0. 3.40/22.71 Sergio Castellanos Summary of 10/23/2012
Mechanical Engineering Department
Massachusetts Institute of Technology, Cambridge, MA (USA)

1. 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.

2. 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

3. 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, (2009)

4. 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)

5. 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)

6. 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).

7. 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).

8. 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
[2] Image from
[3] Brown, L.M. “Frank Reginald Nunes Nabarro MBE” Biographical Memoirs of Fellows of the Royal Society (2009)

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

10. 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)

11. 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]

12. 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

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