(Dr. Iwona Jasiuk, advisor)
"Composites at Micro- and Nano-Scale and a New Approach to the Problem of a Concentrated Force on a Half-Plane"
The embedding of inclusions in a host matrix to make composites and obtain material properties not achieved by either phase alone has been a common practice for many years. Recently, experimental techniques have been developed to allow the scale of inclusions to go down to nano-size. The nano-scale borders on the limits of continuum mechanics theory, and, as a result, current micromechanics theories may not accurately predict the effects of the nano-sized inclusions.
This research addresses the issues involved in characterizing, testing, and modeling of nanocomposites by comparing the size effects of micro- and nano-sized inclusions. Micro- and nano-sized inclusions were added to the matrix and the resulting composites were tested and characterized. The experimental data was be used to determine how well current micromechanics theories predict the effects of nano-scale inclusions.
Nanoindentation has become an essential testing mechanism in attempting to further understand the effects of nano-sized inclusions. Analytically, an indentation can be viewed as a concentrated force on a half-space. This problem can be examined using a new micromechanics-based approach that allows one to solve boundary value problems for ductile materials that obey a power-law creep behavior. The technique omits the constitutive equation describing dilitancy and uses energy optimization to arrive at the solution. By using the technique, the problem at hand can be examined in terms of non-linearity as opposed to being limited to the linear case. This ability provides much greater understanding of what happens with a force on a half-plane beyond the linear range and what are the failure mechanisms at the application of force.