Crack-Tip Parameters in Polycrystalline Plates with Soft Grain Boundaries
Publication: Journal of Engineering Mechanics
Volume 134, Issue 1
Abstract
Two micromechanical models are used to calculate the statistical distributions of the stress intensity factor of a crack in a polycrystalline plate containing stiff grains and soft grain boundaries. The first is a finite-element method based Monte Carlo procedure where the microstructure is represented by a Poisson–Voronoi tessellation. The effective elastic moduli of the uncracked plate and the stress intensity factor of the cracked plate are calculated for selected values of the parameters that quantify the level of elastic mismatch between the grains and grain boundaries. It is shown that the stress intensity factor is independent of the expected number of grains, and that it can be estimated using an analytical model involving a long crack whose tip is contained within a circular inhomogeneity surrounded by an infinitely extended homogenized material. The stress intensity factor distributions of this auxiliary problem, obtained using the method of continuously distributed dislocations, are in excellent agreement with those corresponding to the polycrystalline microstructure, and are very sensitive to the position within the inhomogeneity of the crack tip. These results suggest that fracture toughness experiments on polycrystalline plates can be considered experiments on the single grain containing the crack tip, and in turn reflect the effects typical of finite-geometry specimens.
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Acknowledgments
Partial support for R. Ballarini was provided by the MTS Visiting Professorship in Geomechanics at University of Minnesota’s Department of Civil Engineering. G. J. Rodin acknowledges the support of the National Science Foundation through Grant No. NSFCMS 0219839. The writers also thank John P. Dempsey of Clarkson University for useful discussions.
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© 2008 ASCE.
History
Received: Oct 27, 2006
Accepted: Apr 23, 2007
Published online: Jan 1, 2008
Published in print: Jan 2008
Notes
Note. Associate Editor: Bojan B. Guzina
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