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 imper- fections, 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 21 grande 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 VON ABGES~HRE~KT~~ BETA-~SSING

Die Festigkeit von abgeschrecktem CuZn wird durch Leerstellen erhiiht, die bei der raschen Ordnung- sumwandlung 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 Ver- setzungen 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 Beta- Messing 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

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 investigation. Ardley(4) suggested that Fig. 1 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.

* 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 210

BROWN: THE CAUSE OF THE STRENGTHESIKG IN QUEP;CHED BETA BRASS “11

DEGREE OF LONG RANGE ORDER PRIOR TO QUENCHING

‘“r-

0 I I I I I I I I 200 250 300 350 400 450 500 55(

OUENCHING TEMPERATURE ‘C

FIG. 1. Yield point immediately after quenching vs. quenching temperature.

OUENCHING TEMPERATURE ‘C

x 500

0 445

5 40-

-26 -25 -24 -23 -22 -21 -20 -19 -19 -17 -I

IN t -15,4DO/RT (HR - l/OK)

FIG. 2. Decay of the strength after quenching as a function of time and annealing temperature. Each curve corresponds to a different quenching temperature.

Cottrell(5) interpreted Fig. 1 differently in that he

attributed the maximum to an effect of the size of

anti-phase domains. According to Cottrell the

strengthening by anti-phase domains is given by

+ 1-q ( 1

where y is energy of the anti-phase domain boundary,

1 is the size of the anti-phase domains, a is a factor

depending on the shape of the anti-phase domains

and b is the interatomic distance. The Cottrell theory

predicts that the function of strength vs. anti-phase

domain size passes through a maximum at a domain

size of about 10 atomic distances; therefore, the

maximum strength in Fig. 1 was associated with this

critical domain size. If Cottrell’s theory were correct,

then a specimen quenched from above T, should

show a maximum in strength during the decay

process. However, the softening curves (Fig. 2)

continuously decrease with time. This behavior is in

contrast to Cu,Au whose strength goes through a

maximum during the annealing of a specimen

quenched from above T,. Additional data will be

given which shows that the Cottrell theory does not

fit beta brass.

More recently Clarebrough(6) detected an internal

friction peak in quenched CuZn. The kinetics of the

decay in the internal friction peak were identical with

the kinetics of decay in strength as determined by

Green and Brown. Clarebrough associated the

quenching effect with an excess of vacancies, but he

did not explain why a quenching temperature below

T, produces the maximum effect. The present

investigation suports Clarebrough’s view that

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

brass in that the ordinate could be yield point,

internal friction, density electrical resistivity or

concentration of vacancies.

212 ACTA METALLURGICA, VOL. 7, 1959

2. EXPERIMENTAL DATA

a. Zknsity measurements

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) Netallo- graphic 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 tempera- tures, 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

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.

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 I I 1

250 300 350 400 450 5

QUENCHING TEMPERATURE ‘C

FIG. 3. Change in density after complete decay &B a function of quenching temperature.

loo

WENCH SPECIMEN THICKNESS

+ WATER ,030” . ‘1 oloo”

SO_ 0 OIL X MOVING AIR A STILL AIR

60-

so , / I 3 1 , L

200 250 300 350 400 450 Tc 500

QUENCHING TEMPERATURE *C

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

13ROWN: THE CAUSE OF THE STRESGTHEKING IX QIJENCHED BETA BRASS 213

The shift in the maximum with cooling rate is

inconsistent with Cottrell’s view that the maximum

strength is associated with a critical domain size of

about 10 atomic distances. 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 produce this same critical domain size.

This conclusion is not consistent with the way in

which anti-phase domains grow.

c. Electrical resistivity

The electrical resistivity of quenched beta brass

was measured as a function of quenching temperature.

The resistivity curves have the same form as those

for strength vs. quenching temperature. Since

resistivity varies monatomically with anti-phase

domain size,(*) the maxima in Fig. 4 cannot be

attribut’ed to the critical size of anti-phase domain

demanded by the Cottrell theory.

3. ANALYSIS

The dat)a in Fig. 4 indicate that strength is not

simply a function of temperature prior to quenching,

but that something significant is taking place during

the quench. Quenching strains and ordinary vacancy

production are eliminated as primary factors, since

quenching strains continuously increase with

quenching temperature and the ordinary vacancy

concentration varies exponentially with temperature.

The strength could only be related to the ordering

that is known to take place during the quench. It

must be concluded that the greater the amount of ordering

that occurs during the quench, the greater is the resultant

increase in strength. (Top curve in Fig. 4). However,

some of the generated strength may decay during the

quench.

After quenching to room temperature all specimens

have essentially complete long range order.(1,2)

Therefore, the less a specimen is ordered prior to

quenching, the stronger it is after quenching provided

no decay occurs during the quenching. However, the

rate of decay as described 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 this treatment. Although specimens

quenched from the critical temperature 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 slowly.

Specimens quenched from lower temperatures increase

in strength even less and the retained streugth is

lower even though their rate of decay is very slow.

It is now possible to reproduce Fig. 1 by a calculation

based on the following assumpt.ions:

(1) Strength is proportional t’o the amount of

ordering during quench.

(2) At all temperature the strength decays in

accordance with the data in Fig. 2.

The following differential equation describes the

change in strength during the quench:

(1)

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

and t is the time. ailr/aS is constant, and is that part

of the equation associated with strengthening.

aiN/& is the rate of decay. The empirical equation(3)

(Fig. 2) describing the rate of decay is given by

d(ln S)/dt = -5300 exp [5.6( I- X,,) ~ 15,40O/RT]

(set-i) (2)

where S, is the equilibrium degree of long range order

at the quenching temperature T,, and T is the

temperature at any time t. The relationship between time and temperature is

obtained from heat transfer considerations. Assuming

Newton’s Law of cooling, the following relationship

is obtained for water quenching to 300°K.

dT/dt = -6K(T - 3OO)lpCD (3)

where K is the heat transfer coefficient, p is density,

C is specific heat, and D is both height and diameter

of the specimen. Combining equations (l), (2) and (3)

dW = dS + (5300 exp [5.6(1 - 8,) - 15,40O/RT])/

[SK( T - 300)/pCD] (4)

Since the specimen is at equilibrium prior to quenching,

the initial conditions are

N =0 at t = 0 and T = T,

The following physical constants were used to solve

equation (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 for different quenching rates.

Some curves show a maximum near the critical

temperature because order changes very rapidly in

214 ACTA IMETALLURGICA, VOL. 7, 1959

400 450 500 550 600 650 700 7so

INSTANTANEOUS TEMPERATURE l K

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 tempera- ture. 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 activa- tion 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 OF THE STRENGTHENING IN QUENCHED BETA BRASS 215

. FAST OUENCH

p 0.6 - x SLOWER QUENCH

f g 0.5 - I- O = 0.4 -

: * 0.3 -

Y co.2 - 4 J

g 0.1 -

I I

200 300 400 500

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 during the decay process. The

internal friction peak observed by Clarebrough was

explained by an excess of vacancies. Anti-phase

domain boundaries do not seem to be primarily

responsible for the strengthening because Cottrell’s

theory indicates that a critical intermediate domain

size has a maximum strength and it is difficult to

imagine that this critical size is shifted to lower

quenching temperatures by decreasing the quenching

rate. The variation in electrical resistivity with

quenching temperature is not consistent with anti-

phase domains.

There is a possible mechanism whereby vacanices

could be generated by ordering. It is a geometric

necessity that anti-phase domain boundaries terminate

on a dislocation.(g) Thus, dislocation pairs of like

sign are jointed by an anti-phase boundary. As the

degree of order increases the dislocations come

closer together so as to minimize the energy of

disorder in the boundary. The interaction is so

strong that at complete order the dislocations should

be about fifteen atom distances apart.lg) Thus,

ordering would cause dislocation movement which

could produce vacancies both by dislocations cutting

dislocations and by climb. The dislocations are more

uniformly distributed in the disordered than in the

ordered state, and this may explain the variation in

rate of decay with initial state of order (Fig. 2) if

dislocations act as sinks during the decay process.

Thus, the strength generated would be associated

with the jogs formed on dislocations which had

moved during the ordering process, and the decay

process would be the annihilation of jogs by the excess

vacancies produced during the rapid ordering.

The author would like to thank John D. Corrie for

making the density measurements.

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

&%TO-&-UCtU’W. Amercian Society for Metals, Cleveland (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).