The Contribution of Dislocation Density and Velocity to the Strain Rate and Size Effect Using Transient Indentation Methods and Activation Volume Analysis


Generally, there are 14 different types of crystal unit cell structures or lattices found in nature. Most metals and many other solids have unit cell structures described as body center cubic (BCC), face centered cubic (FCC) or hexagonal close packed (HCP).

There has been significant research on establishing why FCC structured metals tend to exhibit a size effect under specific loading conditions including indentation, torsion and the fundamental mechanism responsible for this behavior. So far, it has already been proven that the indentation size effect (ISE) is governed by dislocation-based mechanisms in crystalline materials and is caused by the accumulation of geometrically necessary dislocations resulting from a large strain gradient for shallow indents. In addition, the stacking fault energy (SFE) of a material, especially metals, has been found to be directly related to its capacity to work harden. Nonetheless, from the available plethora of literature, no work exists that shows the correlation between SFE, hardness, activation volume and ISE for silver (low SFE), nickel (intermediate SFE) and aluminum (high SFE). Therefore, there is need for detailed experiments to be undertaken so as to resolve the aforementioned issue.

Recently, Old Dominion University scientists: Dr. D. E. Stegall and Professor Abdelmageed Elmustafa from the Department of Mechanical and Aerospace Engineering carryout detailed experimentation for some of the more fundamental variables so a to better comprehend previous observations of the same. Specifically, they examined the strain rate, dislocation densities, and dislocation velocity. Additionally, they sought to establish how the coupled relationships between each and every variable contribute to ISE. Their work is currently published in the research journal, Metallurgical and Materials Transactions A.

In brief, the researchers started by taking measurements of the creep parameters using the constant load indentation experiments that were conducted using a nanoindentation system which was properly isolated from vibrational noise. The samples used were properly prepared according to ASTM standards and kept in a desiccator. Lastly, they performed two types of testing to measure the strain rate sensitivity, constant load creep experiments, and constant strain repeated load relaxation tests.

The authors observed that the dislocation velocity which was calculated based on Orowan’s relation decreased with the increasing hardness at shallow depth of indentation. Moreover, they noted that the accumulation of geometrically necessary dislocations (GNDs) resulting from strain gradient at shallow depth of indentation resulted in the decrease of the dislocation velocity with the hardness at shallow depth of indentation. The researchers also realized that at the depths corresponding to the bulk hardness where statistically stored dislocations dominate the crystal plasticity and the influence of the GNDs diminishes, the change in dislocation velocity was not associated with accumulation of GNDs.

In summary, Elmustafa-Stegall study presented detailed experimental procedures with regard to theoretical hypothesis that stipulate ISE is driven by a dislocation mechanism, specifically the increase in the geometrically necessary dislocation density at shallow depth of indentation due to the presence of a large strain gradient. Altogether, by using the Orowan’s relation, they observed that for silver and nickel, the dislocation velocity when plotted vs hardness, exhibited a bilinear behavior. All in all, their observations are in good agreement with related literature and offer a new technique to carry out detailed experiments for other metals.

The Contribution of Dislocation Density and Velocity to the Strain Rate and Size Effect Using Transient Indentation Methods and Activation Volume Analysis - Advances in Engineering

About the author

Dr. David E. Stegall obtained a Ph.D. in Mechanical Engineering from Old Dominion University in Norfolk Virginia, USA. Dr. Stegall’s research interests are primarily concerned with examining the fundamental dislocation mechanisms associated with the indentation size effect in metals using nanoindentation techniques. He has authored or coauthored numerous articles published in refereed journals and conference proceedings in the areas of nanoindentation and thin films. Dr. Stegall has more than 20 years of experience as a research engineer focusing on materials characterization of advanced materials.

About the author

Dr. Elmustafa is a Professor in the Department of Mechanical and Aerospace Engineering at Old Dominion University and The Applied Research Center –Thomas Jefferson National Accelerator Facility in Norfolk and Newport News, VA. Dr. Elmustafa obtained his Ph.D. in Materials Science and Engineering from the University of Wisconsin-Madison and served as a post-doctoral fellow in the Materials Science and Engineering Department, University of Wisconsin-Madison. He was also a Principal Investigator and Program Manager at Piezomax Technologies, now NPoint Inc. Madison, Wisconsin. He was also a Visiting Research Professor in the Department of Mechanical and Aerospace Engineering at Princeton University, 2003-2005.

Dr. Elmustafa has successfully established a distinguished research program that has been funded by industry, NSF, NASA, Thomas Jefferson National Accelerator Facility (Jlab), and other federal agencies. He strives to foster quality students through excellence in education, teaching and research. He has crafted a vibrant research group, where collaborators, graduate, and undergraduate students work together in an atmosphere that is conducive to research and publication. Dr. Elmustafa principal interest is in the study of Nanoscale Mechanical Behavior of solids researching plastic flow properties and the fundamental atomic scale mechanisms, evaporation and deposition of thin films for activation analysis, study of computational and experimental nanoscale mechanical properties, deformation mechanisms, strain gradient plasticity, dislocation defects, fractures strength of thin films, MEMS, cell mechanics and bulk materials using nanoindentation techniques and classical mechanics. He also researches nanoscale mechanical properties of semiconductors materials such as Silicon-on-Insulator, metal gate hafnium and aluminum oxides, and zinc oxide. Additionally he performs modeling and simulation of nanoscale creep and contact mechanics. Other areas of interest in the biomedical sciences include abdominal mesh for hernia repair, urinary bladder replacement, heterogeneous biodegradable materials for bone fixation, and material systems immune/insensitive to bacteria and fabrication, characterization of wireless sensors.


D.E. Stegall, A.A. Elmustafa. The Contribution of Dislocation Density and Velocity to the Strain Rate and Size Effect Using Transient Indentation Methods and Activation Volume Analysis. Metallurgical and Materials Transactions A, Volume 49a, 2018, page 4649-4658.

Go To Metallurgical and Materials Transactions A

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