PLASTIC DEFORMATION

Dislocations and their role in plastic deformation

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What are dislocations?

� Dislocations are line defects that exist in metals

� There are two types of dislocations: edge and screw

� The symbol for a dislocation is � The dislocation density in annealed

metals is normally ρ = 106/cm2

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Types of dislocations

Edge

Screw

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Dislocation motion⇔plastic deformation

Note: Dislocations normally move under a shear stress4

How does a dislocation move?

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Stress field of a dislocation

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Analog to an electric charge

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Modes of deformation

� Slip

� Twinning

� Shear band formation

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Slip� Dislocations move on a certain

crystallographic plane: slip plane� Dislocations move in a certain

crystallographic direction: slip direction� The combination of slip direction and

slip plane is called a slip system

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Slip…..� Slip planes are normally close-packed planes� Slip directions are normally close-packed

directions

Recall for fcc close-packed planes are {111}Close-packed directions are <110>

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Slip systems

Crystalsystem

Slip plane Slipdirection

Totalnumber ofslipsystems

Activeslipsystems

fcc {111} <110> 12 5

hcp {0001} <2110> 3 2/3

bcc {110}{100}

<111> 48 2

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Dislocation interaction

⊥ ⊥ Repulsion

⊥

Attraction&

Annihilation

Positive Positive

Positive Negative

Note: More positive-positive interactions in reality12

Positive-positive dislocation interaction

� Results in more stress to move dislocations (or cause plastic deformation):called work hardening

� This type of interaction also leads to dislocation multiplication which leads to more interactions and more work hardening

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Twinning

� Common in hcp and bcc structures

� Limited deformation but help in plastic deformation in hcp and bcc crystals

� Occurs on specific twinning planes and twinning directions

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Compare slip and twinning

SLIP TWINNING

HOMOGENEOUS LOCALIZED

COMMON IN FCC COMMON IN HCP &BCC

OCCURS UNDERSTATIC LOADING

OCCURS UNDERSHOCK LOADING

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Shear band formation� Limited non-homogeneous deformation

� Very large localized strain ε~1 or 100%

� Occurs especially under high strain rates

� Mechanism of deformation still unclear16

Plastic deformation ⇔movement of dislocations

Strengthening methods

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Cold working

� Deformation at temperatures below 0.4 Tm

� Dislocation density increases from 106/cm2 to 1010-12/cm2

� High dislocation density results in a large number of dislocation interactions which results in high strength and hardness

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Solid solution strengthening� Interaction between stress fields of alloy

atoms and dislocations� This is the purpose of alloying

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Grain size refinement

� Small grains result in higher strength

� Small grains is equivalent to a large number of grain boundaries in the same volume

� Grain boundaries act as barriers to dislocation motion

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Mechanism

Strength is inversely proportional to grain sizeσ = σ0 + kyd-1/2

Hall-Petch equation

Smaller grains have more boundary area and hence morebarriers to dislocation motion

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Precipitation hardening

� Precipitates are second-phase particles

� Hard precipitates act as barriers to dislocation motion

� Applicable only to some alloy systems

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