Abstract
The single fiber, axisymmetric concentric cylinder model is widely used for analyzing the thermo-elastic stress field in a composite representative volume element. In this study, the concentric cylinder model has been utilized to evaluate the load transfer characteristics in the immediate vicinity of a broken fiber in a unidirectional composite. A number of researchers have studied the stress distributions around discontinuous fibers. The so-called shear lag analysis is frequently used for analysis of stress transfer between fiber and the matrix. However, this simplified approach leads to inaccurate predictions of shear stresses and energy release rates [1]. By developing sets of recurrence relations, McCartney [2] has extended the two cylinder stress transfer model to multiple cylinders and used the technique to study the stress transfer behavior when fiber fracture occurs. Using Reissner’s variational principle, Pagano [3] has developed the axisymmetric damage model to approximate the elastic stress field and energy release rates of bodies composed of concentric cylinders containing damaged regions either as annular or penny-shaped cracks in the constituents and/or debonds between them. This variational model of a concentric cylinder [3] can be easily employed to simulate fiber breakage.
The prediction of micro-mechanical damage initiation and growth in composite materials requires accurate stress and deformation analyses. For the fiber fracture stress transfer problem, singularities are encountered for the axial stress in the matrix in the plane of fiber fracture. In this work, the detailed stress and displacement fields in the neighborhood of fiber break are analyzed using the recursive [2] and variational [3] methods, and compared with the asymptotic stresses around the crack tip [4] and with other numerical methods such as FEM using mesh refinement in the regions of singularity. In this study a comparison of the different solutions is presented highlighting the distance at which leading terms of asymptotic analysis are dominant and the ability of the approximate elasticity solutions to capture the local radial and angular distributions near the crack tip. Also, the assumptions of the more commonly used shear-lag analyses will be critically assessed.
