Three-Dimensional Finite Element Modeling of Realistic Polycrystalline Geometries

Michael Veilleux, Cornell University

Fatigue crack nucleation in metallic alloys depends on several variables, including material properties, boundary conditions, constitutive relationships, and geometry. At the continuum scale, the shape of the structural component is the only geometrical entity affecting the stress and strain fields, and the laws governing crack initiation are primarily empirically based. However, in order to predict accurately crack nucleation with a numerical model, it is imperative to consider the micro-mechanical behavior of the material. For one cubic millimeter of a polycrystalline alloy, the local fields depend upon the irregular geometry of thousands of grains. Each grain has a unique orientation with multiple wedges and notches defining its boundaries, many of which cause stress concentrations contributing to crack nucleation.

As part of a larger effort to model accurately crack nucleation and growth in metallic polycrystals, this work focuses on replicating the realistic geometry in a finite element model. Using data taken directly from Scanning Electron Micrographs (SEM’s) of a 7075-T651 aluminum alloy, a digital replication is created. Each grain is defined by a group of elongated Voronoi cells representing the microstructure of the alloy after a rolling operation. After an entire digital polycrystal is created, the microstructure is meshed and analyzed with millions of linear or quadratic tetrahedral elements. Variable material properties can be applied to each grain to show how the more realistic geometry creates substantially different stress and strain fields than a model with simplified geometries.

Abstract Author(s): Michael Veilleux, Anthony Ingraffea, Gerd Heber, Paul Wawrzynek