Aifantis

Summary

The progressively increasing demands of new science and technology to understand the behavior of materials/components and processes at the micrometer and nanometer regimes has led in the mid seventies to the development of micromechanics. In the mid nineties a new term nanomechanics was used by the author to indicate the forthcoming excessive activity in this field and point out to the need for new constitutive equations and mechanics tools to be developed in relation to the emerging fields of nanotechnology. In fact, it was only a few years earlier, that the first carbon nanotubes were produced in Japan - a unique example for the use of elasticity theory at the nanoscale - and the first bulk nanopolycrystals were produced in Russia. At the same time the first experimental observations on deformation and fracture mechanisms of nanopoly-crystalline thin films were reported by the author and his co-workers in US. It was reported, among other things, that plastic deformation at the nanoscale does not take place through lattice dislocation activity but through grain boundary processes including material rotation and mass diffusion. Moreover, fracture processes occur through nanovoid nucleation and coalescence. Some of these experimental observations were numerically verified a few years later through molecular dynamics (MD) multimillion atom simulations.

A first attempt to develop constitutive equations for describing deformation and fracture at the nanoscale is outlined by the author and co-workers with two specific concepts being advanced: the use of a mixture argument for “bulk” and “grain boundary” states and the resort to non-locality for describing the state of stress and strain at the nanoscale. In very recent years, due to the most promising developments in nanosciences/nanotechnologies in conjunction with the rapidly evolved computational advances, coupled ab initio/atomistic/molecular dynamics/finite element calculations have been employed to simulate the mechanical response of matter at the nanoscale in thin film and bulk configurations within the so-called multiscale modeling approach. A variety of nano-objects, including multilayered films, nanocomposites, proteins, as well as other metal or non-metal and biological nanostructures are modeled within such multiscale modeling framework and new nano-testing procedures and nano-apparatuses have been developed to capture this response experimentally. HRTEM, STM, AFM, micro/nano tensile machines and micro/nano indenters are among some of the new experimental tools for probing the mechanical response of materials and structures at the micro/nano scale and designing MEMS/NEMS devices for a variety of electromechanical and biomedical applications.

In an effort to have a general micro/nano mechanics framework as useful as the continuum mechanics model that has been employed so successfully for the understanding of the mechanical behavior at the macroscale and the design of macroscopic components and structures, a proposal will be presented by a straightforward extension/generalization of the macroscopic continuum model. This generalization is based on the concept of a micro/nano continuum which is capable of exchanging mass, momentum and energy with its bounding surface. While such a model has been suggested by the author more than twenty five years ago, it was not until recently that its implications to elasticity, plasticity, and other continuum theories of structural defects was fully explored. The two new basic ingredients of the model are: a) the appearance of deterministic higher order spatial and time derivatives in the governing equations of mechanical fields; and b) the appearance of stochastic terms due to random effects associated with the nucleation and evolution of deformation events at the micron/nano scale regime.

Several benchmark problems are considered to illustrate the applicability of the proposed framework, as follows: (i) Elimination of Singularities. Gradient elasticity models are shown to eliminate the strain and stress singularities form dislocation/disclination lines and crack tips. On the basis of these solutions new relations can be obtained for the strength, energy and interaction of defects in nanocrystals and new fracture criteria can be derived at the nanoscale. (ii) Internal Stress, Elastic Constants and Yield Strength: Size Effects. Gradient elasticity and gradient plasticity are shown to produce new formulas for the determination of internal stress and elastic moduli in micro/nano multilayers and micro/nano plates under bending. A modification of the well-known Stoney formula is an example. Also the dependence of the elastic modulus on the nanoplate thickness is another interesting example. In this connection, it is pointed out that the size dependence of yield strength of micro/nano columns and the dependence of Young’s modulus/failure stress on nanotube diameter has also been documented. (iii) Micro/Nano Indentation. Various basic formulas that have been used for determining material properties at the macroscale during indentation are revisited by employing gradient elasticity/plasticity with or without stochastic terms. Displacement bursts, load-depth serrations, and size-dependent hardness are all phenomena that are often observed during micro/nano indentation and their proper interpretation can assist in the determination of deformation and fracture properties at these scales. (iv) Localization of Deformation and Multiple Shear Banding. The interesting features of deformation and fracture at the micro/nano scale are concerned with the determination of the critical grain sizes where a plasticity transition mechanism takes place. At the nanoscale (1-100 nm) the critical grain size determines the transition from grain rotation/sliding to massive dislocation motion, which often manifests itself by the appearance of an inverse Hall-Petch behavior. At the ultra-fine grain size regime (100-1000 nm) another plasticity mechanism that occurs is the so-called multiple shear banding which often manifests itself by the appearance of a perfectly plastic behavior in the corresponding stress-strain curve. These two plasticity mechanism transitions will be discussed within the proposed unified material micro/nano mechanics framework.

In concluding, it will be pointed out why new techniques such as fractals, wavelets and time-series are often necessary for capturing details and additional features of micro/nano deformation and fracture. Information on some of the above topics can be found in references [1]-[3] and articles quoted therein.

References

1. Aifantis, E.C., In Recent Advances in Applied Mechanics (Honorary Volume for Academician A.N. Kounadis), edited by T. Katsikadelis, D.E. Beskos and E.E. Gdoutos, NTUA, Athens, 2000, 243-254.

2. Aifantis, E.C., Mech. Mat., vol. 35, 259-280, 2003.

3. Konstantopoulos, I., Tragoudaras, D., Mokios, G., Konstantinidis, A., Zaiser, M. and Aifantis, E.C., Research in Progress.

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