On the stress transfer in fibre-reinforced composites with bonded fibre ends

Abstract

In the conventional shear lag model [1], the fibre end stress is usually assumed to be negligible. This assumption is apparently not justified when the fibre ends are perfectly bonded. The exact condition can only be determined, however, as part of full solutions to a three-dimensional axisymmetrical elasticity problem. This problem is too difficult to be handled by any analytical means. On the other hand, if we assume that the shape of the fibre is prolate ellipsoidal, then Eshelby's famous solution [2] can be used to determine the stress in the fibre. The uniform stress state of the Eshelby solution does not allow the variation of the stress in the fibre to be investigated, particularly near the fibre ends. Recent publications [3, 4] have indicated that a simple but reasonably accurate solution is desirable. The purpose of this letter is to communicate some results regarding this problem. Consider a fibre with radius r0 and length 2I embedded in an infinite matrix. The Young's moduli of the fibre and the matrix are denoted by Ef and Era, respectively. The applied stress at infinity in the direction of the fibre is uniform and is denoted by am. It has been found [5] that the fibre stress along the fibre axis is ( + 1 O" m E m K m + K f