J. Ye, AK Kaw Theoretical and Applied Fracture Mechanics 32(1999)15-25 sliding friction stress can be overestimated if the Indent transverse expansion of the fiber is not taken into account. The Poisson expansion of the fibers under the compressive loads and the consequent of the normal stress across the interface lead to a nonlinear variation of the frictional shear stress Matrix along the embedded fiber length is most often used for modeling the pushout test Base and for the evaluation of the fiber-matrix interface ig. 1. Schematic of a single fiber pushout test. However, SLA models have assumptions such as-approximate shear stress distribution on the interface. and axial stresses in the fiber and matrix focus our attention on the adequacy of using SLa are independent of radial direction. So how ade models in extracting the mechanical properties of quate is the SLA model for extracting the two the fiber-matrix interface mechanical properties of the fiber-matrix inter- The first pushout test was conducted in [2] face? To answer this question, an elasticity model Measured was the force necessary to slip a fiber of the pushout test based on boundary element along part or all of its length by pushing on the method(BEM)was developed. The BEM model is end with an indentor on a flat-end probe. It was then used to extract the two fiber-matrix interface assumed that the fiber and matrix are bonded only properties. The results from the BEM model are frictionally in these composites. In [3, 4] use was compared with the SLA model. Further for a made of a variation of the pushout technique [2] complete study, parametric studies are conducted for measuring the interfacial friction stress. In to compare BEM and SLA results for several these experiments, the force F required to push out rameters such as coefficient of friction, fiber to ort fibers from thin composite specimen was matrix elastic moduli ratios, and fiber volume measured and the friction stress was calculated fractions from a simple force balance analysis, F= 2Trr La where rr is the fiber radius, L the fiber length and or is the shear stress along the fiber-matrix in- 2. Shear-lag analysis of pushout test terface. This assumes that the interfacial shear stress over the embedded length that supports the Fig. 2 is the schematic of the pushout test in the external force is constant. However. a constant shear-lag analysis. It shows a composite geometry shear stress approximation may only be reason- of length L and a uniform pressure loading p on of friction is small. Thi ry short or the the fiber to simulate the indentor load Coulomb neglects the variation of the radial stress normal to the interface due to the poissons effect under pushout loading. Actually, in a pushout test the xternal applied force is compressive that expand the fiber in the transverse direction, thereby in creasing the normal stress and hence the frictional stress at the interface A shear-lag analysis(SLA)[5] was proposed for modeling the pushout test. An exponential de- crease was predicted for the interfacial shear stress along the fiber length. The results showed that the Fig. 2. Schematic of the pushout test for shear-lag analysisfocus our attention on the adequacy of using SLA models in extracting the mechanical properties of the ®ber±matrix interface. The ®rst pushout test was conducted in [2]. Measured was the force necessary to slip a ®ber along part or all of its length by pushing on the end with an indentor on a ¯at-end probe. It was assumed that the ®ber and matrix are bonded only frictionally in these composites. In [3,4] use was made of a variation of the pushout technique [2] for measuring the interfacial friction stress. In these experiments, the force F required to push out short ®bers from thin composite specimen was measured and the friction stress was calculated from a simple force balance analysis, F ˆ 2prfLrrz, where rf is the ®ber radius, L the ®ber length and rrz is the shear stress along the ®ber±matrix in￾terface. This assumes that the interfacial shear stress over the embedded length that supports the external force is constant. However, a constant shear stress approximation may only be reason￾able if the embedded length is very short or the coecient of friction is small. This approximation neglects the variation of the radial stress normal to the interface due to the PoissonÕs e€ect under pushout loading. Actually, in a pushout test the external applied force is compressive that expands the ®ber in the transverse direction, thereby in￾creasing the normal stress and hence the frictional stress at the interface. A shear±lag analysis (SLA) [5] was proposed for modeling the pushout test. An exponential de￾crease was predicted for the interfacial shear stress along the ®ber length. The results showed that the sliding friction stress can be overestimated if the transverse expansion of the ®ber is not taken into account. The Poisson expansion of the ®bers under the compressive loads and the consequent increase of the normal stress across the interface lead to a nonlinear variation of the frictional shear stress along the embedded ®ber length. Shear±lag analysis such as that discussed in [5] is most often used for modeling the pushout test and for the evaluation of the ®ber±matrix interface properties [6]. However, SLA models have assumptions such as ± approximate shear stress distribution on the interface, and axial stresses in the ®ber and matrix are independent of radial direction. So how ade￾quate is the SLA model for extracting the two mechanical properties of the ®ber±matrix inter￾face? To answer this question, an elasticity model of the pushout test based on boundary element method (BEM) was developed. The BEM model is then used to extract the two ®ber±matrix interface properties. The results from the BEM model are compared with the SLA model. Further for a complete study, parametric studies are conducted to compare BEM and SLA results for several pa￾rameters such as coecient of friction, ®ber to matrix elastic moduli ratios, and ®ber volume fractions. 2. Shear±lag analysis of pushout test Fig. 2 is the schematic of the pushout test in the shear±lag analysis. It shows a composite geometry of length L and a uniform pressure loading p on the ®ber to simulate the indentor load. Coulomb friction law is assumed at the interface, and Fig. 2. Schematic of the pushout test for shear±lag analysis. Fig. 1. Schematic of a single-®ber pushout test. 16 J. Ye, A.K. Kaw / Theoretical and Applied Fracture Mechanics 32 (1999) 15±25