Mini-Symposium Topic: Non-Linear Models (dedicated to Ian Duerden)

Stress and Deformation Field in an Elastic Medium Containing a Spherical Crack Subject to Torsion

¹University of Victoria, Victoria, British Columbia, Canada

¹ University of North Carolina at Charlotte, Charlotte, North Carolina, U. S. A.

A torsion problem for a crack that occurs on a spherical surface in an elastic medium is considered. The case where an inclusion is present is also analized. The general analytical solution is sought in terms of series in Associated Legendre functions of the first kind. The coefficients of the series satisfy dual series equations and the problem is reduced to a Fredholm integral equation of the second kind, which in turn, is solved numerically through an infinite system of algebraic equations.

The stress intensity factor is assessed for various values of geometric and material parameters.