Size dependent fracture and plasticity in nanorods [electronic resource]
Keywords: Materials Science and Engineering.

As the technology of micro-scale devices evolves to smaller dimensions, the size dependence of fracture and plasticity at small scales attracts more and more attention. This is driven by the knowledge that many mechanical properties at the sub-micron scale differ from those at the macroscopic scale. For the reliable design of MEMS or NEMS devices, obtaining an understanding of the size-dependent mechanical properties of materials is necessary at small length scales. In the first part of the dissertation, we explore size-dependent fracture of Si nano-pillar (NP) lithium ion battery anodes. Silicon (Si) nanostructures are attractive candidates for Li-ion battery electrodes because they provide both large specific charging capacity and less constraint on the volume changes that occur during Li insertion and extraction. Initially, lithiation induced swelling was modeled by considering the diffusion of lithium atoms through the Si host. However, recent experiments have shown that crystalline Si anodes expand highly anisotropically through the motion of a sharp phase boundary between the crystalline Si core and the lithiated amorphous Si shell. This phenomenon cannot be explained by a lithiation mechanism governed purely by diffusion. Here, we present a phenomenological model for the anisotropic phase boundary motion, which can be understood by the fact that lithiation in crystalline Si is controlled by the reaction kinetics occurring in the narrow regime near the phase boundary between the lithiated Si alloy and crystalline Si. In addition, we develop a microscopic model to describe the size-dependent fracture of crystalline Si NPs during lithiation. We derive a traction-separation law based on the plastic growth of voids, and this law is, in turn, used in a cohesive zone finite element model to describe fracture. The model allows for both the initiation of cracking and crack growth. The initial size and spacing of the nanovoids, assumed to be responsible for the fracture are chosen to conform to recent experiments which have shown the critical diameter of Si NPs to be ~300-400nm. The anisotropy of the expansion is taken into account, and this leads naturally to the observed anisotropy of fracture. It may be possible to use our computed fracture toughness to describe the failure of lithiated Si for other loading conditions and geometries, such as the failure of other Si nanostructures during Li-ion battery cycling. In another part of the dissertation, size dependent plasticity in BCC metals is explored using dislocation dynamics (DD) simulations. We formulate a three-dimensional, DD model of dislocation plasticity in BCC micro-pillars and use it to study size effects and the effects of initial dislocation density and strain rate on strength. The model is based on the molecular dynamics (MD) simulations of Weinberger and Cai who discovered a surface-controlled cross-slip process leading to dislocation multiplication without the presence of artificial pinning points. We find a "smaller is stronger" size effect that can be explained by the competition between the multiplication rate and depletion rate from the surface of the mobile dislocations. Although DD simulations still require higher strain rates than those found in experiments, our DD simulations predict flow stress dependences on pillar size, initial dislocation density and strain rate that are largely consistent with experiments. An analytical model is constructed to rationalize the behavior of the DD model at high strain rates. In summary, we have researched the size-dependence of fracture of Si anodes in a Li-ion battery at the sub-micron scale. In addition, micro-pillar plasticity has been analyzed using dislocation dynamics simulation to understand how dislocation behavior relates to mechanical response in BCC metals. We believe that our mechanical modeling has contributed to the enhancement of our fundamental understanding of the size-dependence of fracture and plasticity at the sub-micron scale.