2044 Journal of the American Ceramic Society-Parthasarathy and Kerans Vol. 80. No 8 Malix fibcr R Fig. 1. Schematic sketch illustrating how the effect of interfacial roughness can be modeled as a radial misfit between the fiber and matrix. away from the plane of the matrix crack. In this situation, the composites that are implied by the maximum misfit stresses fiber slides, relative to the matrix, to different extents along the have received some attention, explicit consideration of the im length of the fiber(Fig. 2). For a fiber pulling out of a matrix plications of the model for specific ceramic composites has not under axial loading, the interfacial normal stress in the un- been considered in any detail. The purpose of this work is to slipped region ahead of the crack tip(region I of Fig. 2)is examine the predicted effects of progressive roughness in more determined by the residual stresses and, to a minor degree detail in selected ceramic composites and the magnitude of the ferences in Poissons ratios and the appli errors that are expected from applying smooth-interface as- region Ill, the normal stress is the sum of the residual stresses sumptions to real composites with rough interfaces and, hence, and the stresses that result from the full effect of the topo- the utility of conventional treatments. Debond length at fiber aphical misfit. Region II extends, with incre isfit fre fracture is probably the single parameter that is most illustra- plicates analysis and results in the questions of tis>on com the crack tip to the beginning of region Ill. This regi tive of composite behavior, because it has a key role in deter- mining the matrix crack spacing, fiber failure sites, apparent ance. For the scenario in region Il, the fracture and sliding fiber strength, pullout length, and total energy dissipation. Un- etween the matrix and the fiber has been handled in detail for fortunately, debond length is rarely measurable. Average fric- simple form of roughness by Parthasarathy et al. 3 Although tion along the fiber is less instructive about composite behav- nat treatment leads to a set of solutions that is suitable for ior; however, it is both intuitively and quantitatively directly nalyses of pullout and pushout data, the solutions are not well related to the measured quantity of force applied to the fiber ted corporation into higher-level-design analyses, be- Consequently, this evaluation of the significance of roughness ause of the additional complications illustrated in Fig. 2 and effects is focused on consideration of debond length and fric- discussed above. It also is not readily apparent how progressivetion oughness will affect particular composite systems. The obv The effects of roughness during progressive debonding were ous first order issue relates to the magnitude of progressive examined by calculating the predicted behavior for rough in- oughness effects: are they significant compared to the constant terfaces using an extension of the treatment of Parthasarathy et roughness region Ill, or can they be neglected entirely? Second, al a copy of the code that is thus developed and used in this are there simplifying approximations that provide adequate re- work can be obtained by writing to the authors. Thes are compared with the predictions of the constant Some of the implications for metal-matrix composites have model 25 where a smooth interface is assumed but th en evaluated by Marshall et al. Although effects in ceramic ness makes a constant contribution to the radial Debur」( Gridgis F Fig. 2. Illustration of the effect of interfacial roughness during progressive debonding away from a matrix crack in a composite under tension. Three different regions-labeled L. Il. and lll. as sh an be envisioned. (See text for detailsaway from the plane of the matrix crack. In this situation, the fiber slides, relative to the matrix, to different extents along the length of the fiber (Fig. 2). For a fiber pulling out of a matrix under axial loading, the interfacial normal stress in the un￾slipped region ahead of the crack tip (region I of Fig. 2) is determined by the residual stresses and, to a minor degree, by differences in Poisson’s ratios and the applied axial stress. In region III, the normal stress is the sum of the residual stresses and the stresses that result from the full effect of the topo￾graphical misfit. Region II extends, with increasing misfit from the crack tip to the beginning of region III. This region com￾plicates analysis and results in the questions of first impor￾tance. For the scenario in region II, the fracture and sliding between the matrix and the fiber has been handled in detail for a simple form of roughness by Parthasarathy et al.31 Although that treatment leads to a set of solutions that is suitable for analyses of pullout and pushout data, the solutions are not well suited for incorporation into higher-level-design analyses, be￾cause of the additional complications illustrated in Fig. 2 and discussed above. It also is not readily apparent how progressive roughness will affect particular composite systems. The obvi￾ous first order issue relates to the magnitude of progressive roughness effects: are they significant compared to the constant roughness region III, or can they be neglected entirely? Second, are there simplifying approximations that provide adequate re￾sults? Some of the implications for metal–matrix composites have been evaluated by Marshall et al.11 Although effects in ceramic composites that are implied by the maximum misfit stresses have received some attention, explicit consideration of the im￾plications of the model for specific ceramic composites has not been considered in any detail. The purpose of this work is to examine the predicted effects of progressive roughness in more detail in selected ceramic composites and the magnitude of the errors that are expected from applying smooth-interface as￾sumptions to real composites with rough interfaces and, hence, the utility of conventional treatments. Debond length at fiber fracture is probably the single parameter that is most illustra￾tive of composite behavior, because it has a key role in deter￾mining the matrix crack spacing, fiber failure sites, apparent fiber strength, pullout length, and total energy dissipation. Un￾fortunately, debond length is rarely measurable. Average fric￾tion along the fiber is less instructive about composite behav￾ior; however, it is both intuitively and quantitatively directly related to the measured quantity of force applied to the fiber. Consequently, this evaluation of the significance of roughness effects is focused on consideration of debond length and fric￾tion. The effects of roughness during progressive debonding were examined by calculating the predicted behavior for rough in￾terfaces using an extension of the treatment of Parthasarathy et al.;31 a copy of the code that is thus developed and used in this work can be obtained by writing to the authors. These results are compared with the predictions of the constant roughness model,25 where a smooth interface is assumed but the rough￾ness makes a constant contribution to the radial clamping Fig. 1. Schematic sketch illustrating how the effect of interfacial roughness can be modeled as a radial misfit between the fiber and matrix. Fig. 2. Illustration of the effect of interfacial roughness during progressive debonding away from a matrix crack in a composite under tension. Three different regions—labeled I, II, and III, as shown—can be envisioned. (See text for details.) 2044 Journal of the American Ceramic Society—Parthasarathy and Kerans Vol. 80, No. 8