Dynamics of a rectilinear isolated crack growing at a constant rate under conditions of antiplane deformation

Abstract

Article [i] discusses the problem of the development of a rectilinear crack under the conditions of antiplane deformation with its arbitrary loading and an arbitrary law of the motion of its ends. The difficulty in the practical application of the solution obtained consists in the need for a consecutive calculation of all the wave diffractions running along the crack from one of its edges to the other. Under these circumstances, for large times (in comparison with the time of the passage of a wave over the length of the crack) it is practically impossible to find a solution. With this aspect, the best properties are those of self-similar solutions, obtained in the problem of the development of a rectilinear isolated crack from zero at a constant rate under the action of the corresponding load. Here the arbitrary law of the loading can be approximated [2] by the sum of self-similar loads. For the case of plane and axisymmetric deformation, several such self-similar problems have been solved [3-9]. In the present article, analogs of these problems for antiplane deformation are considered as a partial case. The consideration of antiplane deformation is explained, on the one hand, by the great mathematical simplicity of this case in comparison with plane deformation and, on the other hand, by the fact that many of the qualitative aspects of the solutions in the cases of plane and antip!ane deformation are common.