Investigation of Normal Fracture Cracks in an Infinite Elastic Medium

In this work, based on the representation of the Papkovich –Neiber displacement and stress through 3 harmonic functions, dual integral equations are obtained, the solution of which is reduced to finding one Helder function. To find this function, a singular integral equation with a Cauchy kernel of the 1st kind is obtained. The solution of this integral equation, proposed by the method of V. D. Kuliyev, is reduced to the Fredholm integral equation of the 2nd kind with a continuous kernel. The main parameter of the mechanics of linear fracture of the stress intensity coefficient is determined and a numerical analysis is carried out. When the crack of a normal fracture is located in an infinite elastic medium, it is shown that both components of the displacement vector are nonzero. This result suggests that the crack is an oblate ellipsoid. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.