Multi-scale simulations of plastic flow and failure
in crystalline solids
Mr. Vikranth Racherla, Ph.D. Candidate
Advisor: Professor John L. Bassani
Department of Mechanical Engineering and Applied Mechanics
University of Pennsylvania
Abstract
The implications of non-associated flow on deformation of crystalline solids
is the focus of this lecture. Conventional macroscopic plasticity
theory is predicated on a simple slip mechanism that is controlled only
by the shear stress on the slip plane in the direction of the slip. We
now know that this is exceptional behavior since, in all but FCC lattices,
the core structure of (screw) dislocations tends to be three dimensional.
As a result, slip depends upon what are commonly called non-glide stresses.
This leads to non-associative constitutive theories at both single and
polycrystal levels of the type that are common for granular (frictional)
materials.
In this work we show that effects of non-glide stresses persist at macroscopic
scale and strongly affect deformation behavior. For example, the critical
pressures at which cavitational instabilities occur are shown to be significantly
affected by non-associated flow. The structure of multi-axial constitutive
equations is studied in detail. In classical rate-independent non-associated
flow we show that uniqueness and stability of solutions to incremental boundary
value problems can be lost even at small deformations. To investigate the
effect on sheet necking, a uniform sheet with a thickness inhomogeneity in
the form of a groove or band is analyzed under plane stress conditions, using
a rate-dependent theory with sufficiently large strain-rate sensitivity;
a considerable effect of non-associated flow is found on the critical sheet
necking strains as well the localized band orientation. To investigate the
instabilities in sheet necking for a nearly rate-insensitive response finite
element analysis are carried out using an implicit dynamics scheme. These
led to the discovery of “strain bursts” as a consequence of non-associated
flow, particularly for deformations near the plane strain state.
Thursday, November 9th
337 Towne Bldg.
2:00 – 3:00 p.m.
