2412 Journal of the American Ceramic SocieryMorvan and Baste Vol 8l. No 9 Table Il. Parameters Used to Assess Interfacial posites s and Relationships to Constituent Properties, J. Am. Ce vans, J.-M. Domergue, and E. Vagaggini, ""Methodology for Re- Interbundle lating the Tensile Constitutive Behavior of Ceramic-Matrix Composites to Con- Radius of the fiber, R(um) stituent Properties,J.Am. Ce Push-Out(Indentation) Tests Minor semi-axis of the bundle in Ceramic-Matrix Composites, J. Major semi-axis of the bundle 1500 in Fiber-Reinforced Brittle Matrix Composites: Basic Problems, "Mater. Sci. Youngs modulus of the fiber, E(GPa) l80 eR. J. Kerans, T. A. Parthasarathy, P, D. Jero, A. Chatterjee, and N. J. Pa- Youngs modulus of the bundle, ino. ' Fracture and Sliding in the Fibre/Matrix Interface and Failure Processes 200 Crack depth, 2a(m) of Hysteresis Observe During Fatigue of Ceramic-Matrix Composites, J Am. Ceram. Soc., 73 Crack width, 2c(um Depth of elementary cell 550 1879-83(1990) "D. Rouby and P. Reynaud, ""Fatigue Behaviour Related to Interface Modi- width of elementary cell, 2x,(um) 3500 fication during Load Cycling in Ceramic-Matrix Composites, Compos. Sci IT. A. Parthasarathy, D. B. Marshall, and R J. Kerans, ""Analysis of the Effect of Interfacial Roughness on Fiber Debonding and Sliding in Brittle Ma- interbundle matrix, and at the microstructure level, which con- Hysteresis Measurements and the Constituent Properties of onships between mesostructure level, constituted by both the bundles and the Ceramic Matrix tal Studies on Unidirectional Materials, J. Am. Ce chanical model used with these accurate measurements of the ram,w. Hutchonna-ndh95) various components of the total strain gives access to the value Pullout in Brittle Composites with Fnit of the interfacial sliding stress during the entire tensile test. In 2S. Baste and J-M van,""Unde the model, the interfacial sliding stress is dependent upon both Matrix Composite Using an Ultrasonic Method,E the elastic and inelastic strains but also upon the transverse crack density and the area upon which the sliding occurs. As a M. Morvan and S. Baste. Effects of Two-Scale transverse result, according to the scale of the composite, the interfacial sliding stress exhibits a different value, because of the nature of Danchaivijit and D K. Shetty,""Matrix Cracking in Ceramic Matrix 2C.-H. Hsueh, operties of Fiber-Reinforced Ceramic Compo sing a Mechanical Properties Microprobe, J. Am. Ce ZL. s. Sigl and A G. Evans, Effects of Residual Stress and Frictional Sliding on Cracking and Pull Out in Brittle Matrix Composites, ' Mech. Mater Cracking in Brittle-Matrix Fiber Composites, ""Acta Metall, 33 [11]2013-21 8,1-12(1989) 27N. Laws, G J. Dvorak, and M. Hejazi, ""Stiffness Changes in Unidirec- keaaoree Evans and F w. Zok, " The Physics and Mechanics of Fibre tional Composites Caused by Crack Systems, Mech. Mater, 2, 123-37(1983) d Brittle Matrix Composites, J. Mater. Sci., 29, 3857-96(1994) Evans, F. W. Zok, and J. Davis, "The Role of Interfaces in Fibe isotropic Solids."Philos. Mag, 36,367-zg es sociated with Cracks in Reinforced Brittle Matrix Composites, Compos. Sci. Technol, 42, 3-24 9B. Audoin and S. Baste. "Ultrasonic Evaluation of Stiffness Tensor Roughness, and Fiber Coatings on Interfacial Properties in Ceramic Compos- Roux, B. Hosten, B. Castagnede, and M. Deschamps, ""Caracterisation Pifabram. Soc., 79[1\13-1 1996) Mecanique des Solides par Spectro-Interferometrie Ultrasonore, Rev. Phys. els of Fiber-Matrix Interfacial Debonding, " JAm. Ceram.Soc,756]1694-96(1992) Audoin and J. Roux, "An Innovative Application of the Hilbert Trans- form to Time Delay Estimation of Overlapped Ultrasonic due to Matrix Cracking in Unidirectional Fiber-Reinforced Composites, ""Mech. oux,"Elastic Wave Propagation in Anisotropic I Lamon, "Interface and Interfacial Mechanics: Intluence on the Mechani 73 in Proceedings of IEEE 1990 Ultrasonics Symposia M2210 cal Behavior of Ceramic Matrix Composites(CMC), ""J Phys. IV, 3, 1607-16 Engineers, Piscataway, NJ, 1990 Voy. Institute of Electronic and D. B. Marshall. " An Indentation Method for Measuring Matrix-Fiber Fri B Hosten, ""Stiffness Matrix Invariants late the Characterization of Composite Materials with Ultrasonic Methods, Ultrasonics, 30 16] 365-71 C-260(1984 "D. B. Marshall and W. C. Oliver. ""Measurement of Interfacial Mechanical L. Guillaumat, Microfissuration des CMCs: Relation avec la Microstruc- rties in Fiber-Reinforced Ceramic Composites, "J. Am. Ceram. Soc. ortement Mecanique""(Microcracking in CMCs: Relation be 8J542-48(1987 PC-H. Hsueh and M. K. Ferber. "Evaluations of Residual Axial Stresses tur d Mechanical Behavior ): Ph. D. Thesis. University of and Interfacial Friction in Nicalon Fibre orced Macro- Defect-Free Cement 3SX. Aubard. Modelisation et Identification du ce Composites, J Mater. Sci., 28, 2551-56(1993). des Materiaux Composites 2D SiC-SiC"(Modeling and Identification of the Fernandez, and M. J. Purdy, ""Determination Composite Materials); Ph. D. Thesis. Un of Interfacial Properties Using a Single- Fiber Microcomposite Test, J. Am ersity of Paris VI, Paris, France, 1992 Ceram.Soc,79]1083-91(1996) =F. E. Heredia, S M. Spearing, A. G. Evans, P. Mosher, and w.A. Curtin, Woven C/SiC Composite under Mechanical Loading. Part 1: Mechanical Char- Mechanical Properties of Continuous-Fiber-Reinforced Carbon Matrix Co acterization, ""Compos. Sci. Techno, 56, 1363-72(1996)mesostructure level, constituted by both the bundles and the interbundle matrix, and at the microstructure level, which con￾sists of both the fibers and the intrabundle matrix. A microme￾chanical model used with these accurate measurements of the various components of the total strain gives access to the value of the interfacial sliding stress during the entire tensile test. In the model, the interfacial sliding stress is dependent upon both the elastic and inelastic strains but also upon the transverse crack density and the area upon which the sliding occurs. As a result, according to the scale of the composite, the interfacial sliding stress exhibits a different value, because of the nature of the bonding. References 1 D. B. Marshall, B. N. Cox, and A. G. Evans, ‘‘The Mechanics of Matrix Cracking in Brittle-Matrix Fiber Composites,’’ Acta Metall., 33 [11] 2013–21 (1985). 2 A. G. Evans and F. W. 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Baste, ‘‘Ultrasonic Evaluation of Stiffness Tensor Changes and Associated Anisotropic Damage in a Ceramic Matrix Composite,’’ J. Appl. Mech., 61, 309–16 (1994). 30J. Roux, B. Hosten, B. Castagnède, and M. Deschamps, ‘‘Caractérisation Mécanique des Solides par Spectro-Interférométrie Ultrasonore,’’ Rev. Phys. Appl., 20, 351–58 (1985). 31B. Audoin and J. Roux, ‘‘An Innovative Application of the Hilbert Trans￾form to Time Delay Estimation of Overlapped Ultrasonic Echoes,’’ Ultrasonics, 34, 25–33 (1996). 32J. Roux, ‘‘Elastic Wave Propagation in Anisotropic Materials’’; pp. 1065– 73 in Proceedings of IEEE 1990 Ultrasonics Symposium (Dec. 4–7, 1990, Honolulu, HI). Edited by B. R. McAvoy. Institute of Electronic and Electrical Engineers, Piscataway, NJ, 1990. 33B. Hosten, ‘‘Stiffness Matrix Invariants to Validate the Characterization of Composite Materials with Ultrasonic Methods,’’ Ultrasonics, 30 [6] 365–71 (1992). 34L. Guillaumat, ‘‘Microfissuration des CMCs: Relation avec la Microstruc￾ture et le Comportement Mécanique’’ (Microcracking in CMCs: Relation be￾tween Microstructure and Mechanical Behavior); Ph.D. Thesis. University of Bordeaux I, France, 1994. 35X. Aubard, ‘‘Mode´lisation et Identification du Comportement Me´canique des Mate´riaux Composites 2D SiC–SiC’’ (Modeling and Identification of the Mechanical Behavior of 2D SiC–SiC Composite Materials); Ph.D. Thesis. Uni￾versity of Paris VI, Paris, France, 1992. 36G. Camus, L. Guillaumat, and S. Baste, ‘‘Development of Damage in a 2D Woven C/SiC Composite under Mechanical Loading. Part I: Mechanical Char￾acterization,’’ Compos. Sci. Technol., 56, 1363–72 (1996). h Table II. Parameters Used to Assess Interfacial Sliding Stress Parameter Interbundle Intrabundle Radius of the fiber, R (mm) 7.5 Minor semi-axis of the bundle, m (mm) 150 Major semi-axis of the bundle, M (mm) 1500 Young’s modulus of the fiber, Ef (GPa) 180 Young’s modulus of the bundle, Et (GPa) 200 Crack depth, 2a (mm) 150 15 Crack width, 2c (mm) 2000 15 Depth of elementary cell, 2x1 (mm) 200 30 Width of elementary cell, 2x2 (mm) 3500 30 2412 Journal of the American Ceramic Society—Morvan and Baste Vol. 81, No. 9