April 1998 Interfacial Bond Strength in SiC/C/SiC Composite Materials 3z 学[m 厂hr LONGITUDINAL TENSILE STRAIN(%) Fig. 1. Tensile stress-strain reinforced with as-received (I)or treated ( NicalonTM fibers, ac diamond indentor that has the same depth area ratio as a Vick (3) Alternate Methods of Estimation of ers diamond indentor. The accuracy of measurements with this Interfacial Parameters from Push-Out Curves quipment is considerably higher than that for microindenta (A) Interfacial Sliding Stress: Bright et al.23 measured the tion. However, the maximum load that can be applied is-0 interface debonding load and the maximum sliding load for N. The fiber-loading history involves the application of a pre- various embedded lengths of fiber. The observed dependence determined constant displacement (or loading)rate, up to a of the maximum sliding load on the initial embedded lengths naximum displacement(or force), followed by a constant un fibers was satisfactorily described by the nonlinear shear lag ding until 95% of the force is removed. Magnitudes of the model. The interfacial properties, including the sliding stress, force and displacement are continuously measured with reso- are derived from the maximum stress(omax)using a regression tions of 2, 4 un and 0.4 nm, respectively. The tests are procedure based on the following equati performed under displacement control as well as load control The sliding distance during nanoindentation tests is gener- ally much smaller than the specimen thickness. The fiber is pushed into the matrix but not through it( the same sample Values for the coefficient of friction, H, of the clamping with geometry as that for microindentation was used esidual stress and for the axial residual stress, oa, can be extracted by fitting the Hsueh equations to the loader k=Emr unloading curves. During unloading. fiber recovery as terized by the ratio of the residual to the maximum displace ependent on alues axial residual stress in the fiber and the poisson's ratio of the fiber(ve. The fiber-end displacement is predicted by the Hsueh model, using an expression similar to Eq. (1) The analysis is independent of the shape of the indentation Because of the pyramidal shape of the diamond indentor, the curve; therefore, it can also be applied to composites that have measured displacement must be corrected, due to indentor pen- strong interfacial bonds (B) Interfacial Shear Strength: Because the stress field surface of the loaded fibers). The depth of diamond penetration along the debond must be approximated in most cases, the applied load. Because the latter parameters evolve during the interfacial cracking, is extracted directly from the debonding test, there is no way of establishing a simple relation for diamond penetration versus the applied load tions:24-27(i) the interfacial shear stress decreases from the A method based on the indentation of transverse fibers was surface of the sample, (ii) debonding initiates when the maxi- used to determine the load-versus-diamond-penetratio mum shear stress exceeds the shear strength of the interface distance curve. Many reproducible indentation tests were per and(iii) the examined cell consists of a fiber embedded in ar formed perpendicular to the fiber axis. Then, an empirical re infinite matrix with a free surfa ace lation for diamond penetration distance was obtained by fitting Assuming that the stresses in the fiber are proportional to the ifference between the axial displacements of the fiber and unloading curves. Thus, it was possible to subtract the diamond of the matrix, considered independently, a simple analytica penetration distance from the displacements that were mea- equation for the initial debond stress Ts has been derived: 25,26 sured during the nanoindentation tests. Only the unloading curves for which the deviation from linearity was the largest ogEr+vm)./Rdiamond indentor that has the same depth:area ratio as a Vick￾ers diamond indentor. The accuracy of measurements with this equipment is considerably higher than that for microindenta￾tion. However, the maximum load that can be applied is ∼0.5 N. The fiber-loading history involves the application of a pre￾determined constant displacement (or loading) rate, up to a maximum displacement (or force), followed by a constant un￾loading until 95% of the force is removed. Magnitudes of the force and displacement are continuously measured with reso￾lutions of 2.4 mN and 0.4 nm, respectively. The tests are performed under displacement control as well as load control. The sliding distance during nanoindentation tests is gener￾ally much smaller than the specimen thickness. The fiber is pushed into the matrix but not through it (the same sample geometry as that for microindentation was used). Values for the coefficient of friction, m, of the clamping residual stress and for the axial residual stress, sa, can be extracted by fitting the Hsueh equations22 to the loading and unloading curves. During unloading, fiber recovery, as charac￾terized by the ratio of the residual to the maximum displace￾ments (U0/Umax) is strongly dependent on the values of the axial residual stress in the fiber and the Poisson’s ratio of the fiber (nf ). The fiber-end displacement is predicted by the Hsueh model, using an expression similar to Eq. (1). Because of the pyramidal shape of the diamond indentor, the measured displacement must be corrected, due to indentor pen￾etration into the fiber (a pyramidal mark is observed on the top surface of the loaded fibers). The depth of diamond penetration is directly related to the fiber hardness, the indent size, and the applied load. Because the latter parameters evolve during the test, there is no way of establishing a simple relation for diamond penetration versus the applied load. A method based on the indentation of transverse fibers was used to determine the load-versus-diamond-penetration￾distance curve. Many reproducible indentation tests were per￾formed perpendicular to the fiber axis. Then, an empirical re￾lation for diamond penetration distance was obtained by fitting a second-order polynomial to the experimental loading and unloading curves. Thus, it was possible to subtract the diamond penetration distance from the displacements that were mea￾sured during the nanoindentation tests. Only the unloading curves for which the deviation from linearity was the largest were analyzed. (3) Alternate Methods of Estimation of Interfacial Parameters from Push-Out Curves (A) Interfacial Sliding Stress: Bright et al.23 measured the interface debonding load and the maximum sliding load for various embedded lengths of fiber. The observed dependence of the maximum sliding load on the initial embedded lengths of fibers was satisfactorily described by the nonlinear shear lag model. The interfacial properties, including the sliding stress, are derived from the maximum stress (smax) using a regression procedure based on the following equation: smax = sc k FexpS 2mkt r D − 1G (6) with k = Emnf Ef~1 + nm! (7) and t = −msc (8) The analysis is independent of the shape of the indentation curve; therefore, it can also be applied to composites that have strong interfacial bonds. (B) Interfacial Shear Strength: Because the stress field along the debond must be approximated in most cases, the interfacial shear strength, ts, which measures the resistance to interfacial cracking, is extracted directly from the debonding stress. The few proposed models are based on similar assump￾tions:24–27 (i) the interfacial shear stress decreases from the surface of the sample, (ii) debonding initiates when the maxi￾mum shear stress exceeds the shear strength of the interface, and (iii) the examined cell consists of a fiber embedded in an infinite matrix with a free surface. Assuming that the stresses in the fiber are proportional to the difference between the axial displacements of the fiber and of the matrix, considered independently, a simple analytical equation for the initial debond stress ts has been derived:25,26 ts = − sd 2 F Ef~1 + nm! Em ln S R rDG −1/2 1 tanh (bt) (9) Fig. 1. Tensile stress–strain curves for 2D SiC/SiC composites with carbon interphases (0.5 mm thick) reinforced with as-received (I) or treated (J) Nicalon™ fibers, according to Droillard.13 Associated mechanisms of interface cracking are also indicated. April 1998 Interfacial Bond Strength in SiC/C/SiC Composite Materials 967