Cavitation at the Ends of an Elliptic Inclusion Inside a Plate Under Tension

Abstract

An oblong elliptic inclusion is perfectly filled in a hole in an infinite plate in the unstressed state. Cavities at the ends of the inclusion will appear as a result of the application of uniaxial stress at infinity in the direction of the major axis of the ellipse. Analytical formulation of the problem leads to a mixed boundary-value problem of the mathematical theory of elasticity. A Fredholm integral equation of the first kind is derived for the normal stress with the range of integration being unknown (corresponding to the unknown region of contact). Applying the theorem which has recently been established based on a variational principle, a transcendental equation is obtained for determining the contact region. Numerical results are given for various values of the elastic constants of both the matrix and the inclusion. Application of the results to fiber-reinforced composite materials is discussed.