500 FABER techniques for the mechanical characterization of fiber-matrix interfaces, and key examples of interface design in brittle matrix composite INTERFACE DESIGN PARAMETERS Brittle matrix composites for structural applications are deemed successful when they exhibit fiber debonding and frictional sliding as cracks propagate hrough the matrix. Such behavior is generally accompanied by notch or flaw lerance as demonstrated in a highly nonlinear stress-strain curve reminiscent of a plastically deforming metal (2). The nonlinearity, however, derives not from plasticity but from initiation and propagation of a series of through-the thickness matrix cracks that are bridged by the brittle fibers. The low toughnes interface is the first requirement to prevent fiber fracture during matrix crack growth. Debonding of fibers alone, however, is not sufficient to provide the notch tolerance. As noted by Thouless Evans(3)and by Cao et al (4), the interfacial sliding resistance t should be small enough to allow for a substantial pullout contribution through frictional dissipation by encouraging fiber fracture at significant distances from the matrix crack plane. It is generally thought that t should be between 2 and 40 MPa(3). A third requirement is that thermal mismatch stresses between fiber and matrix are not substantial enough to cause either fiber or matrix crackin To examine how these parameters are explicitly incorporated into composite performance, we first investigate the analysis of Hutchinson Jensen (5), as modified by Marshall(6), that describes the displacement u of a single crack-bridging fiber in a brittle matrix. The analysis assumes stable, interfacial debonding with interfacial sliding governed by a Coulomb friction law and can be written as +r'-sa where u characterizes the frictional properties of the interface and is inversely proportional to the coefficient of friction u, which is related to the frictional sliding resistance t. A is a dimensionless constant that includes the elastic con- stants of the composite constituents, the volume fraction of fibers, the surface roughness, and the anisotropy in thermal misfit strains, Sro is a direct measure of the radial residual stress, Sa is the applied stress normalized by the peak pplied stress. r" is related to the debond energy and is directly proportional to the interfacial toughness Gic and includes any residual stress. The term SR includes the thermal mismatch strain a and the surface roughness-induced strain 8, which relates to the amplitude of the surface roughness A. Conse quently, a complex relationship between the interface toughness, the frictionalP1: ARK/MBL/rkc P2: MBL/vks QC: MBL/agr T1: MBL May 16, 1997 13:47 Annual Reviews AR034-16 500 FABER techniques for the mechanical characterization of fiber-matrix interfaces, and key examples of interface design in brittle matrix composites. INTERFACE DESIGN PARAMETERS Brittle matrix composites for structural applications are deemed successful when they exhibit fiber debonding and frictional sliding as cracks propagate through the matrix. Such behavior is generally accompanied by notch or flaw tolerance as demonstrated in a highly nonlinear stress-strain curve reminiscent of a plastically deforming metal (2). The nonlinearity, however, derives not from plasticity but from initiation and propagation of a series of through-the￾thickness matrix cracks that are bridged by the brittle fibers. The low toughness interface is the first requirement to prevent fiber fracture during matrix crack growth. Debonding of fibers alone, however, is not sufficient to provide the notch tolerance. As noted by Thouless & Evans (3) and by Cao et al (4), the interfacial sliding resistance τ should be small enough to allow for a substantial pullout contribution through frictional dissipation by encouraging fiber fracture at significant distances from the matrix crack plane. It is generally thought that τ should be between 2 and 40 MPa (3). A third requirement is that thermal mismatch stresses between fiber and matrix are not substantial enough to cause either fiber or matrix cracking. To examine how these parameters are explicitly incorporated into composite performance, we first investigate the analysis of Hutchinson & Jensen (5), as modified by Marshall (6), that describes the displacement u of a single, crack-bridging fiber in a brittle matrix. The analysis assumes stable, interfacial debonding with interfacial sliding governed by a Coulomb friction law and can be written as u u∗ = −ASRo ln µ SRo − Sa SRo − 00 ¶ + 00 − Sa, 1. where u∗ characterizes the frictional properties of the interface and is inversely proportional to the coefficient of friction µ, which is related to the frictional sliding resistance τ . A is a dimensionless constant that includes the elastic con￾stants of the composite constituents, the volume fraction of fibers, the surface roughness, and the anisotropy in thermal misfit strains, SRo is a direct measure of the radial residual stress, Sa is the applied stress normalized by the peak applied stress. 00 is related to the debond energy and is directly proportional to the interfacial toughness Gic and includes any residual stress. The term SRo includes the thermal mismatch strain εT, and the surface roughness-induced strain εsr, which relates to the amplitude of the surface roughness Asr. Conse￾quently, a complex relationship between the interface toughness, the frictional