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Technical Briefs

The Propagation of Star-Shaped Brittle Cracks

[+] Author and Article Information
Nazile B. Rassoulova

Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku AZ1141, Azerbaijan

J. Appl. Mech 77(4), 044502 (Mar 31, 2010) (5 pages) doi:10.1115/1.4000900 History: Received May 30, 2008; Revised August 19, 2009; Published March 31, 2010; Online March 31, 2010

The paper studies the dynamical propagation of star-shaped cracks symmetrically arranged in an elastic thin plate, subjected to the action of instantly applied, comprehensively (uniformly) stretching stresses, which implies a self-similar problem with homogeneous stresses and velocities of particles. Occurrence of such motion patterns is established through experiments. By using the Smirnov–Sobolev functional-invariant solutions method and a careful choice of mappings, the problem is reduced to some boundary value problem of the theory of complex variable functions, and exact analytic solution of the original problem, including a closed-form solution for important stress intensity coefficient near the end of the crack, is derived. We also establish a fundamental theoretical limit imposed on the number of cracks—there has to be at least three cracks.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Existence of star-shaped cracks experimentally verified

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Figure 2

Choice of coordinate system

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Figure 3

Two domains in z1,2 planes

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Figure 4

Two domains in ξ1,2 planes coincide on real axis

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