Date of Award

Fall 2016

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Mechanical Engineering

Committee Director

A. A. Elmustafa

Committee Member

Gene Hou

Committee Member

Dipankar Ghosh

Committee Member

Yousuf Mohammed

Committee Member

Helmult Baumgart


The indentation size effect (ISE) in metals is described as the rise in hardness with decreasing depth of indentation and contradicts conventional plasticity behavior. The goal of this dissertation is to further examine the fundamental dislocation mechanisms that may be contributing to the so-called indentation size effect. In this work, we examined several metals and alloys including 99.999% Aluminum (SFE ~200 mJ/m2), 99.95% Nickel (SFE ~125 mJ/m2), 99.95% Silver (SFE ~22 mJ/m2), and three alloys, alpha brass 70/30 (SFE >10 mJ/m2), 70/30 nickel copper (SFE ~100 mJ/m2), and 7075 AlZn (SFE ~125 mJ/m2) to study the effect of stacking fault energy on the ISE. The current work sought to address several objectives including; 1) Verify the existence of an ISE and the bilinear behavior of various FCC metals using single indentation test platform and the same tip for various stress decades: 2) Examine the thermally activated mechanisms that could contribute to the ISE via the kinetics of plastic deformation based on indentation experiments for constant load creep and load relaxation as well as classical uniaxial testing to study the coupled relationship between strain rate, dislocation density, and dislocation velocity: 3) Examine the possible contribution of stacking fault energy (SFE) on the ISE by comparing pure metals over a wide SFE range as well as the effect of alloying. We demonstrate that all the metals tested exhibit a clear ISE using a new approach that included the use of a single machine and using a single tip capable of reaching depths of 30 μm. This eliminated any uncertainty in measurements when comparing data for any metal across the nano to micro-range (from 0.07 mN to 10 N). It was found that the pure metals should be examine separately from the alloys when examining any dependency on SFE. Activation volume analysis, based on indentation creep experiments, was used to examine the stress dependency of the activation volume for each metal. We verified through various experiments across a wide stress range that the ISE has a kinetic signature similar to that found in uniaxial testing for work hardening. We propose an analysis of the ISE in terms of Orowan’s equation which relates the strain rate to dislocation density and dislocation velocity. We performed indentation creep tests across a wide loading range to measure the strain rate sensitivity of the hardness and determine the activation volume. We found that when the data were fitted to the Orowan relation, and the GND dislocation density was assumed to increase according to strain gradient plasticity theory for an ISE, the hardness increased as the dislocation velocity decreased along with the activation volume. To confirm these observations, we developed a new indentation test protocol to perform repeated load relaxation tests in indentation to examine the dependence of dislocation velocity and density on the relaxation strain rate. We found that the relaxation data matched our assumptions that were based on the indentation creep experiments. As the hardness (stress) increases, the ratio of the dislocation velocity decreases, while the dislocation density increases, and the activation volume decreases. We fitted the dislocation velocity data to the bilinear behavior model introduced by Elmustafa and Stone (2003) and found that the dislocation velocity measurements for the pure metals showed a distinct bilinear behavior with increasing stress. The bilinear velocity data in the nano-region had a different slope compared to the data measured at deeper depths of indentation. These findings support the theory that at shallow depths of indentation the ISE is dominated by dislocation-dislocation interactions. Finally, to address the SFE issue, we conducted a variety of indentation tests including standard load control testing and indentation creep. We showed that while a weak correlation of the ISE with SFE is observed for the pure metals tested, the influence of SFE for all metals and alloys cannot be made.

This work, in its entirety, adds to the understanding of the mechanisms that influence the ISE and contributes valuable data and methodologies for future investigators on which to draw.