Electronic Thesis and Dissertation Repository

Thesis Format

Integrated Article


Doctor of Philosophy


Mechanical and Materials Engineering


Klassen, Robert J.


In the area of mechanics of materials, the classic theories cannot describe the material behaviour as the volume of deformation or sample size is small enough to be compared with the size scales of the imperfections of the crystal. So, there has been a great deal of interest in investigating the plasticity of micron and nano-sized materials, in the last 20 years. As a Ph.D. research project, the deformation mechanism at small scales of fcc metals is studied based on dislocations behaviour. The effect of main parameters that haven’t been studied in detail, including, crystal orientation, pre-existing faults, grain boundaries, and free surface is considered. Atomistic simulation is used to investigate the deformation at nanoscales and experimental observation is used to tailor findings at the submicron scale.

The coupling effects of crystallographic orientation and internal structural defects on the load distribution at the onset of plasticity are investigated during Au nanoindentation to clarify the anisotropic characteristics of material responses to crystallographic orientation. In the absence of pre-existing defects, deformation is dominated by nucleation of Shockley partial dislocations regardless of crystal orientation. When the nanoindentation depth is greater than about 2 nm the dislocation density becomes less variable and the indentation hardness and dislocation density reach stable and constant values. The relation between H and √ρ is crystal orientation dependent. Indentation simulations in the presence of sessile dislocation loops in the structure show that the greatest reduction in the pop-in load happens for the [111] oriented sample. Indentation near a defect can lead to small, subcritical events that lead to a smoother pop-in at the onset of plasticity.

The influence of GB on the plasticity is mainly related to the misorientation angle, its intrinsic structure, and GB energy. Our simulation on various symmetric <110> tilt GBs with a wide range of misorientation angles show that high energy GBs affect the dislocation nucleation beneath the indenter and accommodate plasticity by providing the necessary dislocations to make the imposed deformation.

The simulation results of Au nanopillars show that the plasticity always starts with the nucleation of dislocations at the free surface and the crystal orientation affects the subsequent microstructural evolution. The Schmid factor of leading and trailing partials plays a decisive role in leading to the twinning deformation or slip deformation. [100] oriented pillars deform by the glide of the twin boundary planes while [110] and [111] oriented pillars deform by the slip of stacking fault loops and planes. A significant difference is observed in the strength of pillars of the same size with different orientations. The power-law equation exponent is completely dependent on the crystal orientations and a weak or no size effect is observed in the compression of [100] and [110] oriented Au pillars with sizes less than 40 nm. In the absence of free surface, the nucleation of initial dislocations happens in much higher stress and trapping of dislocations in the pillar will result in the smooth increase of stress with strain.

Experimental micro-compression of sub-micron and micron-sized (0.7 – 3 μm) Au spheres at different strain rates showed an increase of yield stress with decreasing the sphere diameter (the yield point increases from 24MPa to 227MPa for 3 µm and 0.7 µm spheres, respectively with a loading rate of 0.005mN/s). The apparent activation volume (V*) remains almost constant, ranging 1.6-2.4b3 with changes of strain up to 20% for the smallest sphere while it ranges 8.6-10.6 b3, 9.4-10.2 b3, and 8.9-10.5 b3 for the 1.5μm, 2.2μm, and 3μm diameter spheres respectively. These results indicate that the operative mechanism in the deformation of considered spheres is correlated with their size. Our obtained data for apparent activation volume (V*) and energy (Q*) suggest that the dislocation-obstacle limited glide mechanism is dominant or plays the main role in the deformation of larger spheres while the smallest sphere deformed by dislocation nucleation and starvation mechanism.

The force-displacement curves of the W and Al2O3 coated samples display a significantly higher strength than the non-coated samples. Analyses of the V* and Q* show a significant increase for the W coated samples comparing the noncoated ones. Values of apparent activation energy changed from 0.062-0.091 (eV) to 0.297-0.430 (eV) for the 0.7 μm spheres by having the W coating layer which reflects the activation of dislocation-obstacle mechanism in the coated layer samples and indicates the surface nucleation and exhaustion mechanism activation in the noncoated samples of 0.7 μm diameter size.

Summary for Lay Audience

The mechanical properties of materials change distinctly when specimen dimension changes to smaller than a few micrometers. With the continuing development of small-scale structures with small dimensions in the micron range, there is an impending need for understanding the fundamentals of plasticity at the micron and nanoscale. In the area of mechanics of materials, classic continuum-based theories describing the material behaviour become inaccurate when the deformation volume being considered is very small, on the size scale of the actual crystal imperfections. In this thesis, the operative deformation mechanisms of face-centered cubic (fcc) small-scale material volumes is studied using both laboratory experimentation and numerical atomistic-simulation. New data are presented on the effect of crystal orientation, pre-existing crystal defects, grain boundaries, and free surfaces on the operative mechanisms of dislocation nucleation and dislocation-obstacle interactions.