ournal J. Am Ceram Soc, 80 [8]20413-55(1997) Predicted Effects of Interfacial Roughness on the Behavior of Selected Ceramic Composites Triplicane A. Parthasarathy* T and Ronald J Kerans United States Air Force Wright Laboratory Materials Directorate, Wright-Patterson AFB, Ohio 45433-7817 Potential effects of interfacial roughness in ceramic com- MPa of interfacial shear stress of frictional sliding. 9 Such posites were studied using a model that included the pro- hbe fibera increasing contribution of roughness with rela- understanding before one can intelligently select or design the atrix interface. A parametric approach was used te Initially, the source of the radial clamping stress had been study interfacial roughness in conjunction with other pa- assumed to be mostly due to the residual stresses that result rameters such as the strength, radius, and volume fraction from the thermal mismatch between the fiber and the matrix of the fiber. The progressive roughness contribution during Now, two more factors have been identified as being equally initial fiber/matrix sliding caused a high effective coeffi- important in determining the sliding resistance. First, the path cient of friction, as well as an increased clamping stress of the interfacial debond crack can cause roughness of the which led to rapidly changing friction with increasing sliding surfaces, which can significantly increase the sliding debond length Calculated effects implied a potentially sig resistance. Second, the compliance of any interfacial layer pre nificant contribution to the behavior of real composite sys- sent can significantly affect how the mismatch strains, which tems and the necessity for explicit consideration in the in- result from differential thermal expansion or roughness, are terpretation of experimental data to understand composite accommodated. The significance of the second factor is onl behavior correctlY. In a tension test, the poisson's contrac- beginning to be recognized and is discussed elsewhere, 20, 21 tion of the fiber may negate the effects of roughness, allow whereas the former has received more attention and is the ing an"effective constant shear stress"()approximation. subject of the present work. In particular, interfacial roughness This was evaluated using a piecewise linear approximation may have a significant role in the design of oxidation-resistant fiber/matrix interface control, which is the key technological posite stress-strain behavior; for the Nicalon/SiC system, challenge to the use of ceramic composite, 2,23 based on oxide be obtained from fiber pushout tests and/or matrix crack coatings are being investigated (for a brief review, see Ker- ans2). The focus of these investigations is the achievement of sufficiently low shear strength to allow impinging matrix L. Introduction cracks to deflect along the interface and bypass fibers without fiber failure. this characteristic is essential. However the to- phy of the interfacial fracture surfaces may differ greatly those of conventional interphases(mostly carbon, some interface debonding and sliding 1-3 Those details are, in turn, BN). This will necessitate explicit attention to interfacial determined by the toughness of the interface, the sliding fric- roughness in the design of the fiber coating system, which, in tion, and the stress state. The resistance to sliding per unit area turn, requires a thorough understanding of the phenomena that of the interface is usually considered either to be a constant or are involved The relative magnitude of the effect of roughness was shown to obey the Coulomb friction law, i. e, the product of the co- to be high, using the fiber pushback or"seating drop.mea- efficient of friction and the radial clamping stress across the fiber/matrix interface or, more accurately, the debonding crack surements.8, 24 Initial modeling of the effect of roughness was faces. Within this framework, fiber pushout and pullout exper ments have been used to measure the interfacial friction coef- facial roughness of amplitude h results in a mismatch strain of ficient and radial clamping stress in composites. -l8 However, h/R, where R is the fiber radius(Fig. 1). This roughness attempts to extend these one or two parameters to a detailed induced strain simply adds to the thermal mismatch strain. This understanding of the influence on macroscopic fracture behav or have had limited success. Qualitative inferences have be the fiber and matrix surfaces mate completely made and frictional shear stresses in the range of 2-50 MPa nal position) and (ii) when the fiber slides, relative to the ma lave been correlated with"good"composites. However, com trix, through a distance greater than a characteristic half-period posites with excellent properties have been obtained with >100 of the roughness, the fiber develops the mismatch strain hIRe Experimental work has shown that this approach reasonably captures the major aspects of actual behavior, 6 however, the choice of the value of h that properly describes a real surface is Evans--contributing editor ambiguous. Recent works27-30 have clarified this somewhat; however, more work is required all these developments have addressed the effect of rough ness on the sliding of a fiber along its entire length, relative to ript No. 191659. Received July 29. 1996: approved Materia s Directorate sliding. However, to model the fracture behavior of a compos- the matrix, as in a pushout or pullout test during""steady-state unde Air Force Contract No. F-33615-91-C-5663 4 ite, it is important to consider the effect of roughness on a tWith UES, Inc, Dayton, OH 454 debond crack as it propagates along the fiber/matrix interface 2043Predicted Effects of Interfacial Roughness on the Behavior of Selected Ceramic Composites Triplicane A. Parthasarathy*,† and Ronald J. Kerans* United States Air Force Wright Laboratory Materials Directorate, Wright-Patterson AFB, Ohio 45433–7817 Potential effects of interfacial roughness in ceramic com￾posites were studied using a model that included the pro￾gressively increasing contribution of roughness with rela￾tive fiber/matrix displacement during debonding of the fiber/matrix interface. A parametric approach was used to study interfacial roughness in conjunction with other pa￾rameters such as the strength, radius, and volume fraction of the fiber. The progressive roughness contribution during initial fiber/matrix sliding caused a high effective coeffi￾cient of friction, as well as an increased clamping stress, which led to rapidly changing friction with increasing debond length. Calculated effects implied a potentially sig￾nificant contribution to the behavior of real composite sys￾tems and the necessity for explicit consideration in the in￾terpretation of experimental data to understand composite behavior correctly. In a tension test, the Poisson’s contrac￾tion of the fiber may negate the effects of roughness, allow￾ing an ‘‘effective constant shear stress’’ (
) approximation. This was evaluated using a piecewise linear approximation to the progressive roughness model in an analysis of com￾posite stress–strain behavior; for the Nicalon/SiC system, the effective
value was lower than the values that would be obtained from fiber pushout tests and/or matrix crack spacings. I. Introduction THE major aspects of the mechanical behavior of ceramic composites are determined by the details of fiber/matrix interface debonding and sliding.1–3 Those details are, in turn, determined by the toughness of the interface, the sliding fric￾tion, and the stress state. The resistance to sliding per unit area of the interface is usually considered either to be a constant or to obey the Coulomb friction law, i.e., the product of the co￾efficient of friction and the radial clamping stress across the fiber/matrix interface or, more accurately, the debonding crack faces. Within this framework, fiber pushout and pullout experi￾ments have been used to measure the interfacial friction coef￾ficient and radial clamping stress in composites.4–18 However, attempts to extend these one or two parameters to a detailed understanding of the influence on macroscopic fracture behav￾ior have had limited success. Qualitative inferences have been made and frictional shear stresses in the range of 2–50 MPa have been correlated with ‘‘good’’ composites. However, com￾posites with excellent properties have been obtained with >100 MPa of interfacial shear stress of frictional sliding.19 Such phenomenological studies need to be extended to a mechanistic understanding before one can intelligently select or design the best material for the desired application. Initially, the source of the radial clamping stress had been assumed to be mostly due to the residual stresses that result from the thermal mismatch between the fiber and the matrix. Now, two more factors have been identified as being equally important in determining the sliding resistance. First, the path of the interfacial debond crack can cause roughness of the sliding surfaces, which can significantly increase the sliding resistance. Second, the compliance of any interfacial layer pre￾sent can significantly affect how the mismatch strains, which result from differential thermal expansion or roughness, are accommodated. The significance of the second factor is only beginning to be recognized and is discussed elsewhere,20,21 whereas the former has received more attention and is the subject of the present work. In particular, interfacial roughness may have a significant role in the design of oxidation-resistant fiber/matrix interface control, which is the key technological challenge to the use of ceramic composites in high-temperature structural applications. Many approaches20,22,23 based on oxide coatings are being investigated (for a brief review, see Ker￾ans20). The focus of these investigations is the achievement of sufficiently low shear strength to allow impinging matrix cracks to deflect along the interface and bypass fibers without fiber failure; this characteristic is essential. However, the to￾pography of the interfacial fracture surfaces may differ greatly from those of conventional interphases (mostly carbon, some BN). This will necessitate explicit attention to interfacial roughness in the design of the fiber coating system, which, in turn, requires a thorough understanding of the phenomena that are involved. The relative magnitude of the effect of roughness was shown to be high, using the fiber pushback or ‘‘seating drop’’ mea￾surements.8,24 Initial modeling of the effect of roughness25 was based on a simple approximation that proposed that an inter￾facial roughness of amplitude h results in a mismatch strain of h/Rf , where Rf is the fiber radius (Fig. 1). This roughness￾induced strain simply adds to the thermal mismatch strain. This model assumes that (i) the roughness is nonaxisymmetric (thus, the fiber and matrix surfaces mate completely only at the origi￾nal position) and (ii) when the fiber slides, relative to the ma￾trix, through a distance greater than a characteristic half-period of the roughness, the fiber develops the mismatch strain h/Rf . Experimental work has shown that this approach reasonably captures the major aspects of actual behavior;26 however, the choice of the value of h that properly describes a real surface is ambiguous. Recent works27–30 have clarified this somewhat; however, more work is required. All these developments have addressed the effect of rough￾ness on the sliding of a fiber along its entire length, relative to the matrix, as in a pushout or pullout test during ‘‘steady-state’’ sliding. However, to model the fracture behavior of a compos￾ite, it is important to consider the effect of roughness on a debond crack as it propagates along the fiber/matrix interface A. G. Evans—contributing editor Manuscript No. 191659. Received July 29, 1996; approved January 8, 1997. Research was performed, in part, at the Wright Laboratory Materials Directorate under U.S. Air Force Contract No. F-33615-91-C-5663. *Member, American Ceramic Society. † With UES, Inc., Dayton, OH 45432. J. Am. Ceram. Soc., 80 [8] 2043–55 (1997) Journal 2043