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Nanotechnology and Materials Systems Analysis of Bending of Micro Beams William Grant Whittington Senior Aerospace Engineering Texas A M University Advisor Dr Amine Benzerga This Research Experience for Undergraduates Site is Sponsored By Air Force Office of Scientific Research U S Air Force Department of Defense National Science Foundation NSF Grant No 0453578 Run simulations for samples ranging from 1 to 5 microns in height geometrically similar Determine impact of size for samples in bending Determine contributions of SSDs Statistically Stored Dislocations and GNDs Geometrically Necessary Dislocations to the overall bending response Continuum theory predicts that all material properties are size independent Experiments Simulations show that beams under tension show increased strength when dimensions are on the order of nanometers tens of microns Improved strength of small samples is due to the behavior of dislocations and dislocation sources For small beams dislocation sources are limited in size and require higher stresses to activate Source behavior may also be interrupted by the presence of free surfaces preventing plasticity from setting in until a higher stress state In bending GNDs are also formed and may affect the material response Used 2D discrete dislocation dynamics code that employs 3D effects developed by Benzerga et al Bending moment normalized by a reference moment Mref 1 6 h2 MYref 1 6 Y h2 is the bulk yield stress in tension Y is the yield stress of the specific specimen in tension 8 7 6 M Mref M MYref 5 4 3 2 1 0 0 1 2 3 4 Sample Height microns 5 6 M Mref Shows contribution of SSDs and GNDs together varies as h 1 8 M MYref Shows contribution of GNDs varies as h 1 1 Demonstrates that both contribute to size strengthening 4 5 4 M M REF M MYREF 3 5 3 2 5 2 1 5 1 0 5 0 0 1 2 3 4 Sample Height microns 5 6 Shows contribution of SSDs Although the method of separation of the two types of sources may not be entirely accurate this demonstrates that while



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