9.1 - Elasticity / plasticity & slip planes / systems

Give the definitions of plasticity & elasticity

• PLASTICITY

→ ability of a material to undergo permanent deformation w/ rupture

→ irreversible / permanent deformation: once the applied stress is removed, it won’t return to its original shape, HOWEVER, if another stress is applied, it can still deform

→ macroscopic scale = plastic deformation

→ microscopic scale = movements of dislocations through the material when the applied stress exceeds the elastic limit → permanent change in the atomic arrangement

• ELASTICITY

→ ability of a material to return to its original shape & size after the applied stress is removed

→ macroscopic scale = reversible, temporary deformation

→ microscopic scale = slight displacement of atoms from their equilibrium position, but the bonds are not broken because the applied stress isn’t high enough to break them (<elastic limit). Atoms return to their original position once the stress is removed

What happens at an atomic scale during elastic deformation?

→ an external stress that doesn’t exceed the elastic limit is applied

→ atoms are slightly displaced, the distance between them slightly chsnges

→ bonds stretch / compress but don’t break

→ this configuration / change is retained as long as the external stress is applied

→ once the stress is removed, the attractive / repulsive net force due to the change in the distance between atoms pulls/pushes the atoms back to their equilibrium position

What’s the Hooke’s law? (Formula & when we apply it)

Sigma = stress

E = Young’s / elastic modulus (stiffness = rigidité)

Epsilon = strain (elongation)

→ only applies in the elastic region

What happens at an atomic scale during plastic deformation?

→ a stress that exceeds the elastic limit is applied

→ movements of atoms via movements of dislocations

→ atomic bonds break → permanent change in the atomic arrangement

What are plastic deformations constrained to?

Why?

Can only take place in certain planes & directions → slip planes & slip directions

Because movement in these planes / directions requires smallest critical shear stress (min. shear stress required to initiate the movement of dislocations)

Give the definition of slip planes & slip systems

• slip planes = planes (atomic layers) with densest packing (closed packed) & large plane spacing

• slip systems = combination of slip planes & slip directions → describe deformation of metals

How many slip systems are there in FCC crystal structures?

Draw a slip plane in a FCC unit cell

What deformability is thus obtained?

• 4 slip planes (parallel slip planes are put together and counted as 1) {111}

  → 2,5,7 // 1,3,8

  → 4,5,7 // 1,3,6

  → 6,8,1 // 2,4,7

  → 6,8,3 // 2,4,5

• 3 slip directions <110>

• 12 independent slip systems (4×3)

→ good plastic deformability

How many slip systems are there in BCC crystal structures?

Draw the different possible slip planes in a BCC unit cell

What deformability is thus obtained?

• 48 slip systems → only 12 are mainly activated (the others are activated when significant higher stresses are applied)

• less dense packed slip systems than FCC

• moderate deformability

How many slip systems are there in HCP crystal structures?

Draw the different possible slip planes in a HCP unit cell

What deformability is thus obtained?

• 12 slip systems → only 1 mainly activated (the others are activated at higher temperatures)

• low plastic deformability

Classify the FCC, BCC, and HCP structures according to their deformability

1. FCC: very good deformability

2. BCC: moderate deformability

3. HCP: low deformability

What’s the definition of a good deformability?

Good deformability = ability of a material to deform its lattice structure w/ damage <=> as many usable slip systems as possible

What kind of forces can cause an atomic plane to slide?

→ shear forces (acting // to slip planes)

(Normal forces which act perpendicular to slip planes will only cause elongation / compression of the crystal lattice in their direction but no lateral displacement)

→ if a force is applied at an angle to a slip plane, the displacement onto the slip plane will only be driven by the component of the force that is // to it)