Chapter 7 Recovery, Recrystallization, Grain Growth

8/10/2019 Chapter 7 Recovery, Recrystallization, Grain Growth

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Chapter 7Recovery, Recrystallization, Grain Growth

7.1 Phenomena and terminology

Plastic deformation strain hardening dislocations

Annealing decrease in strength, increase in ductility

Recrystallization reconstruction of the grain during annealing of deformed metals. proceeds by generation and motion of high angle grain boundaries or grain boundaries migration.

Recovery a rearrangement of dislocation or annihilation of dislocations.

Dynamic recrystallization, dynamic recovery processes occur during deformationStatic recrystallization, static recovery - processes occur during annealing treatment after cold forming

Recrystallization

-Primary recrystallization- also called discontinuous recrystallization- nucleation and nucleus growth

- the dislocation density in metal is not removed

homogeneously

- grain boundaries migration

- Continuous recrystallization or in-situ recrystallization

- occur to the metal subjected to large cold deformation or

the metal which the grain boundaries migration isstrongly impede, i.e. dispersion of a secondary phase.

- a new microstructure has been formed without the

migration of high angle grain boundaries.

- occurs homogeneously

If the degree of prior cold forming is small

- nucleation cannot occur

- existing grain boundaries migrate locally and remove the

dislocation structure in the swept volumes

(SIBM strain induced grain boundary motion) fig 7.3.

- not all grains are deformed equally

- during SIBM : a less deformed grain grows into the

adjacent grain of higher energy and removes the

deformed microstructure.


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If the heat treatment is continued after complete primaryrecrystallization, grain size increases, grain growth, occurs in 2modes

- Continuous or normal grain growth

average grain size continuous increases

- Discontinuous or abnormal grain growthAlso called Secondary recrystallization

only a few grains grow rapidly while the other grains grow

slowly or not at all

Discontinuous grain growth: secondary recrystallization

- the grain size distribution does not remain self-similar

- during secondary recrystallization 2 types of distribution

develop

1. the slowly-growing grains becomes smaller and finally

disappears.

2. the rapidly-growing grains the few abnormally growing grains significantly changes

the average grain size, ln Dm,a and the max frequency,

fmax increase with increasing annealing time untilcompletion, fig. 7.6.

Continuous or normal grain growth

- the average grain size ln Dm is shifted to larger valuesthe maximum and the standard deviation remain

unchanged, fig. 7.6 a.

- called self-similarity

- From a graph of distribution VS ln(D/Dm) the normalized

logarithmic grain size

The distribution does not change during normal grain

growth

The integral of the distribution has a constant value.

Tertiary recrystallization

Normal grain growth usually ceases if the grain size becomescomparable to the smallest specimen dimension (sheetthickness)

In some cases (thin sheet) discontinuous growth of a fewgrains is observed after continuous growth has come to an end

Called Tertiary recrystallization

- because of its discontinuous appearance

- to distinguish from discontinuous grain growthowing to different energetic reasons.


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7.2 Energetics of recrystallizationIf grain boundary of area dA is displaced by distance dx,

the Gibbs free energy changed G = - p dA dx = - p dV 7.1

dV is the volume swept by the moving grain boundaryp = - dG/dV 7.2

p - is the driving force- the gained free energy per unit volume (J/m3)- can be considered as a force acting per unit area

on the grain boundary (N/m2)- pressure on the grain boundary

The driving force for primary recrytallization is the storedenergy of the dislocation.The deformed metal - dislocation density ~ 1016 m-2

The recrystallized grains - dislocation density ~ 1010 m-2

The energy of a dislocation/unit lengthEd = ()Gb2 G = shear modulus 7.3

b = Burgers vectorIf - a dislocation density

The driving force for primary recrystallizationp = Ed = ()Gb2 7.4

For 1016 m-2G 5.104 MPa p = 10 MPab 2.10-10 m ~ 107 J/m3

~ 2 Cal/cm3

The driving force for grain growth Total grain boundaries area is reduced

Assume - the consumed grains have a cubic shaped - diameter of grain boundary - grain boundary energy (J/m2)

I The driving force for discontinuous grain growth(secondary recrystallization)

The driving force on a boundary sweeping such a volumeequals

p = (3d2)/d3 = 3/d 7.5

3 factor - each of the 6 faces of cubic is shared by2 adjacent grains

If the consumed grainsd = 10-4 m p 0.03 MPa 1 J/m2 3x104 J/m2


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The driving force for primary recrytallization is greater byorders of magnitude than for the discontinuous grain growth(or secondary recrystallization)

Therefore, the grain growth proceed very slow or becomefaster at higher temperature.

II The driving force for continuous grain growth

Grain boundary always be a curvature. The force acts on

the curved boundary in the direction towards the center ofcurvature to become straight line. Grain boundary areareduces. The driving force on a boundary segment thepressure on a curved surface. (The driving force forcontinuous grain growth)

p = 2 / R 7.6

R - radius of curvature (assume ~ grain size)

But the curvature is small the radius of curvature is

substantially larger than the grain size (by factor of 5-10)

Therefore, the driving force continuous grain growth e.q. 7.6is about 5-10 times smaller than for discontinuous graingrowth e.q. 7.5 (the secondary recrystallization)

III The driving force for tertiary recrystallization iscaused by the orientation dependence of the free surfaceenergy. The grain will grow at the expense of its neighbor ifits surface energy, o, is smaller than that of its neighbor. Fig.7.9, thin sheet thickness h, width B, grain size is largercompared to the thickness. The grain boundaries moveperpendicular to the sheet plane.

The driving force for tertiary recrystallization

p = (2 o) / h 7.7

o = 02 - 01

For o 0.1 J/m2 p 2x10-3 MPa

h 10-4 m 2x103 J/m3

Since - surface energy depends on the ambient temperature

o can be made larger, or change sign by selecting an

appropriate annealing atmosphere.

Therefore, tertiary recrystallization depends on the annealingtemperature.


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7.3 Deformation microstructure

Deformed metals can recrystallize.

Recrystallization can proceeds from a deformed metal.

Deformed metal dislocation motion influenced by solute

atoms, precipitates

- by other dislocations, dissociation of the

dislocation.

The normalized stacking fault energy SF /Gb *SFcontrols the dissociation width of the dislocations.

- the smaller *SF the larger is the width

- increasing the width

cross slip or climb become more difficult

- obstacles can not be as easily circumvented

- work hardening increases

- material with low stacking fault energy, the flow stresscan reach the level required to activate mechanical twinning.Twinning is a major deformation affects microstructure.

At large degrees of deformation

- for fcc deformed microstructure can have twin orabsence of twin depending on

- the magnitude of *SF- deformation temperature

At low degree of deformations

- dislocation are not homogeneously distributed

- dislocations form cell structure with distribution of cell sizes

- cell walls has high dislocation density

- inside a cell has relatively low dislocation density.

- the character and appearance of a cell structure depends on

- the material- determined by the normalized stacking fault

energy, *SF- degree of deformation

- deformation temperature

With increasing temperature, larger *SF- thickness of the cell wall decreases

- until eventually sharp subgrain boundaries are formed

- cell interior becomes depleted of dislocations

The degree of deformation affects - the cell size

- misorientation between

adjacent cells

with increasing degree of deformation

- the average cell size decreases

- the orientation difference between adjacent cells increases

At large stains, deformation inhomogeneities

- tend to form a globular cell structure

- bands in tensile test

- shear bands in rolling (inclined 35o to rolling plane)

- orientation quite different from the matrix orientation.


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7.4 Recovery

A cold worked metal contains dense dislocations networks.

The recovery (stage of annealing) is

- concerned with the rearrangement of these dislocations toreduce lattice energy

- does not involve the migration of high angle grain boundaries

- the rearrangement of dislocation assist by thermal activation- the dislocation rearrange to form cell walls, fig. 10.15

(Smallman). This process is called Polygonization.Dislocations all of one sign align themselves into walls toform small-angle or sub-grain boundaries

- during deformation a region of the lattice is curved

- formation of excess edge

dislocations parallel to the axis

of bending

- during annealing - dislocations form sub-grain boundaryby align themselves into walls.

Polygonization - sub-boundary formation

- dislocation climb change arrangement from

horizontal to a vertical grouping.

- the process involves migration of vacancies to or

form edge dislocations.

- vacancies removes also the strain energy of

dislocation decreaseshardness decreases dislocations density decreases

electrical resistivity decrease because of vacancies decrease


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7.4 Recovery

Two dislocations with Burgers vectors b1 and b2 . The

interaction force

F = b2 = [(Gb1b2)/2rd(1-)]coscos2 7.11

rd - distance between the dislocations - angular coordinate, = 0o on the slip plane

- Poisson ratio

On the same slip plane:

-dislocation with the same sign repel (force is positive)

-dislocation with the opposite sign attract (force is negative)

Fig. 7.15

-If antiparallel dislocations on the same slip plane meet, theyrecombine and annihilate

-If antiparallel dislocations on the adjacent slip plane

vacancies form dislocation climbs

even if dislocations are several lattice apart, they can

annihilate by climb.

-the equilibrium arrangement of two parallel dislocations is anarrangement of one above the other, = 90o. e.q. 7.11, F=0, this arrangement is low-angle symmetrical tilt boundary

(LATB). The energy of each dislocation is substantiallydecreases.

If Zd number of dislocations per unit length in this arrangement,

The energy per unit area

LATB = Zd [{Gb2/4(1-)} ln(rd/2b) + EC] 7.12

EC - energy of dislocation core

= b/r d 7.13

1/rd = /b = Zd number of dislocations per unit

length in LATB

LATB = (K1 K2 ln ) 7.14

K1 = Ec/b - K2 ln 2 7.15

K2 = Gb/4 (1-) 7.16

Screw and mixed dislocations can also form low angleboundaries. They can form network of many low angle grainboundaries (sub boundaries). The energy is much smaller thanthe energy of the same dislocations distributed randomly in thecrystal.


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From eq. 7.12

Polygonization formed, LATB

Because LATB tend to combine in order to decrease rd-but this will cause to increase high angle grain boundaries

can be generated

Climb and cross slip control recovery

depend on the normalized stacking fault energy *SF are promoted by increasing stacking fault energy

materials with high *SF strong recovery

e.g. fcc (Al) and most of bcc metals, high stacking fault

tend to recovery.

but Ag, Cu (fcc) but have low stacking fault energy show

little tendency to recovery.

Dynamic recovery

- recovery process occur during deformation at elevated temp

- decrease work hardening rate

- dislocations form cell walls or sub grain boundaries (in thecase of strong recovery)

- extent of recovery depends on the type and prior arrangementof the dislocations

- in deformation inhomogeneities (kink bands in tensiledeformed single crystals) sub grains form during deformation, butin other area dislocations remain disordered.

Fig. 7.20: recovery does not need incubation time butrecrystallization does.

- the kinetics are different

- but the property changes are similar.


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Fig. 7.21.

Al hardness of deformed Al changes due to recovery

(stacking faults energy)

Cu hardness changes due to recrystallization.

After some annealing time recrystallization can occur then

hardness change linearly with the crystallized volume fraction.

In most case

- recovery competes with, but also promote recrystallization

- recovery leads to the formation of nuclei for primaryrecrystallzation.

In some materials under special circumstances

- recovery can be strong enough to suppress completely

recrystallization

7.5 Nucleation

In order to generate nucleus for recrystallization, threecriteria have to be met, fig. 7.22.

1. Thermodynamic instability

In order to initiate recrystallization the nucleus to be larger

than a critical size. The critical nucleus radius depends on thedriving force as in eq. 7.17.

The critical nucleus radius

rc = 2/p = 4 / Gb2 7.17

- Because of the low driving force for recrystallization

- The nucleation rate is too small to initiate recrystallization

Assume:

- pre-existent nucleus in deformed microstructure which is adislocation cell or sub grain.

- therefore recovery process is needed to activate adislocation cell nucleation for recrystallization.


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2. Mechanical instability

- inhomogeneous dislocation distribution

- a local imbalance of sub grain sizes developed during theincubation period by recovery process.

Both cause imbalance driving force causenucleus start to grow.

3. Kinetic instability

- The surface of nucleus (or the grain boundary) must bemobile to make nucleus grow and only high anglegrain boundaries have sufficient mobility. Thegeneration of a mobile high angle grain boundaryfrom a deformed microstructure is one of the mostdifficult steps of nucleation of recrystallization.

- the proposed mechanisms which are still in discuss:discontinuous sub grain growth, nucleation at prior

grain boundaries and deformation inhomogeneities.

Considering all 3 criteria

- nucleation is always connected to recovery process whichoccur in incubation period of recrystallization

- on the other hand recovery and recrystallization arecompeting processes because recovery decreasesthe driving force for recrystallization

- In materials with strong recovery high *SF like Al,discontinuous recrystallization can be delayed oreven suppressed.

7.6 Grain boundary migration

The grain boundary moves under the driving force p (J/m3).Atom detaches from the shrinking grain and attachesto the growing grain, thermal activated diffusion jumps.The free energy of each atom pb3 where b3 is theatomic volume.

v is the velocity of grain boundary, the displacement

per unit time , eq. 7.18.

All typical recrystallization temperature T > 0.4 Tm thesmall driving force for recrystallization

pb3


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The mobility of a grain boundary

- A small concentration of impurities strongly influences grainboundary mobility since impurities tend to segregate at thegrain boundary and exert a drag force on the boundary uponits motion high activation energy Qm.

- Depends on the orientation relationship between adjacentgrain.

m = m () 7.22

- rotation angle, - rotation axis

example: high mobility of Al - 40o < 1 1 1 >

Zn - 30o < 0 0 0 1>

Fe-3%Si 27o < 1 1 0>

- impurities tend to segregate at high angle grain boundary.Impurities will drag grain boundary and grain bowing becomeless mobile. Coincidence boundaries is highly orderedstructure have highly mobility because of its less prone tosegregation. With an increasing content of solute atoms, grainboundary migration is reduced.

7.7 Kinetics of primary recrystallization

The deformed metals containing high dislocation density isthermodynamically unstable at all temperatures.Recrystallization removes dislocations and can be consideredas a phase transformation without a true equilibriumtemperature. But the kinetics recrystallization are frequentlydescribed in terms of recrystallization temperature in order to

complete in a certain time (around 1 hour).Recrystallization

- is thermally activated

- depends on Boltzmann factor , expQ/kT

- small change of temperature cause large changes in time.

- But changes in time cause small change of recrystallization

temperature.

Primary recrytallization

The nucleation rate = (dZN/dt)/(1-x) 7.23The growth rate v = dR/dt 7.24

X = VRX/V - recrystallized volume fraction

t - annealing time

R - the radius of a grain

ZN - the number of observed nuclei per unit volume

- the number of nuclei generate per unit time and per

volume in the uncrystallized volumeAssume: nuclei is sphere and isotropic growth.


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Fig. 7.35 measured recrystallized volume fraction X as afunction of annealing time, t, for cold deformed aluminium.

X = 1 exp{-(t/tR)q} 7.25

tR - characteristic time for recrystallization

time necessary for recrystallization to go to completion

In order to obtain tR : definedX(tR) = 1 (1/e) = 0.63

The value of X can be 0.99.

If X close to 100% - deviation from eq. 7.25.

The value of X should be an intermediate one, in order toobtain sensible tR.

If tR, d, x, q known and v can be calcualted.

If grain is sphere (isotropic growth)

nucleation occurs homogeneously and v remain

constantX(t) = 1 - exp [ -(/3) v3t4] 7.26

tR = [(/3) v3]t1/4 7.27

d 2 v tR = 2(3v/ )1/4 7.28

d obtained from eq. 7.28 is only roughly estimated but itgives right order-of-magnitude even though deformation and

annealing conditions also can affect the value of d.

v = vo exp(-Qv/kT) 7.29

= o exp(Q/kT) 7.30

Qv and Q activation energies

vo and o independent of temperature

The recrystallized grain size depends on temperature.

d = (48vo/ o)1/4 exp (Q - Qv )/4kT 7.32

- an increase of the growth rate lead to a a larger grain size

- an increase of the nucleation rate at constant growth rateleads to finer grain size.

Influence: -primary recrystallization

- Degree of deformation

Degree of deformation increase

- and v increase

- affect more strongly than v

- the recrystallized grain size

- The smaller the grain size prior to deformation, the smallerthe recrystalized grains.

- Alloying elementsLow concentration of alloying element - and v are

reduced in the same extent.

d depends on ratio v/ , if v/ has a small changes, thechange of d is also small.

If v and vary in the same extent has little effect ond.


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7.10 Recrystallization in multiphase alloys

The presence of second phases has a substantially influence

on recrystallization.- coarse particles speed up the recrystallization process

- fine dispersion of particles strongly hinderedrecrystallization

Particles influence on the deformation structure, nucleationand grain boundary migration.During deformation:

The hard particles dislocations cannot cut but have to go

around

Nucleation and grain boundary migration

The large particles help the nucleation by particle-stimulatednucleation (PSN). Finely dispersed particles are less influencefor nucleation but they hinder dislocation motion (recovery) andgrain boundary migration (due to a back driving force on grainboundary).

When the grain boundary contacts with a particle, particlesurface replaces part of the grain boundary and the respectivegrain boundary is reduced.

When the grain boundary detaches from the particle, the partof grain boundary has to be regenerated.

The respective retarding force (Zener force) or the backdriving force on grain boundary

pR = -(3/2) f/Rp

Rp - the radius of the particles

f - the volume fraction of the particles

- the grain boundary energy

f/Rp - the degree of dispersion

Only the effective driving force peff= p + pR is available for

grain boundary migration, pR is negative. peff may be small.

In heterogeneous alloys with a high degree of dispersion

- the back driving force can become large

recrystallization is retarded.

- benefit for commercial application, the particles stabilizegrain size after primary recrystallization. Because Zener force islarge, grain growth become small or even suppressed

For example:f = 1% Zener force 0.1 MPa

rP = 1000 A The same order of magnitude or

= 0.6 J/m2 larger than the driving force for grain

growth.


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7.11 Normal grain growth

After completion primary recrystallization, the grains arestain-free. In equilibrium state, all grain have 6 corners. Allboundaries are straight, fig. 7.48.

In single phase metal:

- contact angle = 120o because surface tension of most

grain boundaries is similar.

In multiphase alloys:

- contact angle can be different from 120o because of

different surface tension at interface boundaries. In /brass at triple junction of one and two is 95o .

2 D

If a grain has a number of edges different from 6 for instant

5-sided grain, fig 7.48.1. To attain equilibrium at least one grain boundary iscurved. There is a force acting on the curve boundary towardthe center of curvature to minimize grain boundary area.

2. The angle must be different from 120o equilibrium

3. To establish equilibrium; the other grain boundaries haveto readjust by migration.

4. again cause grain boundary curvature and repeat 3.

Therefore, a stable equilibrium can never be reestablished.The grain with 6 sides straight line

The grain with more than 6 sides has concave curvature

large grain and become larger

The grain with less than 6 sides has convex curvature

small grain and become smaller and disappear

3 D

The contact angle at 4 grains meet is around 109o. Therefore,in 3 D granular structure is never possible to establishinterfacial equilibrium.

The average grain size during isothermal annealing can bepredicted

D Ktn

n = 0.5 - for high purity metals and for annealing

temperature close to Tmn = 0.2 0.3 - for commercially pure metals fig. 7.51.


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Grain growth in thin sheet

The grain growth will slow down if average grain size reach

the size of the smallest specimen dimension.If the grain boundary touches a free surface, a triple junction

between the grain boundary and 2 external crystal surface isgenerated.

The formation of a (thermal) groove along grain boundary,fig. 7.52. If the grain boundary migrate, this groove has to bedragged along or left behind.

The retarding force independent of the depth of the groove

pGR = - 2GB / h s

h specimen thickness s - surface energy

GB - grain boundary energy

This retarding force reduces the growth rate of grains incontact with the surface and grain growth cease at the grainsize ~ 2 times of the sheet thickness.

Material contains precipitates

- the continuous grain growth is limited by Zener drag.

Zener force, pZ = - 3 f/dpf - volume fraction of particle

dp diameter of particle

- a maximum grain size depends on the dispersion of thesecond phase.

- the grain growth terminates if the driving force and retardingforce are equal

2 / = 3 f/dp

- constant relating radius of curvature of grain boundariesand grain size.

The terminal grain sizedmax = (2/3) 1. dp/ f 7.42

dp increases with annealing temperature


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7.12 Discontinuous grain growth (Secondary

recrystallization)

Discontinuous grain growth most of the grains remainstable except for the growth of a few grains.

Occurs in 2 phase materials during annealing close tosolvus temperature.

- during annealing precipitates locally dissolve and initiategrain growth while the remaining grains remain stabilized bythe precipitates.

- the locally growing grain become very big. They canovercome Zener pinning (drag) and consume near by smallgrain pinned by Zener drag.

The critical grain size for a grain to grow discontinuously into

a matrix with precipitate

d > avg d/ (1 - avg d/dmax) 7.43

avg d - average grain size of the pinned grain structure

dmax - maximum grain size according to eq.7.42

Discontinuous grain growth occurs during annealingabove critical temperature. There are small amount of high

angle grain boundaries comparing to the low angle grainboundaries. HAGB - high mobility can grow and finallyconsume the low mobility grain boundaries.

7.13 Dynamic recrystallization

Dynamic recrystallization

- occur during plastic deformation at elevated temperature

T > 0.5Tm- evidence in flow curve, fig. 7.54, with a single peak or

oscillation of the flow curve

- is associated with a sudden loss of strength, fig. 7.55.- can occur during creep recognized by a sudden

increase of creep rate, fig. 7.56.

- the critical values of stress and strain at which dynamicrecrystallization is initiated depend on material anddeformation.

- many concentrated alloys and dispersion strengthenedmaterials do not recrystallization dynamically, fig. 7.57.

- the flow stress to set-off dynamic recrystallization

decreases with increasing deformation temperature, fig. 7.58.and decreasing strain rate, fig. 7.59.

Dynamic recrystallization

- is important for hot forming

- keeps the flow stress level low requires low deformationforces.

- increase ductility, fig. 7.60

- dynamic recrystallized grain size is directly related to flow

stress.- the flow stress increases, the grain size decrease, fig. 7.61.

- the recrystallized grain size can be adjusted by selectdeformation condition

- the recrystallized grain size does not depend on the initialgrain size, but strongly affected by the deformation schedule.


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Chapter 7 Recovery, Recrystallization, Grain Growth