Publications Details

Development of Advanced Continuum Models that Incorporate Nanomechanical Deformation into Engineering Analysis

Zimmerman, Jonathan A.; Jones, Reese E.; Templeton, Jeremy A.

Materials with characteristic structures at nanoscale sizes exhibit significantly different mechanical responses from those predicted by conventional, macroscopic continuum theory. For example, nanocrystalline metals display an inverse Hall-Petch effect whereby the strength of the material decreases with decreasing grain size. The origin of this effect is believed to be a change in deformation mechanisms from dislocation motion across grains and pileup at grain boundaries at microscopic grain sizes to rotation of grains and deformation within grain boundary interface regions for nanostructured materials. These rotational defects are represented by the mathematical concept of disclinations. The ability to capture these effects within continuum theory, thereby connecting nanoscale materials phenomena and macroscale behavior, has eluded the research community. The goal of our project was to develop a consistent theory to model both the evolution of disclinations and their kinetics. Additionally, we sought to develop approaches to extract continuum mechanical information from nanoscale structure to verify any developed continuum theory that includes dislocation and disclination behavior. These approaches yield engineering-scale ex-pressions to quantify elastic and inelastic deformation in all varieties of materials, even those that possess highly directional bonding within their molecular structures such as liquid crystals, covalent ceramics, polymers and biological materials. This level of accuracy is critical for engineering design and thermo-mechanical analysis is performed in micro- and nano systems. The research proposed here innovates on how these nanoscale deformation mechanisms should be incorporated into a continuum mechanical formulation, and provides the foundation upon which to develop a means for predicting the performance of advanced engineering materials.