Some considerations of evaluation of interfacial frictional stress from the indentation technique for fibre-reinforced ceramic composites

Recent studies of fibre-reinforced (or whisker-reinforced) ceramic composites have revealed that a substantial improvement in toughness is achieved via the fibre pullout or bridging mechanism. Optimal conditions for toughening of these composites require an unbonded or a weakly bonded fibre-matrix interface that allows frictional sliding between the fibre and the matrix [1-3]. These requirements have prompted recent studies of interfacial properties of composites with frictional interfaces [4-11]. The fibre pullout test is not widely used, due to problems of sample preparation and inconsistent experimental results [4]. Conversely, the indentation technique has been used extensively to evaluate the interfacial frictional (shear) stress (IFS) [4-7]. Using this technique, an indentor is used to push on the end of an embedded fibre. Thick and thin samples* have been adopted such that partial sliding and push-out of the fibre occur, respectively, when the fibre is subjected to the indentation force (i.e. compressive loading). For the thick sample the average IFS is evaluated from the load-displacement relationship and the sliding length of the fibre based on force equilibrium considerations [5, 6]. For the thin sample the uncertainty in determining the sliding length is avoided and the average IFS is calculated from the thickness of the sample and the minimum force required to push out 'the fibre [7]. Both analyses ignore the variation of the IFS along the sliding length. However, when the fibre is subjected to compression in the axial direction, transverse expansion (i.e. the Poisson effect) of the fibre occurs which induces compressive stresses at the fibre-matrix interface and causes the IFS to vary due to Coulomb friction [8-10]. Consequently, the following questions must be raised. (1) Is the IFS constant along the entire sliding length? (2) If not, does the average value of the IFS bear any physical significance? (3) Can the IFS measured by compressive loading represent the value appropriate to fibre pullout in tension during cracking? The first question has been addressed previously. Theoretical analyses in recent studies show that when the end of the embedded fibre is subjected to a compressive load, the IFS is not constant, decreasing along the fibre length underneath the loaded surface due to the Poisson effect of the fibre [8-10]. The third question has also been analysed. The results show that when Poisson's ratio of the fibre is zero (i.e. no transverse strains due to axially applied stresses) the IFS is constant and has the same value along the sliding length for both fibre pullout and push-down. For Poisson's ratios greater than zero, compared with fibre push-down, fibre pullout has a lower IFS and a longer sliding length for the same magnitude of the load [11]. The purpose of the present study is to answer the second question: i.e. is the average IFS an intrinsic property of the composite when the fibre is subjected to compression (or tension)? In other words, does the average IFS depend on the load for the thick sample and on the thickness of the sample for the thin sample? The geometry used in the present study is a composite cylinder model [12]. A fibre of radius a is embedded in a coaxial cylindrical shell of matrix with