MIT OpenCourseWarehttp://ocw.mit.edu3.22 Mechanical Properties of MaterialsSpring 2008For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.3.22 Mechanical Behavior of MaterialsDefect Nucleation in Crystalline MetalsTim Rupert, Aparna Singh, Kang ShinYoung, Hyunjung YiMIT Department of Materials Science and EngineeringCambridge, MA 02139 USA[1] Van Vliet, Krystyn J., et al. “Quantifying the early stages of plasticity through nanoscale experiments and simulations.” Physical Review B 67 (2003): 104105.Image removed due to copyright restrictions. Please see Fig. 9a,b,c in [1].3.22 Mechanical Behavior of Materials• Defect nucleation plays an important role in defect-free material volumes or if system size is reduced to the submicron level• The stress required to nucleate a dislocation homogeneously sets an upper bound for the effectiveness of our strengthening mechanisms• Understanding defect nucleation is part of the puzzle for understanding the breakdown of Hall-Petch scaling in nanocrystalline materials[2] Detor and Schuh. “Tailoring and patterning the grain size of nanocrystalline alloys.” Acta Materialia 55 (2007): 371-379.[3] Van Swygenhoven, H., P. M. Derlet, and A. G. Frøseth. “Stacking fault energies and slip in nanocrystalline metals.”Nature Materials 3 (June 2004): 399-403.Big PictureHardness as a function of grain size. [2]Defect nucleation from grain boundaries. [3]Courtesy Elsevier, Inc., http://www.sciencedirect.com. Used with permission.Image removed due to copyright restrictions. Please see Fig. 1b,c in [3].3.22 Mechanical Behavior of MaterialsMicroscopic mechanism[4] Minor, A. M., et al. “Direct observations of incipient plasticity during nanoindentation of Al.” Journal of Materials Research 19 (January 2004): 176-182.In-situ TEM micrographs from [4], illustrating the response of an Al grain to nanoindentation. • When a bond breaks in shear, a new bond will usually form immediately afterwards between the new atomic neighbors. This process of bond breaking and reformation controls defect nucleation.• The stress needed to cause such an event should correspond to the theoretical shear strength we calculated in class.• A defect should nucleate when this stress is reached to relieve the high strain energy built up at this pointImage removed due to copyright restrictions. Please see Fig. 3 in [4].3.22 Mechanical Behavior of Materials[5] Johnson, K. L. Contact Mechanics. Cambridge, UK: Cambridge University Press, 1985.[6] Van Vliet, Krystyn J., et al. “Quantifying the early stages of plasticity through nanoscaleexperiments and simulations.” Physical Review B 67 (2003): 104105.Defect nucleation should occur when our shear stress is maximum and near the theoretical shear stress.Shear stress plot along the depth of the indented material by using 2D indentation model. [5]Nucleation of dislocation at z=0.78a in bubble raft model. [6]0.00 0.05 0.10 0.15 0.20 0.25 0.30-10-8-6-4-20Principal Shear Stress/P0 (τ1/P0)Depth, z/a (set zsurface=0)Maximum shearstresswhen z/a=0.78Prediction & Optimization2D material analogs (bubble raft models), molecular dynamics simulations, and in-situ TEM indentation all support the predicted result.Image removed due to copyright restrictions. Please see Fig. 2 in