Mode-I elliptical crack in an infinite elastic body. I. Crack-face displacement for the polynomial law of loading

For a mode-I embedded elliptical crack in an infinite elastic body, we propose a modified procedure for the calculation of the weight function and stress intensity factor based on our earlier development. Analytical and numerical values of the stress intensity factor along the crack front have been obtained for different cases of the polynomial law of loading. We propose an approach to the determination of the crack-face displacements from the stress intensity factor values, in which the Rice energy-balance equation, Dyson's theorem, and the theory of crack translation in a nonuniform stress field are used. An expression of closed form for the elliptical crack-face displacement for a polynomial law of loading of any degree has been derived, which can be employed in solving three-dimensional problems of the elasticity theory for cracked bodies.