Stress intensity factor for an elliptical crack under arbitrary normal loading

Abstract

Harmonic stress function and the stress intensity factor for an elliptical crack embedded in an elastic solid and subjected to an arbitrary internal pressure are derived in this paper. The internal pressure is assumed to be expressible in terms of a polynomial of x and y as σ zz = − p( x, y) where p( x, y) = A 00 + A 10 x + A 01 y + A 20 x 2 + A 11 xy + A 30 y 2 + A 30 x 3 + A 21 x 2 y + A 12 xy 2 + A 03 y 3. The stress intensity factor for the elliptical crack subjected to this polynomial loading reduces to the solutions given by Green and Sneddon when all coefficients A ij except A 00 are zero and by Kassir and Sih when all coefficients except A 10 are zero. The solution is then used to determine the transient stress intensity factor of an elliptical crack embedded in a thick plate, one side of which is subjected to a sudden temperature change. Other possible applications of this solution, such as an elliptical crack in a large beam in pure bending, are also discussed in this paper.