Analysis of a Sector Crack in a Three-Dimensional Voronoi Polycrystal With Microstructural Stresses

[+] Author and Article Information
M. S. Wu, J. Guo

Department of Engineering Mechanics, University of Nebraska-Lincoln, W317.4 Nebraska Hall, Lincoln, NE 68588-0526

J. Appl. Mech 67(1), 50-58 (Sep 15, 1999) (9 pages) doi:10.1115/1.321151 History: Received April 21, 1999; Revised September 15, 1999
Copyright © 2000 by ASME
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Grahic Jump Location
A typical Voronoi grain generated by the algorithm described in Section 2
Grahic Jump Location
The probability distributions of (a) the number of faces of a grain and (b) the number of edges of a grain face in a three-dimensional Voronoi tessellation
Grahic Jump Location
The Eshelby procedure of (a) cutting, (b) straining, and (c) welding for estimating microstructural stresses in a polycrystal
Grahic Jump Location
Point forces P acting on a grain face: (a) P is normal to the grain face, (b) P is tangential to the grain face
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(a) Body force doublet of density fzz and body forces of densities fx and fy acting at the point (ξ,η,0) within the crack plane. (b) Triangular finite elements and polygonal regions within crack used to obtain the resultant force boundary conditions.
Grahic Jump Location
Convergence of the normalized Mode I stress intensity factor along the crack edge with increase in the number of triangular elements
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Two grains used to investigate the dependence of the stress intensity factor of a sector crack on crack length, elastic anisotropy, crack angle, and remote stress state; (a) the crack plane is almost normal to the Z-direction, (b) the crack plane is about 45 deg to the X-axis and Z-axis
Grahic Jump Location
Variation of the Mode I stress intensity factor along the circular edge with the projected position x3/a, and dependence of the stress intensity factor on the crack length
Grahic Jump Location
Dependence of the Mode I stress intensity factor on the elastic anisotropy ratio (A for cubic materials and Ah for hexagonal materials)
Grahic Jump Location
Variation of the Mode I stress intensity factor with the orientation κ of one grain
Grahic Jump Location
Dependence of the Mode I stress intensity factor on the remote biaxial tension stress state. Discrepancies between results computed with and without microstructural stresses can be very significant.




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