National Science Review
2: 133–136, 2015
PERSPECTIVES
MATERIALS SCIENCE
Atomistic modelling of deformation and failure mechanisms in
nanostructured materials
Xiaoyan Li1,∗ and Huajian Gao2,∗
Over the past two decades, there has been
a whirlwind of worldwide research activities on nanostructured materials, with
the long-term promise to tailor-design
material properties from the nanoscale
and up. In this grand effort, computation is playing an increasingly important
role in complementing experiments to
unravel fundamental principles that underlie mechanical behaviours and properties (e.g. deformation and failure) of materials with a characteristic length scale
below 100 nm. For such materials, atomistic modelling is an especially suitable
tool, in combination with other mesoscopic and continuum approaches, for
identifying the dominant deformation
and failure mechanisms. A comprehensive review on the atomistic modelling
and relevant multiscale approaches to
material research can be found in the literature [1]. Figure 1 shows a schematic
illustration of two typical atomistic modelling strategies, the so-called ab initio
molecular dynamics (AIMD) and classical molecular dynamics (CMD) simulations. AIMD provides by far the most
accurate description of atomic interactions by considering the electronic structure of materials, and is therefore capable of reliably predicting the energetic,
electronic, transport, as well as mechanical properties of nanostructured materials. Unfortunately, at this point of time,
AIMD is still an expensive computational
tool limited to relatively small systems
spanning hundreds of atoms and tens
of picoseconds. In comparison, CMD
simulations can deal with systems containing tens of millions of atoms sub-
ject to nearly instantaneous (up to a few
nanoseconds) loading and deformation.
In CMD simulations, an empirical potential is typically used to describe interatomic forces that generally include both
bonded forces associated with the chemical bonding and non-bonded forces such
as the van der Waals and electrostatic
forces. In principle, the empirical potential should reflect not only the pairwise but also many-body effects through
ad hoc functional approximations obtained from fitting against detailed quantum simulations or experimental measurements of material properties. For example, the recently developed reactive
force field is an emerging potential that
can model reactive bond order during
the formation and breakage of chemical bonds. Due to their atomic-scale
resolution and increasingly accurate de-
Tim
~10-12 s
Length
~1 nm
~10-11 s
scription of atomic/molecular interactions, CMD simulations have become the
most broadly used computational strategy to investigate mechanical behaviours
of nanostructured materials during the
last decade, and are now routinely used
to detect nanoscale processes and structures which are often inaccessible to experiments due to limitations in instruments or visualization techniques. Due to
the limited space, here we present a few
representative examples, as a thin slice of
recent progresses in computational material science, on application of molecular
dynamics (MD) simulations (primarily
CMD) to study the deformation and failure of nanostructured materials (including nanocrystalline/nanotwinned metals,
nanotubes, and graphene).
MD simulations have achieved
much success in investigating plastic
~10-10 s
~10-9 s
~10 nm
Nanotube
~100 nm
Nanocrystalline/Nanotwinned metals
Fullerene
Charge
Nanoparticle
Ab-initio molecular
dynamics
(Quantum mechanics)
Graphene
Classical molecular dynamics
(Reactive force field, empirical interatomic potentials )
Figure 1. A schematic illustration of atomistic modelling strategies. Representative length and time
scales for AIMD and CMD simulations are indicated along the axes. Some typical nanostructured
materials (such as fullerene, nanoparticle, nanotube, graphene, and nanocrystalline/nanotwinned
metals) are showed as illustrative examples for different characteristic length and time scales accessible in atomistic modelling.
C The Author(s) 2014. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. All rights reserved. For Permissions, please email:
[email protected]
~10-8 s
134
PERSPECTIVES
Natl Sci Rev, 2015, Vol. 2, No. 2
deformation mechanisms in nanocrystalline metals. Full atomistic simulations
on three-dimensional (3D) systems
with size up to 100 million atoms [2]
revealed that, as the mean grain size
decreases, there exists a transition from
dislocation- to grain boundary (GB)mediated deformation mechanisms
below a critical grain size, giving rise to a
softening mechanism called the inverse
Hall–Petch effect which is opposite to
the traditional Hall–Petch law that the
flow strength of material be proportional
to the inverse square root of grain size.
Quasi-3D MD simulations [3] predicted
the occurrence of deformation twinning
through continuous dislocation slip in
nanocrystalline Al, a phenomenon subsequently observed in experiments via
transmission electronic microscopy. Further simulations on different fcc metals
[4] demonstrated that the deformation
mechanisms (partial/full dislocation slip
and twinning) strongly depend on the
generalized stacking fault energy. These
results from MD simulations outlined a
comprehensive deformation mechanism
map for nanocrystalline metals.
Over the last decade, nanotwinned
metals have emerged as a new class of
hierarchically structured materials with
high density of nanoscale twins embedded in micron- or submicron-sized
grains. Due to the presence of twin
boundaries (TBs) with high symmetry and low energy, nanotwinned materials exhibit an exceptional combination of ultra-high strength, good tensile
ductility, and superior resistance to fracture, fatigue, and wear. MD simulations
[5] coupled with nudged elastic band
method revealed the atomic-scale reactions responsible for dislocation slip
transfer through a TB, and suggested
these reactions as the rate-controlling
mechanisms contributing to the hardening and ductility of nanotwinned metals. Ultra-large-scale MD simulations [6]
on fully 3D systems led to the discovery that, as the twin thickness is reduced, there exists a deformation mechanism transition from dislocation cutting
through TBs to detwinning due to the
nucleation and motion of partial dislocations along the twin planes. This find-
ing corroborates and explains experimentally measured relation between strength
and twin thickness, which exhibits a
transition from Hall–Petch strengthening to softening at a critical twin size.
Combined with experimental results, the
simulations further led to a scaling law
between the strength of nanotwinned
metals and two characteristic dimensions of the material, the mean grain
size and twin thickness. MD simulations
also played a critical role in revealing
two distinct deformation mechanisms—
shear localization and detwinning—in
nanotwinned nanopillars with orthogonal and slanted TBs, and a twin size
controlled ductile–brittle transition [7].
These simulations were performed side
by side with experiments to reveal the
dominant atomic-scale processes that are
responsible for deformation and fracture
in nanotwinned materials and structures.
There have also been successful
examples in using MD simulations to
explore deformation and failure mechanisms in low-dimensional materials
such as carbon nanotubes (CNTs)
and graphene. MD simulations of multiwalled CNTs under pure bending
[8] produced atomic-level rippling
structures in excellent agreement with
experimental observations, and revealed
a twisting deformation mode of inner
tubes induced by the interlayer lattice
mismatch associated with curvature. It
was recently discovered through MD
simulations of bicrystalline graphene under uniaxial tension [9] that the strength
of polycrystalline graphene strongly
depends on the detailed arrangement of
pentagon–heptagon defects (equivalent
to dislocations) along GBs. This was later
verified by experiments on nanoindentation of polycrystalline graphene via
atomic force microscopy. MD simulations [10,11] were also used to study
the fracture behaviours of polycrystalline
graphene, with predicted crack propagation paths [10] and fracture toughness
[11] in good agreement with those
observed/measured
experimentally.
The relationship between mechanical
strength of graphene and various defects
(dislocations, pre-cracks, and GBs)
should play important roles in guiding
practical applications of graphene in
advanced nanodevices.
In spite of considerable progresses/advances made in using MD
simulations to model deformation and
failure mechanisms in nanostructured
materials, there is still a big gap in
quantitative comparisons between
MD simulations and experiments. So
far MD simulations are only capable
of providing qualitative insights in
deformation mechanisms, rather than
quantitative predictions of experimental
measurements, in most studies. The
primary reason for this gap is that MD
simulations have the inherent limitations
in spatial and temporal scales, with
loading rates typically several orders of
magnitude higher than those accessible
in experiments. It is noted that, although
many mechanical properties of materials
are sensitive to the loading rate, the
high loading rates in MD often do not
qualitatively alter the physical nature of
deformation. To overcome the intrinsic
limitations of MD, one potential solution
is to establish multiscale modelling by
coupling MD with mesoscopic or continuum methods. Another is to rely on the
constantly improving capacity and performance of supercomputers (with Peta
FLOPS and even faster speed at present)
and the developments of more accurate
and efficient algorithms. In addition, the
development of interatomic potential
for diverse types of complex materials
(material genome), especially alloys and
complex materials, remains an important
direction of research in the near future.
These developments will inevitably make
atomistic modelling more realistic, predictive and useful in materials research,
reduce/bridge the gap between MD
simulations and experiments, and move
us towards the long-term objective of
‘material by design’ via computation.
Xiaoyan Li1,∗ and Huajian Gao2,∗
1 Department of Engineering Mechanics, Tsinghua
University, China
2 School of Engineering, Brown University, USA
∗ Corresponding authors.
E-mail: [email protected];
huajian [email protected]
PERSPECTIVES
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doi: 10.1093/nsr/nwu049
Advance access publication 19 August 2014
COMPUTER SCIENCE
The impact of AI: can a robot get into the University of Tokyo?
Noriko H. Arai
The ‘Todai Robot Project (Can a robot
get into the University of Tokyo?)’
was initiated by the National Institute
of Informatics (NII), the Japan’s only
general academic research institution
of informatics, in 2011 as an AI grand
challenge. The goal of the project is
to create an AI system that answers
real questions on university entrance
examinations. This paper reports the
current status of the project including
the underlying technologies we have
developed thus far, and the results we
obtained from evaluations.
There have been various types of AI
challenges in the past: the chess and
shogi matches against professional players, the quiz show challenge against human champions. Todai Robot Project
is unique mainly in the following two
senses. First, it targets the integrated intelligent tasks rather than single ones. Examinees must take tests of eight subjects,
two social studies, two sciences, Japanese
(including Japanese and Chinese classics), English, and two mathematics. The
tasks require not only the development
of ground-breaking underlying technologies in various AI research areas but also
their interdisciplinary research synthesis.
Second, it enables us to compare the
performance of the software and numerous well-educated students. University
entrance examinations in Eastern Asian
countries, including Japan, are known to
be quite competitive and they cover various skill areas and fields. More than half
a million high school graduates take National Center Test for University Admissions (NCTUA), standardized multiple
choice style tests, every year in Japan, and
less than top 3% students are allowed to
take the second written test specially designed to select entrants of the University
of Tokyo.
Our research team developed a
testbed [1,2] that utilized the resources
taken from the history problems asked
in NCTUA, and organized international
evaluation tasks at NTCIR-9, 10 and
11. The participants pursued mainly two
approaches to solving history questions.
One is traditional statistical factoid
approach. Kanayama and Miyao [3]
manually converted original true/false
world history questions to a set of
factoid-style questions and achieved
an accuracy of 65% on the NCTUA
data by employing Watson’s factoid QA
engine as the backend system. Kano [4]
developed domain-independent and
language-independent keyword-based
system, and achieved an accuracy of 51%
on the same data. The other approach
is to combine a logical inference engine
based on their semantic representation
with a statistical classifier. Considering
that the accuracy rate of Watson at Jeopardy! Challenge was 69%, it was most
likely some deeper language analysis
Figure 1. Overview of math solver.