The cause of the strengthening in quenched beta brass

THE CAUSE

OF THE

STRENGTHENING

IN QUENCHED

BETA

BRASS*

N. BROWN? Quenched CuZn is strengthened by vacancties which are generated by the rapid disorder-to-order transformation. The quenching temperature which produces maximum strength is a function of quenching rate. The strength immediately after quenching depends on the number of trapped imperfections, where the number is proportional to the amount of ordering during the quench minus the amount of decay during the quench. The vacancies probably originate from the strong int5raction between dislocations in the presence of long range order. Density change, effect of cooling rate, activation energy for decay, electrical resistivity and Clarebrough’s work on internal friction support the idea that the strength of quenched beta brass is associated with vacancies rather than anti-phase domains. LA

CAUSE

DU

DURCISSEMENT

DANS

LE

LAITON

/?I TREMPE

Le laiton /I trempe est rendu plus resistant par les lacunes qui sont creees lors de la transformation rapide ordre-desordre. La temperature de trempa qui produit le maximum de resistance est une fonction de la vitesse de trempe. La r&istance directement apres trempe depend du nombre ~imporf~tions pieg&es. Ce nombre est proportionnel au degre d’ordre atteint au cows de la trempe diminue de l’effet de trempe. Les lacunes ont oomme origine probable la forte interaction entre les dislocations en presence d’ordre 21grande distance. La variation do densite, l’effet de la vitesse de refroidissement, l’energie d’activation du processus, la resistivite Blectsique ainsi que le travail de Clarebrough sur la friction interne sont en accord avec l’idee que la resistance du &ton /l trempi: ext associee aux lacunes plutot qu’aux domaines antiphases. DIE

URSACHE

DES

FESTIGKEITSANST~GS BETA-~SSING

VON

ABGES~HRE~KT~~

Die Festigkeit von abgeschrecktem CuZn wird durch Leerstellen erhiiht, die bei der raschen Ordnungsumwandlung erzeugt werden. Die Abschrecktemperatur, die sn der ho&&en Festigkeit fiihrt, ist eine Funktion der Abschreckgeschwindigkeit. Die unmittelbar nach dem Abschrecken erreichte Festigkeit hilngt von der Zahl der festgehaltenen Fehlstellen ab, diese Zahl ist proportional dem Betrag der Ordnungseinstellnng wiihrend des Abschreckens minus dem wahrend des Abschreckens ausgeheilten Betrag. Die Leerstellen entstehen wahrscheinlich durch die stacke Wechselwirkung zwisohen Versetzungen im ferngcordneten Zustand. Die Dichtelinderung, der EinAuss der Abkiihlgeschwindigkeit, die Aktivierungsenergie des Ausheilens, der elektrisehe Wider-stand und die Befunde von Clarebrough iiber die innere Reibung ~~rst~tzen die Annahme, dass die Festigkeit von ab~schreck~m BetaMessing mit Leersteilen und nicht mit Antiph~en-Dom~nen verkntipft ist.

1. INTRODUCTION

The effects of quenching beta brass have been studied by many investigators. Smith(l) studied the effect of quenching on electrical resistivity and hardness, and concluded that beta brass always has essentially complete long range order after quenching and that the effects of quenching are associated with the size of anti-phase domains. Chipman and Warren(s) measured the superlattice lines of quenched and slowly cooled beta brass, and concluded that the quenched state had the same amount of long range order as the equi~brium state. Thus, it is generally concluded that beta brass orders so rapidly that even * This work was supported by the Office of Ordnance Research, United States Army, and the Atomic Energy Commission. Received April 14, 1958. t School of Metallurgical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania. ACTA METALLURGICA,

VOL. 7, MARCH

I959

a water quench cannot freeze-in an appreciable amount of disorder. Green and Brawn(3) further investigated the effect of quenching beta brass (Fig. 1) and also studied the kinetics of the decay process which occurs after quenching (Fig, 2). The result of Green and Brown (Fig. 1) has since received two different interpretations both of which are believed to be wrong in the light of the present Ardley(4) suggested that Fig. 1 investigation. represents strength as a function of various amounts long range order. In other words, Ardley stated that the quenched state has the degree of long range order which corresponds to its quenching temperature. However, Smith,(i) and Chipman and Warren(2) have shown that water quenching does not freeze-in an appreciable amount of disorder; therefore, Ardley’s interpretation is wrong.

210

BROWN:

THE

CAUSE

OF

THE

STRENGTHESIKG

DEGREE

OF

LONG

RANGE

IN

ORDER

QUEP;CHED

PRIOR

BETA

TO

QUENCHING

I 450

500

“11

BRASS

‘“r-

I 200

0

I 250

I

I 300 OUENCHING

FIG. 1. Yield point immediately

I 400

350 TEMPERATURE

I

I 55(

‘C

after quenching vs. quenching temperature.

OUENCHING TEMPERATURE x

500

0

445

‘C

5 40-

-26

-25

-24

-23 IN

-22 t

-21

-15,4DO/RT

-20 (HR

-

-19

-19

-17

-I

l/OK)

FIG. 2. Decay of the strength after quenching as a function of time and annealing temperature.

Cottrell(5) interpreted attributed

Fig. 1 differently

the maximum

anti-phase

domains.

strengthening

Each curve corresponds to a different quenching temperature.

in that he

to an effect of the size of According

by anti-phase

to

Cottrell

the

domains is given by

contrast

to Cu,Au

maximum quenched

whose

during from

the

above

strength

goes through

annealing T,.

of

a

Additional

a

specimen

data will be

given which shows that the Cottrell theory does not fit beta brass.

+

1-q (

where y is energy of the anti-phase 1 is the size of the anti-phase depending

domain boundary,

domains,

distance.

that the function

a is a factor

domain size passes through

domains

The Cottrell theory

of strength a maximum

Clarebrough(6)

friction peak in quenched

on the shape of the anti-phase

and b is the interatomic predicts

More recently

1

vs. anti-phase at a domain

size of about 10 atomic distances; therefore, the maximum strength in Fig. 1 was associated with this

detected

CuZn.

an internal

The kinetics of the

decay in the internal friction peak were identical with the kinetics Green

of decay

and

quenching

Brown.

in strength

associated

effect with an excess of vacancies,

did not explain why a quenching T,

as determined

Clarebrough

produces

investigation

the

maximum

suports

temperature

effect.

The

Clarebrough’s

by the

but he below present

view

that

critical domain size. If Cottrell’s theory were correct, then a specimen quenched from above T, should

quenching beta brass produces an excess of vacancies beyond the usual type of vacancy production. It turns out that Fig, 1 is a general type curve for beta

show a maximum in strength during the decay However, the softening curves (Fig. 2) process. continuously decrease with time. This behavior is in

internal friction, density concentration of vacancies.

brass

in that

the

ordinate

could electrical

be

yield

point,

resistivity

or

ACTA

212 2. EXPERIMENTAL

METALLURGICA,

The CuZn contained 51.4 wt.% Cu. Grain size was 1-Z mm and the sample was from the same heat of metal as used in the prior investigation.(3) Netallographic examinations showed the alloy to be single phase at all temperatures. Density measurements were made by the displacement method(‘) which detects changes in density of &0.0002 g/cm3. These measurements were carried out on 318 in. diameter specimens water quenohed from different temperatures, and were repeated on the same specimens after a low temperature anneal for a time which completed the decay. The change in density during decay was plotted against quenching temperature (Fig. 3). A maximum occurs at about 450” and the curve has the same general shape as that in Fig. 1. Thus, the strengthening is associated with a density change. This change cannot be attributed to residual strains which

I

The rate of decay as measured isothermally (Fig. 2) suggested that an appreciable amount of decay could occur during the water quenching of the 318 in. specimens on which Fig. 1 is based. In order to minimize the amount of deeay which might occur during the quench, the quen~h~g rate was increased by using 0.03 in. thick specimens. With the thin specimen the maximum strength is produced by quenching from the critical temperature. Specimens were quenched at slower cooling rates. Slower cooling not only reduces the maximum strength attainable, but also shifts the quenching temperature which produces the maximum (Fig. 4).

I

I 300

1

I

350 QUENCHING

7, 1959

are expected to behave monotonically with quenching temperature. If the density change were associated with the disappearance of anti-phase domains, then it is expected that the change would vary inversely with the size of those domains.

DATA

a. Zknsity measurements

250

VOL.

400 TEMPERATURE

450

5

‘C

3. Change in density after complete decay &Ba function of quenching temperature.

FIG. loo

WENCH

SO_

+ .

WATER ‘1

0 X A

OIL MOVING AIR STILL AIR

SPECIMEN

THICKNESS

,030” oloo”

60-

so

, 200

250

/

I

300

350

QUENCHING

1

3

400 TEMPERATURE

450

,

Tc

L

500

*C

Frc. 4. Effect of quenching rate on the yield point immediately after quenching.

THE

13ROWN:

The

shift

OF

in the maximum

inconsistent strength

CAUSE

with Cottrell’s

is associated

THE

with

STRESGTHEKING

cooling

rate is

view that the maximum

with a critical domain

about 10 atomic distances.

size of

Such an interpretation

of

Fig. 4 leads to the conclusion that water quenching from above 450°C and cooling in still air from about 340°C both This

produce

conclusion

this same critical

is not

which anti-phase

consistent

domain

size.

with the way

in

IX

QIJENCHED

BETA

213

BRASS

It is now possible to reproduce Fig. 1 by a calculation based on the following (1) Strength

assumpt.ions:

is proportional

ordering during quench. (2) At all temperature

t’o the

the

strength

accordance with the data in Fig. 2. The following differential equation

amount

of

decays

in

describes

the

change in strength during the quench:

domains grow.

(1)

c. Electrical resistivity The

electrical

resistivity

of quenched

beta

brass

was measured as a function of quenching temperature. The resistivity for

curves have the same form as those

strength

resistivity domain

vs.

quenching

varies size,(*)

temperature.

monatomically

the

maxima

with

in Fig.

attribut’ed

to the critical

demanded

by the Cottrell theory.

Since

anti-phase

4 cannot

size of anti-phase

be

domain

strains

prior to quenching,

is taking place during

as primary

continuously

temperature

and

varies exponentially

The strength

could

only

factors,

ordinary

at the

quenching

temperature

exp [5.6( I-

vacancy

to the ordering It

(Top curve in Fig. 4).

However,

After quenching to room temperature long

all specimens

range

order.(1,2)

Therefore,

the less a specimen

is ordered

quenching,

the stronger it is after quenching provided

no decay occurs during the quenching. rate of decay as described

prior

However,

between

by Fig. 2 and the cooling

rate, as determined by quenching medium and size of specimen, will affect the amount of decay that occurs

during

quenched

this treatment.

from

the critical

Although

temperature

specimens and above

generate the highest strength, this strength ma,y not be the maximum

because decay is large.

A specimen

quenched from an intermediate temperature will generate less strength in comparison, but will retain maximum

strength

because

it decays

more

Specimens quenched from lower temperatures

slowly. increase

in strength even less and the retained streugth is lower even though their rate of decay is very slow.

and

T

is the

time and temperature

is

Assuming

the following

relationship

for water quenching to 300°K. dT/dt = -6K(T

-

3OO)lpCD

where K is the heat transfer coefficient,

(3)

p is density,

C is specific heat, and D is both height and diameter of the specimen.

Combining

equations

dW = dS + (5300 exp [5.6(1 -

(l), (2) and (3)

8,) -

[SK( T -

15,40O/RT])/

300)/pCD]

(4)

Since the specimen is at equilibrium prior to quenching, the initial conditions are N =0

to the

T,,

at any time t.

some of the generated strength may decay during the quench.

(2)

degree of long range order

Law of cooling,

with temperature.

be related

complete

X,,) ~ 15,40O/RT]

temperature

The relationship

is obtained

to take place during the quench.

essentially

equation(3)

obtained from heat transfer considerations. Newton’s

that occurs during the quench, the greater is the resultant

have

The empirical

the rate of decay is given by

d(ln S)/dt = -5300

with

must be concluded that the greater the amount of ordering increase in strength.

(Fig. 2) describing

since

increase

the

concentration that is known

is not

strains and ordinary vacancy

are eliminated

quenching quenching

significant

Quenching

production

that strength

of temperature

but that something

aiN/& is the rate of decay.

where S, is the equilibrium

The dat)a in Fig. 4 indicate

the quench.

and t is the time. ailr/aS is constant, and is that part of the equation associated with strengthening.

(set-i)

3. ANALYSIS

simply a function

where AT is strength, X is degree of long range order,

The following equation

at

t = 0

physical

and

constants

T = T, were used to solve

(4)

K = 0.08 and 0.16 cal cm-2 see-1 “C-1 C = 0.09 cal g-l “C-l p = 8.3 g cm-3 D = 0.94 cm T = 738°C (critical temperature) The relationship between S, and T, was obtained from X-ray data.t2) A numerical method of solution was used.

The results of the calculation

are given in

Figs. 5 and 6, which show the strength that existed during the quench Some curves show temperature

because

for different a maximum order changes

quenching rates. near the critical very

rapidly

in

214

ACTA

400

450

500

IMETALLURGICA,

550

INSTANTANEOUS

VOL.

7, 1959

650

600 TEMPERATURE

700

7so

lK

FIU. 5. The strength that existed during the quench W, a function of the specimen temperature. The intersection of each curve with the abscissa determines the quenching temperature.

0 INSTANTANEOUS

TEMPERATURE

*K

FIG. 6. Same as Fig. 5 for a different quenching rate.

that region. The intersection of the curves with the ordinate gives the strength retained at room temperature. In Fig. 7 the strength retained after quenching is plotted against quenching temperature. The two quen~h~g rates were chosen so as to encompass the uncertainty in the heat transfer coefficient. The curve in Fig. 7 is a calculated version of Fig. 1. The agreement between the calcuated and experimental curves is surprisingly good. The assumptions on which the calculation was made appear to be justified in the light of the variety of independent data used to make the calculation.

4. DISCUSSION

The analysis and experiments substantiate the argument that rapid ordering, which occurs by quenching, strengthens beta brass. It refutes the viewpoint that the as-quenched strength is only a function of the initial state. The experimental evidence does not indicate that the size of anti-phase domains is the primary cause of strengthening. Vacancies are probably involved because the activation energy for the decay process is 15,400 cal/mole(3*s) compared to about 36,000 oalfmole for self-diffusion in the ordered region,@) and because there is an

BROWN:

THE

CAUSE

0.6-

p

OF

.

FAST

x

SLOWER

THE

STRENGTHENING

IN

QUENCHED

BETA

215

BRASS

OUENCH QUENCH

f g 0.5 IO = 0.4 : *

0.3

-

Y co.2 4 J g

-

0.1 I

I 200

300

500

400

OUENCHING

TEMPERATURE

OC

FIG. 7. Calculated strength retained after quenching as a function of quenching temperature. The curves are derived from Figs. 5 and 6 by plotting the intersection with ordinate vs. the intersection with abscissa.

increase

in density

internal

friction

explained domain

by

during

an excess

boundaries

responsible theory

of

do

not

indicates that

quenching

process.

by Clarebrough

vacancies. seem

for the strengthening

to

this

strength

critical

temperatures

The

uniformly

was

ordered state, and this may explain the variation

Anti-phase be

primarily

dislocations

Cottrell’s

Thus,

domain

and it is difficult to

size is shifted

by decreasing

to lower

the quenching

The variation in electrical resistivity with rate. quenching temperature is not consistent with antiphase domains. There is a possible could

be generated

sign are jointed degree closer

of

mechanism by ordering.

together

disorder

Thus,

whereby

increases so

in the

as to

about

ordering

fifteen would

could produce dislocations

vacancies

The

As the

dislocations the

distances

dislocation

interaction

of

is so should

apart.lg)

Thus,

movement

which

both by dislocations

and by climb.

come

energy

order the dislocations

atom cause

the

pairs of like

boundary.

minimize

boundary.

strong that at complete be

with initial

the

jogs

during

generated

formed

on

the ordering

the decay would

process,

produced

process.

be associated

dislocations

process would be the annihilation vacancies

in

state of order (Fig. 2) if

act as sinks during

the strength

than in the

which

had

and the decay

of jogs by the excess

during the rapid ordering.

The author would like to thank John D. Corrie for

vacanices

It is a geometric

dislocation

by an anti-phase

order

with moved

in the disordered

making the density measurements.

necessity that anti-phase domain boundaries terminate on a dislocation.(g)

distributed

rate of decay

because

that a critical intermediate

size has a maximum imagine

the decay

peak observed

The dislocations

cutting are more

REFERENCES 1. C. S. SMITH, Tmns Amer. Imt. Nin. (Metdl.) Engrs. 152, 144 (1943). 2. D. CHIPMAN and C.WARREN, J. AppZ. Phys. 21, 696 (1950). 3. H. GREEN and N. BROWN, Trctns. Amer. Inst. Min (Met&Z.) Engrs. 197,1240 (1953). 4. G. W. ARDLEY, Actn Met. 3, 525 (1955). 5. A. H. COTTRELL, Monograph: Relations of Properties to Amercian Society for Metals, Cleveland &%TO-&-UCtU’W. (1954). 6. L. M. CLAREBROUGH, Acta Met. 5,413 (1957). 7. J. D. CORRIE, M.S. Thesis. University of Pennsylvania (1958). 8. A. B. KUPET, D. LAZARUS, J. R. MANNING and C. T. TOMIZUKA, Ph,ys. Rev. 104, 1536 (1956). 9. K. BROWN and M. HERMAN, !l’mns Amer. Inst. Min. (Metall.) Engrs. 206, 1353 (1956).