### Inelastic deformation of amorphous metals

L. Anand

Massachusetts Institute of Technology

Department of Mechanical Engineering

Under certain conditions many solids appear in a disordered form; such
solids are referred to as amorphous or glassy. Important examples of
amorphous solids are the current generation of bulk metallic
glasses. When a metallic glass is deformed at ambient temperatures the
inelastic deformation is characterized by the formation of intense
localized shear bands; fracture typically occurs after very small
inelastic strain in tension, but substantial inelastic strain levels
can be achieved under states of confined compression, such as in
indentation experiments. The plastic deformation of amorphous metallic
glasses is fundamentally different from that in crystalline solids
because of the lack of long-range order in the atomic structure of
these materials. Molecular-dynamic computer simulations in the
literature show that at a micromechanical level inelastic deformation
in metallic glasses occurs by local shear transformations in clusters
of atoms (≈ 30 to 50 atoms), and topologically such shear
transformations require a local inelastic dilatation that produces an
elastic strain field in the surrounding material that
autocatalytically then initiates similar shear transformations in
neighbouring volume elements, leading to the formation of shear
bands. These simulations also suggest that a pressure-sensitive
Coulomb-Mohr yield criterion describes the data pertaining to the
onset of inelastic deformations in the numerical simulations quite
well.

The Coulomb-Mohr yield condition is widely used in soil mechanics to
determine the stress required for flow of a granular material;
however, the flow-rule, that is, the equation which governs the flow
behavior for this class materials is generally not agreed upon. In
this talk we will present a complete three-dimensional
elastic-viscoplastic constitutive model for the large deformation
response of cohesive granular materials. The model is a
generalization of the classical two-dimensional (plane-strain)
.double-shearing. constitutive model to three-dimensions, includes the
effects of elastic deformation, and the typical pressure-sensitive and
dilatant, hardening/softening response observed in granular
materials. We apply the new constitutive equations to model the
inelastic deformation of a representative amorphous metallic glass
under isothermal conditions.