MSR/smms/Plasticity.md

#SMMS

cooking recipe -> microstructure -> mechanical behavior

Elastic domain should be big (to resist constraints) But Plastic domain should be easy to attain (to shape the material)

In a isotropic material with a mix of constituants :

E_{tot}=\sum\%_iE_i

The stress-strain curve has a big hypothesis : \dot{\varepsilon}=cste

Everything creep with enough time

(see Rheology)

Movement of dislocations

Dislocation by slipping !dislocations With \vec{b}, Burger's vector

The energy needed to dislocate is mainly to start the dislocation (breaking the first bond +\Delta E) because when a bond is formed, the energy of breaking is regained (-\Delta E). A bit of energy is lost to move the atoms (\delta E), but is is negligible in front of the breaking energy (\Delta E).

Energy for one step :

\Delta E + \delta E - \Delta E = \delta E

Covalent bonds : strong bond, so the material does not dislocate very much -> cracks instead -> brittle material (like rocks)

Metallic bonds : weak bond, so the material can dislocate easily -> plastify -> ductile material.

Dependency to temperature

!Temperature effect on stiffness Heat brings energy to the material, so the dislocations become easier to start -> the material softens

Also : T\downarrow\ \Rightarrow hardness \uparrow\ \Rightarrow ductility \downarrow\ \Rightarrow brittleness \uparrow

There exist a temperature of brittle/ductile transition.

Describing dislocations

!

\Psi = angle between \vec{b} and \vec L (in french "caractère")

\Psi = 90° \Rightarrow edge dislocation (coin) \Psi = 0° \Rightarrow screw dislocation (vis)

Work of a dislocation

!dislocation energy

W=FL\ \ \ W=F_a b=\tau(Ll)b\ \Rightarrow\ \frac{F}{l}=\tau b

Interactions between dislocations

Dislocations can attract or repel each other depending on their burger vector and their dislocation line.

Dislocations can even disappear if two opposite ones come into contact.

Dislocations can be generated from one (Frank-Read sources).

Due to the repelling forces between dislocations, their is a saturation level of the material, when the material is filled with dislocations, the only way to dissipate energy is fracture.

Density of dislocations : \rho = \frac{l}{V} where l is the total length of the dislocations and V the volume. (10^6 is the lowest density we can produce and 10^{16} the highest before failure)

Crystal Twinning (maclage)

\vec{b} can be smaller than the movement needed to realign perfectly the crystal. In that case, multiple dislocations can make a perfect alignment, and that makes a twin crystal, causing an orientation change. !

Shape Memory alloy

Using martensite, one can make a stable configuration of twinned crystal. When under a load it then undergoes "de-twinning" which stores the mechanical load. It can be recovered instantly, but sometimes need a bit of energy (as heat).