Vol. 13, No. 2, 2018

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ISSN: 1559-3959
Fracture initiation in a transversely isotropic solid: transient three dimensional analysis

Louis M. Brock

Vol. 13 (2018), No. 2, 171–190
Abstract

A transversely isotropic solid is at rest, and contains a semi-infinite, plane crack. The axis of rotational material symmetry lies in the crack plane. Application of normal point forces to each face of the crack causes transient 3D growth. The related problem of discontinuities in displacement and traction that exist on regions that exhibit dynamic similarity is first considered. Analytic results are obtained in integral transform space. These lead to equations of the Wiener–Hopf type for the fracture problem. Analytic solutions are again obtained and, upon inversion, subjected to a dynamic energy release rate criterion that includes kinetic energy. A particular form of rapid growth in time of the forces is found to cause crack growth rates that indeed vary with position, but not with time. The influence of anisotropy upon wave speeds and crack edge contour are examined.

Keywords
transverse isotropy, transient, fracture initiation, kinetic energy, crack contour
Milestones
Received: 6 October 2017
Accepted: 13 February 2018
Published: 27 May 2018
Authors
Louis M. Brock
Department of Mechanical Engineering
University of Kentucky
Lexington, KY
United States