Deformation & Strength

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Chapter 8:

Deformation andStrengthening

Mechanisms

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Deformation and StrengtheningMechanisms

Plastic deformation caused bydislocation movement.

Slip systems (slip plane, slip direction). Resolved Shear Stress

Strengthening Mechanisms

Recovery, Recrystallization, GrainGrowth

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Deformation Mechanisms (Metals)

Theoretical strengths ofperfect crystal weremuch higher than those actually measured.

It was believed that this discrepancy in

mechanical strength could be explained bydislocations.

On a macroscopic scale, plastic deformationcorresponds to the net movement of large

numbers of atoms in response to an appliedstress.

Interatomic bonds rupturing and reforming.3


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Edge and Screw Dislocations

In an edge dislocation, localized latticedistortion exists along the end of an extrahalf-plane of atoms.

A screw dislocation results from sheardistortion.

Many dislocations in crystalline materials

have both edge and screws components;these are mixed dislocations.

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Dislocation motion leads to plastic deformation.

An edge dislocation moves in response to a shear stress applied in adirection perpendicular to its line.

Extra half-plane atA is forced to the right; this pushes the top halves

of planes B, C, D in the same direction.

By discrete steps, the extra 1/2-plane moves from L to R by

successive breaking of bonds and shifting of upper 1/2-planes. A step forms on the surface of the crystal as the extra 1/2-plane

exits.

Dislocation Motion

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Formation

of a step on

the surface

of a crystal

by themotion of

(a) edge

dislocation

and (b)

screw

dislocation.


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The process by which plastic deformation isproduced by dislocation motion is called slip(movement of dislocations).

The extra

-plane moves along the slip plane. Dislocation movement is similar to the way a

caterpillar moves. The caterpillar hump isrepresentative of the extra -plane of atoms.

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Slip


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When metals are plastically deformed, some fraction (roughly 5%)

of energy is retained internally; the remainder is dissipated as heat.

Mainly, this energy is stored as strain energy associated withdislocations. Lattice distortions exist around the dislocation line.


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Slip Systems

Dislocations move more easily on specific planes and inspecific directions.

Ordinarily, there is a preferred plane (slip plane), and

specific directions (slip direction) along which dislocations

move.

The combination of slip plane and slip direction is called

the slip system.

The slip system depends on the crystal structure of the

metal.

The slip plane is the plane that has the most dense

atomic packing (the greatest planar density).

The slip direction is most closely packed with atoms

(highest linear density). 9


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Slip Plane {111}:most dense atomic packing,

Slip Direction 110:highest linear density,

Slip System FCC example


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Stress and Dislocation Motion

Edge and screw dislocations move inresponse to shear stresses applied along aslip plane in a slip direction.

Even though an applied stress may betensile, shear components exist at all butthe parallel or perpendicular alignments tothe stress direction.

These are resolved shear stresses (R).

Crystals slip due to resolved shear stress.

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Resolved Shear Stress, R


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Condition for dislocation motion:

Critical Resolved Shear Stress

In response to an applied tensile orcompressive stress, slip (dislocation movement) in a

single crystal begins when the resolved shearstress reaches some critical value, crss.

It represents the minimum shear stress

required to initiate slip and is a property of thematerial that determines when yieldingoccurs.

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Deformation in a single crystal

For a single crystal intension, slip will occuralong a number ofequivalent and most

favorably oriented planesand directions at variouspositions along thespecimen.

Each step results from themovement of a largenumber of dislocationsalong the same slip plane.

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On the surface of a polishedsingle crystal, these stepsappear as lines (slip lines).

Slip planes & directions (, )

change from one crystal toanother.

Rwill vary from one crystal toanother.

The crystal with the largestRyields first.

Other (less favorably oriented)crystals yield later. 300 m

Dislocation Motion in Polycrystals

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Polycrystalline Copper


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In addition to slip (dislocation movement), plastic deformation canoccur by twinning.

A shear force can produce atomic displacements so that onone side of the plane (the twin boundary), atoms are locatedin mirror image positions to atoms on the other side.

Twinning may favorably reorient slip systems to promote

dislocation movement.

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Deformation by Twinning


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Strengthening

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The ability of a metal to deform plasticallydepends on the ability of dislocations to move.

Hardness and strength are related to how

easily a metal plastically deforms, so, byreducing dislocation movement, the mechanicalstrength can be improved.

Greater mechanical forces will be required toinitiate further plastic deformation.

To the contrary, if dislocation movement is easy(unhindered), the metal will be soft, easy todeform.


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1. Grain Size Reduction

2. Solid Solution Alloying3. Strain Hardening (Cold Working)

Strengthening Mechanisms


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Grain boundaries are barriers to slip. Barrier "strength increases with misorientation.

Smaller grain size: more barriers to slip.

1. REDUCE GRAIN SIZE

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Hall-Petch Equation:


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Impurity atoms distort the lattice & generate stress. Stress can produce a barrier to dislocation motion.

Smaller substitutional impurity Larger substitutional impurity

Impurity generates local shear at Aand B that opposes dislocationmotion to the right.

Impurity generates local shear at Cand D that opposes dislocation motionto the right.

2. Solid Solutions

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Solid Solution Strengthening in Copper

Effects of Nickel (solute)

content in Copper (host) -Tensile strength (a), Yieldstrength (b) and Ductility,% Elongation (c).


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Room temperature deformation. Common forming techniques used tochange the cross sectional area:

-Forging -Rolling

-Extrusion-Drawing

3. Strain Hardening

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Ti alloy after coldworking.

Dislocations entangle

one another duringcold work.

Dislocation motionbecomes more difficult.

Dislocations DURING COLD WORK

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Dislocation density (d

) increases: Carefully prepared sample: d ~ 103 mm/mm3

Heavily deformed sample: d ~ 1010mm/mm3

Ways to measure dislocation density:

OR

Yield stress increasesas d increases:

40m

Result of Cold Work

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Yield strength (y) increases.

Tensile strength (TS) increases. Ductility (%EL or %AR) decreases.

Impact of Cold Work

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What is the tensile strength & ductility after cold working?

Cold Work Analysis

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Effect of Heating After %CW

The influence ofannealingtemperature (1hour) on thetensile strength

and ductility ofa brass alloy.Grain size isshown as afunction ofannealing

temperature.


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Isotropicgrains are approx. spherical,equiaxed & randomly oriented.

Anisotropic (directional)since rolling affects grainorientation and shape.

Anisotropy - Polycrystals

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before rollingafter rolling

rolling

direction-

Grains areelongated


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Annihilation reduces dislocation density.

Recovery

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During recovery, some of the stored internal strain energyis relieved through dislocation motion due to enhancedatomic diffusion at the elevated temperatures.

There is some reduction in the number of dislocations. Physical properties (electrical and thermal conductivity)

are recovered to theirpre-cold worked states.


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Recrystallization

Even after recovery is complete, the grains arestill in a relatively high strain energy state.

Recrystallization is the formation of a new set ofstrain-free and equiaxed grains that have low

dislocation densities (pre-cold work state). The driving force to produce the new grain

structure is the internal energy difference betweenstrained and unstrained material.

The new grains form as very small nuclei andgrow until they consume the parent material.

Recrystallization temperature is 1/3


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Brass: shows several stages of recrystallization andgrain growth.

Partialreplacement of CWgrains;

After 4 seconds

Complete recryst.after 8 seconds

Initial recrystallization;After 3 seconds,580C

33% CW grains

Further Recrystallization

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Recrystallization with temperature vs %CW foriron. Fordeformations less than 5% CW, recrystallization will not occur.


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GRAIN GROWTH

After recrystallization iscomplete, the strain-freegrains will continue togrow if the metal specimenis left at elevatedtemperatures.

As grains increase in size,the total boundary areadecreases, as does the

total energy. Large grains grow at the

expense of smaller grains.


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Grain diameter versus time for grain growth at specifictemperatures (log scale). Brass Alloy example

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