3.40/22.71 Sergio Castellanos Summary of 10/23/2012 Mechanical Engineering Department Massachusetts Institute of Technology, Cambridge, MA (USA)

Stress-Strain σ A C Constitutive Relations: B ε εplastic εelastic ε σ Strength [A] Ductility [B] Toughness [C] B ε E [Pa] εplastic εelastic ε σ Upon unloading εtotal = εplastic + εelastic I.e. Springback Hysteresis Loop.- Dissipation converts useful mechanical energy into heat.

Inelastic Processes Plasticity Phase Transformation Fracture Energy (V) Potential Energy (V) Potential Non-Periodic Periodic Cleavage Opening Slip Displacement V”=0 Total Metal-Metal Coordination remains constant One-off dissipation mechanism

Inelastic Processes in Metals Easier to follow the path of plasticity (sustainable dissipation) Fracture toughness: Resistance against crack propagation Material KIC-Max [MPa/m0.5] Cu 107 Ag 105 Fe 150 Ni W SiC 5.1 B-Si3N4 10 TiC 3 MgO 2.8 NaCl 0.19 Metallic Ionic Covalent S. Ogata and J. Li “Toughness scale from first principles” J. Appl. Phys. 106, 113534 (2009)

Inelastic Processes in Metals Easier to follow the path of plasticity (sustainable dissipation) Fracture toughness: Resistance against crack propagation B=Bulk Modulus G=Shear Modulus Ω=Cell Volume KIC function of: Bonding energy Ideal strength Bandgap Ionicity Shear Weak = Energy  Dislocation Spread = KIC S. Ogata and J. Li “Toughness scale from first principles” J. Appl. Phys. 106, (2009) 113534

Flow in the presence of Diffusion: Creep Input Output … σ ε ε(t-to) σo εo to to t t Different stages on Creep: Progression towards steady state flow (s.s. dislocation density – gen.) Static recovery counterbalances new dislocation generation Terminal failure (e.g. necking in tension test)

Deformation-Mechanism Map Frost, Harold Jefferson, and M. F. Ashby. "Deformation-mechanism maps: The plasticity and creep of metals and ceramics.” Pergamon Press, Oxford, UK (1982).

Deformation-Mechanism Map Limit on Ideal Shear Strength Low T plasticity by dislocation glide and twinning Limited by: Discrete obstacles Lattice Friction Displacive Power Law by Glide / Glide + Climb Limited by: Glide processes Lattice-Diffusion controlled climb Core-Diffusion controlled climb Breakdown Harper-Dorn Dynamic Recristallization Mixed Diffusional Diffusional Flow Limited by: Lattice-Diffusion (Nabarro-Herring) GB Diffusion (Coble) Interface-reaction controlled Frost, Harold Jefferson, and M. F. Ashby. "Deformation-mechanism maps: The plasticity and creep of metals and ceramics.” Pergamon Press, Oxford, UK (1982).

Diffusional Does not involve dislocations. Through bulk or along free surfaces Diffusional Coble (Surface) Nabarro-Herring (Lattice) , Low T , High T Dsurface>>Dbulk Dsurface comparable Dbulk - [1] Image from http://en.wikipedia.org/wiki/Frank_Nabarro [2] Image from http://news.stanford.edu/news/2009/july27/herring-physics-obit-073109.html [3] Brown, L.M. “Frank Reginald Nunes Nabarro MBE” Biographical Memoirs of Fellows of the Royal Society (2009)

Hall-Petch: Smaller is Stronger Copper M.A. Meyers et al. “Mechanical Properties of nanocrystalline materials” Progress in Materials Science 51 (2006), 427-556

Surface Dislocation Nucleation Nucleation Stress value computed Transition predicted from collective dislocation dynamics to signle dislocation nucleation Geomtry = Long Range Elastic Interaction (Corner/Image) T. Zhu et al. “Temperature and Strain-Rate Dependence of Surface Dislocation Nucleation” PRL 100, (2008) 025502

Ultra-Strength Materials This implies that properties (thermal conductivity, transmittance, etc) can be modified while in the elastic regime. Elastic-Strain Engineering Hydrostatic: phase transformation [1] Yanming Ma et al. “Transparent Dense Sodium” Nature 458, (2009) 182 [2] Images from ti-fr.com, nutritionresearchcenter.org [1] DoE (Taguchi) [2]

Elastic-Strain Engineering M Γ K M Synthesize Strain and Measure Force Measure Strain Numerical Prediction Graphene Carbon Nanotubes Bulk Nanocrystals AFM Synchrotron In-situ TEM DFT

Cool (or Hot?) Application: Photovoltaics [1] Challenges: - Thermalization Losses - Non-Absorption Losses [2] [1] Image: http://en.wikibooks.org/wiki/Microtechnology/Semiconductors [2] Ji Feng et al. “Strain-Engineered Artificial Atom as a Broad-Spectrum Solar Energy Funnel” Nature (2012) Accepted