We use molecular mechanics (MM) simulations with the tight-binding (TB) potential to study local and global instabilities in initially defect-free finite specimens of gold crystals deformed in shear, simple shear, tension/compression, simple tension/compression, and triaxial tension/compression. The criteria used to delineate local instabilities in a system include the following: (i) a second order spatial derivative of the displacement field having large values relative to its average value in the body, (ii) the minimum eigenvalue of the Hessian of the potential energy of an atom becoming nonpositive, (iii) and structural changes represented by a high value of the common neighborhood parameter. A specimen becomes globally unstable when its potential energy decreases significantly with a small increase in its deformations. It is found that the three criteria for local instability are satisfied essentially simultaneously at the same atomic position. Deformations of a specimen are quite different when it is deformed with some bounding surfaces free from external forces as opposed to essential boundary conditions prescribed on all bounding surfaces. It is found that the initial unloaded configuration (or the reference configuration) of the minimum potential energy has significant in-plane stresses on the bounding surfaces and nonzero normal stresses at interior points. In tensile/compressive deformations of a rectangular prismatic nanobar the yield stress defined as the average axial stress when the average axial stress vs. the average axial strain curve exhibits a sharp discontinuity depends upon the specimen size; a similar result holds for simulations of shear deformations. Specimens deformed with essential boundary conditions on all bounding surfaces experience instabilities at a higher value of the average strain than identical specimens deformed similarly but with one or more pairs of opposite bounding surfaces traction free. For the former set of deformations, the response of a specimen prior to the onset of instability is the same as that of a hyperelastic body with the strain energy derived from the TB potential and deformations obeying the Cauchy-Born rule. Specimens with some traction free bounding surfaces experience local instabilities prior to the onset of a global instability but the two instabilities occur simultaneously in specimens with essential boundary conditions prescribed on all bounding surfaces. It is believed that because of residual stresses in the reference configuration, the average axial stress at yield in compression is nearly one-half of that in tension. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/37734 |
| Date | 01 June 2009 |
| Creators | Pacheco, Alejandro Andres |
| Contributors | Engineering Science and Mechanics, Batra, Romesh C., Hendricks, Scott L., Farkas, Diana, Hyer, Michael W., Watson, Layne T., Cramer, Mark S. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | apacheco_dissertation.pdf, SED_CERTIFICATE_OF_COMPLETION.PDF |
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