimens of thicknesses up to at least 5 mm, in contrast with the small-fiber-diameter Nicalon/SiC system (Fig. 4), where the seating drop is not predicted for reasonable choice of roughness parameters. These are consistent with experimental findings (see text). August 1997 Predicted Effects of Interfacial Roughness on the Behavior of Selected Ceramic Composites 2049