Contours for planar cracks growing in three dimensions

Brock, Louis

doi:10.2140/jomms.2015.10.63

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Contours for planar cracks growing in three dimensions

Louis Milton Brock

Vol. 10 (2015), No. 1, 63–77

DOI: 10.2140/jomms.2015.10.63

Abstract

A three-dimensional dynamic steady state analysis for extension of a semi-infinite plane crack is considered. Fracture is brittle and driven by loads applied to the crack surfaces. An analytical solution is obtained, and examined in light of two criteria: energy release (rate) and strain energy density. Introduction of a quasipolar coordinate system allows, for each criterion, generation of a nonlinear first-order differential equation for the distance from the origin to any point on the crack edge. These in turn give insight into the crack contour generated by the crack edge. In particular, for loading by compressive point forces, the equation generated by the energy release (rate) criterion is solved exactly. Calculations depict a crack edge contour that tends to the rectilinear, but deviates markedly from that near the point forces.

Keywords

3D, dynamic, criteria, analytic solution, crack edge contour, crack edge location

Milestones

Received: 27 September 2014

Accepted: 16 December 2014

Published: 12 February 2015

Authors

Louis Milton Brock
Department of Mechanical Engineering University of Kentucky 265 RGAN Lexington, KY 40506-0503 United States

Vol. 10, No. 1, 2015

Louis Milton Brock

Abstract

Keywords

Milestones

Authors