Abstract: An internal variable theory has been proposed to account for the essential microstructures
during inelastic deformation. The framework of the theory is built on the basis of well known
dislocation dynamics to provide the concept of an internal strain tensor as the most fundamental
deformation state variable. The plastic and inelastic strain rate tensors are then naturally defined and
also a kinematics relation among them can further be derived from the time rate of change of this
internal strain tensor, which in fact accounts for the evolution of microstructures during inelastic
deformation. To complete the theory, the constitutive relations between the various stress variables
and their conjugate deformation rate variables are then derived based on the dislocation kinetics. The
theory is then further extended to describe the structural superplasticity, taking this slip zone model
with dislocation pile-ups as the major accommodation mechanism for grain boundary sliding. The
experimental results obtained from the various crystalline materials are then presented and compared
with each other in relation to the internal variable theory for inelastic deformation.
Abstract: It is commonly believed that continuum mechanics theories may not be applied at the
nanoscale due to the discrete nature of atoms. We developed a nanoscale continuum theory based on
interatomic potentials for nanostructured materials. The interatomic potential is directly incorporated
into the continuum theory through the constitutive models. The nanoscale continuum theory is then
applied to study the mechanical deformation and thermal properties of carbon nanotubes, including
(1) pre-deformation energy; (2) linear elastic modulus; (3) fracture nucleation; (4) defect nucleation;
(5) electrical property change due to mechanical deformation; (6) specific heat; and (7) coefficient of
thermal expansion. The nanoscale continuum theory agrees very well with the experiments and
atomistic simulations without any parameter fitting, and therefore has the potential to be utilized to
complex nanoscale material systems (e.g., nanocomposites) and devices (e.g., nanoelectronics).
Abstract: Design has traditionally involved selecting a suitable material for a given application.
A materials design revolution is underway in which the classical materials selection approach is
replaced by design of material microstructure or mesostructure to achieve certain performance
requirements such as density, strength, ductility, conductivity, and so on. Often these multiple
performance requirements are in conflict in terms of their demands on microstructure.
Computational plasticity models play a key role in evaluating structure-property relations
necessary to support simulation-based design of heterogeneous, multifunctional metals and alloys.
We consider issues related to systems design of several classes of heterogeneous material systems
that is robust against various sources of uncertainty. Randomness of microstructure is one such
source, as is model idealization error and uncertainty of model parameters.
An example is given for design of a four-phase reactive powder metal-metal oxide mixture for
initiation of exothermic reactions under shock wave loading. Material attributes (e.g. volume
fraction of phases) are designed to be robust against uncertainty due to random variation of
microstructure. We close with some challenges to modeling of plasticity in support of design of
deformation and damage-resistant microstructures.
Abstract: The present paper summarizes the crystallographic dependence of the displacement burst
behavior observed in nanoindentation using two single crystalline aluminum (Al) materials and
copper (Cu) with three kinds of surface indices, namely (001), (110) and (111). From the critical
indent load at the first burst, the critical resolved shear stresses (CRSSs) of the collective dislocation
nucleation were estimated in reference to molecular dynamics (MD) simulations. These are almost
one-tenth of the shear modulus, which are close to the ideal values. We explain the nanoplastic
mechanics by a comprehensive energy balance model to describe the linear relation between the
indent load and the burst width of the first displacement burst and by the nucleation model consisting
of three-dimensional discrete dislocations to evaluate the number of dislocations nucleating. The
distance between the emitted dislocation loops of Al is found to be fairly large. Thus, Al is expected
to exhibit a less tangled network of dislocations just below the indentation than Cu, which has a lower
stacking fault energy.
Abstract: Cavitation instabilities have been predicted for a single void in a ductile metal stressed
under high triaxiality conditions. In experiments for a ceramic reinforced by metal particles a single
dominant void has been observed on the fracture surface of some of the metal particles bridging a
crack, and also tests for a thin ductile metal layer bonding two ceramic blocks have indicated rapid
void growth. Analyses for these material configurations are discussed here. When the void radius is
very small, a nonlocal plasticity model is needed to account for observed size-effects, and recent
analyses for the influence of such size-effects on cavitation instabilities are presented.
When a metal contains a distribution of micro voids, and the void spacing compared to void size
is not extremely large, the surrounding voids may affect the occurrence of a cavitation instability at
one of the voids. This has been analyzed for a material containing a periodic distribution of
spherical voids with two different void sizes, where the stress fields around larger voids may
accelerate the growth of smaller voids. Another approach has been an analysis of a unit cell model
in which a central cavity is discretely represented, while the surrounding voids are represented by a
porous ductile material model in terms of a field quantity that specifies the variation of the void
volume fraction in the surrounding metal.
Abstract: The formability of a Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass has been investigated in the present study
in relation to the heating rate. A series of extrusion tests after rapid heating has been performed in a
laboratory scale together with sheet forming tests after slow heating for comparison purpose. The basic
processing map based on dynamic materials model (DMM) and compression test data has been utilized to
evaluate feasible forming conditions. The macroscopic formability, classified by fully formed, partially
formed or a catastrophic fracture, is found to have a good correspondence with the iso-efficiency contour in
the processing map. The region of high power dissipation efficiencies with η>0.8 is found to be broaden by
avoiding crystallization events due to reduced exposure time in extrusion process with a faster heating rate.
Abstract: The dynamic buckling caused by propagation of a stress wave in single-wall carbon
nanotube subjected to impact torque is investigated. The single-wall carbon nanotube is modeled by a
cylindrical shell with semi-infinite length, and the dynamic buckling under impact torque is reduced
to a bifurcation problem caused by the propagation of torsion stress wave. The bifurcation problem
can be converted to solving a group of nonlinear algebraic equations. The numerical computation is
carried out, and the effects of the different parameters on dynamic buckling are discussed. It is found
that if critical buckling time of the carbon nanotube is different, the corresponding buckling model is
different, too. Relation between the critical buckling stress and the critical buckling time is given.
Molecular-dynamic simulations of torsional deformation of a single-wall carbon nanotube have been
used to obtain the critical buckling strain, which is 0.064. In this work, the critical buckling strain
obtained by the continuum model is 0.061, which is very close to the value 0.064. Single-wall carbon
nanotubes have very much powerful anti-impact torque, and the critical buckling shearing stress can
reach up to 132GPa.