August 1997 Predicted Effects of Interfacial Roughness on the Behavior of Selected Ceramic Composites 2047 Friction stress nal Fort。r From Urstaliny toringo on for Ks引 6-3(hal" pcriod; Rrs danl Strcss Relative Fiber/Matrix Displaceme 8) Fig. 3. Schematic sketch of the effect of progressive roughness on the interfacial friction stress at a selected point on the fiber friction stress. the total friction stress asymptotically measured T approaches the The calculated average friction stress, including Poisson effect, is shown plotted for the control set in Fig. 4(a), for progressive model predictions. Theg. 5(b, al t by Eldridge in a SCSa/RI et al 38 Their results are shown in F along with the lower amplitude of roughness in Fig 4(b), and for two different progressive roughness periods in Figs. 4(c), and(d). In all cases, an equivalent smooth model clearly helps rationalize the dependence of T on the fiber with a clamping stress equal to the maximum(region Ill) maximum load of the cyclic push-in tests clamping stress of the rough fiber is plotted for comparison The average friction stress that is plotted in Fig. 4(a)retains the same basic character as the schematic in Fig 3, with the fea-(2) Effects of Roughness on Debond Length tures smoothed by the distributed nature of the transitions along The effect of the interfacial roughness amplitude h on the the length of sliding fiber. The roughness amplitude has the debond length was studied as a function of the fiber stress. Thi expected effect on the amplitude of the peak in friction stress fect for the Nicalon/Sic comBo ite system is shown in Fig. 6 Fig. 4(b)). Note that because d is held constant, 0 decreases as The behavior at low fiber stresses and debond lengths is showr the roughness decreases, and, hence, the initial slope also is in Fig. 6(a), and the behavior at stresses near the fiber strength decreased In Figs. 4(c)and(d), the amplitude is held constant(taken as 1.5 GPa)is shown in Fig. 6(b). It is clear that rough and the period is varied, which leads to even more- interesting ness decreases the debond length significantly for a given fiber behavior. As the period is decreased, the slope and the am stress. When the roughness amplitude is >10 nm, the debond tude of the effect both increase. It is evident from Figs. 4(c)and length decreases rapidly for a fiber stress of 1.5 GPa; at 30 nm )that the rough-fiber friction can be either lower or higher the debond length is <150 um than the smooth-fiber case and that the smooth -fiber value can As shown in Fig. 6(a), there are two distinct regions to each be asymptotically approached from either above or below. This curve for nonzero roughness amplitudes, for reasons discussed ather remarkable result means that the nature and even exis earlier. The first is the portion of the debonding that is the tence of a pushback seating drop 8, 28 will be dependent on the development of region Il. The transition occurs at the inception shape (or 0), not just the amplitude h of the roughness. The of region Ill, and, for the remainder of the debonding process, predicted seating drop is proportional to the difference in there is no change in the length of (and contribution from) values between the maximum constant roughness model (slid region II: the entire increase in debonded length is in the form ing friction)and the progressive roughness model; note that of increasing region Ill. It is evident that the region lll contri- this varies with the debond length, which can be taken to be the bution is dominant for roughness amplitudes of up to 10 nm. specimen thickness in fiber pushout/pushback tests. Physically, For larger roughnesses, region lI has a significant effect on the the thickness dependence comes from the fact that, at the bot- total debond length until fiber fracture tom of the seating drop, the fraction of the fiber that is fully The development of two different regions has a consequence seated in its original position decreases as the thickness do in the relationship between matrix crack spacing and pullout lengths. At lower stresses, the debond lengths are shorter than Fiber pushback tests have shown a significant seating drop in what a constant roughness model (which assumes region Ill the SCS6/glass system. 2 The predictions for this system along the entire fiber) would have predicted. This should lead shown in Fig. 5(a), in which the rough-fiber case is plotted with to relatively small matrix crack spacing; howeve the constant roughness approximation for two cases: one with and using this behavior at low stresses to predict the pullout minimum clamping(residual stress only, or no roughness)and lengths(which are dependent on debond lengths at stresses the other with maximum clamping stress(residual stress+ near fiber fracture)will underestimate the pullout length. The roughness-induced clamping stress, as in region III). The rough debond length at high stresses is dominated by region Ill be- fiber does indeed start at almost the same frictional stress havior, which is assumed in the constant roughness model that for a smooth fiber and gradually increases to the maximum Consequently, the relationship between matrix crack spacing value(rough-fiber)at large debond lengths. Thus, for speci- and pullout length will be significantly different than that pre- mens mm thick, a significant load drop will be predicted in dicted using a constant roughness model or, for similar reasons, seating drop experiments. The predicted dependence of the a constant T modelfriction stress; hence, the total friction stress asymptotically approaches the region III bound. The calculated average friction stress, including Poisson’s effect, is shown plotted for the control set in Fig. 4(a), for a lower amplitude of roughness in Fig. 4(b), and for two different periods in Figs. 4(c), and (d). In all cases, an equivalent smooth fiber with a clamping stress equal to the maximum (region III) clamping stress of the rough fiber is plotted for comparison. The average friction stress that is plotted in Fig. 4(a) retains the same basic character as the schematic in Fig. 3, with the fea￾tures smoothed by the distributed nature of the transitions along the length of sliding fiber. The roughness amplitude has the expected effect on the amplitude of the peak in friction stress (Fig. 4(b)). Note that because d is held constant,  decreases as the roughness decreases, and, hence, the initial slope also is decreased. In Figs. 4(c) and (d), the amplitude is held constant and the period is varied, which leads to even more-interesting behavior. As the period is decreased, the slope and the ampli￾tude of the effect both increase. It is evident from Figs. 4(c) and (d) that the rough-fiber friction can be either lower or higher than the smooth-fiber case and that the smooth-fiber value can be asymptotically approached from either above or below. This rather remarkable result means that the nature and even exis￾tence of a pushback seating drop18,28 will be dependent on the shape (or ), not just the amplitude h of the roughness. The predicted seating drop is proportional to the difference in
values between the maximum constant roughness model (slid￾ing friction) and the progressive roughness model; note that this varies with the debond length, which can be taken to be the specimen thickness in fiber pushout/pushback tests. Physically, the thickness dependence comes from the fact that, at the bot￾tom of the seating drop, the fraction of the fiber that is fully seated in its original position decreases as the thickness de￾creases. Fiber pushback tests have shown a significant seating drop in the SCS6/glass system.24 The predictions for this system are shown in Fig. 5(a), in which the rough-fiber case is plotted with the constant roughness approximation for two cases: one with minimum clamping (residual stress only, or no roughness) and the other with maximum clamping stress (residual stress + roughness-induced clamping stress, as in region III). The rough fiber does indeed start at almost the same frictional stress as that for a smooth fiber and gradually increases to the maximum value (rough-fiber) at large debond lengths. Thus, for speci￾mens <3 mm thick, a significant load drop will be predicted in seating drop experiments. The predicted dependence of the measured
value (average
) on the debond length (or load/ stress on the fiber) has recently been validated experimentally in a SCS6/RBSN system using a cyclic push-in test by Eldridge et al.38 Their results are shown in Fig. 5(b), along with the progressive model predictions. The progressive roughness model clearly helps rationalize the dependence of
on the maximum load of the cyclic push-in tests. (2) Effects of Roughness on Debond Length The effect of the interfacial roughness amplitude h on the debond length was studied as a function of the fiber stress. This effect for the Nicalon/SiC composite system is shown in Fig. 6. The behavior at low fiber stresses and debond lengths is shown in Fig. 6(a), and the behavior at stresses near the fiber strength (taken as 1.5 GPa) is shown in Fig. 6(b). It is clear that rough￾ness decreases the debond length significantly for a given fiber stress. When the roughness amplitude is >10 nm, the debond length decreases rapidly for a fiber stress of 1.5 GPa; at 30 nm, the debond length is <150 m. As shown in Fig. 6(a), there are two distinct regions to each curve for nonzero roughness amplitudes, for reasons discussed earlier. The first is the portion of the debonding that is the development of region II. The transition occurs at the inception of region III, and, for the remainder of the debonding process, there is no change in the length of (and contribution from) region II; the entire increase in debonded length is in the form of increasing region III. It is evident that the region III contri￾bution is dominant for roughness amplitudes of up to 10 nm. For larger roughnesses, region II has a significant effect on the total debond length until fiber fracture. The development of two different regions has a consequence in the relationship between matrix crack spacing and pullout lengths. At lower stresses, the debond lengths are shorter than what a constant roughness model (which assumes region III along the entire fiber) would have predicted. This should lead to relatively small matrix crack spacing; however, interpreting and using this behavior at low stresses to predict the pullout lengths (which are dependent on debond lengths at stresses near fiber fracture) will underestimate the pullout length. The debond length at high stresses is dominated by region III be￾havior, which is assumed in the constant roughness model. Consequently, the relationship between matrix crack spacing and pullout length will be significantly different than that pre￾dicted using a constant roughness model or, for similar reasons, a constant
model. Fig. 3. Schematic sketch of the effect of progressive roughness on the interfacial friction stress at a selected point on the fiber. August 1997 Predicted Effects of Interfacial Roughness on the Behavior of Selected Ceramic Composites 2047