Stress-displacement relation of fiber for fiber-reinforced ceramic composites during (indentation) loading and unloading
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I. INTRODUCTION Studies of fiber-reinforced ceramic composites have revealed that a substantial improvement in fracture resistance is achieved via the fiber pullout or bridging mechanism. Optimal conditions for toughening of these composites require an unbonded or a weakly bonded fiber/ matrix interface that allows frictional sliding between fibers and the matrix.1"3 These requirements have prompted recent studies of interfacial properties, especially the interfacial frictional stress (IFS), of composites with frictional interfaces.4"10 The indentation technique has been used extensively to evaluate the IFS.4"8 In this method, an indenter is used to push on the exposed end of an embedded fiber along the axial direction of the fiber such that sliding occurs at the fiber/matrix interface. By assuming a constant IFS along the sliding length, the stress-displacement relation of the fiber has been analyzed to determine the IFS.4"6 However, theoretical analyses in recent studies show that the IFS is not constant along the sliding length due to Poisson's effect of the fiber. 910 When the fiber is subjected to compression in the axial direction, transverse expansion (Poisson's effect) of the fiber occurs, which induces compressive stresses at the fiber/matrix interface and increases the IFS through Coulomb friction. As the exposed end of the embedded fiber is compressively loaded in its axial direction, the axial compressive stress in the fiber and, hence, the IFS decrease with an increase in distance underneath the loaded surface because of the stress transfer from the fiber to the matrix through interfacial shear.9 Conversely, in the case of fiber pullout, the IFS increases along the sliding length underneath the loaded surface.10 The purpose of the present study is to account for the nonconstant IFS (Poisson's effect) in the development of
rigorous solutions for the stress-displacement relation of the fiber during axial compressive loading and unloading. Unbonded fiber/matrix interfaces subject to Coulomb friction and residual radial clamping stresses are considered. First, the stress distributions along the sliding length during loading and unloading are shown. Next, the effects of the residual clamping stress, Poisson's ratio of the fiber, and the coefficient of friction on stressdisplacement curves during loading and unloading are illustrated. Then, a methodology is demonstrated based on the present analysis to determine the magnitude of the clamping stress, the coefficient of friction, and the IFS distribution along the sliding length. Finally, the applicability of the present analysis to the case where bonding exists at the interface is discussed. II. STRESS ANALYSIS The same geometry of a composite cylinder model11 used in previous studies910 is adopted in the present study. A semi-infinitely long fiber with a radius, a, is embedded in a coaxial cylindrical shell of a matrix with an outer radius, b, such that a2/b2 corresponds to the volume fraction of fibers in the composite. As shown in Fig. 1, r is the distanc
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