MECHANICAL RESPONSE AND ELASTIC INSTABILITY OF CUBIC BULK AND NANOSCALE MATERIALS

Abstract

The Born-Hill elastic stability theory has been applied to study mechanical response and elastic instability behavior of many bulk materials under various loading conditions. The scope of this work involves further investigation on cubic bulk materials. More importantly, the elastic stability theory is used to analyze the mechanical response and elastic instability behavior of nanoscale materials such as nanoplate, nanowire, and nanotube. Atomistic simulations including molecular dynamics (MD) simulation, molecular statics (MS) and density functional theory (DFT) are employed to predict mechanical response of materials. In the study of bulk materials, influence of transverse stresses to [100]-direction on the ideal tensile strength of face-centered-cubic materials is considered under the framework of the elastic stability theory. We especially emphasize on the different effects of symmetric and asymmetric loadings. It is found that the ideal tensile strength is largely dependent on the transverse stresses. When the transverse stresses are symmetric, the ideal strengths increase linearly with the transverse stresses. However, when the transverse stresses are asymmetric, the ideal tensile strength reduces considerably even though both of the lateral stresses are tensile. Cubic materials under the asymmetric transverse stresses can exhibit another interesting phenomenon: negative Poisson’s ratio along principal directions. Surface stress is a key parameter to determine the characteristic of nanoscale materials and it reflects the size-dependence of nanoscale materials. A simple and efficient method is presented to calculate surface stress even at finite strain. In the study of nanoplates, we provide numerical and theoretical evidences that negative Poisson’s ratios are found in nanoscale metal (001) plates under finite strains. Under the same conditions of crystal orientation and loading direction, materials with a positive Poisson’s ratio in bulk form can display a negative Poisson’s ratio when the material’s thickness approaches the nanometer scale. We show that this behavior originates from a unique surface effect that induces a finite compressive stress inside the nanoplates, and from a phase transformation induced by elastic instability that causes the Poisson’s ratio to depend strongly on the amount of stretch. In addition, we discuss the effects of the thickness and temperature on the mechanical behavior of the nanoplates. As the thickness decreases, the amount of compressive stress increases. As a result, the metal nanoplates become more auxetic. Higher temperatures cause the phase transformation to occur sooner. Thus, strongly auxetic nanoplates can be obtained by raising the temperature. Poisson’s ratios of nanoplates with different metals exhibit largely different from each other, even though Poisson’s ratios of the corresponding bulks are almost the same. In the study of nanowires, we provide numerical and theoretical evidences that a global deformation, which has no relation to dislocations or defects, is a failure mode of metal nanowires. This finding breaks the belief during the last several decades that nanowires only fail with nucleation and propagation of dislocations or defects. Such deformation can be named as local deformation. Furthermore, 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 stability theory whereas they fail with a local deformation by the nucleation of dislocations at high temperatures. In addition, we address a discussion on this competition between the global and local deformations in terms of the shapes of cross-section of nanowires that are critical to the initiation of dislocations. There always exist the transient temperatures below which the nanowires fail by the global deformation and over which they fail be the local deformation. In addition to the study of failure modes in nanowires, we investigate the effect of the cross-sectional shape on Poisson’s ratio of the nanowires. Furthermore, simple methods are provided to design metal nanowires and nanotubes with a negative Poisson’s ratio.