Theoretical Study Of Elastic And Magnetoelastic Bending Character Of Nanofilms

Nanofilm materials are of great importance in modern nanoscience and nanotechnology. With the development of material science and manufacture technology, the nanofilm materials are widely used in nano-electromechanical system (NEMS) devices. However, the properties of nanofilms are differ from micron film counterparts. Their elastic, magnetoelastic and bending properties are all affected by surface effect. While theoretical discussion of the elasticity, magnetoelasticity and bending characters and the surface effects on these characters are lagging all along. And some basic problems such as Young’s modulus, Poisson’s ratio and magnetostrictive coefficient are still controversial. The nanofilms usually carry lowered symmetry correspond to bulk counterpart because of the small thickness. But there are few researches in this important character. Therefor, this article is concentrating on elasticity, magnetoelasticity, and bending of nano-bilayer system induced by epitaxy, bending of single nano-film induced by surface stress, magnatostrictive bending of nano-bilayer cantilever, and general unified bending theory for all devices driven by isotropic and anisotropic stimuli. Based on these theory, the further discussions on the stress and strain within the system, as well as neutral plane of the bending system in NEMS are presented.Firstly, nanofilms carry on lowered symmetry correspond to bulk counterpart induced by surface relaxation. The elastic and magnetoelastic properties along film thickness direction are different from those along inplane directions. One needs introduce new elastic and magnetoelastic constants to interpret the properties of nanofilms. The symmetry lowing and the corresponding additional new constants are of great importance in theoretical description of mechanical properties of nanofilms. The cubic symmetry is lowered to the tetragonal one in ultrathin nanofilms. For isotropic materials, the bulk materials are spherically symmetric while nanofilms are cylindrically symmetric.Based on the nanofilm energy density under cylindrical symmetry and the principle of minimal free energy, the equation of Hooke’s law for nanofilms was rewrote, the stress-strain relation in nanofilms was obtained, Young’s modulus, Poisson’s ratio, biaxial modulus and their anisotropic property due to the lowered symmetry for cubic crystal nanofilms were researched. The translational symmetry and rotational symmetry in film thickness direction of the cubic crystal can not be kept in nanofilms, this induced the spherical symmetry lower to the cylindrical one in nanofilms, and there appear a new elastic coefficient and there is no bulk counterpart. These characters of nanofilms induced the anisotropy of Young’s modulus and Poisson’s ratio.Secondly, the proposed theory is applied to the bending of a single free standing nanofilm induced by surface stress i.e. the modified Stoney formula. And the bending of a bilayer nanofilm system induced by epitaxy i.e. modified Timoshenko formula. In the bending problem of single nanofilm induced by surface stress, this work modified Stoney formula furthermore by considering the thickness of surface slice. When the surface slice thickness approaches zero, this theory will coincident with result of Core-surface theory. And the bending of single nanofilm by anisotropic surface stress is discussed in this article. For the bilayer nanofilms, curled-up Si-Si and InAs-GaAs tube were discussed, and corresponding numerical results were compared with experiments, and achieved a much better agreement with the experimental results was. This suggests that the nanofilms bending theory present in this article is reasonable.Thirdly, the thickness dependent magnetostrictive coefficient is derived under the cylindrical symmetry. Based on the four-parameter theory, the magnetostrictive bending of magnetic film-nonmagnetic substrate nanocantilever is dicussed. In the cylindrical symmetry magnetostritive theory, the manetostrictive strains of Fe nanofilm are discussed and the numerical result is compared with experiment. The result is gives nice agreement with experiment. The theory resolved the minimum of the Fe nanofilm thickness dependent magnetostriction. The numerical results suggest that the new magnetostrictive theory in this paper is reasonable. Due to the Core-surface theory is accepted by people, this thesis investigated the nanometer cantilever four-parameter bending theory under the Core-surface model.Finally, based on the four-parameter model, the bending problem of micron and nano-bilayer cantilever under anisotropic strains is studied. The results contain Timoshenko formula and the four parameter model of magnetostrictive bending theory. The anisotropic neutral planes were discussed in this thesis,12 neutral planes with different direction and different style were found. These neutral planes are researched, classified and compared with each other.