      Nanotechnology and Materials Systems – Analysis of Bending of Micro BeamsWilliam Grant WhittingtonSenior, Aerospace EngineeringTexas A&M UniversityAdvisor: Dr Amine BenzergaThis Research Experience for Undergraduates Site is Sponsored By:Air Force Office of Scientific Research, U.S. Air Force, Department of DefenseNational 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 bendingDetermine 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 independentExperiments/Simulations show that beams under tension show increased strength when dimensions are on the order of nanometers-tens of micronsImproved 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 activateSource 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 *  * h2MYref = 1/6 * Y* h2 is the bulk yield stress in tensionY is the yield stress of the specific specimen in tension      %$" %$" %$" %$" &'&'&'&'(((())))       $  $  $  $0123456780 1 2 3 4 5 6Sample Height (microns)M/Mref M/MYref      *$*$*$*$M/Mref – Shows contribution of SSDs and GNDs togethervaries as ~h-1.8M/MYref – Shows contribution of GNDsvaries as ~h-1.1Demonstrates that both contribute to size strengthening       $  $  $  $00.511.522.533.544.50 1 2 3 4 5 6Sample Height (microns)M/MREF - M/MYREF      *$*$*$*$Shows contribution of SSDs. Although the method of separation of the two types of sources may not be entirely accurate, this demonstrates that while both dislocation types contribute to the strengthening, SSDs contribute more.varies as ~h-3.3      + + + + Test