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Chapter 1
INTRODUCTION
1.1 STRENGTH OF NANO-COMPONENTS
With recent developments in and miniaturization of electronic
devices because of the increasing demand for high-density
integration, the size of elements has been approaching a few
nanometers. In an extreme, the atom-by-atom structure of atomic-
scale elements, e.g., carbon nanotubes, comes in sight for future
applications. Industry has intensely developed devices on the
micrometer or nanometer scale that have multifarious functions—
namely the micro-electro-mechanical system (MEMS) and nano-
electro-mechanical system (NEMS), including small sensors and
actuators. The stress applied to a nano-component stems from
various sources, such as mechanical loading (e.g., polishing), residual
stress, and thermal elongation mismatch in processing as well as
service. Hence, to ensure reliability, nano-components should be
carefully designed on the basis of mechanical conditions. Because
they are composed of various materials with different nano-size
geometries, the stress concentration originating from their shapes
plays a critical role in the fracture mechanisms of nano-components.
Moreover, to realize high-density integration of the components in
devices, small materials with different mechanical properties (e.g.,
elastic modulus) are adhered each other without an interlayer or
with an ultrathin one. Since the mismatch of deformation often
Fracture Nanomechanics
Edited by Takayuki Kitamura, Hiroyuki Hirakata, Takashi Sumigawa and Takahiro Shimada
Copyright © 2011 by Pan Stanford Publishing Pte. Ltd.
www.panstanford.com
2 Introduction
brings about inner stress, its interface is the most critical site in
terms of a fracture.
In a complex process from a viewpoint of mechanics, such
as the nano-imprint technique, where a thin film is removed
along the interface (intentional delamination) after it is formed
on a substrate, the interface strength is of central importance,
and constitutive understanding of the fracture phenomenon is
inevitable for its precise process management. The key issue in
the technology is to spontaneously control the interface strength;
adhesion and exfoliation. This clearly points out that we need
fundamental knowledge of “fracture” not only for prevention of
device malfunction but also for fabrication in the future technology
of nano-components, namely from fracture prevention to fracture
design. For this purpose, it is essential to understand both the
mechanism and mechanics of material strength, such as deformation
and failure characteristics of nanometer-scale materials.
1.2 FRACTURE NANO-MECHANICS IN STRUCTURE
We cannot understand the strength of nano-components without
considering the geometric factor, because the structure brings
about various functions on a material. Structure can be classified
into two categories, external (or global geometry) and internal (or
understructure). The former indicates the shape of a component,
e.g., films, bars, dots, while the latter does the organization or the
pattern in the material, e.g., crystallographic grains, dislocation
patterns. It is well known that both structure and size strongly
affect fracture behavior.
Before a detailed discussion, we would like to identify our
standpoint concerning fracture mechanics on the nanometer scale
in terms of material structure. There are mainly two types of issues
that we have to consider:
1. Multi-scale investigation focusing on the hierarchical effects of
structure:
The target is a material with the external structure of
micrometer to meter size (macromaterial) and the internal
one of nanometer size (e.g., nanocrystal). Of course, interaction
Fracture Nano-mechanics in Structure 3
among different scales of structure (e.g., dislocations/grain
boundaries) plays key role in the fracture process.
2. Nano-scale investigation, where the component size itself is in
nanometer scale:
The external structure on the nanometer scale is targeted; e.g.,
nano-components, such as nano-films, nano-bars, and nano-
dots. The internal structures are atomic arrangement and
electronic structure in this case. The research aims to elucidate
the fracture behavior considering the atomic scale implicitly.
In the context of deformation and fracture on the nanometer
scale, these two standpoints share common fundamentals in the
mechanics, but remarkably differ in the following points. While
the volume decreases in the third power of the reference length
with the shrinkage of small components, the surface/interface
area does so in the second power. Thus, surface and interface
often have critical influence on fracture in nano-components.
Moreover, the size difference between “external” and “internal”
structure is a crucial factor, although both multi-scale and nano-
scale investigations aim to elucidate the fracture process and
mechanics under the interaction between phenomena on each
scale level. In nano-scale investigation, the scale of stress (or strain)
concentration region stemming from the external structure is close
to the one of the internal structure (e.g., atomic arrangement). In
other words, the internal structure directly affects the fracture
mechanism of the whole component. Since this must bring about
strong impact on the fracture criterion, one fundamental question
that comes up is the applicability of a conventional concept based
on the continuum mechanics because of the discrete structure of
atomic arrangement.
We can distinctly recognize the philosophical difference in the
fracture research between issues 1 and 2 above. The authors, then,
would like to emphasize that this book dedicates to the second
issue: fracture of nano-components. The discussion on the multi-
scale concept (i.e., the first issue) is out of scope because there are
already excellent books available on the subject.
This book focuses on the mechanical effect of surface and
interface on the characteristics of deformation and fracture.
