Calculation of stress concentration caused by a coated particle in polymer matrix to determine adhesion strength at the interface

The mechanical problem of a coated particle embedded within a cylindrical rod under tensile load is considered. The motivation for the calculations is to determine the maximum radial stress at the particle surface as a function of applied load. Assuming that normal stresses at the interface are responsible for debonding, the adhesion strength can be determined from critical loads at debonding initiation. Analytical and finite element solutions of the stress field around a particle under uniaxial load are derived as functions of the mechanical properties of the particle, the matrix and the interphase. A non-linear relation between the true stress and logarithmic strain is considered for the interphase and the matrix. The effect of the interphase on the stress concentration strongly depends on the ratio between the elastic modulus of the matrix and the interphase and on the Poissonʹs ratio of the interphase. The consideration of an interphase leads to a non-uniform stress distribution within the particle. The ratio between the particle diameter and the cross section of the sample has a decisive influence on the shape of the non-linear relation between applied load and maximum radial stress.