In this chapter, conclusions of the dissertation are presented. Molecular statics, molecular dynamics and density functional theory simulations were employed to predict mechanical response of materials. We studied mechanical response and elastic instability of cubic bulk materials and nanoscale materials including nanoplates, nanowires, and nanotubes. In addition, we introduced a simple and efficient method for the calculation of surface stress at finite strain.
For concluding, the striking questions addressed in Chapter 1 are revisited by compendiously summarizing the presented results and discussions from Chapter 3 to Chapter 6:
1. (i)What are the mechanical responses and elastic instability of cubic bulk materials under external loading, especially uniaxial stress and multiaxial stress? (ii) How does ideal strength of bulk materials change under different modes of loading? (Chapter 3).
i. Under mechanical loading, the cubic bulk materials begin at equilibrium states, deform elastically and finally lose their stability. In the case of uniaxial tensile stress along [100]-direction for the FCC metals and Si, there is the branching (bifurcation) of crystal structures at onset of the instability. In particular, there are a large contraction along a lateral direction and a large expansion along the other lateral direction (tetragonal to orthorhombic phase transformation). In the case of uniaxial compressive stress condition along [100]-direction, the FCC metals and Si fail without a large deformation. For Fe BCC, bifurcation phenomenon happens in the case of the tension while in the case of the compression, it loses elastic stability without large deformation. The phase transformation is still observed in the case of bulk materials under multiaxial stress condition with symmetry of transverse stress.
However, under the multiaxial stress condition with asymmetry of transverse stress, the large deformation (the phase transformation) is replaced by a smooth changes of crystal structures along the lateral directions. Consequently, we can observe negative Poisson’s ratio in cubic bulk materials even along principal directions.
ii. Under multiaxial stress condition, the ideal strengths of the FCC materials are largely dependent on the transverses stresses. In the case of symmetric transverse
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stresses, the ideal tensile strength linearly increases as the applied transverse stress increases. However, in the case of asymmetric transverse stress, the ideal tensile strength decreases significantly with increase of the degree of asymmetry, even when both transverse stresses are tensile.
2. Is it possible to obtain surface stress of material under finite strain, and if so how does it change with strain? (Chapter 4).
Yes, it is. As the first time, we provide a simple and efficient method to calculate surface stresses of materials at finite strain. Under a loading condition, surface stresses show strong correlation with mechanical strain.
3. (i) What is mechanical response of nanoplates under mechanical loading? (ii) What is the role of elastic instability and surface effect? (Chapter 5)
i. Under uniaxial stress along [100]-direction, the metallic nanoplates exhibit counterintuitive behavior, i.e., negative Poisson’s ratio at finite strain.
ii. The behavior originates from the branching phenomenon of bulk counterpart, and from the unique surface effect that induces a compressive stress inside nanoplates.
While surface stress induces a compressive stress along the in-plane lateral direction inside nanoplate, there is stress free along the thickness direction. Thus, the induced stresses along lateral directions inside nanoplates are asymmetric. As a result, the sudden branching in the bulk materials is altered by gradual branching in the nanoplates and thus negative Poisson’s ratio in observed. Poisson’s ratio behavior of nanoplates is strongly dependent on the characteristics of the branching of bulk counterparts as well as on the amount of the induced compressive stress. Thickness of nanoplate, magnitude of surface stress and temperature are the key parameters that influence on the Poisson’s ratios.
4. (i) Can elastic stability theory be used to analyze instability behavior of nanowire?
(ii)When/how/where does a metallic nanowire fail? (iii) How do cross-sectional shapes of nanowire/nanotube effect on their mechanical properties? (Chapter 6).
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i. Yes, it can. The stability theory, which is conventionally used to investigate the elastic instability behavior in bulk material, can also be used to analyze the instability of nanowires with some modification.
ii. FCC metal nanowires under loading (tension or compression) along [100]-direction can fail with homogeneous deformation (global deformation), which has no relation to dislocation. At the global deformation mode, nanowires fails with a large contraction along a lateral direction and a large expansion along the other lateral direction. This observation is totally different from the belief during last two decades that nanowires only failed locally as the result of nucleation and propagation of dislocations. The global failure mode is driven by elastic instability.
Furthermore, we found that there is a competition between the global and local deformations, and thermal activation (i.e., temperature) is a critical measure that decides the global or local deformation as the failure mode of nanowires. At low temperatures, metal nanowires fail with a global deformation by the elastic instability theory whereas they fail with a local deformation by the nucleation of dislocations at high temperatures.
iii. Cross-sectional shape of [100] nanowires strongly influences on their material properties. The Poisson’s ratio of symmetric cross-sectional area nanowires such as circular, square is slightly different from that of the bulk counterpart and it is positive. However, with asymmetric cross-section such as rectangle or ellipse, the Poisson’s ratio changes significantly with asymmetry of the cross-section area. We can obtain a negative Poisson’s ratio in proper designed nanowires. Similar to the case of nanoplate, negative Poisson’s ratio in the nanowires is the result of the phase transformation and surface effect. Metal nanotubes can exhibit more auxetic than nanowires because the surface effect in metal nanotubes is larger.
The theory of elastic stability has been developed for nearly eight decades. Many mechanical responses of bulk materials were revealed. Also, the stability theory has served as a powerful tool to estimate strength of materials. This dissertation contributes more examples
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in the study of elastic stability of bulk materials; and more importantly as the first time, we deal with elastic stability problem for nanoscale materials. In order to improve the auxeticity in nanoplates (Chapter 5), nanobelts and nanotubes (Chapter 6), enhancing surface stress of nanoscale materials is a relevant method. Therefore, surface modification to increase surface stress can be a valuable research. Furthermore, based on our study, mechanical response and elastic instability behavior of 0-dimentional nanomaterial (nanoparticle) can be investigated.
Even though there are still many remaining problems in the study of mechanics of nanoscale materials, nanomechanics depicts and provides more and more relevant underlying mechanical properties of nanoscale materials. Along with advances in synthesis and fabrication technology, nanomechanics supports the nanotechnology applications and thus it brings nanoscience achievements to various fields of human life.
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