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RecrystallizationTheoretical & Practical Aspects

27-301, Microstructure & Properties IFall 2006

Supplemental LectureA.D. Rollett, M. De Graef

Materials Science & EngineeringCarnegie Mellon University

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Objectives• The main objective of this lecture is to introduce you

to the process of recrystallization and to prepareyou for a laboratory exercise on this topic.

• You will have mastered the material in this lecture ifyou can describe the process in qualitative terms,can relate it to thermomechanical processing ingeneral and know how to apply Johnson-Mehl-Avrami-Kolmogorov analysis to the kinetics.

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Recrystallization Basics• Recrystallization is essential to thermomechanical

processing of metallic materials. Plasticdeformation stores energy in the form ofdislocations and also distorts the shape of thegrains. Recrystallization restores the material toan undeformed state.

• Static recrystallization occurs on heating thedeformed material to an elevated temperature.

• Dynamic recrystallization occurs during theplastic deformation. This only occurs for hotdeformation at temperatures greater than 0.5 of themelting point.

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Microstructures

The microstructuregradually changesfrom one withelongated,deformed grains toone withundeformed,equiaxed grains.

Aluminum Handbook, Hatch(1984).

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Annealing Processes• Recrystallization is one example of a process that occurs

during annealing of materials. Annealing is simply theexposure of a material to elevated temperature for a specifiedperiod of time. Various thermally activated processesoccur during annealing that the materials engineer seeksto control in order to optimize properties.

• Other processes include recovery, grain growth, carburization,and sintering.

• Recovery is the decrease of dislocation density that occurs bymotion and annihilation of individual dislocations.

• Grain growth is the coarsening of the grain structure bymotion of grain boundaries.

• Carburization is an example of a change of chemicalcomposition near the surface brought about by the presence ofa high chemical potential for carbon (e.g. by having CO in thefurnace atmosphere) during annealing. This is important insteels for producing high hardnesses at the surface of amaterial.

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Recrystallization: mechanisms• The basic mechanism of recrystallization is the

(long-range) motion of grain boundaries thatremoves dislocation density from the material.

• A consequence of the requirement for long-range boundary migration is thatrecrystallization is a thermally activatedprocess.

• In most materials, temperatures > Tm/3 are requiredfor recrystallization to proceed at a measurable rate.

• Why? Grain boundaries are slowed down by thepresence of solute and most practical materialshave significant amounts of solute.

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Recrystallization: measurement• How can we measure recrystallization?• The traditional method is to perform optical

metallography on sectioned samples.Recrystallized grains appear as approximatelyequiaxed grains with uniform color. Unrecrystallizedgrains appear as deformed grains with irregularcontrast.

• Measurement is primarily the area fraction ofrecrystallized versus unrecrystallized material.Stereology tells us that this area fraction isequivalent to the volume fraction of recrystallizedmaterial.

• An easier measurement is hardness whichdecreases during the recrystallization process.

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Recrystallization Characteristics• In order for the boundary between a new grain (nucleus) and

the deformed material to be able to move, it must be a highangle boundary. This is a consequence of the properties ofboundaries, to be described later.

• The requirement that new grains have high angle boundariesmeans that the final grain size and the rate at whichrecrystallization takes place is highly dependent on the strainlevel.

• Higher strains mean greater lattice rotations (from dislocationslip) inside grains and higher stored energies. Therefore theprobability of generating new grains increases with strain andthe driving force increases.

• Increasing probability for nucleation translates directly intoincreased density of nuclei and therefore smaller recrystallizedgrain size.

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Grain size as a function of priordeformation level

• The grain size afterrecrystallization decreaseswith increasing prior strain,i.e. the nucleation densityincreases.

• Example of commercialpurity Al, recrystallized at600°C (1.5h) after 2 (top), 6,8 & 10% (bottom) reductionin tensile strain.

• Note that these are verysmall strains compared tocommercial practice.

• Next slide shows industrialdata on grain size, also forcommercial purity aluminum.

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Strain dependence

• In most materials, the grain size after recrystallizationdecreases as the strain increases. For most applications,small grain size is desirable. Certain applications, however,require large grain size, and so small strains are sometimesused.

• Note that the heating rate has essentially no effect on theoutcome of recrystallization.

Aluminum Handbook, Hatch (1984).

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Strain effect on kinetics• Recrystallization takes place more rapidly as the deformation

strain increases. This work was performed at Carnegie Tech.

[Humphreys]

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Temperature dependence• The growth of new grains requires motion of grain

boundaries. Boundary migration occurs by thetransfer of atoms across the boundary which is adiffusion-like process.

• Solutes have a strong effect on boundaries becausethe interaction leads to segregation (generally anexcess of solute on the boundary). In effect, movingthe boundary forces the solute to move with it.

• A suitable measure of the “reaction rate” is the timefor 50% recrystallization.

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Temperature Effect on Rex kinetics• Recrystallization is a

thermally activatedprocess and thereforeproceeds more rapidlyas the temperatureincreases.

• Note that the rate ofrecrystallization ismeasured by the timerequired for 50%recrystallization.

[Humphreys]

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Impurity effects on recrystallization

R. Vandermeer and P. Gordon, Proc.Symposium on the Recovery andRecrystallization of Metals, New York,TMS AIME, (1962) p. 211.

F. R. Boutin, J. Physique, C4,(1975) C4.355.1/T

decreasing Fe content

increasing Cu content

V (cm.s-1)

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Nucleation & Growth• Based on the microstructural characteristics (a

different type of material appears as dispersed‘particles’ and grows to the point of replacing thedeformed material), recrystallization is classified asa ‘nucleation & growth’ phenomenon.

• Although treating recrystallization as a nucleation &growth process is perfactly adequate, more detailedexamination shows that it is actually a continuouscoarsening process. The coarsening is, however,so highly heterogeneous that classification dependson the length scale at which it is characterized.

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Nucleation & Growth• Two steps are required for recrystallization to

proceed:– (a) nucleation of new grains that are dislocation-free– (b) growth of the new grains into the dislocated matrix

Deformed matrixNew grains

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Source of stored energy• Martin, Doherty & Cantor distinguish between

microstructural changes driven by chemical energyand change driven by strain energy.

• Recrystallization is a process of microstructuralchange driven by strain energy.

• We will examine the details of plastic deformationlater in the course. For now, it is sufficient to knowthat plastic deformation requires a high level ofdislocation activity on at least 5 slip systems in eachgrain. Dislocations intersect and multiply leavingbehind a highly irregular structure. This storage ofdislocation line length is the direct cause of workhardening and is the strain energy that drivesrecrystallization.

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Nucleation Issues• Nucleation in recrystallization must be a

heterogeneous nucleation process because thedriving force is too small to sustain homogeneousnucleation.

• Estimate of driving force, E:– Energy per unit length of dislocation ≈ Gb2

– Thus energy/volume, E ≈ Gb2ρ– Typical cold worked dislocation density, ρ = 1015.m-2

– For Al, G = 27GPa, b =0.28nm,E ≈ 2 J.m-3 ( = 2MPa)– For a boundary energy σ = 0.5 J.m-2, the critical nucleus

size, rcrit = 2σ/Ε2 ≈ 0.25µm,which is a very large (too large!) critical radius.

• Therefore nucleation in recrystallization must beheterogeneous.

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Heterogeneous Nucleation• Nucleation of recrystallization therefore occurs on

defects in the material.• Sites for nucleation:

– Prior grain boundaries (strain induced boundary migration,SIBM)

– Deformation bands or shear bands, i.e. regions of non-uniform rotation of the lattice

– Coarsening (recovery) of a subgrain structure– Coarsening (recovery) of dislocation structure near to

coarse particles; this is called Particle StimulatedNucleation (PSN).

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Growth of New Grains• The interface between a new grain and the

deformed (unrecrystallized) material (“matrix”) is agrain boundary.

• Grain boundaries vary in their mobility, M, i.e. theconstant of proportionality between migration rate, v,and driving force, E.

• Assume a linear relationship: v = ME.• The driving force is exactly the stored energy

estimated previously.• (HAGB) High angle grain boundaries (θ>15°) are

typically far more mobile than (LAGB) low angleboundaries (by orders of magnitude).

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Laboratory 1 - Introduction• The objectives of the first Lab are as follows:

– Demonstrate recrystallization– Develop metallography skills– Ability to measure grain size– Ability to measure hardness– Demonstrate effect of strain on recrystallized grain size– Demonstrate effect of temperature on recrystallized grain

size– Demonstrate effect of strain on hardness– Demonstrate effect of temperature on hardness– Demonstrate the Hall-Petch effect– Promote critical thinking about the reasons for the variations

in grain size and hardness observed

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Lab. 1- Apparatus• The approach is to deform a rectangular piece of

brass and then anneal it in a temperature gradient.The brass specimen is machined to have a wedgeshape so that when it is deformed (rolled), the strainvaries from the thin side to the thick side.

• Download the Lab Manual from Blackboard in orderto obtain further details.

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Lab. 1- Apparatus, contd.• The specimen is suspended by a wire within an

induction coil. The lower end dips into a beaker ofwater in order to maintain one end at (a maximumtemperature of) the boiling point of water.

WaterWater

HOT

COLD

InductionCoil

Procedure: applyheat and observethe temperature atthe top of thespecimen (T/C).Stop the heatingonce T=900°C; cutthe wire so that thespecimen falls intothe water and isquenched.

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Lab 1 - Expected Results• Hardness: before recrystallization, the hardness should

increase with increasing strain (hint - relate this to what youknow about stress-strain behavior in metals).

• After recrystallization, the grain size will increase withincreasing temperature, but decrease with increasing priorstrain.

• Also after recrystallization, the hardness will increase withdecreasing grain size (Hall-Petch effect) in the recrystallizedareas.

• Note: a critical part of the Lab is to obtain high quality imagesof the grain structure so that you can measure grain size. Themetallography involved requires skill and effort. Also,computer-based submissions are required (Word, or LaTex).

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What is a Grain Boundary?• Grain boundaries control the process of

recrystallization. This suggests that it is worthknowing something about the structure andproperties of boundaries.

• Regular atomic packing disrupted at the boundaryby the change in lattice directions.

• In most crystalline solids, a grain boundary is verythin (one/two atoms).

• Disorder (broken bonds) unavoidable forgeometrical reasons; therefore large excess freeenergy. This interfacial energy is analogous to thesurface tension in a soap bubble (and manyinvestigations on grain growth have been made withsoap froths).

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Crystal orientations at a g.b.

gA

gB

gCgD

TJABC

TJACB

gBgA-1

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Grain Boundary Structure• High angle boundaries: can be thought of as two

crystallographic planes joined together (with or w/o atwist of the lattices).

• Low angle boundaries are arrays (walls) ofdislocations: this is particularly simple to understandfor pure tilt boundaries [to be explained].

• Grain boundary energy increases monotonically withmisorientation as a consequence of increasingdislocation density.

• Transition: in the range 10-15°, the dislocationstructure changes to a high angle boundarystructure.

• The grain boundary mobility increases abruptly atthis transition in structure.

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LAGB to HAGB Transitions

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25

EnergyMobility

En

erg

y,

Mo

bili

ty

Angle (°)

c2=1.-0.99*exp(-.5*(c0/15)^9)

c1=c0/15.*(1.-ln(c0/15.))• The Read-Shockley equationdescribes theenergy of lowangle boundaries.• An exponentialfunction is usefulfor describing thesharp transition inmobility from low-to high-angleboundaries

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Example: tilt boundary = arrayof parallel edge dislocations

• Low angle boundaries are arrays of parallel edgedislocations if the rotation between the lattices issmall and the rotation axis lies in the boundaryplane. In this example, the rotation axis betweenthe two crystals is perpendicular to the plane of thepicture.

b