Modifications of fibre pull-out analysis

Abstract

CHUN-HWAY HSUEH Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA The interracial properties of fibre-reinforced compo- sites can be evaluated for the results of single-fibre pull-out tests. The shear lag model [1-10] has been used extensively to analyse the stress transfer be- tween the fibre and the matrix, and to interpret the result of a single-fibre pull-out test. To obtain analytical solutions for a single-fibre pull-out, approximations of the analysis are required. For example, the stress transfer between the fibre and the matrix is modelled by a simple relationship between the axial stress gradient in the fibre and the interracial shear stress [1-10]. The radial depend- ences of the axial stresses in both the fibre and the matrix are generally ignored [1-8]. Since the radius of the matrix is generally much greater than that of the fibre in the single-fibre pull-out test, the radial dependence of the axial stress in the matrix is included in Hsueh's analyses [9, 10]. However, to obtain this radial dependence, an approximate shear stress distribution in the matrix is adopted. This shear stress nearly satisfies the free surface condition when the radius of the matrix is much greater than that of the fibre [9, 10] which, in turn, provokes questioning of the eligibility [8] of Hsueh's analyses. Also, the correlations between the exact equilibrium equation and the equations dictating both the stress transfer between the fibre and the matrix, and the shear stress distribution in the matrix have not been addressed. As a complement to the previous study [9], the purposes of the present study were two-fold. First, the correlations between the exact equilibrium equation and the approximate equilibrium equations adopted in the shear lag model were addressed. Secondly, the shear stress adopted in the previous studies [9] was modified to satisfy the free surface condition, and the corresponding differential equation governing the axial stress distribution in the fibre is presented. The results based on this modification are then compared with previous re- sults [9]. The idealized specimen for a single-fibr e pull-out and the corresponding shear lag model is shown in Fig. 1. A fibre with a radius of a is located at the centre of a coaxial cylindrical shell of matrix with outer radius b, which is much greater than a. The radial and the axial co-ordinates are r and z, respectively. An axial stress, or0, is applied to pull out the fibre, and the matrix is fixed at the bottom surface. For an axially symmetric geometry, which has the cylindrical polar co-ordinates r, 0 and z, the