In this independent study project, the problem of interfacial stress concentrations was considered from the perspective of shear lag solutions. We considered a fiber encased by a coaxial matrix sheath. An applied axial load on the sheath can increase the interfacial shear stress towards the ends of the fibers within the composite. This concentration of shear stress at the ends can cause debonding and failure of the composite. Because of the shear lag phenomenon, axial stress is maximum at the half-length of the fiber and decreases towards the ends. Conversely, the transference of stresses from matrix to fiber causes the shear stress to be zero at the midpoint of the fiber and then drastically spike at the end of the fiber. This problem has been long studied through shear lag approaches. This paper studies in detail a new shear lag approach for a fiber with stiffness that varies along its length, and documents how a piecewise functionally graded fiber, linearly decreasing in stiffness from the mid-point towards the end, can alleviate this shear concentration, reducing the risk of failure. The derivation is recounted here, and the solution methods and numerical techniques I developed to solve the equations is described. A parametric study was performed in which stress fields associated with functionally graded fibers were compared to a reference case with fibers of constant stiffness. Results show that functional grading of fibers, when chosen within a specific range, can substantially alleviate stress concentrations.

Document Type

Final Report

Author's School

McKelvey School of Engineering

Author's Department

Mechanical Engineering and Materials Science

Class Name

Mechanical Engineering and Material Sciences Independent Study

Date of Submission