Strengthening mechanisms in internally oxidized silver-based alloy single crystals

STRENGTHENING

MECHANISMS

IN

ALLOY

INTERNALLY

SINGLE and

S. MAHAJANtS

OXIDIZED

SILVER-BASED

CRYSTALS* L.

HIMMELts

The internally oxidized Ag-based alloy single crystals containing nearly similar atomic fractions of Mg and Cd differ markedly in their strength values. It is inferred that, besides the dispersion being on a finer scale in the Ag-Mg alloy (alloy A), MgO particles must exist in the constrained state and these internal strain fields could contribute substantially to the observed strengthening. However in the Ag-Cd alloy (alloy B) the constrained strain is high enough to relax itself by the nucleation of dislocations around the particles. The yield stress and the Cottrcll-Stokes ratio in the internally oxidized alloy A crystals are very temperature sensitive; arguments for rationalizing these observations have been developed. In the internally oxidized alloy B crystals, yielding is controlled by the Orowan mechanism and the variations in the Cottrel-Stokes ratio with temperature are similar to those in pure Ag. MECANISMES

DE

CONSOLIDATION

D’ARGENT

DANS

AYANT

DES

SUB1

UNE

MONOCRISTAUX OXYDATION

D’ALLIAGES

A

BASE

INTERNE

Les monooristaux d’alliages a base d’argent ayant subi une oxydation interne, dont les concentrations en atomes de Mg et Cd sont presque semblables, presentent des differeneces tres nettes quant aux valeurs de leur resistance meoanique. Les auteurs supposent que, la dispersion &ant d’ailleurs faible dans l’alliage Ag-Mg (alliage A), des particules de MgO doivent exister a l’etat contraint, et ces champs de deformation interne pourraient contribuer de fapon non negligeable Q la consolidation observee. Cependant, dans l’alliage Ag-Cd (alliage B), la deformation due L ces contraintes est suffisamment importante pour produire une relaxation par nucleation de dislocations autour des partioules. La contrainte 8, la limite elastique et le rapport de Cottrel-Stokes dans les cristaux de l’alliage A ayant les auteurs exposent des arguments subi une oxydation interne sont t&s sensibles fi la temperature; Dans les cristaux de l’alliage B ayant subi une oxydation interne, la limite interpretant ces observations. Blastique est oontrBlCe par le mecanisme d’orowan, et les variations avec la temperature du rapport de Cottrell-Stokes sont analogues a celles se produisant dans l’argent pur. VERFESTIGUNGSMECHANISMEN

NACH

EINER

INNERER

OXIDATION

SILBERREICHEN

VON

EINKRISTALLEN

LEGIERUNG

Silberreiche Legierungseinkristalle mit nahezu gleichen Anteilen an Mg oder Cd zeigen nach innerer Oxidation stark unterschiedliche Festigkeitswgrte. Wir kommen zu dem SohluB, daR in der Ag-MgLegierung (Legierung A) eine feinere Dispersion vorliegt, dad aber aul3erdem im verspannten Zustand MgO-Teilchen vorhanden sein miissen, deren inneres Spannungsfeld betriichtlich zur beobachteten Verfestigung beitragen kann. Die von der Verspannung herriihrende Dehnung ist in der Ag-Cd-Legierung (Legierung B) jedoch grol3 genug, urn durch die Bildung von Versetzungsringen urn die Teilchen eine Relaxation herbeizuftihren. Die FlieDspannung und das Cottrell-Stokes-Verhaltnis sind im innerlich oxidierten Kristall A stark temperaturabhangig. Es werden Argumente fur dieses Verhalten gegeben. In innerlich oxidierten BKristallen ist das FlieDen durch den Orowan-Mechanismus kontrolliert und die Temperaturabhangigkeit des Cottrell-Stokes-Verhiiltnisses ist iihnlioh wie in reinem Silber. 1. INTRODUCTION

After

internal

containing

oxidation

nearly

the

identical

study silver-based

atomic

fractions

magnesium (alloy A) and cadmium (alloy markedly in their hardness values; the differences variation

have

been

rationalized

alloys

in terms

in sizes of the dispersed phases.

of

B) differ observed of the

It has been

was initiated

characteristics after the

internal present

to investigate

of single crystals oxidation; paper.

stress (measured

these results constitute It is observed that the yield

at O-1 per cent offset) and also the

flow stress of internally strong

the deformation

of alloys A and B

temperature

oxidized

A crystals exhibit a

dependence,

whereas

suggested that because the binding between magnesium

stress in the dispersion

and oxygen

is insensitive to the changes in temperature

to oxygen, second

is much stronger than that of cadmium under identical

phase particles

oxidation

conditions

the

in alloy A should

be smaller

in size than in alloy B and consequently

should be

distributed

on a finer scale.(r)

to verify this hypothesis ture

dependence

METALLURGICA,

VOL.

with the Orowan mechanism

the yield

B crystals and this is

of yielding.(s)

These results imply that there is an inherent difference between the characteristics

in the

20,

2. EXPERIMENTAL

the temperatwo

alloys,

a

* Received December 29, 1971; revised April 13, 1972. t Department of Materials Science and Engineering and the Inorganic Materials Research Division, Lawrence Radiation Laboratory, University of California, Berkeley, California. 3 Now at: BellLaboratories, MurrayHill, NewJersey 07974. Department of Chemical Engineering and $ Now at: Material Sciences, Wayne State University, Detroit, Michigan 48202. ACTA

alloy

of the two dispersions.

As it should be possible

by examining

of yielding

consistent

hardened

NOVEMBER

1972

DETAILS

The details of alloy preparation, crystal growth, homogenization anneal and internal oxidation procedure are given in the preceding paper, subsequently referred to as part I .(3) The only differences are that in the present investigation the crystals were oriented with their [OOl] direction parallel to the tensile axis and all of them were oxidized for 24 hr. 1319

1320

ACTA

METALLURGICA,

The tensile tests which were carried out were of two types: (i) determination of yield stresses at various temperatures; and (ii) measurements of the reversible changes in flow stress with temperature.‘4) All tests were performed with a standard Instron testing machine; an auxiliary unit was incorporated into the load cell circuit which allowed the zero to be suppressed in ten equal steps. Using zero suppression and operating the machine at its highest sensitivity, it was possible to obtain a stress sensitivity of ~0.1 per cent over the entire load range employed. Tests were carried out by immersing the crystals in the following fixed temperature baths: (i) liquid nitrogen, 77’K; (ii) n-pentane, 141°K; (iii) dry iceacetone mixture, 194°K; (iv) ice and water, 273°K; (v) boiling water, 373°K. The reversible changes in flow stress with temperature were measured by deforming the crystals alternately at two different temperatures at a tensile strain-rate of 2.2 x low5 set-l. The usual procedure in carrying out this type of test was to deform the crystal first at one temperature, partially relax the load to maintain the alignment, change to another bath, and then to continue deformation at the new After changing baths a standard temperature. period of 5 min was allowed for equilibrium to be reestablished before resuming the test. Since the total elongation obtainable at 273°K was ~10 per cent or less at the lowest temperature, the strain increment between the temperature changes was usually held to ~0.5 per cent. It almost always proved feasible to carry out at least five or six complete reversals in temperature, by which time a constant flow stress ratio had generally been obtained. In all cases cycling was continued until it became apparent that the maximum load had been reached and that fracture of the specimen was imminent. In order to check the validity of the aforementioned experimental technique, a few tests were carried out on pure silver single crystals. The observed values of the flow stress ratios were in fairly good agreement with those of Basinski.c5) Some of the crystals were chemically analyzed and were found to contain on the average NO.79 at. ‘A Mg and ~0.83 at. o/0 Cd. Assuming that these solute elements are completely oxidized during the internal oxidation treatment, the volume fractions of MgO and Cd0 produced are estimated to be NO.92 x lop2 and 1.38 x 10e2, respectively. 3. RESULTS 3.1 Stress-strain

behaviour

The tensile stress-strain curves of the internally oxidized crystals of alloys A and B, obtained at

VOL.

20,

1972

Tensile FIG. 1. Stress-strain

strain.

%

curve of internally oxidized alloy A crystal at 273°K.

273”K, are reproduced in Figs. 1 and 2, respectively. It is apparent that (i) initially the work hardening rates (0) are very high in both alloys, but 0, is considerably higher than t!JBand (ii) alloys A and B differ markedly in their hardening responses. Considering that the tensile yield stress (measured at 0.1 per cent offset) of Ag crystals of identical orientation, saturated with oxygen at 873°K for 24 hr, is ~1.2 kg/mm2, it is inferred that iniernal oxidation causes substantial hardening in both alloys. 3.2 Temperature-dependence

of tensile yield stress

The observed variations in the ratios of tensile yield stress (o,-measured at 0.1 per cent offset)

22’5(

I IO

I 5

12.5 0

Tensile FIG. 2. Stress-strain

strain,

%

curve of internally oxidized alloy I3 crystal at 273’K.

&a.

3. The variation of (a,/G) with hmpereture in in&rnaily oxidized alloy A crystals.

and shear modulus (G) with temperature in the iuternally oxidized alloys A and B crystals are depicted in Figs. 3 and 4, respectively; G’s at va.rious temperatures were computed From the rest&s of ~eigl~bours and Alem. It is apparent that in alloy A (o;/G) is highly temperature sensitive, whereas in alloy B the ratio, allowing for the experimental scatt.er, does not vary with temperature. 3.3 Reversildc!changes in ~&I’LL, stresLu The ratios of the flow stresses (cF), obtained on cycling from a high temperature to a low temperat~e and after correcting for the temperature dependence of the shear modulus, are plotted as a function of temperatax in Figs. 5 and 6; superimposed on these curves are the ratios for Ag single crystals obtained by Basinski. c5) It is emphasized that each ratio is an average of at least five to six values and the scatter between each value was generally Iess than 10 per cent. From these results it is inferred that in alloy B the flow stress ratios are very sensitive to the tzemperature changes and they differ markedly from those for pure Ag, whereas in alloy B the ratios essentially foliow the pattern of pure Ag.

6 50

I

1

100

150

I zoo

Temperature, Fm.

G

I

I

I

250

300

350

OK

4. The variation of (oJG) with temperature in internally oxidized alloy 23 orystals.

Temperature,

'K

FIG. 5. The variations in the Cottroll-Stokes ratio, after correcting the changes in shear modulus, with temperature ‘in internally oxidized alloy A crystals

After internal oxidation of alloy A the second phase particles were discernible only at very high magnifications (an example is shown in part I)! and ~50 A was estimated to be an upper limit for the particle diameter. These areas were also examined under two-beam dynamical diffraction condition ; in the presence of a very large number of particles it was very difficult to establish unequivocally the existence of the black-rehire images, characteristic of the smalf defect clusters.t7’ In the internally oxidized alloy B crystals Cd0 particles were identified by electron diffraction” The micrographs, using the Cd0 reflections, were obtained from the surfaee region as well as from the interior of the specimen. Prom these micrographs tlhe variations in the particle diameter were investaigated and the results are illustrated in Fig. 7 ; the average particle diameters in the surface region and in the interior are ~150 and -275 if, respectively, Furthermore, the interface dislocations appeared to be

1

400

FIG;. 6. The variations in the Cc&bell-Stokes ratio, after correcting for the changes in shear modulus, with temperature in internally oxidized alloy B crystals.

1322

ACTA

n

METALLURGICA,

(a)

150

200

250

diameter,

20,

1972

It is therefore

very likely that the internal

strain fields are present in alloy A crystals. Assuming

that in alloy A crystals c is made up of

three components: (i) oLVf-the flow stress of Ag single crystals of identical orientation saturated with

IL

_ Particle

to occur.

1

,

VOL.

oxygen needed

at 873°K for 24 hr; (ii) o,,-the stress to move the dislocations in the presence of

internal

strain

fields;

quired to overcome the dislocations

300

and (iii) cr,,--the

and the particles

from that of the matrix.

#

stress re-

the repulsive interaction having

between

G different

Taking the particle radius

(R) = 25 A, volume fraction of the dispersed phase (f) = 9.2 x lop3 and using the results of Gerold and Haberkorn(li) and Fleischer,(i2) it is estimated that cAE and cat should be ~23.6 respectively.

and 4.65 kg/mms,

Since the observed

cJV1(at 0.1 per cent

offset) at 273°K is 1.2 kg/mm2, ol/ is calculated -29.45

to be

kg/mms.

Considering that the observed value is 33.4 kg/mms, the fit between the estimated 2

-100

200

150

250

Particle

350

300

diameter,

and observed

400

FIG. 7. Histograms illustrating the size distribution of the particles in the internally oxidized alloy B crystal: (a) supface; and (b) interior regions. A thickness of 1500 A was used in computing the number of patricles/cn?.

associated vicinity

but in no case were

with the particles,

prismatically

punched

out

loops

observed

in

the

of the particles. 4. DISCUSSION

Assuming

the particles

to be spherical

ined strain (E) in the inclusions the following

the constra-

can be estimated

from

relation given by Mott and Nabarro :(*) 3K, c =

3K,

+ 4G,

16

Substituting

the

G,

to be 15.5 x 10n dyn cm-2. K, = 15.5 x 10”

= 3.38 x loll

dyn

cm-2

and

dyn

cm-2,

6 = 3 x 1O-2

in the above

relation, it is estimated that at 273°K cMso should be ~2.3 x 10-2. The data on the elastic properties

of Cd0

are not available,

but using the

same values as for MgO &odo is estimated to be ~10.8 x lop2 at 273°K. Combining these evaluations with

the conclusions

of Brown

and

of linear

from their respective

coefficients

expansion. Based on the available data it is estimated that when the temperature is lowered from 273 to 77”K, the lattice parameters

of Ag and MgO should

decrease by 1.39 x 1O-2 and 9.55 x 10e3 A, respectively. It is therefore inferred that in alloy A cry&& &yg,, increases on lowering the temperature or vice versa and thus c should increase or decrease. It is suggested responsible

that this feature

for the strong

may be principally

temperature

Woolhouse,

it is suggested that in alloy B &C&ocould be completely relaxed by the spontaneous nucleation and multiplication of dislocations around the particles, whereas in alloy A +rgo is too small for this relaxation process

G with temperature observed

variation

pure Ag crystals,

by the crystals. the variation

in MgO are not available. in the stress-strain saturated

for 24 hr, with temperature bution

dependence

in the same manner

as does aae, but the data regarding G,

of the matrix and S the unconstrained

for

could be

evaluated

oat could vary with temperature

misfit parameter. Taking C,, = 28.92 x 101r dyn cm-2 and C,, = 8.80 x 1On dyn cm-2 for MgO,@) K, is computed

of Ag and MgO

caused by the change in testing temperature

of the yield and flow stresses exhibited

where K, is the bulk modulus of the particle, shear modulus

values is satisfactory.

The changes in lattice parameters

fi

of The

behavior

with oxygen

of

at 873°K

suggests that the contri-

of oM to the temperature

sensitivity

of the

yield and flow stresses is negligible.(13) Based

on

the

substructural

part I, taking into account

results

reported

the variation

in

in particle

sizes from the surface to the interior and using Ashby’s formalism

of the Orowan mechanism,(14)

6, in alloy ~11

B crystals

at 273°K

kg/mm2 ; the observed

The agreement in this alloy

is satisfactory yielding

temperature

to be

value is 10.25 kg/mm2. and it is inferred that

is controlled

mechanism ; the observed

the average

is estimated

insensitivity

by the Orowan of o,/G to the

is also consistent with this assessment.

MAHAJ.%N

The similarities alloy

HIM;MEL:

AXD

between

STRENGTHENING

the flow stress ratios of

crystals a,nd Ag (Fig. 6) could be rationalized

B

as follows. The substructural features of this dispersion hardened alloy are essentially simiIar to those which develop

during the deformation

to large st’rains,(r5) except strain

level.

identical

It is therefore

oscillating

of pure Ag crystals

that they form at a lower envisaged

temperatures,

that for the

their

flow stress

ratios should be similar. It is also visualized that, in carrying out the CottrellStokes type experiments,

the realignment

tions in going from high to low temperature negligible

for the following

are oriented fractions

of dislocashould be

reasons:

(i) the crystals

for mult~iple slip and

(ii) the volume

of the second phase particles are moderately

high.

OXIDIZED

CRYSTALS

of this work by the U.S.A.E.C.

would

is gratefully

Dr. C. N. Reid

for a critical reading of the manuscript

and the support

1323

acknowl-

REFERENCES 1. J. L. MEIJERING and M. J. DRUYPESTEYN, Philips Res. Rep. 2, 81 (1947). on internal Sfresses in JTfetals 2. E. OROXVAN, ~~~~0~~~~ nnd AEloys, p. 457.- Institute of M&aIs (1948). 3. S. MAHAJAN and L. HIMNEL, ~4cta Met. 20, 1313 (1972). 4. A. H. COTTRELI, and R. J. STOHES, Proc. R. Sot. A233, Ii

~195.51. \-~--, 5. Z. S. BASIXSKI, Phil. Nay. 40, 393 (1959). Phus. 6. J. R. NEZHBOVRS and G. _A. ALERR, 1 Rec. 111. 707 (1958).

7. U. ESRMASN and M. WILICEXTS,Phys. Status Solidi 8. 9. 10. 11.

14.

like to thank

IN

edged.

13. 13.

ACKNOWLEDGMENTS

The authors

MECHANISMS

15.

4, Ii53

(19641. k. F:‘Mon and F. R. N. NABARRO. Pmt. P&p-. Sot. 52, S6 (1940). D.-H. tkTXG, IWE. Mag. 8, 833 (1963). L. M. H~owr; and G. R. WOOLKOI~~~, Phil. Xczg. 21, 339 (197O\ ‘v. G&O~LD and H. HABERKORN. Phys, Statzts Solidi 16, 675 (1966). R. L. FLEISCHER, Acta Net. 8, 598 (1960). S. MAIIAJ.4N, Ph.D. Dissertation, ~~niwrsit~ of California (1965). ik F: ASHBY, Oxide Dispersior~ Streru$heni?lg, p. 143. Gordon and Breach (1968). D. M. MOON and W. H. ROBINSON, Cnn. J. Phys. 45, 1017 (1967).