Publication 26-CNA-008
Finite-width Adiabatic Shear Banding and Dislocation Patterning in Mesoscale Polycrystalline Aggregates
Siddharth Singh
Department of Civil and Environmental Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
ssingh3@andrew.cmu.edu
Rajat Arora
Apple, Inc.
N. Seattle, WA 98109
Janith Wanni
Department of Materials Science and Engineering
University of Wisconsin-Madison
Madison, WI, 53706
Charles Adkins
Department of Materials Science and Engineering
University of Wisconsin-Madison
Madison, WI, 53706
Raymond Rasmussen
Department of Mechanical Engineering
University of Wisconsin
Madison, WI 53706
Noah J. Schmelzer
Department of Civil and Systems Engineering
Johns Hopkins University
Baltimore, MD 21218
Dan J. Thoma
Department of Materials Science and Engineering
University of Wisconsin-Madison
Madison, WI, 53706
Curt A. Bronkhorst
Department of Mechanical Engineering
University of Wisconsin
Madison, WI 53706
Amit Acharya
Department of Civil & Environmental Engineering
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213
acharyaamit@cmu.edu
Abstract: Dynamic shear banding under adiabatic conditions in a mesoscale polycrystalline aggregate is studied using a model of mesoscale dislocation mechanics and experiments. The model involves a length scale related to hardening induced by excess/polar/geometrically necessary dislocation (GND) density, and utilizes a simple classical crystal plasticity model with isotropic Vocelaw hardening. Simulations of statistically representative volume elements of a polycrystal determined from experimental samples are conducted. Studies in 2-d (section) and 3-d capture the experimentally observed finite-width shear bands and the formation of low-angle subgrain boundaries even in the absence of heat conduction in the model, as well as size-dependent strengthening for grain sizes from 1 to 20 $\mu m$. The 2-d and large-scale 3-d simulations, the latter involving 1 million finite elements, provide access to the progressive evolution of material strength, stress state, and temperature in the course of large deformations. GND distributions accumulate at grain boundaries and form patterned structures within grain interiors, offering insight into the microstructural changes that precede failure in adiabatic shear bands. Mesh-converged, delocalized and localized plastic flow to very large deformations without softening is observed for a significant range of parameters, reflecting a competition between GND hardening and thermal softening in setting the non-softening steady state in the absence of other ductile damage mechanisms in the model.
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