Stresses in Fiber-Reinforced Composites With Imperfect Bonding

Abstract

The axially symmetric problem of an infinite elastic fiber embedded into an infinite matrix of different thermomechanical properties is considered. It is assumed that the composite contains imperfections in the form of interface cracks or a broken fiber. The integral equations for the singular part of the problem are obtained by considering concentrated dislocations on the fiber-matrix interface and using the results as Green s functions.The resulting system of singular integral equations is solved, the expressions for stress intensity factors at the points of singularity and the strain-energy release rate are obtained, and a numerical example is given.

Fracture problems in composite materials

“…Similar results for an elastic fiber imbedded into an elastic matrix having perfect adhesion except for an axisymmetric interface crack are given in [8].…”

“…In crack problems the input functions f, (i = 1,2) are the components of the traction vector on the crack -6-surface and the unknown functions Pi are defined by [2][3][4][5][6][7][8] *1…”

Two bonded half planes with a crack going through the interface

“…In this type of studies it is usually assumed that the composite medium consists of perfectly bonded elastic components and the localized imperfection may be idealized as a plane crack or as a flat elastic inclusion. The problem of a finite crack lying parallel to or at a bimaterial interface in composites with various geometries was discussed in [1][2][3][4][5]. The similar problem for a flat inclusion was studied in [6].…”

“…An up-to-day review of the general fracture problems in composite materials and a summary of some of the known results may be found in [7]. The distinguishing feature of the solutions given in [1][2][3][4][5][6][7] as well as the other known solutions which appeared in literature within the past decade is that the strength of the stress singularity at the imperfection front is -1/2 and, in the case of a crack, the quasi-static stress state in the neighborhood of the crack front remains autonomous as the crack propagates. That is, aside from a slight change in a multiplicative constant known as the stress intensity factor, the asymptotic nature of the stress state in the vicinity of the crack front remains unchanged.…”

Mixed Boundary-value Problems in Mechanics

“…The solution of the wedge problem shown in Figure 8 with r` and without a crack initiating at thi apex will appear elsewhere. The application of the technique described in this section to singular integral equations of the second kind with complex coefficients may be found in [31], [33], [42] and [43]. Extension of the technique to a system of equations in which A, B, and k(x,y) are square matrices is given in [44] and [251. : .…”