Wave displacement field at a half-space surface caused by an internal crack under twisting load

A nonstationary axisymmetric problem concerning mode-III elastic wave generation in an elastic cracked half-space is considered. The problem is formulated in the Fourier time transform domain. An integral representation of displacements is selected in the form of Helmholtz potentials with unknown densities that characterize the crack-opening displacements. The problem of determining the functions of the crack-opening displacements is reduced to solving two-dimensional boundary integral equations. The dependences of the elastic displacements at the half-space surface on the crack depth and distance from the epicenter are found for various functions describing the time dependence of the crack load.

► A dynamic problem concerning the determination of the elastic displacement field in a half-space with a crack is considered.
► An integral representation of displacements is selected in the form of Helmholtz potentials.
► The dependences of the elastic displacements at the half-space surface on the crack depth and distance from the epicenter are found.