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Summary of 10/23/2012

Sergio Castellanos

Mechanical Engineering DepartmentMassachusetts Institute of Technology, Cambridge, MA (USA)

Stress-Strain

2

Constitutive Relations: Strength [A] Ductility [B] Toughness [C]

σ

ε

A

B

C

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

3

• Plasticity• Phase

Transformation

• Plasticity• Phase

Transformation

• Fracture• Fracture

Pot

entia

lE

nerg

y (V

)

Slip DisplacementP

oten

tial

Ene

rgy

(V)

Cleavage Opening

Total Metal-Metal Coordination remains constant

One-off dissipation mechanism

V”=0

PeriodicNon-Periodic

Easier to follow the path of plasticity (sustainable dissipation) Fracture toughness: Resistance against crack propagation

Inelastic Processes in Metals

4

Material KIC-Max [MPa/m0.5]

Cu 107

Ag 105

Fe 150

Ni 150

W 150

SiC 5.1

B-Si3N4 10

TiC 3

MgO 2.8

NaCl 0.19

S. Ogata and J. Li “Toughness scale from first principles” J. Appl. Phys. 106, 113534 (2009)

MetallicIonicCovalent

Easier to follow the path of plasticity (sustainable dissipation) Fracture toughness: Resistance against crack propagation

Inelastic Processes in Metals

5

S. Ogata and J. Li “Toughness scale from first principles” J. Appl. Phys. 106, (2009) 113534

• KIC function of:- Bonding energy- Ideal strength- Bandgap- Ionicity

•

€

˜ K =K IC

B⋅Ω1

6 B=Bulk ModulusG=Shear ModulusΩ=Cell Volume

Shear Weak = Energy Dislocation Spread = KIC

Flow in the presence of Diffusion: Creep

6

σ

t t

ε

toto

Input

σo

εo

ε(t-to)

Output

Different stages on Creep:1. Progression towards steady state flow (s.s. dislocation density – gen.)2. Static recovery counterbalances new dislocation generation3. Terminal failure (e.g. necking in tension test)

…

Deformation-Mechanism Map

7

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

8

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

Limit on Ideal Shear Strength

Low T plasticity by dislocation glideand twinning Limited by:

Discrete obstaclesLattice Friction

Power Law by Glide / Glide + ClimbLimited by:

Glide processesLattice-Diffusion controlled climbCore-Diffusion controlled climbBreakdownHarper-DornDynamic Recristallization

Diffusional FlowLimited by:

Lattice-Diffusion (Nabarro-Herring)GB Diffusion (Coble)Interface-reaction controlled

DisplaciveDisplacive

DiffusionalDiffusional

MixedMixed

9

•Does not involve dislocations.

• Through bulk or along free surfaces

•Does not involve dislocations.

• Through bulk or along free surfaces

Diffusional

[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)

-

Nabarro-Herring(Lattice)

Coble(Surface)

, High T, Low T

Dsurface>>Dbulk Dsurface comparable Dbulk

Hall-Petch: Smaller is Stronger

10

Copper

M.A. Meyers et al. “Mechanical Properties of nanocrystalline materials” Progress in Materials Science 51 (2006), 427-556

Nucleation Stress value computed

Transition predicted from collective dislocation dynamics to signle dislocation nucleation

Geomtry = Long Range Elastic Interaction (Corner/Image)

Surface Dislocation Nucleation

11

T. Zhu et al. “Temperature and Strain-Rate Dependence of Surface Dislocation Nucleation” PRL 100, (2008) 025502

Ultra-Strength Materials

12

€

τcrit >τ shear _ ideal

10=

G

10

ε elastic >1

100=1%

This implies that properties (thermal conductivity, transmittance, etc) can be modified while in the elastic regime.

Hydrostatic: phase transformation

[1] Yanming Ma et al. “Transparent Dense Sodium” Nature 458, (2009) 182[2] Images from ti-fr.com, nutritionresearchcenter.org

[1]

€

d(Ppty) = ∂ε ⋅∂(Ppty)

∂ε> 0Elastic-Strain Engineering

[2]

DoE(Taguchi

)

DoE(Taguchi

)

Elastic-Strain Engineering

13

Synthesize Strain and Measure Force

Measure Strain

E

M Γ K M

NumericalPrediction

• Graphene• Carbon Nanotubes• Bulk Nanocrystals

• AFM • Synchrotron• In-situ TEM

• DFT

Cool (or Hot?) Application: Photovoltaics

14

[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

Challenges:- Thermalization Losses - Non-Absorption Losses

[2]

[1]