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High temperature compressive creep of sintered nickel

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Title:
High temperature compressive creep of sintered nickel
Added title page title:
Compressive creep of sintered nickel
Creator:
Tarr, Walter Ralph, 1945-
Publication Date:
Copyright Date:
1973
Language:
English
Physical Description:
xi, 129 leaves. : illus. ; 28 cm.

Subjects

Subjects / Keywords:
Deformation ( jstor )
Densification ( jstor )
High temperature ( jstor )
Nickel ( jstor )
Particle density ( jstor )
Particle size classes ( jstor )
Porosity ( jstor )
Sintering ( jstor )
Stress tests ( jstor )
Surface areas ( jstor )
Dissertations, Academic -- Materials Science and Engineering -- UF
Materials Science and Engineering thesis Ph. D
Metals -- Creep ( lcsh )
Nickel ( lcsh )
Sintering ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis -- University of Florida.
Bibliography:
Bibliography: leaves 122-128.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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University of Florida
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Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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14039012 ( OCLC )
ADA8621 ( NOTIS )

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HIGH TEMPERATURE CO IPRESSIVE CREEP
OF SINTERED NICKEL














BY


TWALTER IALTPI' TARR


A DISSERTATION PRESENTED TO THE GHLADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA
1973


































DEDICATED TO THE ,IEE.IORY OF


FLORENCE LYNNE WILLIAMS


















ACK NOWSLEDI EXNTS


The author wishes to thank Dr. F. N. Rhines, chairman of the

supervisory committee, for guidance in this research and in putting it

together as a unified concept.

The author wishes to thank Dr. R. T. DeHoff for the large

amount of time he expended in discussing this work.

The author is indebted to Dr. E. D. Verink, Jr. for personal

and professional guidance.

The author wishes to thank Dr. E. H. Hadlock and Dr. J. F.

Burns for serving on his supervisory committee, and Mr. T. 'I. Sloan

for assistance in sample preparation and quantitative metallography

data.

The author thanks Mrs. R. V. Ilitchead for all her help

throughout the years.

The financial support for this research by the Atomic Energy

CommissiGn was appreciated, and is hereby acknowledged.


















TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS . . . . . . . . ... . . . iii

LIST OF TABLES . . . . ... .. . .. . . . vi

LIST OF FIGURES . . . ... . . . . . . . . vii

ABSTRACT . . . . . . . . . . . . xi

CHAPTER

1 INTRODUCTION . . .... . . . . . 1.

1.1 General Characteristics of the Sintering Process 1
1.2 Background and Previous Investigations of
Sintering . . . . . . . .. .. 4
1.3 General Characteristics of the Creep Process .. 8
1.4 Background and Previous Investigations of
the Creep Process . . . . . . . . 9
1.5 Dislocation Modelin .. . . . . 10
1.6 Purpose and Scope of This Research . . . . 16

2 MATERIAL SPECIFICATIONS . . . . . . . .. 1

2.1 Material . . . . . . . . .. .. . 18
2.2 Particle Sizes Used . . . . . . ... .18
2.3 Sample Preparation . . . . . . ... 21
2.4 Experimental Investigation into the Creep
of Sintered Nickel . . . . . . . .. 25

2.4.1 Equipment (Creep Apparatus) . . . .. 25
2.4.2 Test Conditions . . . . . . 31

2.5 Experimental Procedure . . . . . . . 31

3 EXPERIMENTAL RESULTS . . . . . . . .. 33

2.1 Der.sification and Shrinkage in Sintering ... . 33
3.2 Calibrate AL in Creep as a Function of Particle
Size, Density, Load, Temperature, and Time . . 43

3.2.1 Particle Size Effect . . . . . 49
3.2.2 temperature Effect . . . . . .. 49
3.2.3 Effect of Starting Density . . . .. 49
3.2.4 Stress Effect . . . . . . ... 55














TABLE OF CONTENTS (Continued)


CHAPTER Page
3 (Continued)

3.3 The Quantitative Microscopy of Sintered
Nickel Creep Samples . . . . . ... 55

3.3.1 Quantitative Microscopy on Polished
Surfaces . ... . . . . . 55
3.3.2 Quantitative Microscopy on Fracture
Surfaces . . . . . . ... 73

4 DISCUSSION OF RESULTS . . . . . . ... 88

4.1 Description of Physical Aspects of
a Sample Undergoing Creep . . . . .. 88
4.2 Sintering Process in Creep . . . . .. 92
4.3 Creep . ... . . . . . . . 94

4.3.1 Particle Size Effect .... . . 95
4.3.2 Temperature Dependence . . . .. 96
4.3.3 Density Effect .... . . . . 97
4.3.4 Stress Effect . . . . . ... 98

4.4 Specimen Examination . . . . . .. 100
4.5 Quantitative Microscopy in the Creep of
Sinter Bodies . . . . . . ... 104
4.6 Summary . . . . . . . . ... 115

5 CONCLUSIONS .... .............. 120

BIBLIOGRAPHY . . . . . . . . . . . 122

BIOGRAPHICAL SKETCH .. . . . . . . . . 129


















LIST OF TABLES


Table Page

1. Chemical analysis of the Sherritt-Gordon nickel
powders used in the experimental work . . . ... 19

2. Loose stack densification data for -20, 30i, 57.,
and 115k1 nickel powders at 11000C, 12500C, 1350C and
the corresponding calculated incremental average
shrinkage rates . . . . . . . .... . 41

3. Creep data containing before and after densities,
loads, temperatures, total creep, total test time,
and Andrade constants e a, and n . . . ... 45

4. Quantitative microscopy data of polished sections
Creep Samples and Loose Stack Sintered Samples . .. 56

5. Quantitative metallography of fracture surfaces . . 79

6. Calculations of the components of the stress activated
sintering model . . . . . . . .... ... 110
















LIST OF FIGURES


Figure Page

1. Intraparticle porosity in the nickel powder ...... 20

2. Scanning electron photomicrographs of -20 and 30w
nickel powders . . . . . . . ... 22

3. Scanning electron photomicrographs of 57p and 115p
nickel powders . . . . . . . . . 23

4. Creep furnace in operation. . . . . . .. 27

5. Molybdenum creep rig with sample in test position . . 28

6. Stainless steel plate supporting the molybdenum creep
rig . . . . . . . . . . . . . 29

7. Working surface of creep apparatus as in operation . 30

G. Dunsification curves for the four pDrticle sizes when
loose stack sintered at 11000C . . . . . ... 35

9. Densification curves for the four particle sizes when
loose stack sintered at 12500C . . . . . ... 36

10. Densification curves for the four particle sizes when
loose stack sintered at 13500C . . . . . ... 37

11. Shrinkage rates of -20p, 30i, 57al, and 115p nickel
powder specimens at 11000C . . . . . . . 38

12. Shrinkage rates of -204, 30p, 57p, and 115p nickel
powder specimens at 1250'C . . .. . . . . 39

13. Shrinkage rates tL/L /hr for --20U, 30p, 57p and 115p
nickel powders at 130C . . . . . 40

14. The creep of 80% dense nickel samples of four different
size fractions versus time at 11000C and 500 P.S.I. . 50

15. The creep of 80% dense nickel samples of four different
size fractions versus time at 900C and 1000 P.S.I. . 51.
















Figure


1Ga. The creep of 80, dense nickel samples of four different
size fractions versus time at 7000C nud 1000 P.S.T .....

16b. Creep curves of 100% dense samples made from -20p, 30p,
and 115, particle size fractions at 1000 P.S.I. and
900 C . . . . . . . . . . . . . .

17. The dependence of the creep of 80% dense 115p particle
size samples on temperature at a constant load of
1000 P.S. . .. . . . . . . . . . .

18. The effect of starting density on creep of samples made of
115i powder and tested at 900C and 1000 P.S.I. . . .

19. The effect of starting density on creep of samples made
from 1154 powder and tested at 1100C and 500 P.S.I. . .

20. The effect of starting density on creep of samples made
from 1151i powder at 11000C and 250 P.S.I. . . . . .

21. The effect of starting density on creep of samples made
from 115,; powder and tested at 1100'C and 100 P.S.. . .


LTST OF FIGIUES (Continued)


Page


53




54



61



62



63



64


22a. The effect of stress on 65% dense samples


powder and tested at 1100C .

22b. The effect of stress on 65% dense
powder and tested at 1100'C . .

23. The effect of stress on 70% dense
powder and tested at 1100C . .

24. The effect of stress on 75% dense
powder tested at 11000C .. ..

25. The effect of stress on 80% dense
ponder tested at 11000C .. ..

26. The effect of stress on 85% dense
powder and tested at 11000C . .

27. The effect of stress on 80% dense
powder and tested at 900C . .


samples



samples



samples



samples



sample es


samples


made from 115 it



made from 115p



made from 115p



made from 115p



made from 115l



made from 115l


made from 115i


viii














I1ST OF FIGURES (Colnti nued)


Figure Page

28. Surface area (S ) versus volume fraction porosity (VV

for the 30p, 5711, and 135- nickel powders loose stack
sintered to different densities . . . . .. 72

29. S versus V for crept 115u samples compared to S

versus V for loose stack sintered samples . . . 74

30. Anisotropy in surface area of crept samples, plotted
as a function of the amount of creep . . . .. 75

31. Apparatus used to fracture notched, sintered samples
for quantitative metallography of fracture surfaces . 77

32. The percent fracture area versus percent creep under-
gone by 63% dense, 115 samples at 700'C . . .. 78

33. Number of intersections of fracture outline with test
probe per unit length of probe, Lf, plotted against
Lf'
percent creep undergone by 63% dense, 115p samples
at 7000C . . . ....... . . . ... 81

34. Number of fracture areas per unit area of exposed
fracture, NAf, plotted against percent creep undergone

by 63% dense, 115, samples at 700'C . . .... . 82

35. AAf versus percent density for samples of -20p, 30p
48p, and 115L samples . . . . . . . 83

36. Total creep after two hours for five densities at
11000C with A. = 1510 P.S.1. . . ... . .. 84
Af

37. Total creep after two hours for three densities at
11000C with a = 3020 P.S.I. . . . . . ... 85
Af

38. Normalized fracture stress and area fraction of
fractured surface plotted against volume fraction
porosity for sintered nickel tensile bars . . . 87

39. Model showing change in state of stress of a sintered
pore fruo the addition of an external compressive
load . . . . . . . . ... ... .. . 90












LIST OF FIGURES (Continued)


Figure Page

40. Density change undergone by 80% dense creep samples
at various temperatures and varying amounts of creep . 93

41. Creep of -20 samples at four densities at 1100C
with AAf = 1500 P.S.I. ............... 102


42. Creep curves of 100% dense, -20p and 1154 samples
at 11000C and 1500 P.S.I. . . . . . . . ... 105

43. Model used in the analysis of creep and stress
assisted sintering . . . . . . . . . . 109

44. Total creep in test versus percent calculated from
the model to be stress activated sintering . .. . .112

45. Total time of test versus % h as calculated from
asthe model
the model ...... ............................ 114












Abstract of Di.ssrtation Presented to the
Graduate Council of the University of Florida in Partial
Fulfillment of the Requiremients for the Degree of Doctor of Philosophy


HIGH TEiMPELLRATURE COPIRESSIVE] CREEP
OF SINTERED NICKEL

By

WALTER RALPH TARR

August, 1973



Chairman: Dr. Frederick N. Rhines
Major Department: Materials Science and Engineering


Compressive creep of sintered nickel was performed under the

following range of conditions,

Temperature 700C 900C

Load 25 P.S.I. 4000 P.S.I.

Density 60% 100%

Particle size -20P 115p.

The data show that the creep rate was determined by the load on an

effective cross section of material which was determined to be the

fracture cross section in tension. This cross section called the area

fraction of fracture surface is designated AAf. The effect of sinter-

ing on the creep process was determined to be primarily one of return-

ing the pore shape to isotropy after the pore was deformed in creep.

















CHAPTER 1


INTRODUCTION




The powder metallurgy field has been an art throughout much

of history. With the application of materials science and quantita-

tive microscopy, the geometric processes through which a loose powder

aggregate goes during the sintering process are well established.

The fabrication of parts by the use of powder metallurgy techniques

and the application of these parts in the severe environments of high

temperature, high load, and sometimes high neutron flux demand an

understanding af how a porous material acts under severe conditions.

An aggregate of powder possesses more energy than a solid piece

of the same material of the same mass because it contains more surface

area. This energy, called surface energy, comes from the fact that

there is an imbalance of energy associated with atoms situated next to

a free surface.

When particles which are in contact with each other are heated

to a high temperature, but below their melting point, they weld together

and densify into a solid mass which may approach the theoretical bulk

density of the material. This densification process is called sinter-

ing and is driven by the surface energy possessed by the powder aggre-

gate [1,2,3,4,5,6].











Another phenomenon seen primarily at high temperature is creep,

which is the time dependent strain of a material under a stress.

The driving force for creep is the stress applied to the part. This

time dependent strain of a part in service becomes critical where close

tolerances are required for long times under severe operating condi-

tions. An example of severe conditions encountered by porous materials

is that of sintered fuel elements for reactors. The sinter body must

be reasonably dimensionally stable at high temperatures, high stress,

and high neutron flux. Applications such as fuel elements wed the

problems of the sintering and creep processes so that a knowledge of

how a porous body reacts under load at high temperature and the phys-

ical changes that take place in the structure becomesnecessary.


1.1 General Ch-racteristicF of
the Sintering Process

Loose stack sintering is the term applied to the phenomena by

which an aggregate of finely divided particles welds together and densi-

fies at high temperature. This densification requires neither melting

nor the application of an external load. A reduction in surface area

is effected with densification with the attendant reduction of surface

energy and thus the total energy of the system. Due to the complexity

of the geometric changes taking place during sintering, the topological

approach to the evolution of the microstructure of a sinter body devel-

oped by Rhines [71 will be used as a basis for description of the

changes that take place as a mass of loose powder proceeds from sepa-

rate parts to a single dense body.











The sintering process is conveniently thought of as possessing

three stages [1,8]. The first stage is characterized by the welding

and growth of particle contacts and the smoothing of particle surfaces.

The topological state, i.e., genus, fixed by the original stacking,

remains constant during this process. The particle network is striv-

ing for a minimum surface energy for its given topological state.

As the surface total force/unit area is greatest at areas of highest

curvature, the largest geometric changes take place at weld necks,

particle corners, and fine tips in dendritic powder, where this force is

the largest. The surface energy expended in rounding the internal sur-

face is wasted as far as densification is concerned as no process which

acts solely on the surface can contribute significantly to the densifica-

tion of the particle compact. The weld necks grow and surface rounding

continues until a minimal surface for the given topological state has

been effectively achieved. Further reduction in surface area can come

about only by reducing the genus, i.e., connectivity of the pore network;

i.e., second stage sintering. Second stage sintering is the stage in

which the pore network goes from a completely interconnected state to

a completely isolated state. As the connections between pores, or

channels, are pinched off, a new minimal surface area state prevails

corresponding to the now topological state. This direct dependence of

minimal surface area on state can be seen in the fact that during second

stage sintering, the surface area per unit volume, SV, decreases lin-

early with increase in density. Channel closure persists until all

porosity is isolated. Particle identity is generally lost during











second stage. Third stage sintering is concerned with chat happens to

the isolated pores. As time proceeds, conglobation of the remaining

porosity occurs. The large pores grow at the expense of smaller pores,

thus the average pore size becomes larger [9]. Some reduction in total

porosity also is characteristic of third stage. Total removal of all

porosity from the interior of a sinter body rarely, if ever, occurs

solely under the action of the sintering force (surface tension) in

the finite time of sintering operations. Densification occurs in all

three stages of sintering and the three stages overlap in the times in

which they occur.



1.2 Background and Previous Investigations
of Sintering

Sintering has been used in the manufacture of products from

particles of all classes of solids: metals, ceramics, glasses, and

organic [1]. Commercial sintering is seldom loose stack sintering,

but commonly uses pressure on the powder aggregate to promote densifi-

cation or a liquid phase for the same purpose. Most processes that

involve sintering constitute one or more of the following:

1. Loose stack sintering. The loose powder stack is heated to

a temperature near its melting point and densification

occurs with time.

2. Pressed and sintered. Kuch or most of the densification of

the powder aggregate is achievedd by the application of high

pressure precedLng the sinterjng operation. Densification

from the pressure occurs by plastic deformation and/or

roarrangmelnent of the pjarticles.











3. Hot pressing. The application of pressure during the sintering

process [4].

4. Liquid phase sintering. Sintering with the aid of a liquid

phase [2,10].

The geometry of a loose stack of particles such as is found in

normal, practical sintering appears complex. Some of the approaches

that have been put forward to help in the understanding of sintering

are the use of equi-sized particles, only two particles [11], a string

of particles [12], a particle on a plane surface [13], three wires

twisted together [41, spools of wire [4], constant temperature, and

controlled atmosphere. The study of sintering in these relatively

simple cases has given insight uito the growth of weld necks and some

understanding of the densification phenomenon, decrease in the relative

volume of porosity, but have been generally unsuccessful in explaining

the total sintering of even a simple shape which contained a large

number of particles. Mathematical models can be formulated for

simple cases and with the use of known physical parameters, mechan-

isms have been inferred. A basic fault with all the foregoing geo-

metrically reduced experimental models is that the information is

1-or 2-dimensional and practical sintering is complex 3-dimensional.

Some investigations of the three stages of sintering will now be

presented.

The first stage of sintering includes weld neck growth and

surface rounding. Surface rounding can be accomplished by evaporation

of material from convex surface and condensation on concave, or l oss

convex, surface f'2,10]. Su.I'ace and volume diffusion [7,141 can cause












surface rounding by the net transfer of material from convex surface to

concave surface. It should be noted that neither evaporation-

condensation nor surface diffusion can cause significant densification

in a powder aggregate [1,4,7]. It is thought that the growth of weld

necks can be caused by several mechanisms. They are: evaporation-

condensation [15], surface diffusion [4,11,12,16,17], volume diffusion

[4,7,10,11,15,18,19,20], viscous flow [2,4], and plastic flow [7,20,21,

22,23,24]. It is also believed that densification requires both creep

and concurrent surface area minimization [25]. Calculations using the

surface tension value obtained for copper (1400 dynes/cm) have shown

that plastic flow is possible at least in the early stages of neck

growth where contact area is very small [4]. Observations of weld

necks formed in loose stack sintering experiments show that there is

at least one of the mechanisms capable of surface rounding in operation

during neck growth. The rounded neck surface could not have been

created by plastic flow alone. In metal systems having low vapor

pressure [11], the rate of weld neck growth, as indicated by experi-

ments with particles on plane surfaces and pairs of particles, is

believed to be either surface diffusion or volume diffusion controlled

or both. Kuczynski [11] found for copper that surface diffusion was the

dominant mechanism for small particles and low temperatures, while for

large particles and high temperatures, volume diffusion was dominant.

Second stage sintering is characterized by densification of the

body and the isolation of the pores that remain [1,7,8,9].











The connectivity of the porosity goes to zero [7]. There are three

material transport mechanisms that various authors believe capable of

causing densification. They are: creep [7,8,20,22,26], volume dif-

fusion [4,14,26,27,28,29], and grain boundary diffusion [14,22,23;

29,30,31,32]. Sintering done under small loads [20,24] indicates that

there is no change in mechanism as the sinter body densifies. This

information supports the plastic flow theory. Support for the grain

boundary diffusion theory may be found in the lowered sintering rate

[27] after grain growth. Wire model experiments also show decreased

pore size in the vicinity of grain boundaries. Volume diffusion of

vacancies to the external surface from the internal pores has been

generally discounted due to large distances involved [7].

Third stage sintering is usually defined as the elimination

and/or coarsening [9] of the remaining isolated porosity. Plastic

flow is believed responsible for elimination of pores by some and a

theoretical model [22] for the shrinkage of these isolated pores by

plastic flow has been derived. Coarsening of large pores at the ex-

pense of disappearance of smaller surrounding pores can be accomplished

only by volume diffusion [91. It has been shown by several authors

[2,14,30] that the presence of grain boundaries can cause a signif-

icant increase in total densification; however, grain boundaries are

not required for densification [4,9]. Volume diffusion is postulated

by some [14,27,28] as the mechanism of pore shrinkage; whereas, others

[7] believe volume diffusion of vacancies from an internal pore to the

external surface cannot effect any significant densification of the

total body. Densification rates based on volume diffusion data












indicate that the times required for densification are unreasonable

and that geometry would require that the sinter body densify from the

external surface inward, contrary to experimental observation [9,33].

It can be seen from the preceding paragraphs that considerable

discussion of the exact nature of sintering still remains along with

considerable, seemingly conflicting, experimental evidence. There is

at present no formula in the literature into which one may insert the

physical properties of a metal or a ceramic powder and predict the

densification of a compact from a loose stack to a fully dense mass.


1.3 General Characteristics
of the Creep Process

Creep is defined as the time dependent strain undergone by

a material when subjected to a stress at constant temperature [34,35,

36,37,38,39]. At elevated temperatures where recovery processes are

relatively active, small stresses which are a fraction of the tensile

strength are capable of causing plastic deformation in metals. Some

materials will show this phenomenon when subjected to room temperature

tensile tests at different strain rates. This may be seen in the

stress-strain curves of pure metals such as aluminum and zinc where

the stress-strain curve of the tensile bar pulled at the slower strain

rate shows a greater strain for a given stress.

Constant load tensile creep is generally thought of as

possessing three stages [34,40]. The first stage is a period of

decreasing creep rate where work hardening mechanisms are dominant

[41]. In the creep of polycrystalline samples, the grains with orien-

tations favorable to shear are the first to deform. This inhomogeneous











deformation produces elastic as well as plastic strains and these

elastic strains are recoverable vith time if the specimen is unloaded.

This recoverable creep is called inelastic creep. The second stage

is considered a stage of constant creep rate where the rate of work

hardening being produced by the deformation is exactly counteracted

by recovery processes [42,43] and/or reduction in cross-sectional

area of the sample [39]. The third stage is generally characterized

by an accelerating creep rate, intergranular cavity formation (at

high temperature) [44,45,46] neckin:- (at low temperature) [44], and

ultimate failure. Constant stress and constant load compressive

creep in ductile metals generally exhibits only the first stage of

creep, and thus generally shows a inonotonically decreasing creep rate

throughout a test [47].


1.4 Background and Previous Investigations
of the Creep Process

Creep is seen to be a sensitive function of temperature and for

a given structural state has been shown to have an Arrhenius temper-

ature dependence. Creep is therefore generally considered to be a

thermally activated process [34,36,37,38]. Activation energies calcu-

lated from strain rate versus temperature data are usually close to the

activation energies of self-diffusion when the creep temperature is

between 0.5 and 1.0 T [34,,3,3,481. There is nuch discussion concern-

ing the exact mechanism that allows creep to proceed. Some of the

irnnsport processes proposed as controlling the kinetics of the high

temperature creep process are: diffusionni crce-p (XNbarro-llerring crcep!












[36,40,49,50,51]) and others [52,53], dislocation intersection and jog

formation [34,54,55,56], and climb of dislocations [36,56,57].


1.5 Dislocation Modelling

There are many formulas that have been used to model the first

and second stages of creep [58,59]. Some of the equations have elements

which match known physical parameters, whereas others are strictly

empirical.

A few of the well-known creep laws or formulas will now be

presented with explanations based on physical parameters where possible.

Logarithmic creep [34,40], e = aLog (t) + c. Log creep has

been found in organic, glasses, metals, and ceramics and is generally

found in experiments of moderate to low creep rates, small strains, and

temperatures below 0.4 T This type of creep has a monotonically
m

decreasing rate such as found in the transient, 1st stage of creep

curves. Log creep can logically be reasoned to be a result of exhaus-

tion of energy barriers to deformation capable of being overcome by the

applied stress on a sample and local thermal fluctuations [34]. As the

material deforms, the barriers to further deformation (dislocations,

etc.), increase, thereby requiring more energy to overcome them and

cause further deformation [60]. In constant stress creep there exists

a constant external stress plus the thermal fluctuations. Thermal

fluctuations are capable of helping overcome normal lattice coherency

(Peierls force), but as deformation proceeds, these regions requiring

minimum force to push a dislocation through are used up and only regions











requiring more energy (higher activation energy) remain. Thus the

creep rate decreases. The log creep equation cannot account for

steady state creep.
1/3
Andrade creep [59,61,62,63,64], e = bt This type of creep

has essentially no acceptable theory to explain it. The reason for the

widespread use of the Andrade formula for transient creep is that many

researchers [47,65,66] have found that it can be successfully used in

plotting experimental results. The Andrade creep formula generally

fits better in creep experiments where large creep strains and temper-

atures greater than about 0.4 T are involved. The basic Andrade creep
m

equation will not fit curves where steady state creep has been involved,

for steady state creep requires a linear term in time [40]. The fit

of the Andrade creep formula can be improved in cases where steady

state has occurred by the addition of a linear term, e=kt (k= const.).

A term for instantaneous strain on loading, eo 67,68], is also fre-
1/3
quently added, thereby making the Andrade equation, = e + bt +kt.

For monotonically decreasing creep rates, the linear term, kt, is

omitted. A constant creep rate (for a constant stress), implies that

some recovery of the creep sample is taking place during the creep

experiment. This dynamic recovery [69,70] is most likely cross-slip

and climb. Under some conditions of stress and temperature, a combi-

nation of the log and Andrade creep equations fit the data best.

Theory has of course been left far behind. Some authors do not find

stage two creep for constant stress tensile tests [68,71] and observe

a monotonically decreasing creep rate from the onset of loading to the

initiation of failure.











Diffusional creep (habarro-Herring creep). Diffustonal creep

is believed by many authors to be stress directed self-diffusion.

Atoms diffuse away from grain boundaries under compressive stress to

grain boundaries under tensile stress, resulting in sample elongation

in the tensile direction. The nature of diffusional creep is such

that very high temperatures, very low loads, and a fine grain size are

required for it to be the dominant creep mechanism. The strain rate

for Nabarro-Herring creep may be given by the equation,


S= (aD/L2) (6/kT),

2
where a = const. about 5 for uniaxial stress, 6 is an atomic volume ch

where b is the Burgers vector and c is a constant about 0.7, D is the

diffusion coefficient, and L is the grain diameter. That creep obey-

ing this equation exists has been shown by several authors [36,40,49,

50,56].

None of the foregoing creep and creep rate equations is capable

of modelling or predicting the occurrence of or the results of massive

recovery such as recrystallization. Generally, when recrystallization

occurs during a test, the creep rate increases [72,73].

There are many variables affecting the creep rates of materials,

some of which are temperature, shear modulus, grain size and subgrain

size, stacking fault energy, stress, composition, and diffusion rate.

The manner in which some of these parameters are known or thought to

affect creep will now be discussed.

Temperature. Creep is generally considered a thermally activated

process because it has an Arrhenius temperature dependence; therefore,












the temperature at which a material undergoes creep deformation is of

primary importance. Creep is usually thought of as a high temperature

phenomenon, 0.3 to 1.0 Tm, primarily because its effects are most com-

monly observed in this temperature range. However, creep has been

reported at temperatures below 100K. Thermally activated processes

are exponential functions of temperature; i.e., f(e ), and

for most materials, AHc, the apparent creep activation energy, is such

that recovery processes become reasonably active above about 0.3 T .
m

Diffusion. Self-diffusion is now generally accepted as being

the ultimate controlling process in most high temperature creep [38].

Nabarro-Herring creep is generally thought to be stress directed volume

diffusion (though not by all researchers)[51,52]. Climb of edge dis-

locationF also has diffusion of vacancies to nr from the dislocation

core as the rate controlling step. Many experimentally determined

high temperature creep activation energies for most metals and many

ceramics are found to be identical to or very near the activation

energy of self-diffusion. Creep rates are found to change abruptly

with an abrupt change in diffusivity and in the same proportion.

An example of this is found in the phase transformation of iron.

In ceramic compounds, the high temperature creep activation energy is

usually close to that of the diffusivity of one of the elements of

which the compound is composed.

Shear modulus [38]. The dependence of shear modulus on

temperature is generally ignored. This is usually not critical, but

significant deviations from creep rates predicted by self-diffusion data











have been corrected by introducing the temperature dependence of the

shear modulus into the creep equation [74].

Stacking fault ene rgy. In general, the lower the stacking

fault energy, the lower the creep rate [35,38,75,76,77]. A low stack-

ing fault energy allows widely split partial dislocations which must

recombine for the dislocation to climb. Stacking fault energy is also

a determining factor in the size of the substructure units (subgrains),

formed during deformation.

Grain size. That grain size can in many cases have an effect

on the creep rate of a material is accepted by most investigators [38,70,

78,79,80]. Some authors show that a small grained material has a lower

creep rate than the same material in large grain form at one temper-

ature, while others see the opposite at another temperature [80].

Other authors have found a grain size effect only below a certain

grain size [78]. The amount of grain boundary is that property which

grain size determines which is of interest in creep. Grain boundaries,

being discontinuities in a structure, act as barriers to the movement

of dislocations. If the grain size is small enough for a significant

portion of the work hardening to be a result of dislocations piling up

at grain boundaries, then one could envision the effect of changing

grain size (amount of grain boundary), in this grain size region.

If one decreased grain size increasedd grain boundary area), there

should be a decrease in creep rate and vice versa. If, however, the

grain size is large enough that the pileup of dislocations at grain

boundaries is insignifi c.nt compared to pileups in the interior of the











grain, then varying the grain size would be expected to have little

effect on creep rate. The grain size at which grain size becomes an

important factor in determining creep rate depends upon properties of

the material such as stacking fault energy and morphology (precipitates,

etc.), although there is no uniformly accepted trend. The amount of

grain boundary shear may also be tied to the amount of grain boundary.

Grain boundary shear is the phenomenon in which the volume of a grain

adjacent to a grain boundary shears to a greater extent than the bulk

of the grain due to accelerated recovery [35,36,81] (generally poly-

gonization)[82], of the crystal in this region. It has been shown in

bicrystals [81] that a significant portion,40%, of total shear can in

some cases be attributed to grain boundary shear. Some authors state

that grain boundary shear can be a significant portion of total creep

in polycrystalline metals, while others discount its effect. Grain

boundary shear appears to be important to the formation of cavities

[83,84,85] leading to the commonly observed intercrystalline failure

of high temperature creep samples [86].

Stress. The effect of stress on creep of materials and the

resultant structure is complex. The stress dependence of creep is

generally divided into three regions [7]. The low stress region
1 5
where e :a intermediate a 5 and high stress region where

e a e, b = constant. Most creep tests and engineering applications

are concerned with the intermediate stress region where ; is propor-

tional to a The effect of stress (strain rate) on structure is

a complex function of temperature, stacking fault energy, modulus,











composition, etc., i.e., the mobility of dislocations and recovery

processes. Generally in metals which form substructures, at a given

temperature, the higher the stress and consequent strain rate the

finer the substructure formed. The subgrain size formed in high

temperature creep seems to be independent of deformation (creep or

cold work), previous to a given test [35]. If, during a creep test

the stress is changed, a new subgrain size will be formed which is

characteristic of the new stress [35]. Recent work in pure aluminum

indicates that increasing the temperature (and consequent strain rate)

during a creep test will reduce subgrain size [82].

The primary problem in trying to determine the exact nature

and influence of each of the aforementioned parameters is that it is

difficult, if not impossible, to alter any one without affecting some

or all the others. This is probably the basis of much of the conflict

reported in the literature.


1.6 Purpose and Scope of This Research

The purpose of this research is to provide insight and quanti-

tative data relating to the structural states through which a sintered

nickel specimen goes during a compressive creep test. The nature of

the interaction between the creep of sinter bodies and concurrent sinter-

ing is studied. Structural changes in a sinter body can most easily

be studied through the use of quantitative metallography. Many of the

well-known quantitative metallographic functions are used. They are:

AA V, S, NL, and NA. A new quantitative metallographic function has-
been defined during the course of this research which has proved to beV
been defined during the course of this research which has proved to be










n useful tool in predicting the strenrths of sinter bodies. This func-

tion, AAf, is a measure of the load bearing area in a sinter body.

A is the standard A count taken on the fracture areas of a fractured

sinter body. Vhen a sinter body is fractured, the fracture should take

the path of least resistance, i.e., the weakest section. Thus, the

measure of the area covered by fracture relative to the total cross

section of the sinter body should be a measure of load bearing area in

the sinter body.

'his research encompasses a 400C temperature range, a 4000P.S.I.

load range, particle sizes from -20 pI to 115 ', and densities from loose

stack to 100% dense. The response of sintered nickel bodies under

various combinations of these parameters has been studied and presented.

The creep and creep rate data have been modelled to the equation

c = C + atr and the effect of the various parameters on this equation

are presented.















CHAP ER 2


MATERIAL SPECIFICATIONS




2.1 Material

The material used in the experimental creep work was nickel

powder purchased from the Sherritt Gordon Company. The nickel powder

was received in two lots, one of predominantly fine particle size

(-270 mesh) and the other of predominantly coarse particle size

(-48 + 200 mesh). The chemical analysis of each lot is given in

Table 1. The powder was produced by an electrolytic process which

resulted in an irregular particle at small size fractions which became

more spherical as the powder size increased. All particles had a

lumpy surface texture resembling that of a blackberry. The individual

particles were not always solid and upon metallographic preparation

intraparticle porosity could be seen as shown in Figure 1. Fractures

of low density specimens of the coarse, -120 + 149, 115 ,L, size frac-

tions occasionally showed that the outer layer of one of the particles

was torn from it at the point of fracture.


2.2 Particle Sizes Used

The powder, as received, was sieved through a set of U.S.

Standard sieves made by the W. S. Tyler Company. Three of the size

fracioins used were sieve cuts froLm this series. The three size




















Table I. Chemical analysis of the Sherritt-Cordon
nickel powders used in the experimental
work.

Property Lot -1 Lot F2

Composition wt ,

Nickel (includes Cobalt) 99.9 99.9

Cobalt 0.061 0.110

Copper 0.006 0.005

Iron 0.004 0.014

Sulfur 0.016 0.034

Carbon 0.005 0.016




Apparent Density (gm/cc) 4.61 3.76




Dominant Size Range (-4S +200) -270
(mesh)


























































Figure 1. Intraparticle porosity in the nickel powder.











fractions from the Tyler sieves wroc: (1) coarse (-120 + 140, 115 .),

(2) intermediate (-230 + 270, 57 I.), and (3) fine (-400 + 500, 30 2).

A fourth size fraction was prepared by taking the fines which passed

through the 500 sieve and further sieving it on screens in an Allen-

Bradley Sonic Sifter. The size fraction used from this sieving was the

powder which passed through the 20 L screen, designated -20 p. Scanning

electron microscope photographs of these four size fractions may be

seen in Figures 2 and 3. Specimen notation throughout the work is

keyed by both a letter and a number. The letter denotes the size

fraction from which the samples were prepared and the number denotes

the chronolog-cal order of testing. The notation is ,s follows:

A = --400 + 500, 30 microns (J)

B : -230 + 270, 57 microns (p)

C -120 + 140, 115 microns (p)

-20 microns = -20 microns + 0 (average 11 I).



2.3 Sample Preparation

The procedure for manufacturing the loose stacki sintered speci-

mens was the following. Previously sized powder was poured into a

graphite mold containing 10 to 12 flat-bottomed holes .375 inch in

diameter and .75 inch in depth. The mold so charged was then inserted

into a nichrome wound, silica tube, presintering furnace which was

maintained at 1000"C. The atmosphere in the presintering furnace \as

wet hydrogen. PresinterLng time was I hour, after which the graphite

boat was withdrawn front the furnace 1and tihe lightly sintered blanks

were tapped out of the mold Ind the rm;od Iwas reused.






















-20 p
2000X

























30pl
100OX


Figure 2. Scanning electron photomicrographs of
-20I and 30p nickel powders.










57 p
500X













1154
500X


4r r
:.< *b ;^ '?.. "
, i'^^B


Figure 3. Scanning electron photomicrographs of
57p and 1154 nickel powders.











The temperatures used for sintering varied from 11000C to

14000C. The sintering furnaces were globar heated and had high purity

impervious alumina tubes. The boats in which the presintered blanks

were placed for sintering were also of high purity alumina. Any mate-

rial with any appreciable trace of silica in the sintering environment

resulted in destruction of the sintering blanks due to liquation at

the surface of the blanks or, in some cases, complete melting. The

dissociation of the water in the wet hydrogen atmosphere provided a

back-pressure of oxygen which effectively retarded any SiO transport at

sintering temperatures.

Samples above 93% relative density were made by hot-pressing

the powder in a graphite mold at 1200'C. A 1-inch diameter blank was

made in this way which was 91% dense. This large blank was then

annealed in wet hydrogen at 1000C and cold-pressed at 70,000 P.S.I.

to 96.5% relative density. Several nominally identical high density

specimens were than electro-discharge machined from this blank and

annealed. Samples which were 100% dense were first hot-pressed to

97% relative density, annealed and swaged. All hot-pressing was done

in graphite molds. This procedure resulted in the contamination of

the specimen with enough carbon to cause melting at 14000C. The

samples were therefore given a decarburizing treatment at 10000C

which consisted of 1 hour in a slightly oxidizing atmosphere com-

mercial tank nitrogen, followed by 30 minutes under hydrogen.

Density measurements were made by using a wax impregnation

Archemedes method. The sample was weighed (dry weight), impregnated











with wax, and weighLed again (wax weight). The impregnated sample was

then supported by a fine wire and weiglhcd while immersed in waLer

(II 0 weight). The wire weight was the weight of the wire suspended

in the water. The density was determined from the following equation::


3 Dry weight
Density (gn./cm 3) = Dry weight
Wax weight (H20 weight Wire weight)


Relative density could then be obtained by dividing by 8.906 gm/cm,

the theoretical x-ray density of nickel. If the desired density of

nickel had not been reached, the wax was burned out in air and the

blank returned to the sintering furnace for further sinteriig. This

process was repeated until the blnnk had a measured density equal to

the density desired, 0.5%.

A blank of the desired density was then machined on a

Schaublin 70 high precision lathe. The specimen was a right circular

cylinder with a tolerance of 0.0002 inch on the diameter and with the

ends within 0.0002 inch of being parallel.



2.4 Experimental Investigation into
the Creep of Sintered Nickel

The experimental investigation of sintered nickel was done in

compression, encompassing a wide range of loads, temperatures, par-

ticle sizes, and densities.


2.4.1 Equipment (Creep Apparatus)

The creep apparatus consisted of a globhr furnace with an

impervious alumina tubc in which the sam.pl;le and loadij' rig w.'ro

inserted for tihe test. A complete vie. of the creep apparatus in












operation is shown in Figure 4. The loading rig in vhich the sample

1
was placed for testing consi steL of three inch diameter aolybderumi
2

rods bolted to a 1-- inch diameter molybdenum base plate which sup-

ported the samples. Loading was effected by means of a fourth -inch

diameter molybdenum rod which used the three support rods as guides

(see Figure 5). The support rods were bolted to a stainless steel

plate which was bolted to a large aluminum plate a.hich served as the

working surface for the remainder of the creep apparatus. The stainless

steel plate also had a gas outlet in it as well as holes for the load-

ing rod and measuring thermocouple which was positioned next to the

test sample. A photograph of this part may be seen in Figure 6.

Loading was accomplished by a 3 to 1 lever which had a ball bearing

pivot. The load was transferred to the loading rod from the lever

arm through a ball bearing set inLo a piece of steel. This ball bear-

ing had a flat ground on it on which the dial gage rested. With the

dial gage directly over the sample, one could read deflection of the

sample directly during the test. The dial gage had a range of 0.4
-4 -5
inch and direct readings to 10 inches with estimates to 10 inches.

The height of the lever arm pivot and the dial gage was adjustable to

accommodate different length specimens. The working surface of the

apparatus is shown in Figure 7.





































































Figure 4. Creep furnace in operation.

































































Figure 5. Molybdenum creep rig with sample
in test position.

































































Figure 6. Stainless steel plate supporting
the molybdenum creep rig.


















































Figure 7. WVorking surface of crop apparatus
as in operation.


c L~4L_ 1












2.4.2 Test Conditions

The range of conditions of the test parameters is as follows:

1. Temperature 700'C 1100C

2. Load 25 P.S.I. 4000 P.S.I.

3. Density 60%-100% Rel. Density

4- Atmosphere Wet Hydrogen.


2.5 Experimental Procedure

A specimen machined to the desired size was measured with

a micrometer before inserting into the creep apparatus while outside

the furnace. The specimen sat on an alumina disk and had one rest-

ing on it. The loading rod was then lowered onto the sample to avoid

sample movement and consequent misalignment during insertion of the

rig into the furnace. The ri; was lowered into the hot zone of tho

furnace, at which time the loading rod was lifted from the sample and

remained off until the sample temperature had risen to test temperature

and the creep test was to begin. While the sample was coming to temper-

ature, as measured by a thermocouple placed next to the sample, the

lever arm was placed over the loading rod and the dial gage was locked

into place directly over the rod. When the test was to begin, the

loading rod was lowered to contact the sample, an initial dial reading

was taken, and the load applied at time zero, to, for the start of the

test. Dial readings were taken at intervals to record the creep curve

and a temperature reading at the same time. At completion of the run,

the load was removed from the sample and the entire rig was removed from

the hot zone of the furnace. The loading rod was lifted from the sample











immediately at the end of the test. Elapsed time from the end of the

creep test, removal of load and loading rod from the sample, to

removal of the sample from the furnace hot zone was generally 3 to

5 minutes.

All creep work was done in a hydrogen atmosphere to prevent

oxidation of the sample and the molybdenum creep apparatus.

When the sample had cooled, the final length was measured

and the per cent error of creep measurement was calculated according

to the following formula:

(DO-D ) (L1 -L2) X 100
% Error = L
(L1 2


where

D = Initial dial reading

D = Final dial reading

L = Initial sample length as measured by micrometer

L2 = Final sample length as measured by micrometer


This error was usually less than 6%. If the error was greater than

15%, the test was automatically discarded.
















CHAPTER 3


EXPERIMENTAL RESULTS




The experimental work was designed to provide information on

the creep of sintered nickel under conditions of varying particle size,

density, temperature, and load. Studies of sintering kinetics were

performed on the various particle size powders independent of creep

testing. Densification rates of loose-stack sintered specimens can be

translated into lineal shrinkage which may be significant in compres-

sive creep testing. The density was monitored both before and after

creep testing. Quantitative microscopy was used as a means of -follow-

ing the evolution of microstructure in loose stack sintering as well as

in creep testing.


3.1 Densification and Shrinkage
in Sintering

The densification (shrinkage) of nickel powder aggregates was

measured as a function of particle size, density, temperature, and time.

The first step needed to understand the creep of sintered nickel was to

determine the sintering kinetics of the various powders. This infor-

mation was needed to determine what fraction of the length change in

a creep test was ascribable to loose stack sintering phenomena in a

compressive creep test.











As a powder aggregate sinters andc densities, the lineal

dimensions decrease. TI the sintering is isotropic (under no force

except that of surface tension), the lineal shrinkage may be calcu-

lated according to the following equation:


S 11"3 ,1 -VVoIi3
1 1 --(1)
o 1
LO



where Lo is the initial length, o is the initial density, VVo is the

initial volume fraction porosity, and o and V are final states,

respectively. From equation (1), the amount of strain in a creep test

that is attributable to loose stack sintering may be subtracted from

the total strain. The densification curves for the four particle

sizes used in the creep experiments at three temperatures are given

in Figures 8 to 10. The incremlental average shrinkage rates versus

percent density, corresponding to the densification curves are given

in Figures 11 to 13. The incremental average lineal shrinkage rate

is calculated according to the following formula:


AL/L /hr = 1 La (tl)/p (t2 t2-t1 (2)


where p (t ) and p (t2) are the densities after sintering for times

t and t2, with t2 >t The AL/Lo/hr is calculated between each time

interval and is plotted versus the density at the end of the time

interval a (t2) All densification and corresponding I.AL/Lo/hr data for

Figures 8 to 13 are given in Table 2. Loose stack wintering and creep

are parallel mcchlanjtisns In the shortening of a porous sintlred saiple

in compressive creep. Any change in the creep conditions lhich WOould











100-










SOL


4oL I I
0 30 60 90 120 150 180 210 240 270 30'
t (hrs)

Figure 8. Densification curves for the four particle sizes when loose stack sintered at 1100C.












100


o -2o0p
C 30P.
A 574-
>: 115s.


II I I I
0 30 60 90 120 150 180 210 240 270
t (hrs)

Figure 9. Densification curves for the four particle sizes when loose stack sintered at 1250'C.




























0 -20L
S30p
A 57u
}< 115k


100



90


Li


*.'





i


0


30 60 90 120 150 180 210 240 270
t (hrs)
Figure 10. Densification curves for the four particle sizes when loose stack sintered at 1350C.















A -20oi


0.1










0.01


40 50 60
% Density


70 50 90 100
70 50 90 100


Figure 11. Shrihinge rates of 320, 30p, 57 L, and 1151 nickel
powder specii-mlns at 1100"C.


115 i


0.001 L


0.0001


0.00001
30








1.0 ,


S-20-
X 30
S57 p

L 1151p

0.1


A







0.01 "\





o ,




0.001











0.0001










0. 00001 1
30 40 50 60 70 80 00
R Uc'nsity
Figur' 12. Shrinl: ,ae rlats of -20;i, 30, 571, and 115p
nickel powder spc'cimen.s aL 1250C.





1 .


A -20 .



O 57

E 115.


0.1











0.01










0.001











0.0001










0.00001 I 1
40 50 60 70 80 90 100
% Density
Figure 13. Shrinkage ratcs AL /L /hr for -201, 30, 57, and
1135' nickel pon'dCers at 1350 C.










Table 2. Loose stack densification data for -20 i, 30, 57p, and 1151
nickel powders at 11000C, 12500C, 1350'C and the correspond-
ing calculated incremental average shrinkage rates.


Particle Size, Temp.

Loose Stack, po (%)

-20p 11000C

p =31.5%

-20[L 12500C

p =31.5%

-20 L 1350C

p =31.5%


42.5%



42.2%



42.77,


57p

S= 45.33%
o

57 p

P 45.2%

57

p =0 46.6%


115p

O

115p

Po



O


56.32%



56.5%



56.3%


Total

time (hrs) = t

% p after t



% p after t

AL/L /hr
0

% after t

AL/L /hr
o


.25

52.5

.626

53.04

.637

57.88

.734


11000C % p after t

AL/L /hr
o

12500C % p after t

AL/L /hr
o

13500C % p after t

AL/Lo/hr




AL/I, /hr
o
1250C % p after t

AL/Lo/hr
13500C % p after t

AL/L /hr
o




13500C % p after t

AL/L /hr
0




1100C % p after t

AL/L /hr
0

123000 5; p after t



13500C %; after t

o


.5

54.67

.0536

55.91

.0696

63.8

.128


47.5

.0728

51.75

.1315

57.31

.187


47.3

.0282

49.68

.0620

53.88

.0945


57.0

.00798

57.45

.0111

57.71

.016.1


57.75

.0362

60.73

.0544

71.6

.0754


50.24

.0370

53.72

.0248


2

59.7

.011

66.31

.0289

79.7

.0351


52.12

.0122

57.08

.0200


64.58

.0129

73.04

.0159

86.00

.0125


54.63

.00778

60.73

.0102


60.53 64.20 69.24

.0361 .0194 .0124


48.56

.0174

50.81

.0149

55.25

.0167


57.0

0

57.84

.00451

58.67

.011


49.62

.00717

52.27

.00940

56.76

.00895


57.22

.00128

58.39

.0315

59.64

.00545


51.01

.00458

54.10

.00570

59.12

.00675


57.90

.00197

59.36

.00274

60.68

.00287










Table 2 (Extended)






8 16 32 64 128 256 294

70.13 76.78 83.07 89.08 92.77 95.18

.00678 .00361 .00164 .000719 .00021 .0000665
+ .5hr .5hr + 3hr
79.96 86.79 91.07 94.11 96.11 97.25

.00743 .00317 .00103 .000335 .000104 .0000314

90.13 92.88 94.58 95.98 97.67 98.43

.00388 .00125 .000377 .000153 .0000906 .00002


56.63 61.12 66.15 72.71 80.18 82.23

.00298 .00314 .00163 .00097 .000501 .0000501

65.43 70.93 77.17 83.51 88.73 92.96

.00614 .00332 .00173 .000812 .000313 .0000928

74.72 82.28 88.33 91.24 93.59 95.32

.00627 .00395 .00147 .00033 .000132 .0000367


52.01 54.06 56.61 59.91 63.33 66.36

.00161 .00160 .000953 .000585 .000366 .0000621

56.15 59.17 62.33 67.2 71.53 78.39

.00308 .00216 .00107 .000774 .000322 .000181

62.00 66.55 73.05 77.96 85.22 88.22

.00393 .00292 .00191 .00067 .000457 .000104


58.21 58.81 59.57 61.45 63.42 64.97

.00445 .000427 .000267 .000322 .000163 .0000483

60.17 61.04 62.61 64.56 66.34 70.74

.00113 .000597 .000527 .000318 .000141 .000128

62.11 63.87 66.64 69.58 72.91 76.83

.00193 .00116 .000878 .000446 .000242 .000104










increase the reLuLa i i.ajprtance oA' init 'in'" w'illh rcspec'L to tha of

creep will increase thui portion of ith- n'a-ucd stLirin which is

attributable to sintel,'iuTt and vice vwru,. For cxaipL e, at a _iven

temperature aId coiI'pressive strain rat, a samp e of lover density

and lower lond wiouidl iave a greatLu port ioi of its strain at'h ibnuabei

to sintering thnn ono. of higT'hr d'inpity a'nd higher load.

The densificat.i.oni rates aru entirely consistent, iwith the

finest nickel powd:o'ir tirtriong Ifstr 1 i haLi the coEiarsl r povdelr at each

density and temperature level. It can easily be seen that tie shrinL-

age 'ilrt.s dtuo ii loo(,n st;cI h sint.er'in r wuld br lower :for t poraitunr'es

lov.'er than those ir 'Pah e 2 ind for densities hiiigher tllhn those in

tile tab le. Dons ir i ca t ont i'a:cs fCol a]] po',.dcs fit t"il f ol lowing

cq']uation:

F -n e-QiT-*'( l) m
p e::p (a(D ) ) (3)
L o _J


whcre P is a porosity pn'an.cter equal t I.' 'V, ,.'ihere 1V is tie

porosity at tijn (L), and V, is Lth loose slack porosity, Do is the

starting particle size mi.Urois, T = lK t _u tlmo (h1's), Ri is the gas

constant, 1.987 cal/moleIK, a 1550, n = 1, Q = 16,200 cal/mole, and

m 0.4. The -20, po'w;'idei had an eftective D of 11..



3.2 Calibral e AL in Crocp as a Function
of Partlicle Sit", Density, Load,



TW'e mAnt Ihl 'osL o li e oexpou't'l .1 creep wo.'Or' hl b on the

ci'raceriza:t n o if Te .:ffuC of the di r.'ent coiditiJ on of creep

t n c ;[irg. T oer'c -,,re .4 l ln'e i": sc lri'. of cr'c p testt" 3c *ra Lt o sot)p; ':!tL











the effects of par:ticle size, dcns.i iy, t.e'miperatnre, anld lond )n cr ep

rates and total creLt. The dant obtlined1 wi're curve fitted to an

Anldrade type equa Ji on.


I = + at (4)
o


The exponent of imi.;, n, varied witlih stress as dijdl c ind a. These

"constants" were Iplotted as a function of stress o the niniilm ilt Rm a sulplile

cross section (oA f), for samples of the 11511 particle size crept

at 11000C. Fromi the functionall depeinden ,e of these constants, Co

a, and n, one can then write an equation thal mieodels creep of the

115p particle size samples as a furcLion of stress at 1100C. This

equation is:

oA Af .)-. 2'46

e QoA ,, 12 XAI 2.146 100 /(



Creep data on all sas-mnles used in this research are given in Table 3.

A basic assuml'ption hias been made in the t ests that ,ere

undertaken to model the effects of temipcrature, load, and density.

This assumption v.as th th the dcnsilication effect of sintering is

negligible. This means that the dimensional change in a creep sample

caused by loose stack sintering dcns iication during a test was smnll

cnou'h to be igl nor To this end, the l sie ryst fraction of pov.'der

was used in milost e':pcr nts, wic h t.ie c lioice of the other conditions

to be held constant selected accorli'~,Ily.











Table 3. Creep data containing before and after densities, loads, temperatures,
total creep, total test time, and Andrade constants e a, and n.

Part. p p
Size Before Temp. Load After Time Creep a n Fi
SC P.S.I. % (min) % o

C21 115 84.G 1100 1000 S8.2 300 12.5 1.36 .333 .614 20
C22 115 85.1 1100 500 89.4 100l 5.25 .'164 .0074 .937 19
C23 11 84.9 1100 250 82.2 3020 5.12 .16 .0069 .817 20
C::d 115 85.7 1100 100 86.0 4050 2.10 .0053 .136 .32 20

C25 11l 75.8 1100 1000 79.8 21 15.5 1 3.13 .404 24
C31 115 80.0 1100 500 86.2 534 10.96 .251 .512 .513 -

C32 115 79.8 1100 250 79.4 1770 6.05 .19 .00 .92 20

CS3 115 80.2 1100 100 82.9 3450 1.24 .00407 .00313 .77 21
(. 115 64.8 1100 500 70.0 21 16.02 2.54 3.75 .42 19

Cu6 115 65.2 1100 250 60.2 60 10.36 .225 2.12 .3S 20
( 11 61I.7 1100 100 G8.8 300 7. S2 .864 .217 .59 21

(CS 115 64.63 1100 50 68.5 1746 9.28 .162 .124 .5 22
C41 115 69.2 1100 1000 76.4 10 15.32 2.61 4.81 .425 23

C42 115 70.2 1100 100 75.4 1910 G.10 .0093 .0012 .83 21
C43 115 65.57 1100 1000 3 19.02 3.9S 7.5 .43 22

C44 115 o0.2 900 1000 81.17 122 3.71 .S 1.13 .293 15
C47 115 80.3 000 1000 80.95 120 4.72 .105 .99 .32 18
C,8 115 69.9 900 1000 74,10 60 6.18 .0027 1.7 .313 18











Table 3 (Continued)


p
Before Temp.
% C

81.7 1100

65.27 1100

G1.54 1100

85.00 1100

75.1 1100

70.1 1100

63.G3 1100

100 1100


CSS


C90
COl


C92

C93

CO94

C104










.99


C5 1
.15
Ni35

381
pal S


p
Load After Time Creep
P.S.I. % (min) %


628 83.84 120 1.82 .214 .226 .403

167 66.SG 120 8.50 0 .65 .54 22

333.8 67.4 120 16.37 .613 1.42 .490 22

1257 85.47 120 8.53 .59" .41 .75 -

375 75.72 120 1.19 .470 .112 .737 24

755 78.43 120 9.05 .361 1.09 .434 24

67,88 65.19 120 5.00 .050 .258 .620 22

1500 100 120 5,66 '0


900 1000


1100

1100

700

900


900

1100

700


120 4.07 0


500 80.7 120

500 U1.28 120

2000 80.01 150

1000 100 14410


1000 81. 120

500 80.69 120

2000 80.'3 150


6.21 .363

5.S9 .388

3.73 .625

1.29 .244,


3.S2 .219

5.50 .272

3.18 .620


.335

.099




.195


.267

.125

.217


.529 1




cl88 16


.501 ic
.230 16


.544 15

.78 1,i

.192 10


P-rt.
Size


80.4

80.0

79.7



100


79.5

79.5

79,7










Table 3 (Continued)
Part. P P
Size Before Temp. Load After Time Creep Fi'
-v .% C P.S.I. (min) o

C.9 115 79.7 900 500 81.25 2730 4.19 .186 .009 .47 27
C0o 1183 0.0 900 2000 87.48 54 8.17 .0075 2.07 .334 27

C13 l, 9G.4 900 1000 97.35 2380 2.73 31 .28. .265 1 '
CO5 15 79.9 900 4000 85.02 6 17.23 1.91 10. 1 .25 27
Co 115 79.7 1000 1000 85.5 120 7.53 .149 1.55 .326 17
C.37 11 80.1 1100 1000 85.3 120 10.53 .416 1.3 .426 17
C58 115 79.9 850 1000 80.4 120 2.92 .3GS .482 .35 17
C59 115 79.7 700 1000 80.2 630 2.80 .472 .267 .342 17
C6O 115 75.1 900 2000 78.3 120 12.50 .801 2.S3 .293
CG2 115 75.1 900 2000 79.2 60 10.1 .761 2.97 .277
C, 115 100 900 1000 100 1410 2.07 .000 .550 .180 IC"

C70 115 80.0 700 2000 80.1 150 2.94 .029 .30(3 .75 :6
C7 I 115 74.94 1100 250 70.13 450 5.4 .586 .0095 .G45 20
C75 115 70.6 1100 250 74.09 120 8. 8 .251 ,338 .322
C7G 115 70.05 1100 500 74.96 180 12.23 .67 1.71 .432 19
C77 115 74.6 1100 500 77.92 IS0 9.23 .10S 1.3 .376 19
CSO i15 79.9 1100 500 82.77 120 4.71 .251 .387 .512 14

CS,- 115 80.3 700 2000 83.61 150 2.6S .44 .220 19 13
CSG 115 66.4 1100 25 65.793 540 .977 0 .0078 .7GS 2
C87 115 70.02 1100 250 70.99 360 S.64 0 .469 .498 20










Table 3 (Continued)


Part. p p
Size Eefore Temp. Load After Time Creep
p % C P.S.I. (min) %


-20L 95 -20 SO,29 1100

-t0, 9G -20 80.13 900

-:20; 977 -20 79.59 700

S-2; a -20 SO.O 1100

-2U9 102 -20 100 1100

-20, 105 -20 60.17 1100

-20. 1CG -20 70.47 1100

-20: 10S -20 79.5 1100

-20.: i09 -20 100 1100


650 87.09 120 18,4 .171

1000 83.1 120 7.1 .115

2000 0.,37 120 4.71 .73

500 85.34 120 13.05 .252

1000 100 1440 .5 59

292.5 79.98 10 18.05

405 77.72 60 17.5 -

517.5 84.G6 120 15.22 -

1500 100 120 5.0 -


Fig.



.745

.88 15

.82 16a

.777 11

.185 1Gb

10

40
40

140











3.2.1 Particle Size I flFct

i There wire fou1 r pnartic le s:L'zes test efd under creelp conditions.

They were: -20], -I00 1 500(i0O)[, -2U10 270(57 T) ad -120 + 1,10(115j).

Comparisons of the creep of the thrI.e pcaricle sizes were run at tlrcu

different load-'c;lpcrature combilnatlious, 1100''C and 500 P.S.. ,

9000" and L000 P.S. I., and 700 C and 2000 P.S.I. fTh results of Lhese

twelve tests may be soen in F'igures 14 to 16a. For tilh c tests, all

samples started at SO,; dense. In all cases, the finer the povdr frtom

which the sample was miade, Lhe gj-ieaer the percent creo p :at the enr of

the two-lhour crucIp losts. The wide dij foerence in the amount of creep

cannot be explained from sl inkage due to loose stack sintering densi-

fication. Sampnl es of the various ponders at 100',- relative density

shoiwedi tlint their fine r the starting poo t'der, the _lor.'er the creep rate.

This effect at 100' densit-y ji due to '11i purity of the nickel povder

decreasing with decreasing particle size, Figure 1Gb and Table 1.


3.2.2 Temperature Effect

The temperature effect on creep uws studied in a series of 80%

dense, 1154 samples und-er a load oF 1000 P.S.I. The creep curves for

these five samples mr3y be seen in iguire 17. 'Ihe results are as

expected, with total cr ap1 and creep rate Inclrcasing ,itih incr'oasing

temperat-ure.


3.2.3 Effect of Staurting Do-usity

Th eIffect of csrArilng d ensit-y on cre.p rate was predicLaile

with toial creep 'di c re.) rate incre iig v.11h i dtecj-' ase in density












1/


12





/







r -


LG o A79
/ ,.






S 115p, cso
0
t (min)r



2Fiu crep of s of f0









un l 500 P.S.I.
















.7

'i'


5 L


4--

3

,/ c-


30 A4

SA 57 15
2 .
2 ,LI ~115s C4









O L I __ _
0 40 s0 120
t (min,
n^?!










t (lniln


6
5

-1
4

4


Figure 15. Thei ceep of 80% douise nickel samDples of four different
size fractions versus tiu.e t 900'C ndi 1000 P.S.I.





















\V



Sf,
r/'




I' -S






-204 97
S 30p A82
A 57, BS3
I- 7' [ 1151l C84


0 40 so 120
t (min)


Figure 16a. The creep of 80% denr-e nic';ol samples of four
different size fractions versus time at 700C
and 2000 P.S.I.















o 115 C64
2A 30 u, A99






.5 -








vII



l Ij-


0.0 I
0 200 40000 0 800 1000 1200 1400 1G00
t (Main)


Figure 16b. Creep curves of 100% dense samples made from -20p, 30u, and 115- particle
size fractions at 1000 P.S.I. and 9000C.















0 11000C C57


S t/ A 1000C C5G

9000 C C44

( 850'C C5S
4 -
S, 700C C59

3


K --





1 .




0 40 SO 120 160 200 240 280 320 360
t (min)

Figure 17. The dependence of the creep of 80%SO dense 115p particle sire sample-s
on temperature at a constant load of 1000 P.S.I.











for a set temperature and load. Figures 18 to 21 show the results of

varying the density of samples while holding particle size, temperature,

and load constant.


3.2.4 Stress Effect

The creep rate of sintered nickel increases with an increasing

stress. Figures 22 to 27 show the results of creep experiments over

a wide range of loads and densities at two temperatures. In each series,

the temperature, density, and particle size wereheld constant.


3.3 The Quantitative Microscopy of
Sintered Nickel Creep Samples

Quantitative microscopy has been established as a useful tool

for the description of microstructures. In the course of this work,

quantitative microscopic measurements were taken as a means for undpr-

standing microstructural changes that occurred when a porous body

underwent creep.


3.3.1 Quantitative Microscopy on
Polished Surfaces

The quantitative microscopic measurements were first taken on

samples in the as sintered state for use as controls, then on samples

which had undergone creep testing. The quantitative metallographic

data taken on polished sections of loose stack sintered samples and

crept samples may be found in Table 4. A plot of SV versus porosity

is given in Figure 28 for 30w, 57p, and 115i loose stack sintered

samples. On crept samples, quantitative metallography data were taken

in two directions, one parallel to the creep direction and one













Table ,1. QO'anti itl .i\-c miCcros-copy dl:L:


Loud p buflor
P1.. I. g/i.ctis


P;FrL.
Size



15



115



115



115



U1,5
115



115



115



115



115



115



115
115
115



115






























1i 0


Tel:,P.
C




1100



1100








1100



1100



1100

1100



1100


1100



900



900



900



900


af [er Creep) S


1000



500



1000



500



1000



500



500



250







1000



1000



500



2000


7.51



7.5



6.76



6.71



7.13



7.13



6.24



6.23



6.21



7.13



6.23



7.11



7.13


7. 85



7.96



7.10



7.12



7. 7S



7.68



6. 95



G.84



G.S1



7. '1



6.60



7. 2



7.79


12. 5



5.25



15.5.



13.37



13.09



10.96



13.4



12.05



15. 32



4.72



G.18



1.19



S. 17


128.16
141.4

121.58
123.20

213.57
232.30

191.28
204.32

128.55
160.24

157.16
177.34

210.72
224. 52

227.70
231.62

249.44
262.44

165.10
173.08

2-1. 8
248.60

173.24
178.96

152.7"
180.7


on polished sections.


Creep ,Sam1p c:s












Table 4 (Extended)
Creep Samples

xO-3 xO-3 O4
SV = ANL A r X103 o 0 (1cm)
net net (cm)



9.48 29.8 23.24 37.14
.8875 9.36 1.013 29.21 20.37 32.96

9.56 30.0 24.70 35.10
.9863 8.77 1.09 27.5 22.35 34.63

14.50 36.1 16.91 38.06
.9193 10.86 1.33 34.1 14.69 34.99

9.32 29.3 15.31 42.01
.9361 9.88 .944 31.0 15.19 39.33

10.71 33.6 26.16 39.49
.8022 10.43 1.03 32.8 20.45 31.68

8.18 25.7 16.32 35.00
.8878 -10.43 .784 32.8 18.48 31.15

10.27 32.3 15.31 41.76
.9385 9.05 1.135 28.4 12.66 39.10

8.10 25.4 11.17 40.81
.9833 7.90 1.025 24.8 10.72 40.13

7.51 23.6 9.45 37.80
.9506 7.98 .9406 25.1 9.48 35.93

8.41 26.4 16.01 46.23
.9538 7.38 1.145 23.1 13.34 44.09

9.13 28.7 11.85 42.88
.9729 10.27 .9729 32.3 12.98 41.72

7.82 24.6 14.18 43.29
.968 6.99 1.11 22.0 12.27 41.91

8.69 27.3 17.93 33.04
.8424 9.56 .9091 30.0 16.61 27.83











Table 4 (Continued)
Creep Samnples



Part. Temp. Loidl p before p after Creep SV
Size C P.S.I. gm/c3 mc3 C



137.68
C51 115 900 4000 7.12 7.84 22.14 174.38

143.72
C55 115 900 4000 7.12 7.58 17.23 172.48

295.80
E54 57 900 1000 7.09 7.25 3.82 306.37

-20, 852.88
105 -20p 1100 292.5 60.17 69.98 18.05 904.10

-20p. 504.3
108 -20p 1100 517.5 7.08 7.54 15.22 518.3












Table 4 (Extended)
Creep Samples


SSV =NL TA x10-3
net


.7895


.8332


.9654


.9489


- 12.05
- 10.15

- 10.07
- 8.57

- 30.42
- 28.33

- 689.4
- 776.3


981.7
.9230 999.5


-3 4 4
n TA x10 Xxl
net (1/cm) (cm)


1.187


- 37.8 27.49 34.89
- 31.9 18.29 27.55


31.6 22.02 34.62
1.175 26.9 15.61 34.89

95.6 32.31 25.21
1.074 89.0 29.05 24.34

-2165.8 -2524.55 14.02
.8881 -2438.8 -2697.5 13.31

-3084.2 -6115.8 12.12
.9822 -3140.0 -6055.8 11.86













Table 4 (Continued)

Loose Stack SinLioed Samples


6
Part.
Size (3)
p. cm


30 7.81

7.23

6.65

6.11

5.35

4.96


57 4.85
5.08

5.52

5.98

7.05


115 5.49
5.95

6.31

7.09

7.45


H \


Porosity (-1)
(cm )


.104 293

.158 556

.221 790

.283 923

.354 1230

.397 1370


.462 845

.393 708

.368 701

.322 624

.176 407


.402 417

.333 281

.287 254

.224 179

.131 126


92 -5 -1
(cm )x10 (cm ) (cm)


2.62 -894 .0014

2.05 -369 .0011

5.15 -652 .0011

5.44 -589 .0012

5.84 -475 .0011

-12.8 -934 .0011


4.84 -573 .0021

1.95 -275 .0022

2.84 -'05 .0020

2.36 -378 .0020

1.87 -459 .0017


.914 -219 .0038

.082 29.1 .0047

.202 79.5 .0045

.237 -132 .0050

.286 -227 .0042














4.0

3.0




1.0


0 500 1000 1500 2000 2500 3
-i t (min)


00


>< C-48 70%

o C-47 80%


E C-53 96%

A C-64 100%


7.0


SL I I I I I I I I

0 20 40 60 80 100 120 140 160 180 200
t (min)

Figure 18. The effect of starting density on creep of samples made of 115L powder and
4--+,i -, nnor and 1000 P.S.I.


PI




~
=/














[ C-34

A C-76


C-77

Sc-so

<>C-S2


6.0

o 5.0
o

u 4.0

3.0

2.0

1.0


400 600
t (min)


800


0 20 40 GO SO 00 120 140 160 ISO 200
0 0--------00
t (min)

Figure 19. The effect of starting density on creep of samples made fro 115 powder
and tested at 11000C and 500 P.S.I.













8.0
7.0-





.0
3.0 1

1.0

0 500 1000 1500 2000 2500 300C


85%


80o



705



C;55


12.0 L


t (min)

Fi'iGuLr 20. The effect of starting density on creep of samples made from 1154 powder at
11000C and 250 P.S.I.













SC-37 65%

SC-42 70%

SC-33 80%






8.0 -



6.0

6.0 -,/ .- .






2.0



0o.o -t' ,r i- --- ------ --! D
0 200 400 600 SO0 1000 1200 1400 1600 1800 2000
t (min)

Figure 21. The effect of starting density on creep of samples made from 115P powder
and tested at 11000C and 100 P.S.I.


























X C-43 1000 P. S.I.

( C-34 500 P. S, I

C-90 333.8 P.S.I.

[ C-3G 250 P.S.I.

/ C-89 167 P.S.I.

( C-94 67.88 P.S.I.


t (min)
Figure 22a. The effect of stress on 651% dense samples made from 1154 powder and tested
at 11000C.

































o C-37 100 P.S.I.

[] C-38 50 P.S.I.

- C-86 25 P.S.I.


10.0


S.0




6,0
5"



4.0




2.0




0.0


0 180 360 540 720 900 1000 1260 1440 1620 1800
t (min)


Figure 22b. The effect of stress on 65% dense samples made from 115" powder and tested
at 11000C.














( C-41 1000 P.S.I.
] C-42 100 P.S.I.
S6
X C-76 500 P.S.I.
A C-87 250 P.S.I.

3




. 0


t (min)

Figure 23. The effect of stress on 70% dense samples made from 115. powder and tested
at 11000C.














o C-25 1000 P.S.I.

15L C-74 250 P.S.I
> C-77 500 P.S.I.
C7 A C-92 375 P.S.I.
12 / C-93 755 P.S.I.
















0
"'---




Ji^i


0 50 100 150 200 250 300 350 400 450 500
t (min)


Figure 24. The effect of stress
at 11000C.


on 75% dense samples made from 115u powder tested

















0
Q)

U
^ 3


0 C-80 500 P.S.I.

SC-57 1000 P. S.I.

< C-33 100 P.S.I.

< C-32 250 P. S. I.


1600 2400
t (min)


3200 4000


0 20 40 60 SO 100 120 140 160
t (min)

Figure 25. The effect of stress on 80%/ dense samples made from 115P powder tested
nt 11000C.



















100 P.S. I.

250 P. S.I.

500 P. S.I.

1000 P.S.I.


> C-24

( C-23

E C-22

C c-21


0 100 200 300 400 500 600 700 800 900 1000
t (min)
Figure 26. The effect of stress on 85% dense samples made from 115p powder and tested
at 11000C.













14 -



1A-
12 C-49 500 P.S.I

o C-47 1200 P.S.I. I
2 C-50 2000 P. S. I.





8 5




0 1 2 3 5
t (min)

.--












0 20 40 60 80 100 120 140 160 180
t (min)
Figure 27. The effect of stress on 80% dense samples made from 115lu powder and tested
at 900*C.









16001-


0 30p,

1400

0 57L



1200 A 1154



30p
1000

0


800


1 57


600





400




200




0 1
.5 .4 .3 .2 .1 0
V porosity


Figure 28. Surface area (S ) versus volume fraction porosity (V )
for the 301, 57p, and 115p nickel powders loose stack
sintered to different densities.











perpendicular to the creep direction, rather than randomly as is

generally done. This counting in specific directions shows the

anisotropy created in the pore structure by creep deformation.

In loose stack sintering, S varies linearly with VV once the

conditional minimal surface area has been reached in second stage

sintering. The effect of creep in all cases has been to increase S

relative to the S of a loose stack sintered sample which is of the

same density as the creep sample after a creep test. This may be seen

in Figure 29 where S is plotted versus VV for many crept samples of

115. powder and all points lie to the high side (surface excess side)

of the loose stack sintered line.

An anisotropy factor was defined as

Property in perpendicular direction
Property in parallel direction

The anisotropy of SV, QSV, is plotted versus percent creep in Figure 30.

Anisotropy varied roughly linearly with percent creep in the 30p

nickel samples, but showed much scatter in the 57p and 115p, samples.


3.3.2 Quantitative Microscopy
on Fracture Surfaces

Fractured surfaces of sintered and sintered and crept samples

were also amenable to quantification by quantitative metallography.

The quantitative metallographic parameters used in the quantification

of fracture areas were: AAf, NLf, and NAf. These quantitative metal-

lographic measurements were taken from irregular internal surfaces

which were exposed when the porous samples were fractured. Note must

be made that these measurements are not taken from plane polished










400






350






300






250


O
El




1. [


Figure 29. S versus V.
V for loose
V


--- ---- --- -^- -------
.3 .2 .1 0
Vv (porosity)
for crept 115pA samples compared to S versus
stack sintered samples.


100 P.S.I. C 1100"C
250 P.S.I. @ 11000C
500 P.S.I. @ 9000C
500 P.S.I. @ 1100C
1000 P.S.I. @ 900C
1000 P.S.I. @ 11000C
2000 P.S.I. @ 9000C
4000 P.S.I. @ 9000C
Loose Stack 0 1300C











\o


Cq Q










A A (30 p)

( B (57,,)
( C (115 L)


A
A


I 1 A
5 10 15
% Total Creep


25 30
25 30


Figure 30, Anisotropy in surface area of crept samples, plotted
as a function of the amount of creep. Data include
a broad range of sample configurations and test
conditions.


1.03


1.02 -


1.01


1.00


.99


.98


.97


.96


.95


.94












surfaces as in most quantitative metallography. The AAF measurement

is defined as the area fraction of fractured surface and is simply the

fraction of the total projected area occupied by fracture. NLf is the

line intercept count taken on the perimeters of the fractured areas.

The NAf count is simply the number of distinct fracture areas

recorded per unit area.

A series of four samples, three of which were crept and one

control sample, made from 1154i nickel powder were measured for AAf'

NLf, and NAf. All samples were notched and then fractured in the

apparatus shown in Figure 31. The notched sample was inserted into

the apparatus with the notch toward the bottom. The knife edge was

rested against the sample opposite the notch. The apparatus, thus

assembled, was then iimmersed in a container of liquid nitrogen.

When the nitrogen boil subsided, the knife edge was struck a sharp

blow with a hammer, fracturing the specimen. The fracture mode was

completely ductile. A section of the fracture surface was cut out with

a jeweler's saw, with care taken not to include any area deformed by

the knife edge. These sections were than mounted and inserted into

a scanning electron microscope. All counting was done by using

a 5 X 5 grid of points and lines held against the display tube by the

tube cover plate.

The AAf NLf and NA counts on the 1154 samples were taken at

500X magnification. The results of the -change in AAf with percent

creep are shown in Figure 32. All quantitative metallography data

taken on fracture surfaces are in Table 5. The NLf and NAf counts
Lf AM

















C


Figure 31. Apparatus used to fracture notched, sintered samples
for quantitative metallography of fracture surfaces.















































0 1 2 3 14 5 6 7 6 o J IU Lj I IZ i 'i "
% Creep

Figure 32. The precent fracture area versus percent creep undergone by
63% dense, 115p samples at 700'C.
















Table 5. Quantitative meLallography of fracture surfaces.


Quantitative microscopy of fractured as sintered samples


Particle Size

115i


p '7

56.5

63.0

70

75

80



45.5

62.0

70.75

76.5


AAf

0

.045

.1655

.25

.331


0

.13

.18

.285


Particle Size

30


-20 .


Loose stack density.


Quantitative metallography of fractured creep samples


Particle Size % Creep


0

3.05

8.17

15.12


o -

41.8

51.2

70.79








31. 5

62.66

79.64


AAf

0

.0873

.2057








0

.213

.345


AAf

.015

.0713

.0715

.1028


,Af

14.2 X103

3
12.9 X10

12.5 x10
16. 3
16.8 :;10


NLf

59.75

55.93

65.95

96.07











versus percent creep on the fractured ureas (Figures 33 and 34) have

an initial decrease in value with percent creep, then increase as

expected. The initial decrease in Nf and Nf leading to these minima

is attributed to the close proximity of the initial contacts between

particles. These multiple contacts derive from the lumpy, blackberry-

shape of these nominally spherical surfaces, With small compressive

strains, these multiple contacts coalesce, initially decreasing both

NL and N. For smooth spherical powders, the NLI and A measure-
L At -"LI Af

ments on the fractured surfaces would be expected to increase with

increasing creep from the outset.

A series of AAf measurements was made on samples made from

different size fractions of powder at various densities. Figure 35

shows the results of these AAf measurements plotted versus V porosity.

The specific AAf values may be found in Table 5. It is clear from

these curves that AAf is sensitive to particle shape, i.e., loose stack

density, at low densities. The plots of AA for the different particle

sizes converge in the range of 0.3 to 0.2 VV porosity and are identical

from 0.2 to 0.0 V. porosity. These data were used to calculate the

creep loads which would give the same normalized stress on the load

bearing areas of two series of 115 creep samples. From the results

in Figures 36 and 37, the postulate that AAf is a measure of load

bearing area is substantiated. Severe distortion of the areas around

the fractures made it difficult to distinguish fracture from distorted

metal surrounding the fracture at density levels above 80) denlse.















100




90




SO




70




50 s




50




40 I _ _ I _L -- -- 1 -- 1 -- I r_ _
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
% Creep

Figure 33. Number of intersections of fracture outline with test probe per
unit length of probe, N L, plotted against percent creep undergone

by 63% dense, 115pi samples at 7000C.















17,000


16,000




15,000




S14,000




13,000




12,000 -



11,000 .

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
% Creep
Figure 34. Number of fracture areas per unit area of exposed fracture, NAf'

plotted against percent creep undergone by 63%. dense, 115p samples
at 700'C.












0.9 115,
0 48s
Q 30
-20
0.8




0.7
/ /



0.6 A /




0'.5




0.4 -




0.3




0.2




0.1




0.0 1-,L___ __
30 40 50 60 70 80 90
%' Density

Figure 35. AA versus percent dcnsiLy lor samples of -20l, 30'p,
4SiL, and 115l samples.






























A
A-9 .5
Ei C-94 .045


() C-70

A C-92

SC-80

( C-104


.16G

.25

.331

1


0 (P.S.I.)
67.88

250

375

500

1500


65 70 75 80 85 90 95 10
% Density


Figure 36. Total creep after two hours for five densities at 11000C with CAAf
Af


1510 P.S.I.


4 !



















[] C-76

A C-93

0 C-57


Figure 37. Total creep
with a =
AAf


AAf

.166

.25

.331


70 75 80 85
% Density

after two hours for three densities at 1100C
3020 P.S.I.


a (P. S. I.)

500

755

1000







86



Room temperature tensile tests were made on specimens of varying

densities and varying starting particle sizes. A plot of normalized

fracture stress plotted versus VV porosity may be seen in Figure 38 [87].

As can be seen, the tensile strength of the sintered samples follows

Af, the minimal sample cross section measured on the fracture surface.














1.0
1.O..-.--- --------------------------------------- -----------


0 Fracture stress
70,000 P S.I.
/
.8 -
0 A O0




a .6 O
.G O



so
> 00
.6 .5 .4 ..3 .2 .





.2



o o


.6 .5 .4 .3 .2 .1 0
V V Porosity







Figure 38. Normalized fracture stress and area fraction of
fractured surface plotted against volume fraction
porosity for sintered nickel tensile bars.
















CHAPTER 4


DISCUSSION OF RESULTS




4.1 Description of Physical Aspects
of a Sample Undergoing Creep

This research was performed with the objective of gaining an

understanding of the nature of high temperature creep deformation of

porous sintered nickel. To this end, a general survey was made with

particle size, temperature, load, and density as the variable param-

eters. Quantitative microscopy of polished sections and of fracture

surfaces was used extensively to determine the structure and geometry of

samples in the as sintered state and to follow the structural changes

which took place during creep as a means to provide insight into the

process of creep in porous sintered nickel.

The question now arises as to what happens to a porous sinter

body when loaded compressively at high temperature. With the applica-

tion of the load, the body begins to deform. The first part of this

deformation is simply the elastic response of the sample to the stress

and is not time dependent. Further deformation which is time dependent

(i.e., creep) also begins at the time of loading. As the deformation

proceeds, the energy state which exists in the pore-solid interface by

virtue of surface tension is disrupted. This disruption is the change

of shape of this internal interface. The sample is under a triaxial










compressive stress from surface tension and although the value of the

force exerted by surface tension on the sinter body may vary locally

according to the Gibbs equation for pressure across an interface;

eq. G, the net effect is a hydrostatic compression on the sample

as a whole.

1 1
P = --,{ +-- (6)



where AP is the pressure differential across an interface, y is

the surface tension and rl and r2 are the normal radii of curvature

at a point on the surface. The application of the external compressive

creep load alters this uniform compressive stress by increasing the

load on the sample in the vertical direction and sample deformation

(with attendant flattening of pores) changes the surface tension stress

pattern further. A model of a spherical pore (radius r) is used to

illustrate the changes in stress distribution (Figure 39).

Figure 39, part a, describes the stress from surface tension

as uniformly hydrostatic throughout; i.e., the curvature is equal at

all points. Part b shows the change in the state of stress on the

material after loading, but before pore deformation. There is an

increase in total force in the vertical direction from the external

load, but the forces from surface tension remain the same. Part c

shows the pore deformed into an ellipsoid. If the deformation has been

uniform, the three axes of the ellipsoid are now (rl, x direction),

(r2, y direction), and (r3, z direction), with rl r2 > r The

radius of curvature at point (0,0,r ) is r in both the x-z and y-z

planes. At point (0,r 2,0) the radii of curvoture are ra in the




Full Text

PAGE 1

HIGH TEMPERATURE C0:.LPRE3SIVE CREEP OF SIKTERED NICKEL BY WALTER RALPH TARR A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OE THE UNIVERSITY OF FLORIDA IN PARTIAL FUI.FILL^U-NT OF THE REQUnmiENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FL0R1J)A 197

PAGE 2

\ DEDICATED TO THE MEMORY OF FLORENCE LYXNE V/ILLIAAIS

PAGE 3

ACKNOWLEDGMENTS The author wishes to thank Dr. F. N. Rhinos, chairman of the supervisory committee, for guidance in this research and in putting it together as a unified concept. The author wishes to thank Dr. R. T. DeHoff for the large amount of time he expended in discussing this work. The author is indebted to Dr. E. D. Verink, -Jr. for personal and professional guidance. The author wishes to thank Dr. E. H. Hadlock and Dr. J. F. Burns for serving on his supei'visory committee, and Mr. T. M. Slean for assistance in sample preparation and quantitative metallography data. The author thanks Mrs. R. V. l.liitehead for all her help throughout the years. The financial support for this research by the Atomic Energy Coirmiissicn was appreciated, and is hereby acknowledged.

PAGE 4

TABLE OF CONTENl'S Page ACKN0\^'LEDG^reNT3 ^^^ LIST OF TABLES ^^ LIST OF FIGURES . , • • '^^^ ABSTRACT ^^ CHAPTER 1 INTRODUCTION ^ 1.1 General Characteristics of the Sintering Process . 1 1.2 Background and Previous Investigations of Sintering '^ 1.3 General Characteristics of the Creep Process ... 8 1.4 Background and Previous Investigations of the Creep Process 9 5 Dislocation Modellin;; 1.6 Purpose and Scope ox This Research 16 IvlATERlAL SPECIFICATIONS ^8 2.1 Material ^^ 2.2 Particle Sizes Used 18 2.3 Sample Preparation 21 2.4 Experimental Investigation into the Creep of Sintered Nickel ^^ 2.4.1 Equipment (Creep Apparatus) ... 25 2.4.2 Test Conditions -^l 2.5 Experimental Procedure -^^ EXPERI^IENTAL RESULTS 33 3.1 Densification and Shrinkage in Sintering 33 3.2 Calibrate AL in Creep as a Function of Particle Size, Density, Load, Tem.perature, and Time .... 43 3.2.1 Particle Size Effect 43 3.2.2 lemperature Effect ^9 3.2.3 Effect of Starting Density 43 3.2.4 Stress Effect 55 iv

PAGE 5

CHAPTER 3 (Continued) TABLE OF CONTEJnTS (Continued) Page 3.3 The Quantitative Microscopy of Sintered Nickel Creep Samples • ^5 3.3.1 Quantitative Microscopy on Polished Surfaces 3.3.2 Quantitative Microscopy on Fracture Surfaces 55 73 4 DISCUSSION OF RESULTS ^^ 4.1 Description of Physical Aspects of a Sample Undergoing Creep ^^ 4.2 Sintering Process in Creep 92 4. 3 Creep ^^ 4.3.1 Particle Size Effect 95 4.3.2 Temperature Dependence S6 4.3.3 Density Effect 97 4.3.4 Stress Effect 98 4.4 Specimen Examination 100 4.5 Quantitative Microscopy in the Creep of Sinter Bodies . 104 4.6 Suiranary 115 5 CONCLUSIONS •'-20 BIBLIOGRAPHY -"-^^ BIOGRAPHICAL SKETCH ^29

PAGE 6

Table LIST OF TABLES 3. Creep data containing before and after densities, loads, temperatures, total creep, total test time, and Andrade constants e , a, and n Page 1. Chemical analysis of the Sherritt-Gordon nickel powders used in the experimental work 19 2. Loose stack densif ication data for -20^:, 30(i, 57p„ and 115'^ nickel powders at 1100^' C, 1250° C, 1350° C and the corresponding calculated incremental average shrinkage rates 41 45 4. Quantitative microscopy data of polished sections Creep Samples and Loose Stack Sintered Samples .... 56 5. Quantitative metallography of fracture surfaces .... 79 6. Calculations of the components of the stress activated sintering model 1^0

PAGE 7

LIST OF FIGURES Figure 1. 2. 9. 10. 11. 12. 13. 14. 15. Page Intraparticle porosity in the nickel powder 20 Scanning electron photomicrographs of -20|j, and SOp22 nickel powders Scanning electron photomicrographs of 57 p, and 115 p, 23 nickel powders 27 Creep furnace in operation Molybdenum creep rig with sample in test position .... 28 Stainless steel plate supporting the molybdenum creep ..... 29 rig Working surface of creep apparatus as in operation ... 30 Densific-.tion curves for the four particle sizes v.'hen loose stack sintered at 1100° C • ^^ Densification curves for the four particle sizes when loose stack sintered at 1250° C ^^ Densification curves for the four particle sizes when loose stack sintered at 1350°C '^ Shrinkage rates of -20^L, ?>0\i, 57^i, and 115i.i nickel powder specimens at 1100° C ' ShrirJ^age rates of -20'^, 30 |i, 57 n, and 115 |i nickel pov/der specimens at 1250^ C Shrinkage rates Lh/L /hr for -2Uu, SOp,, 57 ii and 115(i nickel powders at 13§0°C 40 The creep of 80% dense nickel samples of four different size fractions versus time at 1100° C and 500 P.S.I. . . 50 The creep of S0% dense nickel samples of four different size fr.^ctions versus time at 900° C and 1000 P.S.I. .. . 51.

PAGE 8

LIST OF FIGUKl'S (Cont iniied) Page i-igxire IGa. The creep of 80% dense nickel samples of four different size fractions versus time at 700'^C . nd 1000 P.S.I. S'J 16b. Creep curves of 100% dense samples made from -20ii, SOjj,., and IIS^L particle size fractions at 1000 P.S.I, and 900° C "^ 17. The dependence of the creep of 80% dense 115^1 particle size samples on temperature at a constant load of 1000 P.S.I ^'^ 18. The effect of starting density on creep of samples made of 115^1 powder and tested at 900°C and 1000 P.S.I 61 19 The effect of starting density on creep of samples made from 115 ',J. powder and tested at 1100^ C and 500 P.S.I. ... 52 20. The effect of starting density on creep of samples made from 115 ^i pov.-der at 1100° C and' 250 P.S.I 63 21 The effect of starting density on creep of samples made from 115ii pov/der and tested at 1100° C and 100 P.S.I. ... 64 22a. The effect of stress on 65% dense samples made from 115^1powder and tested at 1100° C *55 22b. The effect of stress on 65% dense samples made from llS^i powder and tested at 1100° C ^^ 23. The effect of stress on 70% dense samples made from 115[i powder and tested at 1100° C ^' 24. The effect of stress on 75% dense samples made from 115 [i powder tested at 1100° C '^^ 25. The effect of stress on 80% dense samples made from 115m, powder tested at 1100° C ^^ 26. The effect of stress on 85% dense samples made from 115^, powder and tested at 1100° C ^^ 27. The effect of stress on 80% dense samples made from 115^ powder and tested at 900° C ^ "

PAGE 9

LIST OF FIGURtS (Continued) Figure 23. Surface area (S^^) versus voIu;,ie fraction porosity (V^) for t]ie 30u, 57 ^i., and 115nickel powders loose stack sintered to different densities 29. S versus V for crept 115u samples compared to S^ 30. ve 32. Tlie percent fracture area versus percent creep undergone by 63% dense, 115 ^i samples at 700*^0 33. Number of intersections of fracture outline with test probe per unit length of probe, X^_j,, plotted against percent creep undergone by 63;; dense, 115 u samples at 700° C 34. Number of fracture areas per unit area of exposed fracture, N , plotted against percent creep undergone by 65% dense, 115^. sampDes at 700'C 35. A versus percent density for samples of -20^.,, 30)i, 48 ji, and 115 |j, samples 36. Total creep after two hours for five densities at 1100°C with a = 1510 P.S.I Af 37. Total creep after two hours for three densities at 1100'= C with a, = 3020 P.S.I \± 38. Noi-malized fracture stress and area fraction of fractured surface plotted against volume fraction porosity for sintered nickel tensile bars 39. -Jodel showing change in state of stress of a sintered pore from the addition of an external compressive load Page 72 rsus V for loose stack sintered samples 74 Anisotropy in surface area of crept samples, plotted as a function of the amount of creep 75 31. Apparatus used to fracture notched, sintered saniples for quantitative metallography of fracture surfaces . . 77 78 81 83 84 85 87 90

PAGE 10

LIST OF FIGURES (Continued) Figure Page 40. Density change undergone by 80% dense creep samples at various temperatures and varying amounts of creep ... 93 41. Creep of -20[i samples at four densities at 1100°C with a. = 1500 P.S.I 102 42. Creep curves of 100% dense, -20|i and llSjj, samples at 1100° C and 1500 P.S.I 105 43. Model used in the analysis of creep and stress assisted sintering 109 44. Total creep in test versus percent calculated from the model to be stress activated sintering 112 45. Total time of test versus % h as calculated from the model f 114

PAGE 11

Abstract of Dissertation Presented to tlie Grnduate rouncil of the University of Fiorida in Partial Fulfillment of the Requireiacnts for the Degree of Doctor of Philosopliy HIGH TE?,n=ERATURE COMPRESSIVE CREEP OF SINTERED NICKEL By WALTER RAI.PH TARR Aug-ust, 1973 Chairman: Dr. Frederick N. Rhines Major Department: Materials Science and Engineering Compressive creep of sintered nickel was performed under the follov/ing range of conditions. Temperature 700° C 900° C Load 25 P.S.I. 4000 P.S.I. Density 60',; 100% Particle size -20}i, 115u. The data show that the creep rate was determined by the load on an effective cross section of material which was determined to be the fracture cross section in tension. This cross section called the area fraction of fracture surface is designated A^^. The effect of sintering on the creep process was determined to be primarily one of returning the pore shape to isotropy after the pore was deformed in creep.

PAGE 12

CHAPTER 1 INTRODUCTION The powder metallurgy field has been an art throughout much of history. With the application of materials science and quantitative microscopy, the geometric processes through which a loose powder aggregate goes during the sintering process are well established. Tlie fabrication of parts by the use of powder metallurgy techniques and the application of these parts in the severe environments of high temperature, high load, and sometimes high neutron flux demand an understanding of how a porous material acts under severe conditions. An aggregate of powder possesses more energy than a solid piece of the same material of the same mass because it contains more surface area. This energy, called surface energy, comes from the fact that there is an imbalance of energy associated with atoms situated next to a free surface. When particles which are in contact with each other are heated to a high temperatiore, but below their melting point, they weld together and density into a solid mass which may approach the theoretical bulk density of the material. ITiis densif ication process is called sintering and is driven by the surface energy possessed by the powder aggregate [1,2,3,4,5,6].

PAGE 13

Another phenomenon seen primarily at high temperature is creep, which is the time dependent strain of a material under a stress. The driving force for creep is the stress applied to the part. This time dependent strain of a part in service becomes critical where close tolerances are required for long times under severe operating conditions. An example of severe conditions encountered by porous materials is that of sintered fuel elements for reactors. The sinter body must be reasonably dimensionally stable at high temperatures, high stress, and high neutron flux. Applications such as fuel elements wed the problems of the sintering and creep processes so that a knowledge of how a porous body reacts under load at high temperature and the physical changes that take place in the structure becomes necessary. 1.1 General Chpracteristics of the £interir;s Process Loose stack sintering is the term applied ro the phenomena by which an aggregate of finely divided particles welds together and densifies at high temperature. This densif ication requires neither melting nor the application of an external load. A reduction in surface area is effected with densif ication with the attendant reduction of surface energy and thus the total energy of the system. Due to the complexity of the geometric changes taking place during sintering, the topological approach to the evolution of the microstructure of a sinter body developed by Rhines C?] will be used as a basis for description of the changes that take place as a mass of loose powder proceeds from separate parts to a single dense body.

PAGE 14

The sintering process is coriTeiiieiitly thought of as possessxng tiree stages [1,8]. The first stage is chaxacterized by the weldizig and growth of particle contacts and the smoothing of particle surfaces. The topological state, i.e., genus, fixed by the original stacking, remains constant during this process. The particle network is striving for a minimum surface energy for its given topological state. As the surface total force/unit area is greatest at areas of highest curvature, the largest geometric changes take place at weld necks, particle comers, and fine tips in dendritic powder, where this force is the largest. The surface energy expended in rounding the internal surface is wasted as far as densif ication is concerned as no process which acts solely on the surface can contribute significantly to the densification of the particle compact. The weld necks grow and surface rounding continues until a minimal surface for the given topological state has been effectively achieved. Further reduction in surface area can come about only by reducing the genus, i.e. , connectivity of the pore network; i.e., second stage sintering. Second stage sintering is the stage in which the pore network goes from a completely interconnected state to a completely isolated state. As the connections between pores, or channels, are pinched off, a new minimal surface area state prevails corresponding to the new topological state. This direct dependence of minimal surface area on state can be seen in the fact that during second stage sintering, the surface area per unit volume, S^, decreases linearly with increase in density. Channel closure persists until all porosity is isolated. Particle identity is generally lost during

PAGE 15

second stage. Third stnge sintering is concerned with what happens to the isolated pores. As time proceeds, conglobation of the remaining porosity occurs. The large pores gro-.v at the expense of smaller pores, thus the average pore size becomes larger [9]. Some reduction in total porosity also is characteristic of third stage. Total removal of all porosity from the interior of a sinter body rarely, if ever, occurs solely under the action of the sintering force (surface tension) in the finite time of sintering operations. Densif ication occurs in all three stages of sintering and the three stages overlap in the times in which they occur. 1.2 Background and Previous Investigations of Sintering Sintering lias been used in the manufacture of products from particles of all classes of solids: metals, ceramics, glasses, and organics [1]. Commercial sintering is seldom loose stack sintering, but commonly uses pressure on the powder aggregate to promote densification or a liquid phase for the same purpose. Most processes that involve sintering constitute one or more of the following: 1. Loose stack sintering. The loose powder stack is heated to a temperature near its melting point and densif ication occurs with time. 2. Pressed and sintered. Much or most of the densif ication of the powder aggregate is achieved by the application of high pressure preceding the sintering operation. Densif ication from tlie pressure occurs liy plastic deformation and/or rearrangement of the particles.

PAGE 16

3. Hot pressing. The application of pressiu'e during the sintering process [-1] . 4. Liquid phase sintering. Sintering with the aid of a liquid phase [2,10]. The geometry of a loose stack of particles such as is found in normal, practical sintering appears complex. Some of the approaches that have been put forward to help in the understanding of sintering are the use of equi-sized particles, only two particles [11], a string of particles [12], a particle on a plane surface [13], three wires twisted together [4], spools of wire [4], constant temperature, and controlled atmosphere. The study of sintering in these relatively simple cases has given insight into the growth of weld necks and some understanding of the densif ication phenomenon, decrease in the relative volume of porosity, but have been generally unsuccessful in explaining the total sintering of even a simple shape which contained a large number of particles. Mathematical models can be formulated for simple cases and with the use of known physical parameters, mechanisms have been inferred. A basic fault with all the foregoing geom.etrically reduced experimental models is that the information is 1or 2-dimensional and practical sintering is complex 3-dimensional . Some investigations of the three stages of sintering will now be presented. The first stage of sintering includes weld neck growth and surface rounding. Surface rounding can be accoKipl ished by evaporation of material from convex surface and condensation on concave, or less convex, surface 12,10]. Surface and volume diffusion [7,14] can cause

PAGE 17

surface rounding by the net transfer of material from convex surface to concave surface. It should be noted that neither evaporationcondensation nor surface diffusion can cause significant densif ication in a powder aggregate [1,4,7]. It is thought that the growth of weld necks can be caused by several mechanisms. They are: evaporationcondensation [15], surface diffusion [4,11,12,16,17], volume diffusion [4,7,10,11,15,18,19,20], viscous flow [2,4], and plastic flow [7,20,21, 22,23,24]. It is also believed that densif ication requires both creep and concurrent surface area minimization [25]. Calculations using the surface tension value obtained for copper (1400 dynes/cm) have shown that plastic flow is possible at least in the early stages of neck growth where contact area is very small [4] . Observations of weld necks formed in loose stack sintering experiiaenls show that there is at least one of the mechanisms capable of surface rounding in operation during neck growth. The rounded neck surface could not have been created by plastic flow alone. In metal systems having low vapor pressure [11], the rate of weld neck growth, as indicated by experiments with particles on plane surfaces and pairs of particles, is believed to be either surface diffusion or volume diffusion controlled or both. Kuczynski [11] found for copper that surface diffusion was the dominant mechanism for small particles and low temperatures, while for large particles and high temperatures, volume diffusion was dominant. Second stage sintering is characterized by densif ication of the body and the isolation of the pores that remain [1,7,8,9],

PAGE 18

The connectivity of the porosity goes to zero [7]. There are three material transport mechanisms that various authors believe capable of causing densif ication. They are: creep [7,8,20,22,26], volume diffusion [4,14,26,27,28,29], and grain boundary diffusion [14,22,23, 29,30,31,32]. Sintering done under small loads [20,24] indicates that there is no change in mechanism as the sinter body densif ies. This information supports the plastic flow theory. Support for the grain boundary diffusion theory may be found in the lowered sintering rate [27] after grain growth. Wire model experiments also show decreased pore size in the vicinity of grain boundaries. Volume diffusion of vacancies to the external surface from the internal pores has been generally discounted due to large distances involved [7]. Third stage sintering is usually defined as the elimination and/or coarsening [9] of the remaining isolated porosity. Plastic flow is believed responsible for elimination of pores by some and a theoretical model [22] for the shrinkage of these isolated pores by plastic flow has been derived. Coarsening of large pores at the expense of disappearance of smaller surrounding pores can be accomplished only by volume diffusion [9]. It has been shown by several authors [2,14,30] that the presence of grain boundaries can cause a significant increase in total densif ication; however, grain boundaries are not required for densif ication [4,9]. Volume diffusion is postulated by some [14,27,28] as the mechanism of pore shrinkage; whereas, others [7] believe volume diffusion of vacancies from an internal pore to the external surface cannot effect any significant densif ication of the total body. Densif ication rates based on volume diffusion data

PAGE 19

indicate that the times required for densif ication are unreasonable and that geometry would require that the sinter body density from the external surface inward, contrary to experimental observation [9,33]. It can be seen from the preceding paragraphs that considerable discussion of the exact nature of sintering still remains along with considerable, seemingly conflicting, experimental evidence. There is at present no formula in the literature into which one may insert the physical properties of a metal or a ceramic powder and predict the densif ication of a compact from a loose stack to a fully dense mass. 1. 3 General Characteristics of t he Creep Process Creep is defined as the time dependent strain undergone by a material when subjected to a stress at constant temperature [34,35, 36,37,38,39]. At elevated temperatures where recovery processes are relatively active, small stresses which are a fraction of the tensile strength are capable of causing plastic deformation in metals. Some materials will show this phenomenon when subjected to room temperature tensile tests at different strain rates. This may be seen in the stress-strain curves of pure metals such as aluminum and zinc where the stress-strain curve of the tensile bar pulled at the slower strain rate shows a greater strain for a given stress. Constant load tensile creep is generally thought of as possessing three stages [34,40]. The first stage is a period of decreasing creep rate where work hardening mechanisms are dominant [41]. In the creep of polycrystalline samples, the grains with orientations favorable to shear are the first to deform. This inhomogeneous

PAGE 20

deformation produces elastic as well as plastic strains and tlicse elastic strains arc recciverablo wifh tinie if tlie specimen is unloaded. This re'coverable ci'oop is called an.elastic creei). The second stage is considered a stage of constant creep rate v/here tlio rate of v/ork }iardening being produced by the deformation is exactly coimteracted by recovery pi'ocesses [42,43] and/'or reduction in cross-sectional area of the sample [39]. The third stage is generally characterized by an accelerating c^reep rate, intci'granular cavity foi'mation (at higli temperature) [44 ,45 , 'le] , necking (at low l emperature) [44] , and ultimate failure. Constant stress and constant load com.pi'essive creep in ductile metals generally exhibits only the first stage of creep, and thus generally shows a monotonically decreasing creep rate tlirougliout a test [47]. 1.4 Background a nd Previous Investigations of the Creep Process Creep is seen to be a sensitive function of temperature and lor a given structural state has been shown to have an Arrlienius temperature dependence. Creep is therefore generally considered to be a thermally activated process [34,36,37,38]. Activation energies calculated from strain rate versus tem.perature data are usually close to the activation energies of self-diffusion when the creep temperature is between 5 and 1 T [34,36,38,48]. There is much discussion concernm ing the exact mechanism that allows creep to proceed. Some of the iransport processes proposed as controlling tl:e kinetics of tlie high temperature creep process are: diffusior.al creep (Xabarro-Ilerring creep

PAGE 21

10 [36,40,49,50,51]) and others [52,53], dislocation intersection and jog formation [34,54,55,56], and climb of dislocations [36,56,57]. 1.5 Dislo cation Modelling There are many formulas that have been used to model the first and second stages of creep [58,59]. Some of the equations have elements which match known physical parameters, whereas others are strictly empirical. A few of the well-known creep laws or formulas will now be presented with explanations based on physical parameters where possible. Logarithmic creep [34,40], e = a Log (t) + c. Log creep has been found in organics, glasses, metals, and ceramics and is generally found in experiments of moderate to low creep rates, small strains, and temperatures below 0.4 T . This type of creep has a raonotcnically m decreasing rate such as found in the transient, 1st stage of creep curves. Log creep can logically be reasoned to be a result of exhaustion of energy barriers to deformation capable of being overcome by the applied stress on a sample and local thermal fluctuations [34]. As the material deforms, the barriers to further deformation (dislocations, etc.), increase, thereby requiring more energy to overcome them and cause further deformation [60]. In constant stress creep there exists a constant external stress plus the thermal fluctuations. Thermal fluctuations are capable of helping overcome normal lattice coherency (Peierls force), but as deformation proceeds, these regions requiring minimum force to push a dislocation through are used up and only regions

PAGE 22

11 requiring more energy (higher activation energy) remain. Thus the creep rate decreases. The log creep equation cannot account for steady state creep. 1/3 Andrade creep [59,61,62,63,64], e = bt . This type of creep has essentially no acceptable theory to explain it. The reason for the widespread use of the Andrade formula for transient creep is that many researchers [47,65,66] have found that it can be successfully used in plotting experimental results. The Andrade creep formula generally fits better in creep experiments where large creep strains and temperatures greater than about 0.4 T are involved. The basic Andrade creep " m equation will not fit curves where steady state creep has been involved, for steady state creep requires a linear term in time [40]. The fit of the Andrade creep formula can be improved in cases where steady state has occurred by the addition of a linear term, e = kt (k= const.). A term for instantaneous strain on loading, s i;67,68], is also frequently added, thereby making the Andrade equation, e = e + Dt + kt. For monotonically decreasing creep rates, the linear term, kt , is omitted. A constant creep rate (for a constant stress) , implies that some recovery of the creep sample is taking place during the creep experiment. This dynamic recovery [69,70] is most likely cross-slip and climb. Under some conditions of stress and temperature, a combination of the log and Andrade creep equations fit the data best. Tlieory has of course been left far behind. Some authors do not find stage two creep for constant stress tensile tests [68,71] and observe a monotonically decreasing creep rate from the onset of loading to the initiation of failure.

PAGE 23

12 Diffusional creep (Xabarra-Herriiig: cxeep) . Dtffustanal creep is believed hy many authors to be stress directed self-diffusion. Atoms diffuse away from grain boundaries under compressive stress to grain boundaries under tensile stress, resulting in sample elongation in the tensile direction. The natvire of diffusional creep is such, that very high temperatures, very low loads, and a fine grain size are required for it to be the dominant creep mechanism. The strain rate for Nabarro-Herring creep may be given by the equation, e = (aD/L^)(crS ^kT) , 2 where a = const, about 5 for uniaxial stress, 6 is an atomic volume cb where b is the Burgers vector and c is a constant about 0.7, D is the diffusion coefficient, and L is the grain diameter. That creep obeying; this equation e:iists has been shown by several authors [36,4Q,4i?, 50,56]. None of the foregoing creep and creep rate equations is capable of modellingor predictingthe occurrence of or the results of massive recovery such, as recrystallization. Generally, v/hen recrystalliza-tion occurs during a test, the creep rate increases [72,73]. There are many variables affecting^ the creep rates of materials, some of which are temperature, shear modtilus , grain size and snbgrain. size, stacking fault energy, stress, composition, and diffusion rate. The manner in which some of these parameters are known or though.t to affect creep will now be discussed. Temperature, Creep is g-enerally considered, a th.ermally activated process because It has an Arrbenius temperature dependence; therefore,

PAGE 24

13 the temperature at which a material undergoes creep deformation is of primary importance. Creep is usually thought of as a high temperature phenomenon, 0.3 to 1.0 T , primarily because its effects are most comm monly observed in this temperature range. However, creep has been reported at temperatures below 10°K. Thermally activated processes ^^ (AHc/RT), , are exponential functions of temperature; i.e., f(e ;, ana for most materials, AHc, the apparent creep activation energy, is such that recovery processes become reasonably active above about 0.3 T^. Diffusion. Self-diffusion is now generally accepted as being the ultimate controlling process in most high temperature creep [38], Nabarro-Herring creep is generally thought to be stress directed volume diffusion (though not by all researchers) [51 ,52] . Climb of edge dislocations also has diffusion of vacancies to or from the dislocation core as the rate controlling step. Many experimentally determined high temperature creep activation energies for most metals and many ceramics are found to be identical to or very near the activation energy of self-diffusion. Creep rates are found to change abruptly with an abrupt change in diffusivity and in the same proportion. An example of this is found in the phase transformation of iron. In ceramic compounds, the high temperature creep activation energy is usually close to that of the diffusivity of one of the elements of which the compound is composed. Shear modulus [38]. The dependence of shear modulus on temperature is generally ignored. This is usually not critical, but significant deviations from creep rates predicted by self-diffusion data

PAGE 25

have been corrected by introducino; the temperature dependence of the shear modulus into tlie creep equation [74], Stacking fault energy. In general, the lov/er the stacking fault energy, the lower the creep rate [35,38,75,76,77]. A low stacking fault energy allows widely split partial dislocations which must recombine for the dislocation to climb. Stacking fault energy is also a determining factor in the size of the substructure units (subgrains) , formed during deformation. Grain size. That grain size can in many cases have an effect on the creep rate of a material is accepted by most investigators [38,70^ 78,79,80]. Some authors show that a small grained material has a lower creep rate than the same material in large grain form at one tem.perature, while others see Lhe opposite "at another temperature [80]. Other authors have found a grain size effect only below a certain grain size [78]. llie amount of grain boundary is that property which grain size determines which is of interest in creep. Grain boundaries, being discontinuities in a structure, act as barriers to the movement of dislocations. If the grain size is small enough for a significant portion of the work hardening to be a result of dislocations piling up at grain boundaries, then one could envision the effect of changing grain size (amount of grain boundary) , in this grain size region. If one decreased grain size (increased grain boundary area) , there should be a decrease in creep rate and vice versa. If, however, the grain size is large enough that the pileuij of dislocations at grain boundaries is insignificant compared to pileups in the interior of the

PAGE 26

15 grain, then varying the grain size would be expected to have little effect on creep rate. The grain size at which grain size becomes an important factor in determining creep rate depends upon properties of the material such as stacking fault energy and morphology (precipitates, etc.), although there is no uniformly accepted trend. The amount of grain boundary shear may also be tied to the amount of grain boundary. Grain boundary shear is the phenomenon in which the volume of a grain adjacent to a grain boundary shears to a greater extent than the bulk of the grain due to accelerated recovery [35,36,81] (generally polygonization) [82] , of the crystal in this region. It has been shown in bicrystals [81] that a significant portion, 40%, of total shear can in some cases be attributed to grain boundary shear. Some authors state that grain boundary shear can be a significant portion of total creep in polycrystalline metals, while others discount its effect. Grain boundary shear appears to be important to the formation of cavities [83,84,85] leading to the commonly observed intercrystalline failure of high tem.perature creep samples [86], Stress. The effect of stress on creep of materials and the resultant structure is complex. The stress dependence of creep is generally divided into three regions [7] , The low stress region 1 • 5 where e °: ct , intermediate e -^ CT , and high stress region where e oc e^'^, b = constant. Most creep tests and engineering applications are concerned with the intermediate stress region v/here e is proportional to a^. The effect of stress (strain rate) on structure is a complex function of temperature, stacking fault energy, modulus,

PAGE 27

16 composition, etc., i.e., the mobility of dislocations and recovery processes. Generally in metals which form substructures, at a given temperature, the higher the stress and consequent strain rate the finer the substructure formed. The subgrain size formed in high temperature creep seems to be independent of deformation (creep or cold work), previous to a given test [35]. If, during a creep test the stress is changed, a new subgrain size will be formed which is characteristic of the new stress [35]. Recent work in pure aluminum indicates that increasing the temperature (and consequent strain rate) during a creep test will reduce subgrain size [82]. The primary problem in trying to determine the exact nature and influence of each of the aforementioned parameters is that it is difficult, if not impossible, to alter any one without affecting some or all the others. This is probably the basis of much of the conflict reported in the literature. 1. 6 Purpose and Scope of This Research The purpose of this research is to provide insight and quantitative data relating to the structural states through which a sintered nickel specimen goes during a compressive creep test. The nature of the interaction between the creep of sinter bodies and concurrent sintering is studied. Structural changes in a sinter body can most easily be studied through the use of quantitative metallography. Many of the well-known quantitative metallographic functions are used. ITiey are: A V S. N and N . A new quantitative metallographic function has' A ' V ' \' ' L A been defined during the course of this research which has proved to be

PAGE 28

a useful tool in predictingt])e stren<;:t]is of sinter bociics. This function A , is a measure of the load bearing area in a sinter body. ' Af A is the standard A count taken on the fracture areas of a fractured Af A sinter body. V.hen a sinter body is fractured, tiie fracture should take the path of least resistance, i.e., the weakest section. Tlius , the measure of the area covered by fracture relative to the total cross section of the sinter body should be a measure of load bearing area in the sinter body. This research encompasses a 400'' C tem.perature range, a4000P. S.T. load range, particle sizes from -20 u to 115 ^.i., and densities from loose stack to 100";; dense. The response of sintered nickel bodies under various combinations of these parameters has been studied and presented. The creep and creep rate data have been modelled to the equation e = e + at^ and the effect of the various parameters on this equation o ai'e presented.

PAGE 29

CHAPTER 2 MTEra. AL SPEC! FI CATI OXS 2.1 Material The material used in the experimental creep work was nickel powder purchased from the Sherritt Gordon Company. The nickel powder was received in two lots, one of predominantly fine particle size (-270 mesh) and the other of predominantly coarse particle size (-48 + 200 mesh). The chemical analysis of each lot is given in Table 1. The powder was produced by an electrolytic process which resulted in an irregular particle at small size fractions which became m.ore spherical as tlie powder size increased. All particles had a lumpy surface texture resembling that of a blackberry. Tlie individual particles were not always solid and upon metallographic preparation intraparticle porosity could be seen as shown in Figure 1. Fractures of low density specimens of the coarse, -120 + 149, 115 [i, size fractions occasionally showed that the outer layer of one of the particles was torn from it at the point of fracture. 2 . 2 P article Sizes Used The powder, as received, was sieved througli a set of U.S. Standard sieves made by the \v. S. Tyler Cuinp;iny. Three of the size fractions used were sieve cuts fro:ii this series. Tlie tlrree size 18

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Table 1. Chemicol analysis of tiie Sherritt-Gordon nickel jjowders used in tlie experimental work. Property Lot ^1 Lot ^2 Composition \vt % Nickel (includes Cobalt) Cobalt Copper Iron Sulfur Carbon Apparent Density (gm/cc) 4.61 3.76 Dominant Size Range (-4S-;-200) -270 (mesh) 99.9

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20 Figure 1. Intraparticle porosity in the nickel powder.

PAGE 32

fractions fro!:i the Tyler sieves were: (1) coarse (-120 ^ 140, 115 a), (2) intermedinte (-230 i 270, 57 ^) , and (3) fine (-400 + 500, 30 \i) . A fourth size fraction was prepared by taking the fines wliich passed through the 500 sieve and further sieving it on screens in an AllenBradley Sonic Sifter. The size fraction used from this sieving was the powder which passed through the 20 ix screen, designated -20 jj.. Scanning electron microscope photographs of these four size fractions may be seen in Figures 2 and 3. Specimen notation throughout the woil-: is keyed by both a letter and a number. The letter denotes the size fraction from which the samples were prepared and the number denotes the chronological order of testing. The notation is as follows: A # = -400 -1500, 30 microns (p.) B ~ '-= -230 + 270, 57 microns (yi) C F = -120 -i 140, 115 microns ('|_l) -20 microns = -20 microns + (average 11 (i) . 2.3 S ampl e Preparation The procedure for manufacturing the loose stack sintered specimens was the following. Previously sized powder was poured into a graphite mold containing 10 to 12 flat-bottomed holes .375 inch in diameter and .75 inch in depth. The m.old so charged was then inserted into a nichrome wound, silica tube, presintering furnace which was maintained at lOOO-'C. The atmosphere in the presintering furnace was wet hydrogen. Presintering time was 1 hour, after which, the graphite boat was withdrawn from the furnace and th.e lightly sinter. ^d blanks were tapped out of t!ic mold and the mold was reused.

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22 -20 p, 2000X 30 |j, lOOOX Figure 2. Scanning electron photomicrographs of -20 )i and 30 p, nickel powders.

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23 57 (J, 500X 115n 500X Figure 3. Scanning electron photomicrographs of 57 ;i, and 115 ^ nickel powders.

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24 The temperatures used for sintering varied from 1100° C to 1400° C. The sintering furnaces were globar heated and had high purity impervious alumina tubes. The boats in which the presintered blanks were placed for sintering were also of high purity alumina. Any material with any appreciable trace of silica in the sintering environment resulted in destruction of the sintering blanks due to liquation at the surface of the blanks or, in some cases, complete melting. The dissociation of the water in the wet hydrogen atmosphere provided a back-pressure of oxygen which effectively retarded any SiO transport at sintering temperatures. Samples above 93% relative density were made by hot-pressing the powder in a graphite mold at 1200° C. A 1-inch diameter blank was made in this way which was 91% dense. This large blank was then annealed in wet hydrogen at 1000°C and cold-pressed at 70,000 F.S.I, to 96.5% relative density. Several nominally identical high density specimens were than electro-discharge machined from this blank and annealed. Samples which were 100% dense were first hot-pressed to 97% relative density, annealed and swaged. All hot-pressing was done in grapMte molds. This procedure resulted in the contamination of the specimen with enough carbon to cause melting at 1400° C. The samples were therefore given a decarburizing treatment at 1000° C which consisted of 1 hour in a slightly oxidizing atmosphere, commercial tank nitrogen, followed by 30 minutes under hydrogen. Density measurements were made by using a wax impregnation Archemedes method. The sample was weighed (dry weight) , impregnated

PAGE 36

with wax, and weighed again (wax weight). Tiic impregnated sanple was tlien supported by a line wire and weighed while immersed in water (H weight). The wire weight was the weight of the wire suspended in the water. The density was determined from the following equation;: 3 Dry weight Density (gm/cm ) --^ ^^^-^T^ight (il^O weigh.t V;ire weight) Relative density could then be obtained by dividing by 8.906 gm/cm , the theoretical x-ray density of nickel. If the desired density of nickel had not been reached, the wax was burned out in air and the blank returned to the sintering furnace for further sintering. This process was repeated until the blank had a measured density equal to the density desired, ± 0.5%. A blank of the desired density was then machined on a Schaublin 70 high precision latlie. The specimen was a right circular cylinder with a tolerance of ± 0.0002 inch on the diameter and with the ends within 0.0002 inch of being parallel. 2.4 Exp erimental Investigation into t he Creep of Sintered Nickel The experimental investigation of sintered nickel was done in compression, encompassing a wide range of loads, Temperatures, particle sizes, and densities. 2.4.1 Equipment (Creep Apparatus) The creep apparatus consisted of a globar furnace with an impervious alumina tube in which ti^c sample and loading rig were inserted for the test. A complete view of the creep apparatus in

PAGE 37

operation is sliown in Figure 4. The loading rig in v.hich the sample was placed for testing consisted of three — incli di ar.eter rnolybdeniiin I'ods bolted to a 1 inch diameter molybdenum base plate which supported the sam-ples. Loading was effected by means of a fourth — incli diameter molybdenum rod which used the three support rods as guides (see Figure 5). The support rods were bolted to a stainless steel plate whicli was bolted to a large aluminum, plate v.hich served as the working surface for the remainder of the creep apparatus. The stainless steel plate also had a gas outlet in it as well as holes for the loading rod and measuring thermocouple which was positioned next to the test sample. A pliotograph of this part may be seen in Figure 6. Loading was accomjjlished by a 3 to 1 lever which had a 'oall bearingpivot. The load was transferred to the loading rod from the lever arm through a ball beai-ing set into a piece of steel. This ball bearing liad a flat ground on it on which the dial gage rested. V/ith the dial gage directly over the sample, one could read deflection of the sample directly during the test. The dial gage had a range of 0.4 -4 -5 inch and direct readings to 10 inches with estim.ates to 10 inches. The height of the lever arm pivot and the dial gage was adjustable to accommodate different length specimens. Tlie working surface of the ai)paratus is shown in Figure 7.

PAGE 38

27 Figure 4. Creep furnace in operation.

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28 Figure 5. Molybdenum creep rig with sample in test position.

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Figure 6. Stainless steel plate supporting the inolybdenim creep rig.

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Figure 7. V/orking surface of creep apparatus as in operation.

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31 2.4.2 Test Conditions The range of conditions of the test parameters is as follows: 1. Temperature 700° C 1100° C 2. Load 25 P.S.I. 4000 P.S.I. 3. Density 60Tc lOO^c Rel. Density 4. Atmosphere Wet Hydrogen. 2.5 Experimental Procedure A specimen machined to the desired size was measured with a micrometer before inserting into the creep apparatus while outside the furnace. The specimen sat on an alumina disk and had one resting on it. The loading rod was then lowered onto the sample to avoid sample movement and consequent misalignment during insertion of the rig into the furnace. The rig was lowered into tlie hot zone of the furnace, at which time the loading rod was lifted from the sample and remained off until the sample temperature had risen to test temperature and the creep test was to begin. While the sample was coming to temperature, as measured by a thermocouple placed next to the sample, the lever ami was placed over the loading rod and the dial gage was locked into place directly over the rod. Wlien the test was to begin, the loading rod was lowered to contact the sample, an initial dial reading was taken, and the load applied at time zero, t , for the start of the test. Dial readings were taken at intervals to record the creep curve and a temperature reading at the same time. At completion of the run, the load was removed from, the sam.ple and the entire rig was removed from the hot zone of the furnace. The loading rod was lifted from the sample

PAGE 43

32 immediately at the end of the test. Elapsed time from the end of the creep test, removal of load and loading rod from the sample, to removal of the sample from the furnace hot zone was generally 3 to 5 minutes. All creep work was done in a hydrogen atmosphere to prevent oxidation of the sample and the molybdenum creep apparatus. When the sample had cooled, the final length was measured and the per cent error of creep measurement was calculated according to the following formula: (Dq -D^) (L^ -L^) X 100 % Error = ^4 W where D Initial dial reading D Final dial reading L = Initial sample length as measured by micrometer L = Final sample length as measured by micrometer , This error was usually less than 6%. If the error was greater than 15%, the test was automatically discarded.

PAGE 44

CHAPTER 3 EXPERIMENTAL RESULTS The experimental work was designed to provide information on the creep of sintered nickel under conditions of varying particle size, density, temperature, and load. Studies of sintering kinetics were performed on the various particle size powders independent of creep testing. Densif ication rates of loose-stack sintered specimens can be translated into lineal shrinkage which may be significant in compressive creep testing. The density was monitored both before and after creep testing. Quantitative microscopy was used as a means of -following the evolution of microstructure in loose stack sintering as well as in creep testing. 3.1 Densif ic ation and Shrinkage in Sintering The densif ication (shrinkage) of nickel powder aggregates was measured as a function of particle size, density, temperature, and time. The first step needed to understand the creep of sintered nickel was to determine the sintering kinetics of the various powders. This information was needed to determine what fraction of the length change in a creep test was ascribable to loose stack sintering phenomena in a compressive creep test. 33

PAGE 45

As a jxiwder aggresate sinters and densifies, the lineal dimensions decrease. If the sintering is isotropic (under no force except that of surface tension), the lineal shrinkage nay be calculated according to the following equation: /3 .1/3 A -Vv^n1/3 ^h^ 1 t2) 1 i—^) (1) o ^ where L is the initial length, p is the initial density, Vy^ is the o o initial volume fraction porosity, and o and V^, are final states, respectively. From equation (1), the amount of strain in a creep test that is attributable to loose stack sintering may be subtracted from the total strain. The densif ication curves for the four particle sizes used in the creep experiments at three tem.peratures are given in Figures 8 to 10. The incremental average shrinkage rates versus percent density, corresponding to the densif ication curves are given in Figures 11 to 13. The incremental average lineal shrinkage rate is calculated according to the following formula: AL/L /hr 1 I ^ ft K-nft ) I /t_-t. (2) ir -.. 1 [D(t^)/p{t^)~j /tg-t^ where p (t^) and p (t^) are the densities after sintering for times t and t with t >t . The AL/L /hr is calculated between each time interval and is plotted versus the density at the end of the time interval p (t ) . All densif ication and corresponding AL, L^/hr data for Figures 8 to 13 are given in Table 2. Loose stack sintering and creep are parallel mechanisms in the shortening of a porous sintered saiaple in comoressive creep. Any change m the creep conditions which would

PAGE 46

Aq^Tsuoa "h

PAGE 47

ATlKUyQ ^j

PAGE 48

ico O <] CtXSUOC[ %

PAGE 49

1.0 0.1 0.01 0.001 0.0001 0.00001 30 40 50 60 70 % Density 90 100 Figaro 11. Shriiiknge rates of -20ij., 30u, 57ii, ami 115|.' nickel IJov.xler spcjciiucriS at 1100"' C.

PAGE 50

1.0 0.1 0.01 0.001 A -20 u. )C 30 fi O 571.L 115 II 0.0001 0.00001 L^Udo 12. 50 I 70 80 60 '-, Density Shrinkage rates oi -20^.1, 30 p., 57 ii, aaid 115 1.'. nickel powder specinens at 1250° C. 90

PAGE 51

l.() :-„ 0.1 0.01 0.001 0.0001 0.00001 40 50 60 Fifiure 13. 70 % Density Slirinkri':',e rates AL/L /hr for o 115^1 nickel powders at 1350^ C 1

PAGE 52

Table 2. Loose slack densi f Ic'.ation data for -20',!, 30p., 57 ji, and llSiJ, nickel pov/ders at 1100° C, 1250" c:, 1350° C and the corresponding calculated incremental average slirinkage rates. Particle Size, Temp. Total Loose Stack, d ("c) time (hr.s) r:= t . 25 .5 1 2 4 ' o 52.5 54.67 57.7 5 59.7 64.58 .626 .0536 .0362 .011 .0129 53.04 55.91 60.73 60.31 73.04 .637 .0696 .0544 .0289 .0159 57.88 63.8 71.6 79.7 86.00 .734 .128 .0754 .0351 .0125 47.5 50.24 52.12 54.63 .0728 .0370 .0122 .00778 51.75 53.72 57.08 60.73 .1315 .0248 .0200 .0102 57.31 60.53 64.20 69.24 .187 .0361 .0194 .0124 47.3 48.56 49.62 51.01 .0282 .0174 .00717 .00458 49.68 50.81 52.27 54.10 .0620 .0149 .00940 .00570 53.88 55.25 56.76 59.12 .0945 .0167 .00895 .00675 57.0 57.0 57.22 57.90 .00798 .00128 .00197 57.45 57.84 58.39 59.36 .0111 .00451 .0315 .00274 57.71 58.67 59.64 60.68 .0164 .011 .00545 .00287 -20|i

PAGE 54

increase the reLati.\o J.^iiKirtanee of Pint crin'j; v,-it,li i-especL to t]!;.!. oC creep will inerense Iruilpoi'tion C)!' tlierii-i'iisiu-ecl Kti'aiii v.'jiich is ;i t L:'il5i)table to Hinl"*.;i'in:;anci vice vevsu. Tor exainple, at a fj;iven tciiiperature and coiiiii.re.osivo strain rate, a samijle o:C lov.er dc:nsjty and lov.'er loaci would luu'c a c.;reater pr;rtion o;f its striiin attritnitablc to sLnteririg th.nn one oi .hi;;'hei' densitj' and hi^Jier load. liie dens j f icatioii rates ai'e entii-ely coasisten.t, witli the finest nickel po'.-:dcM' siritering faster riian the coarser i~jov,-der at eacli density and temperature level. It can ea.sily be seen that tlie shi-inkage rates due to IoijSo stack sintering v.'oulo bo lowei' for teii^peratures lo'.ver tlian ttiose in Table 2 ;nid for densities Jiigiier than those in tlio table. Densi f i ca t" Jon rates for al .1 powders fit the following eci nation: P --= e;:p i a(D ) """ e"'^' " ' ( u )'" ( (3) L o J wlierc! Pisa porositj" parameter equa^l to ^»\"\'\' i A'.'iiere V is tJie Tjoi'osity at ti.me (t) , mid \\r is Hit' loose stack jjorosity, D is tlie ^ o ' o starting particle si/^e iiiici'ons, T "K . t time (h2's) , R is the gas constant, 1.987 cal/mole"K, a :^ 1550, n r1, O rr 16,200 cal/inole, and m = 0.4. The -20;j. powder had an effective D of 11 n. ' o 3.2 Calibi'at;e ;\lj in Creep as a Function of Particle Size, Density, Load, Tempei'atu2-e , and Time The inajri thrust of tlie expej-im..'nlnil crce]) v;or]luis been the characterization of fiie effects of tlie d i P fijre.'it conditions of creep testing. Ihere v,ei'e systematic sei'ies of creep tests rial to sejiarat'-

PAGE 55

tlu; effects ol pai'ticle size, clcr.s.ily, Lenuieriiture, anci load on ci-cop I'ates and toLal creep. The data o]itaira,-d v/oi-e ci'j'Ve fitted to an Andrade type equaljon. e = c -. at". (4) o The exponent of tiiiie, n, varied v,it]i stres-s as did g and a. These o "constants" v.'ei'o jilotLed ;"is a fonction t)f stress on tlic nrinirium Eample cross section (oA ), for sa)iiplcs of the llGu, pai'tj.cle size crept 7\f ' at 1100°C. Froi.i th.e finictional depeiidence of these constants, ', o a, and n, one can Lii^-n write an ctination tJiat models creep of the 115'^. particle size sairiples as a func-.tion of sti'ess at 1100°C. Th.is oq\iation is: .cA . -.246 / Af \ ,aA , , , 1 . 42 .oA ,,,2.146 VlOO /' Creep data on all saniples vised in iliis research ai-e g'ivon in Table 3. A basic assin;!pt.i on lias bev:n made in the tests tliat wei-e un-dertaken to model tlie effects of tempei'ature, load, and density. This assumption v;as that the densifi cation effect of sintei'in;-;is negligible. This means that the dimensional chan.ge in a creejj saiaple caused by loose sLack sintering densif ical ion during a test v;as small enoi'.gh to be ignored. To tlii.s end, tlic lai'gcst size fraction of pov.der was used in ir.ost e.':periri,ents , \vi tli tlie clioice of the other conditions to ]je held constaiifc select'.'d ac'coi';u.e:';l\' .

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M < CD t°~ o o e3 o O rM ^ o 10 M o o Vl

PAGE 57

-I 1 H H yH <-',
PAGE 58

C-l W tO C5 o ^ c ;s o o o o en m ICO tCD o o o o o o o O W C) o -T m

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o o o o o o o

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3.2.1 Parti c l_c S i /. e Itffe c t Tliere were :Ccni:!' ]KnM::Lcle sizes tested \ir,clcj,' creej) conditions. They v/ere: -20,1,, -400 -i500 (30(j,) , -230 ; 270 (57 i.) , and -120 + 110 (115 t;) . Comparisons of tiit' creej^ ol the tlireo particle sizes wei-c I'un a.t Llirec dilfei'ent loa.d-tei:iiiorature comljinations , 1100'-''C and 5()0 P.S.I. , 900-'C and ] 000 P.S.I. , and 700°C and 2000 P.S.I. The results of those twelve tests may be seen iii Fit;ures 11. to 16a. For these tests, all sajnnles st.ai'ted at SO',"', dense. In all cases, (lie finer the pov.xler fi'om whicli tlie sar.iple was riade, the yreaLe^' the percent cree-p at tlie end of the tvvo-hour creci) tests. The wide difference in tlie arrioiint of creep cannot lie explained from sh.3 inka;';e due to loose stack sintering densification. Samij] es of the various powdoi's at 100',, relative density shov/ed that tiie finer the starting pov,c!ei', tlie lo'.ver the creep I'ate, This effect at 100'',:, density is due to ihe puriLj' of the riickel powder decreasing with, decreasingparticle size, Figure 16)3 and Table 1. 3.2.2 TeTiiperature FffecL Th.e tor::.pei-atvii'e effect on creep v/as studied in a series of 80% dense, llSjj, sariiples under a load of 1000 P.S.I. TJie creep curves for these five sanities laay be seen in. Figui-e 17. llie I'esults are as expected, with total crec}; and ci'eep .rate inci'casing with iricreasing ternperatiii'e. 3.2.3 Effect of Starting ]:)onsity The cffc'Ct of s'tai'ling deusitj' on creeiJ I'atc was predictal'ilc v/ith toi:al creep and ci-oep j-ate increasing with u decLvase i)i densit3'

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11 !

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-20i,i 96 O 30(1 A'i5 B 11 5 u C44 80 120 t (iidn) Figure 15. The ct'eefj of 80% deiiso nickel pnmples of four different s.ize fractions versu.s tiiae ;it 900"C and iOOO P.S.I.

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v n/"^ / / rrrcJ A" O ./^-^rA J"^^^' X -20,1 97 Q 30 ^ AS2 A 57'^ BS3 [2] 115 u CS4 40 50 120 t (mill) 160 Figure 16a. Tiio creep of 80% den?;e nickel samples of four different size fractions versus time at 700^ C and 2000 P. S. I.

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o

PAGE 65

dooxj

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55 for a set temperature and load. Figures 18 to 21 show the results of varying the density of samples while holding particle size, temperature, and load constant. 3.2.4 Stress Effect The creep rate of sintered nickel increases with an increasing stress. Figures 22 to 27 show the results of creep experiments over a wide range of loads and densities at two temperatures. In each series, the temperature, density, and particle sizewereheld constant. 3. 3 The Quantitative Microscopy of Si ntered Nickel Creep Samples Quantitative microscopy has been established as a useful tool for the description of microstructures. In the course of this work, quantitative m.icroscopic meas\!rements were taken as a means for understanding microstructural changes that occurred when a porous body underwent creep. 3.3.1 Quantitative Microscopy on Polished Surfaces The quantitative microscopic measurements were first taken on samples in the as sintered state for use as controls, then on samples which had undergone creep testing. The quantitative metallographic data taken on polished sections of loose stack sintered samples and crept samples may be found in Table 4. A plot of S^ versus porosity is given in Figure 28 for 30 ji, 57 |x, and 115 ^j. loose stack sintered samples. On crept samples, quantitative metallography data were taken in two directions, one parallel to the creep direction and one

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Pprt.

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Table 4 (Extended) Creep Samples 57 -3 n s^ = n\

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Tnble 4 (Continued) Creep Samples Part. Temp. Load p before p after C:reep S Size °C P.S.T. . ,3 ,3 % gm/cm gnv cm 137.68 C31 115 900 4000 7.12 7.84 22.14 174.38 143.7 2 C55 115 900 4000 7.12 7.58 17.23 172.48 295.80 B54 57 900 1000 7.09 7.25 3.82 306.37 -20 Li 852.88 105 -20p, 1100 292.5 60.17 69.98 18.05 904.10 -20 H 504.3 108 -20i.i, 1100 517.5 7.08 7.54 15.22 518.3

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59 %-^\ .7895 .8332 .9654 .9489 .9230

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60 Part. Size V30 57 115 Table 4 (Continued) Loose Stack Sintered Samples 6

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da O.I 3

PAGE 73

cIoo.i3

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(:•::, I

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da a. TO %

PAGE 76

cloojo %

PAGE 77

ClOO.TD

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O X <] o

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(i( Cu P-, O S X o~ 0) o H-i O do 3. to

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o o
PAGE 81

70 da a JO 'J,

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clao.TO %

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72 1600 1400 _ 1200 1000 N In "L" 800 600 400 200 . V porosity Figure 28. Surface area (S ) versus volume fraction porosity (V ) for the 30p,, 57 p,, and llSp, nickel powders loose stack sintered to different densities.

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73 perpendicular to the creep direction, rather than randomly as is generally done. This counting in specific directions shows the anisotropy created in the pore structure by creep deformation. In loose stack sintering, S varies linearly with V^^ once the conditional minimal surface area has been reached in second stage sintering. The effect of creep in all cases has been to increase S^^ relative to the S of a loose stack sintered sample which is of the same density as the creep sample after a creep test. This may be seen in Figure 29 where S ^ is plotted versus V for many crept samples of 115|i powder and all points lie to the high side (surface excess side) of the loose stack sintered line. An anisotropy factor was defined as Property in perpendicular direction "' ~ Property in parallel direction The anisotropy of S , QS , is plotted versus percent creep in Figure 30. Anisotropy varied roughly linearly with percent creep in the 30p, nickel samples, but showed much scatter in the 57 ^ and 115|i samples. 3.3.2 Quantitative Microscopy on Fra cture Surfaces Fractured surfaces of sintered and sintered and crept samples were also amenable to quantification by quantitative metallography. The quantitative metallographic parameters used in the quantification of fracture areas were: A,^, N ., and N... These quantitative metalAf Li Ai lographic measurements were taken from irregular internal surfaces which were exposed when the porous samples were fractured. Note must be made that these measurements are not taken from plane polished

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o 400 350 300 250 N CO s s 200. 150 100_ 50 .5 O O n D A o 100 P.S.I. 250 P. S. I. 500 P.S.I. 500 P.S.I. 1000 P.S.I. 1000 P. S. I. 2000 P.S.I. 4000 P.S. I. Loose Stack (3 1100°C @ 1100°C © 900° C (3 1100°C 900° C @ 1100°C @ 900" C @ 900° C @ 1300° C .1 V (porosity) A Figure 29. S versus V for ci'
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1.03 1.02 1.01 A A (30 ^:) O B (57p,) 13 C (115^0 1.00 .99 .98 97 .96 .95 94 .93 "A H A A-. 13 © O A". A 92 91 A .90 89 Figure 30 10 15 20 % Total Creep 25 30 Anisotropy in suz^face area of crept samples, plotted as a function of the amount of creep. Data include a broad range of sample configurations and test conditions.

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76 surfaces as in most quantitative metallography. The A^ measurement is defined as the area fraction of fractured surface and is simply the fraction of the total projected area occupied by fracture. N^^ is the line intercept count taken on the perimeters of the fractured areas. The N count is simply the number of distinct fracture areas ' Af recorded per unit area. A series of four samples, three of which were crept and one control sample, made from llSp, nickel powder were measured for A^_^ , N , and N . All samples were notched and then fractured in the apparatus shown in Figure 31. The notched sample was inserted into the apparatus with the notch toward the bottom. The knife edge was rested against the sample opposite the notch. The apparatus, thus assembled, was then iiimiersed in a container of liquid nitrogen. Wnen the nitrogen boil subsided, the knife edge was struck a sharp blow with a hammer, fracturing the specimen. The fracture mode was com-pletely ductile. A section of the fracture surface was cut out with a jeweler's saw, with care taken not to include any area deformed by the knife edge. These sections were than mounted and inserted into a scanning electron microscope. All counting was done by using a 5 X 5 grid of points and lines held against the display tube by the tube cover plate. The A , N , and N counts on the 115 n samples were taken at 500X magnification. The results of the "change in A^^ with percent creep are shown in Figure 32. All quantitative m.etallcgraphy data taken on fracture surfaces are in Table 5. The N^^ and N^ counts

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7 7 Figure 31. Apparatus used to fracture notched, sintered samples for quantitative metallography of fracture surfaces.

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0)

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'i'J Table 5. Quantitative metallog^'aplly of fractui'e surfaces. Quantitative microscopy of fractured as sintered samples Particle

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versus percent creej) on the fractured iireas (Figures 33 and 34) have ari initial decrease in value with percent creep, then increase as expected. The initial decrease in N and N leading to these minima is attributed to thiS close proximity of the initial contacts between particles. These multiple contacts derive from the lumpy, blackberryshape of these nominally spherical surfaces. V.'ith small compressive strains, these multiple contacts coalesce, initially deci'easing both N ^ and N For smooth spherical powders, the N and X moasureLf Af b t Ai ments on the fractured surfaces would be expected to increase with increasing creep from the ouLset. A series of A measurements was m.ade on sam.ples m.ade from Af different size fractions of powder at various densities. Figure 35 shows the results of these A measurements plotted versus V porosity. Tiie specific A , values m.ay be foinid in Table 5, It is clear fi'om these curves that A ^ is sensitive to particle shape, i.e., loose stack Af density, at low densities. The plots of A for the different particle sizes converge in the range of 0.3 to 0.2 V porosity and are identical from 0.2 to 0.0 V. porosity. These data were used to calculate the creep loads which would give the same normalized stress on the load bearing areas of two series of llSfJcreep samples. From the results in Figures 36 and 37, tlie postulate that A is a measure of load bearing area is substantiated. Severe distortion of the areas around the fractures made it difficult to distinguish fracture from, distorted metal surrounding the fracl:ure at density levels abo\-e 80';, dense.

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^ ri o

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( UtD/x) JV,.

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Figure 35. A ve L 60 70 80 ';; Densitj' rsus percent density for samples of -20i 30', and 1151-L samples.

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Q o Q © <] <> O O s

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o E <<1 13 claajo

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86 Room temperature tensile tests were made on specimens of varying densities and varying starting particle sizes. A plot of normalized fracture stress plotted versus V porosity may be seen in Figure 38 [87], As can be seen, the tensile strength of the sintered samples follows A,., the minimal sample cross section measured on the fracture surface. Af

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1.0 r o Frj'xtAire stress 70,000 P S. I. ^J V , Porosity Figure 38. Normalized fracture stress and area fraction of fractured surface plotted against volume fraction porosity for sintered nickel tensile bars.

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CliAPTER 4 DISCUSSION OF RESULTS 4.1 Description of Physical Aspects of a Sample Undergoing Creep This research was performed with the objective of gaining an understanding of the nature of high temperature creep deformation of porous sintered nickel. To this end, a general survey was made with particle size, temperature, load, and density as the variable parameters. Quantitative microscopy of polished sections and of fracture svirf aces was used extensively to determine the structure and geometry of samples in the as sintered state and to follow the structural changes which took place during creep as a means to provide insight into the process of creep in porous sintered nickel. The question now arises as to what happens to a porous sinter body when loaded compressively at high temperature. With the application of the load, the body begins to deform. The first part of this deformation is simply the elastic response of the sample to the stress and is not time dependent. Further deformation which is time dependent (i.e., creep) also begins at the time of loading. As the deformation proceeds, the energy state which exists in the pore-solid interface by virtue of surface tension is disrupted. This disruption is the change of shape of this internal interface. The sample is under a triaxial 88

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compressive stress from surlacc tension and although the value of the force exerted by surface tension on the sinter body may vary locally according to the Gibbs equation for pressure across an interface; eq. 6, the net effect is a hydrostatic corapression on the sample as a whole. 1 1 ^ (6) where AP is the pressure differential across an interface, y is the surface tension and r^ and r^ are the normal radii of curvature at a point on the surface. The application of the external compressive creep load alters this uniform compressive stress by increasing the load on the sample in the vertical direction and sample deformation (with attendant flattening of pores) changes the surface tension stress pattern further. A model of a spherical pore (radius r) is used to illustrate the changes in stress distribution (Figure 39). Figure 39, part a, describes the stress from surface tension as uniformly hydrostatic throughout; i.e., the curvature is equal at all points. Part b shows the change in the state of stress on the material after loading, but before pore deformation. Tl^ere is an increase in total force in the vertical direction from the external load, but the forces from surface tension remain the same. Part c shows the pore deformed into an ellipsoid. If the deformation has been uniform, the three axes of the ellipsoid are now (r^ , x direction), (r , y direction), and (r z direction), with r -_ r > r The V 2' ' 3 radius of curvature at point (0,0, r.^ is r^ in both the x-z and y-z planes. At point (0,r^,0) the radii ox curvature are r^ in the

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(a) "*-•

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91 r in the x-y plane. Point (r,0,0) has the sane radii b of curvature as point (0,r,,,0). The relative masnitucles of the radii y-z plane and . 2' of curvature are r^ > r^ > r^. The resulting surface tension forces are then "^o.o.rg) v(f;-^ : and 1 ^''(0,r2,0) = ^^r^,0,0) ^ >\r^ r^ Since r and r are both smaller than r it follov.s that the surface a b ^ tension force is greater at points (r_^,0,0) and iO,i\^,0) than at (0,0, r ). This change in curvature causes a potential gradient dovm which a net migration of material can occur. Surface tension forces act toward the center of curvature of a surface and will try to reduce surface area (and total surface energy) by moving a surface toward its center of curvature. The potential gradient thus results in the net migration of material by diffusion to the areas of high curvature from the areas of low curvature. This sintering action results in the reduction of total surface and a reduction in the anisotropy of the surface as measured by the R^ count. There are then two forces working against each other in terms of pore shape; the external load causing the anisotropy through specimen deformation with partial pore collapse in the cree^p direction and the local diffusion action trying to make the porosity Isotropic again. Tlie relative rates of these two actions are measured by the anisotropy of the Nj count across the pore-solid interface.

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92 Compressive deformation of a porous body results in densification through partial collapse of the porosity. There is therefore not as much barreling in a porous body which undergoes plastic deformation as is found in a solid body which cannot alter its volume upon deformation. The densification effected upon a porous sinter body by compressive deformation is seen to be generally slightly higher in high temperature creep than in room temperature compression for the same amount of deformation, Figure 40. 4.2 Si ntering Process in Creep When a porous body is held at high temperature, sintering is expected to take place. Sintering phenomena may be divided into surface changes and volume changes with surface tension as the driving force for both changes. Early in the sintering process, there is a considerable portion of the surface energy expended just in local surface minimization. There is considerable densification in early stage sintering although it is not simply related to the total expenditure of surface. As sintering proceeds , the surface area reaches the minimum it can have for the given density of the sample. From this point, until isolated poros-ity appears, there must be densification for a reduction in surface area to be effected. At this point in the process all interparticle porosity is interconnected and the surface is referred to as a conditional minimal surface. This condition may be thought of as having the surface stretched taut over the solid network. Densification occurs as pore channels are pinched off. As soon as a channel is eliminated, the

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93 20 18 16 14 12 10 Density change f <^in 80% dense 115 [J, deformed at room tem^v perature Q llSp, 1100°C Q 115ii 1000°C ©llSp, 850°C Oll5n 900°C © 115^1 700°C EI -20p, 1100°C [^ -20^i 900°C g -20^1 700°C A 30 p, 1100° C A 30|l 700°C ^ 57 n, 1100°C A 57 jj, 900° C ^ 57p, 700°C J 10 2 3 4 5 6 7 8 % Change in Density Figure 40. Density change undergone by 80% dense creep samples at various temperatures and varying amounts of creep.

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94 surface springs back to a new local minimal surface. This state of conditional minimal surface is maintained until isolated porosity appears. Tlie expenditure of surface energy is linearly related to densif ication, while the system maintains this conditional minimal area state. What is the contribution of loose stack sintering to the total deformation found in a compressive creep test? Using the rate and volume equations (equations 1, 2, and 3 of Section 3.1), one finds that the shortening of a sample due to loose stack sintering in these creep tests is negligible in all cases except in the -20ii (smallest powder) samples where it was a small, but significant portion. As mentioned in Section 4.1, sintering action in these creep tests is primarily localized and it attempts to take the anisotropy out of the surface which is undergoing mechanical deformation in creep. The pore volume is decreased by the creep deformation by collapse in the creep direction. This collapse in the vertical direction is the primary source of the anisotropy in the pore structure. The contribution of sintering in the creep of sinter bodies is local action involving particle size distances attempting to maintain a minimal surface, and pore isotropy. 4.3 Creep Creep rate of a dense specimen depends on many factors. Composition, crystal structure, and morphology of a specimen are material factors and temperature, load, and time are test conditions which alter creep rate. Most samples in this research have two more

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95 variables which are particle size and sample density. Tlie following discussion is concerned with the effects of particle size, temperature, density and stress on the creep of porous nickel samples. 4.3.1 Particle Size Effect It was found that the particle size from which a porous sample was made has a large effect on creep rate. It was always found that the finer the powder from which a porous sample was made, the more the sample would creep under a given set of conditions. It might at first be supposed that the difference in creep rates might be explained by the faster sintering rates of the samples made from the finer powders. Reference to the AL/L /hr values in Table 2 show that the sintering o rates of the different powders are far too slow to make the magnitude of difference seen in these tests. From the chemical analyses of the powder lots received, it is known that the purity of the powder decreased with decreasing particle size. Wlien 100% dense samples made from the different particle sizes were tested, it was found that the finer the particle size from which a sample was made, the less it crept! This result is believed to come from the purity effect as these samples are geometrically identical. That is, with the elimination of internal porosity, there cannot be any sintering phenomena operating. On the other hand, the higher creep rate of fine particle specimens at significant porosity levels (80% dense and less) must be the result of a phenomenon characteristic of the size of the particles from which the samples were made and which has much stronger and opposite effect on creep than the purity difference. Further discussion of the particle size effect follows in Section 4.4.

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96 4.3.2 Temperature Dependence The temperature dependence of creep is generally found to be of the Arrhenius type. From the Arrhenius temperature dependence it is commonly found that high temperature creep activation energies are equal to the activation energy for self-diffusion in fully dense materials. This is usually taken to signify that the ultimate controlling mechanism is diffusion. Activation energy may also vary v.ith temperature [48]. In nickel, the activation energy for creep has been found to decrease the self-diffusion activation energy of 66.5 kcal/mole as the temperature decreases below 700°C and approaches 23 kcal/mole at 500°C [48]. Seeger [88] reports that an activation energy of about 1 ev (23 kcal/mole) is characteristic of dislocation intersection in nickel. In these experiments, the exact nature of the temperature dependence was difficult to determine as the creep apparatus was not capable of fast temperature cycling. The activation energy analysis was therefore performed on separate samples that had the same particle size, starting density, and load, but were crept at different temperatures. To have the samples as structurally similar as possible, the analysis was performed, using the creep rates at equal amounts of creep. The creep activation energies found for the llS^i particle size samples were generally in the range of 23 to 40 kcal/mole which is suggestive of dislocation intersection. As an Arrhenius temperature dependence implies, the creep rate is very sensitive to temperature and increases with increasing temperature. '

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97 4.3.3 Density Effect As a sinter body densifies, the amount of metal per unit cross section increases. For this reason, for a given external load, tlie unit stress on the load supporting cross section is reduced the denser the specimen and less creep occurs. The average cross section of a porous body, A , increases linearly with increase in density. This average cross section is in fact a direct measure of the density. If a sample is 60% dense, then the A is .6, at 80% dense, A^ = .8, and at 100% density, A =1. Another cross section found useful in this J ' A research has been A „. This is considered to be the average minimal cross section in a porous body and is measured by taking an A^ count of the fracture areas exposed when a sample is fractured in tension. A does not increase linearly with increase in density and depends upon the original stacking of the loose powder. The density at which a given particle size stacks when poured into a mold depends upon the particle shape. The more regular the particle (spherical), the higher the loose stack density. Thus the difference in loose stack density found in this research is a result of the smaller particles being more irregular than the larger particles. The finer particles, i.e., -20|j,, also do not appear to be as "filled in" as the 115 (i powders. The density from which A,^, begins to increase with sintering from approx•' A± imately zero is the loose stack density, regardless of what that loose stack density is. The rate of increase of A with increasing sintering densification is slow as the sample starts densifying and the rate increases as densification continues until the density for which this

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98 particle shape (and stacking) reaches its minimal surface area configuration. This minimal area configuration is reached when the A^_^ of a sample intersects the A versus density line that is representative of a sample which had its particles most densely stacked in the loose stack condition, i.e., a sample of smooth, spherical particles. In this research, the 115\i particles closely approximate spheres and normal spherical stacking. Thus it is seen that the A^_^s of the smaller, more irregular powder samples approach the 115[i A^^ versus density line and are identical to this 115^ A^^ line as the samples of the smaller size fractions continue to densify past the point of juncture. A result of this factor is that the A of a sample of a smaller size fraction (in this research) is always equal to or larger than the A^^ of a sample from a larger size fraction. A has been found to be a measure of the load supporting Af area in tensile tests. If the stress is reversed to a compressive test the area supporting the load should be the same. It follows then that for small deformations, in which the load bearing area A^^ does not significantly change, A^^ should be predictive in compression. That this has been found for 115)0, samples is discussed in the next section. 4.3.4 Stress Effect The stress effect is such that an increase in stress produces an increase in creep rate. The stress, a, listed for a given test is the stress on the gross sample cross section. To find the true maximum stress on the minimal cross section, one must divide the listed sample

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99 stress by the A of the sample. The creep stress is the highest on the minimal cross section; therefore, most of the creep deformation is concentrated there, as strain rate is proportional to a where n is usually 3 to 6. All creep tests were constant load tests. This condition leads to a monotonically decreasing effective stress from the outset of creep. In coarse size fraction (llSiJ,) , the load and density effects could be combined into a single term of the use of the A measurement at a particular density. Using the effective stress, a. , on the \f minimal cross section of the 115ii samples, the creep rate remained the same regardless of starting density. For example, an 80% dense sample made from 115^ powder has an A of 0.331. In this case cr = ^ ^^^ = approximately 3cr. At 100% density, ct = -— = a . The postulate ^Af •was made that the area represented by A is the true load bearing area in a porous sintered sample. If this postulate is valid, then a creep load of -^ on an 80% dense sample will produce the same creep as a load of ct on a 100% dense sample. There are further requirements which must also be met for the creep of the 80% and 100% dense samples to be equal. They are: 1. The samples must be metallurgically stable (no grain growth, etc.) throughout the test. 2. Densif ication of the porous sample due to loose stack sintering must be negligible during the test. 3. Creep must not be affected by the scale of the system (grain size, subgrain size, or proximity of surface) over the range of densities involved.

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100 The results of creep tests on two series of 115^l samples at varying densities with a constant may be seen in Fig-ures 36 and 37. Although there is scatter in the results, the agreement is close and justifies the postulate that the A^^ of a sintered sample is the load bearing area. As these tests are constant load tests, the stress on A^ is continually decreasing. As creep proceeds the a, must decrease pro^Af portionally on samples of all densities as the A^^^ increases. In the 100% dense sample, the increase in cross-section is all barreling, whereas in a porous sample, the A^^ increases as well as the gross sample cross-section. The total load supporting cross-section, A^a, where a is the gross sample cross-section, must increase proportionally in the samples of all densities to keep the a equal on all samples as ^Af creep proceeds. If this increase were not proportional, the c on the Af different samples would be different as would the resulting creep rates and the total creep in a given time. 4. 4 Specimen Examination Metallographic examination of 115^ samples that have undergone creep shows virtually no variation in the makeup of the particles in the density range of 60% to 80%. The particles have internal porosity and 5 to 7 grains on a polished cross section. Numerous annealing twins are present as well as occasional serrated grain boundaries. The 100%. 115ii samples had grain diameters up to 1 mm to 3 mm or roughly the same diameter as a 1/8-inch diameter creep sample. The observation of no effect on creep of 115|i particle size samples of a variation in grain size from roughly 40 ti diameter as seen in samples where particle identity is retained, to lOOOy, to SOOOji, grain diameter means that the creep

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101 mechanism is not structure sensitive, i.e., grain size sensitive, in this size range. The effect of particle size on creep shows that the scale of the system is of importance when there is a significant porosity level. The degree of the effect is small until a critical size range is reached. For instance, Figure 14 shows the creep curves of 80% dense samples tested under 500 P.S.I, at 1100°C for four different particle sizes. It can be seen that there is only a small size effect on creep between the 115m. and the 30 p, samples. Tliere is almost a factor of 4 difference in the average particle diameter which produces only a factor of 1.25 difference in total creep in 2 hours. If one now compares the 30 (i sample with the -20^ (11m. average) where there is only a factor of three difference in diameter, one sees that the -20msample has crept 2.2 times as much as the 30|^ sample. Obviously, the scale of the system is much more important in this particle size range than in the size range of 30m. to 115m. I* has previously been shown that at lOOfo density, the creep rate varies directly with the particle size from which the samples were made, Figure 16b. From these two observations (creep at 100% density and creep at 80% density) , one would expect to find creep at constant a^ to be density dependent Af in samples made from the STp., 30m, and -20m powders. The strongest dependency should be fovmd with samples made from the -20m powder. To check the density effect on creep in this size fraction, samples of 60%, 70%, 80%, and 100% density were crept with different starting loads which produced a a. of 1500 P.S.I, in each sample. The results in Figure 41 show an extreme sensitivity to density.

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102 o <^ <] E < O o <3 oo o o S o da a JO %

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103 An explanation of the particle size effect is based on dislocation motion and stoppage. First, consider the deformation of a dense, polycrystalline piece of metal where dislocation glide is the method of deformation and dislocation accumulation is the strengthening mechanism. Next, consider the effect of grain boundaries and subgrain boundaries on the movement of dislocations. Grain and subgrain boundaries are lattice discontinuities through which dislocations often penetrate with much difficulty; therefore, dislocations accumulate behind them. As grain size decreases, grain boundary area increases and a dislocation travels a shorter distance before encountering a boundary, thus the common observance of increased strength and creep resistance with a decrease in grain size. Now im.agine this polycrystalline piece of metal pulled apart at the gr^in boundaries ^nd the effect these boundaries would now have on stopping dislocation movement. When dislocations reach a grain boundary and the boundary is not restrained by another grain or oxide, the dislocation may put a step in the surface, thereby leaving the interior of the grain. This results in negligible strengthening of the crystal. Relate this analysis to the structure of a porous sinter body. If the particle size from which the sinter body is made is large compared to the grain or subgrain size, then the probability of a dislocation being caught by an interior boundary of the particle and causing hardening or strengthening is much higher than the probability of the dislocation traveling to the poresolid interface and escaping as a step on the surface. As a sinter body densifies, the average distance a dislocation would have to travel before

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104 reaching a free surface (pore-solid interface) increases. In the case of the particle size being large compared to the grain or subgrain size so that the dislocations are already caught inside the particle, this increase in average distance is of no consequence. Such is the case with the 115(j, samples where there is a large amount of intraparticle boundary. If however, the particle size is small enough for an active dislocation to have a high probability of reaching the pore-solid interface, then densif ication with the attendant average increase in distance a dislocation must travel to reach a free surface would increase the probability of the dislocation being trapped in the solid. Such is the case with the -20^i. (lip, average) samples. As the -20\i particle size samples densify, they approach the same situation as found in the large particle size samples and at 100% density,, the two are geometrically identical. A comparison of the creep of the lOOfc dense samples made from 115 |j, and -20 [j, powders in Figure 41 show this. The two intermediate particle sizes, 30|i and 57|i, are intermediate cases between the two extremes. Metallographic examination of -20^ samples revealed that the particle were either single crystals or bicrystals and 3\i to 15|j, in size, which is the size generally reported for subgrain in hot worked and crept nickel [35,89]. 4 . 5 Qu antitative Microscopy in the Creep of Sinter Bodies Many quantitative microscopy data were taken in the course of this work. These measurements included A^^ (area fraction), S^ (surface area/unit volume), M^ (total curvavure) , H (average mean curvature) and I (mean pore intercept) on polished sections, and A^^ (area

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105 6 ^

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lOG fraction of fracture surface) , N (number of intersections on fracture surface 'unit length of test line) and N (number of fractures/unit area) on fracture surfaces. The line intercept count, N , was the most widely studied of the measurements on the polished sections. The N count is related to S by the equation N = — S . S , surface Li V Ij ^ V V area/unit volume, was used as one indicator of how the creep process affected the amount of internal surface in a sinter body. The S val•' V ues were determined for the 115(i, 57 n, and 30u. powder samples at various densities in the as-sintered condition (unciept). These "standard" values were then compared with tlie S ^ values obtained from samples which had undergone creep. In loose stack sintering, there is a linear correlation betw^een S and V once second stage sintering and the conditional iiiinimal suiface condition Lf!ve been reached. The effect of creep was to increase the value of S over that which would be assoV ciated with loose stack sintering, Figure 30. Sintering phenomena, especially surface rounding, continually strive to bring the surface area back to the balance line, the S -V equilibrium line. The N count from which the S calculation is made has been used to measure the distortion in the pore-solid interface left by the creep process. Rather than taking the N counts randomly on the polished sections of creep samples, the counts were made parallel to and at 90 degrees to the creep direction. The ratio of these two measurements has been designated by the term QN , N (transverse direction) /N (longitudinal L Li Li direction). For a loose stack sintered sample which has not undergone creep, QN = 1. For crept samples, fiN < 1.

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107 For the porous nickel used in this research, the compressive deformation is thought of as consisting of three parts. Part of the overall study has been to separate and quantify these parts. The first part, called normal creep, is the creep which takes place with no influence from sintering phenomena. This creep is similar to that found in fully dense material, but is nevertheless tied to the geometry of the porous structure. The anisotropy of the N count, .QN^, is taken as the measure of this creep. This measurement reveals the degree of flattening of the internal porosity of a creep sample in the creep direction. This flattening is purely mechanical and would be expected to be maximized when deformation takes place under conditions where thermal readjustment of internal surface is minimal. The second portion of the total deformation is the shrinkage of the sample attributable to loose stack sintering. This is the dimensional change in the creep direction which the sample would undergo due to normal sintering (no load) at the test temperature for the time of the test. This length change may be calculated using equations 1, 2, and 3 of Section 3.1. The third portion of the total sample deformation is attributed to the fact that the creep stress is acting on a porous body rather than on a fully dense bulk sample. This portion is referred to as stress assisted sintering. Stress assisted sintering results from the fact that the creep process results in more than the equilibrium amount of surface that a sinter body of a given particle size, genus, and density were obtained through loose stack sintering and the fact that the porosity has been made anisotropic. Local sintering action

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108 attempts to return the sample to the minimal surface and remove the anisotropy put in by the purely mechanical creep. A simple model was devised for tlie analysis of the different parts that make up the total creep deformation of a porous sinter body. In this model, the porosity lias been segregated to one end, Figure 42a. Figure 42b shows the model divided into the various components of deformation under study. The notation is as follows: L sample length before creep test o L sample length after creep test h , = height of pore before creep test = L (1-% o „ ) pb o before h = height of pore after creep test = L (1-% o ) pa after h height of metal = L (% D ) m o "^ 1j heiglit lost in test due to noi-inal creep px'ocesses an ^ ri---) as measured by anisotropv of N = h — L pa Q h = height lost due to loose stack sintering densif ication us h = height lost in test due to stress assisted sintering as • ° h=h^-h-h-h. as pb pa an us This model is used as a method of following the anisotropy of the pore shape and h and h should not be taken as the actual percentan as ages of the total deformation undergone by a porous creep sample. The results of this analysis are found in Table 6. This analysis has shown that for the IISll particle size sample, h is ' ' us negligible and the total creep may be thought of as consisting of h and h . Figure 43 is a plot of the percent total creep versus an as ^ ^ the percent of the total calculated to be activated sintering. There is

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109 (a) 7TApD L :i'_ Pore after test Metal V' an ~y^ us pa (b) Figure 43. Model used in the analysis of creep and stress assisted sintering.

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110 Table 6. Calculations of the components of the stress activated sintering model. C21 C22 C25 C26 C30 C31 C39 C40 C41 C48 C49 C50 C51 B54 C55 Temp. 1100° C 900° C 84.6 85.1 75.8 75.4 80.0 80.0 70.0 69.9 69.7 69.9 79,7 80.0 80.0 79.5 79.9 -20(1 105 1100°C 60.17 -20^L 108 " 79.5 after

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Table 6 (Extended) 111

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112 18^ 16, C41 1000 14. oT 12 (1) 10 60 Figure 44. 70 80 % h 90 100 Total creep in test versus percent calculated from the model to be stress activated sintering. Sample numbers and corresponding loads (P.S.I,) are given.

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113 a striation of the data according to the starting density of the samples. This striation of the 1100°C, Hop, data with density shows that at a given total creep, the portion of tlie total creep w]iich is attributed to activated sintering is larger the lower the density. Tlie data are further ordered within each density according to the time of testing and load. For a given starting density, the lower the load and longer the test time, the larger the percentage of creep attribvited to stress activated sintering. Figure 44 is a plot of the same samples with time of creep testing plotted versus percent of total creep attributed to activated sintering. With h =0, one has only the two us ' •' remaining parts to add up to the total creep; namely, the normal creep as measured by the anisotropy of the porosity, h , and the stress an activated sintering, h . Any test condition which w'ould reduce the as anisotropy of the porosity w^ould necessarily increase the share of the total creep attributed to activated sintering because the calculation of activated sintering is done by difference. Although the time, temperature, and particle sizes involved in these tests are such that sample length changes due to loose stack sintering are negligible, local rounding takes place with surface diffusion. The longer times involved with creep testing at the smaller stresses result in a loss of anisotropy as measured after the test. This loss of anisoti'opy would then be seen as stress activated sintering. There is further evidence of the density sensitivity of activated sintering. Take the following pairs of samples (C25, 75% dense, 21 min, and C41 70% dense, 10 min), (C26, 75% dense, 120 min and C39 , 70% dense, 130 min), and

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114 1200 1000 800 600 400 200 _ 100 % h Figure 45. Total time of test versus % h as calculated from the model.

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115 (C31, 80% dense, 534 min and C'lO, TC; dense, 420 min) , Figure 45, and observe that in each case, tlie percentage of activated sintering is greater in the lower density sample, althougli tlie times involved are equal to or s]iorter than in the higher density samples. 4,6 Summary All of the pertinent points of the research have been discussed separately in the previous sections of this chapter. The general principles learned from these observations will now be discussed. High temperature creep of porous nickel has shown that sintering as a densif ication mechanism per se does not contribute significantly to the deformation found in these creep experiments. Sintering does, however, command a prominent position in maintaining the internal structure of a porous creep sample. As the creep load continuously deforms a specimen, local sintering forces continuously strive to return the structure to an isotropic, minimal, surface area state as is found in a loose stack sintered sample. The structure of a creep sample after a test is such that it appears to have had an extremely large surface tension in operation, causing the densif ication. Although the internal structure of a creep sample appears as though the creep load has been transformed into a triaxial compressive force, the nearness of the internal shape to isotropy is in fact due to local pore shape change. The significance of this maintenance of isotropy from the standpoint of creep deformation lies in the load bearing area of the sample. The local sintering effect strives to maintain the minimal load bearing cross section, A , in a sample undergoing

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116 creep. This means that to the extent to which the local sintering maintains the minimal cross-sectional area as a specimen densities in creep, the creep load is resisted by tlie minimal amount of cross section possible at a given density. As the starting density of a sample increases, the creep rate for a given temperature and load decreases. Tliis follows from the fact that there is more cross-sectional area resisting the creep load resulting in a lower unit stress. Likewise, an increase i'n creep load increases the creep rate for a given temperature and density because the unit stress on the load bearing area is increased. The increase in creep with increase in temperature is consistent with a general weakening of material, making it less resistant to deformation. This weakening is from faster recovery and lower modulus. The amount of anisotropy of pore outline left in a creep sample after a creep test shows that the denser the sample is, the more anisotropy remains. The reason for this fact is that the deformation is not as confined to the A cross section as in lower densities and thus the disrupAf tion of the pore shape is not as localized as in a low density sample. The local potential gradient for diffusion is not as large, making the process slower. The deformation is more widespread in a high density sample, a fact which increases diffusion distances. The distances involved in the redistribution of surface are also a factor in the rate at which the pore-solid interface approaches isotropy or keeps from being totally flattened in a test. This means that the shorter the distance over which diffusion must occur to change the shape, the faster the shape can change. As there is a factor of 10

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117 difference in average particle size between the 115^i and the -20^, specimens, it is easily seen why a much smaller amount of anisotropy remains in a -20u sample after a test than in a comparable sample of the 115u size fraction. The increase in total load bearing cross section in 115^ samples of the various densities is proportional with creep for the small amounts of creep in the tests in which the dependence of creep on minimal load bearing area was checked. The apparent lack of dependence of creep on load bearing area in the -20^ samples of varying densities is due to two factors. First, the nature of the deformation (movement of dislocations) changes as density changes and second, the change in load bearing area with creep-induced densif ication is not as severe in the 60% to 80% density range as in the lloji, samples. That is, the slope of the A , plot versus density is not as large for the -20p, Af as for the 115^ particle size samples. Thus, one could have a larger creep and creep-induced densif ication in a -20(i sample than in a 115|i, sample and not have decreased the load on the minimum cross section as much as on the minimum cross section of a 115p, sample. The dependence of tensile strength on density has been found to be a function of A which is itself dependent upon the particle shape and the original loose stack density from which sintering began (Figure 35). The reason for the particular dependence of strength on density in sinter bodies can now be understood in the light of this minimal cross section, A . In the density region from 80% to 100% density, all loose stack sinter bodies have the same A . The change in A^ with density in this region can also be considered to be linear with density.

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118 That A can be approximated by a straight line is not surprising in light of the knowledge that many other quantitative mici-oscopic quantities are also linear in this region. The path of the change of A with density is surface tension controlled just as are the quantitative microscopic quantities of S , M^, H, and genus. An important aspect of this linearity of A in this region is that A is entirely independent of starting particle size or original stacking. This can be useful from an engineering standpoint in that one only needs to know the bulk tensile strength of a solid piece of like material to be able to predict the strength of a sinter body in this density region. Ultimate tensile strength has been shown to be directly related to A for nickel [87], Figure 38, and copper [99,91], Modul'.'.s data for a large variety of iron and steel sinter bodies [92] also follow the same curve. The relationship obtained between amount of porosity and tensile strength can be formulated simply from the slope of the A line in the 80% to 100% dense region. The strength of a sinter body at 80% is A (bulk strength) or 0.33 times the bulk strength. The slope of the A versus V line is therefore 3.35. The strength at any density in this linear region can then be expressed as: T(A^) = [1 TT A^ ] T (bulk) por where T(A ) is the strength of the compact in the density range, .8 < A < 1.0, and T (bulk) is the strength of the bulk (100% dense) material. Thus in this conraiercially important density range, one needs

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119 only to know the bulk strength of a material and the relative density to know the strength of the sinter body. The basic elements of the model of high temperature creep of porous, sintered nickel have been reviewed. Creep in the porous nickel samples by this research is seen to depend upon temperature and load in a fully rational manner. The intrinsic properties of the material used, such as chemistry, particle size, and grain size, are all seen as strong factors in determining creep of sintered nickel as well as the internal and external appearances after a test. Hot pressing of metal powders into shapes is completely similar to high temperature compressive creep of porous metal samples and the same phenomena would be found in hot pressing as were found in compressive creeTy.

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CHAPTER 5 CONCLUSIONS The creep of porous sintered nickel and the structure resulting from a compressive creep test have been found to be the result of the interplay of short and long range stresses and the movement of material as a result of these stresses. The long range stress, which is the applied compressive load, deforms the solid network en both a short range and a long range basis. The creep load induced deformation on the scale of the sample as a whole, is simply the sum of the local deformations on the scale of the particle size, less the densif ication. That is, the densif ication of the sample reduces the barreling from what would be required if their density remained the same. The short range stresses are those produced by the surface tension forces that are present at the pore solid interface. These forces are responsible for the redistribution of the pore shape in a creep test. It was found that the faster the material could respond to these forces (increased temperature) or the larger amount of these forces available (lower density, smaller particle size) the less anisotropy would be found in a sample for a given total amount of creep. Tlie distance over whicli these forces must act to move laatcrial was also important (particle size) with the smaller the distance involved, the faster the response to the surface tension. 120

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121 The particle size effect on creep deformation rate has been found to be a result of the morphology of the particles rather than size alone, i.e., grain size relative to particle size. The ease with which a dislocation could reach a free surface was determined by the particle size. The loose stack sintering rate was found to be negligible in all creep samples except those of the finest particle size (-20^,). m general, the effects of surface tension and sintering phenomena were restricted to short range effects such as pore shape and load bearing area, whereas the external load had both short and long range effects on shape of the porosity as well as the sample as a whole. me effective load bearing area was found to be represented by the area fraction of fracture surface, A^^.

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BIBLIOGRAPIiY 1 F. niummler and W. Tomma. "The Sintering Process," Metallurgical Reviews , The Metals and Metallurgy Trust, 1967, p. 69. 9 R L Coble and J. E, Burke. "Sintering in Ceramics," Progress in Cera mic Scie nce, Vol. 3, Editor, J. E. Burke, Pergamon Press, New York, 1963, p. 197. 3 W E Kin-ston and G. F. Huettig. "Fundamental Problems of Sintering Processes," T he Physics of Powder Metallurgy , Editor, W. E. Kingston, McGraw-Hill Book Co., New York, 1951, p. 1. 4 G C Kuczynski. "Theory of Solid State Sintering," Powder Metallurgy , Editor, W. Leszynski, Interscience Publishers, New York, 1961, p. 11. 5. R. A. Gregg. Analysis of the Sintering Force in Copper , Ph.D. Dissertation, University of Florida, 1968. 6. R. A. Gregg and F. N. Rhines. "Analysis of the Sintering Force in Copper," Meta ll. Trans. , Vol. 4, i'j73, p. 1365. 7. F. N. Rhines. "A New Viewpoint on Sintering," Plansee Proc . , 1958, p. 38, S. F. N, Rhines. "Seminar on the Theory of Sintering," T.A. I.M.E. , Vol. 166, 1946, p. 474. 9. F. N, Rhines, C. E. Birchnall , and L. A. Hughes, T.A. I.M.E. , vol. 188, 1950, p. 378, 10. P. Schwartzkopf and R. Kieffer (Editors). "The Mechanism of Sintering (General Principles)," Cemented Carbides , Chap. Ill, p. 55. 11. G. C. Kuczynski. " Self -Diffusion in Sintering of Metallic Particles. T.A. I.M.E. , Feb. 1949, p. 169, Vol. 185. 12 -r L U'ison and P. G. Shewmon. "The Role of Interfacial Diffusion in the Sintering of Copper," T.A.I. M.E . , Vol. 236, 1966, p. 48. 13. G. C, Kuczynski. "Study of Sintering in Glass, J. Appl. Phys . , Vol. 20, 1949, p, 1160, 14. J. White. Basic Phenomena in Sintering Science of Ceramics , Vol. I, Academic Press, New York, 1962, p. 1. 122

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123 15. W, D, Kingeiy and M. Berg. "Study of the Initial Stages of Sintering bjViscous Flow, Evaporation-Condition, and Self-Diffusion," J. Appl. Phys . , Vol. 26, No. 10, 1955, p. 1205. 16. G. C. Kuczynski. "Discussion," T.A. I.M.E. , Vol. 185, 19-19, p. 796. 17. P. Schwed. "Surface Diffusion in Sintcrinj; of Spheres on Planes" (Technical Note), J. of Metals , Vol. 3, 1951, p. 245. 18. N. Cabrera. "Sintering of Metallic Particles" (Note on Surface Diffusion in), T.A. I.M.E . , Vol. 188, p. 667. 19. G. Bockstiegel. "On the Rate of Sintering," J. of Metals , Vol. 8, 1956, p. 580. 20. F. N. PJiines and H. S, Cannon. "Rate of Sintering of Copper under Dead Load," J. of ?,Ietals , Vol. 3, 1951, p. 529. 21. D. L. Johnson. "New Method of Obtaining Volume, Grain Boundary, and Surface Diffusion Coefficients from Sintering Data," J. Appl . Phys . , Vol. 40, 1969, p. 192. 22. J. K. Mackenzie and R. Shuttleworth. "A Phenomenological Theory of Sintering," Proc. Phys. Soc . , Vol. 62, 1949, p. 55. 23. J, G. Early, F. V. Lenel , and G. S. /Instil. "The Material Transport Mechanism during Sintering of Copper-Powder Compacts at High Temperature," T.A. I.M.E . , Vol. 230, 1964, p. 1641. 24. M. J. Salkind, F. V. Lenel and G. S. Ansell. "The Kinetics of Creep during Hot Pressing of Loose Powder Aggregates," T.A. I.M. E . , Vol. 233, 1965, p. 39, 25. F. N. Rliines. Private Communication. 26. G. C. Kuczynski. "The Mechanism of Densif ication during Sintering of Metallic Particles," Acta Met . , Vol. 4, 1956, p. 58. 27. R. L. Coble. "Sintering in crystalline Solids I. Intermediate and Final State Diffusion Models," J. Appl. Phys . , Vol. 32, 1961, p. 787, 28. R. L. Coble. "Sintering in Crystalline Solids II. Experimental Test of Diffusion Models in Powder Compacts," J. Appl. Phys . , Vol. 32, 1961, p, 793, 29. D. L. Johnson and T. M. Clark. "Grain Boundary and Volume Diffusion in the Sintering of Silver," Acta Met. , Vol. 12, 1964, p. 1173.

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124 30. R. L. Coble. "Ceramic and Metal Sintering: Mechanisms of Material Transport and Density Limiting Characteristics," P'undaiiiental Phe nomena in the Material Sciences , Vol. 1, Plenum Press, New York, 1964, p. 11. 31. D. L. Johnson and I. B. Cutler. "Diffusion Sintering I. Initial Stage Sintering Models and Their Application to Shrinkage of Powder Compacts," J. Am. Cer. Soc . , Vol. 46, 1963, p. 541. 32. D. L. Johnson and I. B. Cutler. "Diffusion Sintering II. Initial Sintering Kinetics of Alumina," J. Am. Cer. Soc . , 1963, p. 545. 33. F. N. Rhines. Unpublished data. (Eight pounds of copper powder sintered and sectioned. No density variation was found.) 34. A. H. Cottrell. "The Time Laws of Creep," J. of Mechanics and Physics of Solids , Vol. 1, 1952, p. 53. 35. A. K. Mukherjee, J. E. Bird, and J. E. Dorn. "Experimental Correlations for High Temperature Creep," Trans. A. S. M . , Vol. 62, 1969, p. 155. 36. J. Weertman. "Dislocation Climb and High Temperature Creep Processes," Trans. A. S.M . , V^ol. 61, 1968, p. 680. 37. D. McLean, "The Phj'sics of High Temperature Creep in Metals," Rep. Progress Physics , Vol. 29, 1966, p. 1. 38. 0. D. Sherby and P. M. Burke. "Mechanical Behavior of Crystalline Solids at Elevated Temperatures," Progress in Materials Science , Vol. 13, 1964, p. 325. 39. R. E. Reed-Hill. Physical Metallurgy Principles , D. Van Nostrand Co., Inc., Princeton, New Jersey, 1964, p. 571. 40. H. Conrad. "Experimental Evaluation of Creep and Stress Rupture. Part 1. Experimental Evaluation of Creep," Scientific Paper 6-40104-1-P2, Sept. 29, 1959, Westinghouse Research Laboratories. 41. J. B. Conway and M. J. Mullikin. "An Evaluation of Various Equations for ExTDressing First Stage Creep Behavior," T. A. I.M. E . , Vol. 236, 1966, p. 1496. 42. P. W. Davies and K. R. Williams. "The Tertiary Creep and Fracture of O.F.H. C. Copper over the Temperature Range 335-500°C," J. Inst. Metals , Vol. 97, 1969, p. 337. 43. S. K. Mitra and D. McLean. "Work Hardening and Recovery in Creep," Proc. Roy. Soc, Vol. 295A, 1966, p. 288.

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125 44. A. S. Nemy and F. N. Rhines. "On the Origin of Tertiary Creep in an Aluminum Alloy," T. A. I.M.E . , Vol. 215, 1959, p. 992. 45. A. E. B. Presland and R. I. Hutchinson. "The Effect of Substructure on tlie Nucleation of Grain-Boundary Cavities in Magnesium," J. Inst. Metals , Vol. 92, 1963-64, p. 264. 46. W. Rosenhain and S, L. Archbutt. "On the Intercrystalline Fracture of Metals under Prolonged Application" (Preliminary Paper) , Proc . Roy. Soc . , 1919, p. 55. 47. G. Brinson and B. B. Argent, "The Creep of Niobium," J. Inst . Metals , Vol. 91, 1962-63, p. 293. 48. J. E. Cannaday, R. J. Austin, and R. K. Sorer. "Activation Energies for Creep of Polycrystalline Wire," T. A. I. M. E . , Vol. 236, 1966, p. 595. 49. F. R. N. Nabarro. Proceedings of Conference on Strength of Solids, Physical Society (London), 1948, p. 75. 50. C, Herring. "Diffusional Viscosity of a Polycrystalline Solid," J. Appl. Phys . , Vol. 21, 1950, p. 437. 51. I. M. Bernstein. 'Diffusion Creep in Zirconium and Certain Zirconium Alloys," T.A. I.M.E . , Vol. 239, 1967, p. 1518. 52. R. L. Coble. "A Model for Boundary Diffusion Controlled Creep in Polycrystalline Materials," J. Appl. Phys . , Vol. 34, 1963, p. 1679. 53. R. Lagneborg. "Dislocation Mechanisms in Creep," International Metallurgical Reviews , IMRVBH 17, June 1972, p. 130. 54. P. W. Davies, T. C. Finniear, and B. Wilshir. "A Comparison of Tensile and Compressive Creep Rates," J. Inst. Metals , Vol. 90, 1961-62, p. 368. 55. Y. Ishida, C.-Y. Cheng, and J. E. Dorn. "Creep Mechanisms in Alpha Iron," T.A. I. M.E. , Vol. 236, 1966, p. 964. 56. E. R. Parker. "Modern Concepts of Flow and Fracture," Trans . A. S.M . , Vol. 50, 1958, p. 52. 57. p. Feltham and J. D, Meakin. "Creep in Face-Centered Cubic Metals with Special Reference to Copper," Acta Met . , Vol. 7, 1959, p. 614. 58. S. Bhattacharya, W. K. A. Congrieve, and F. C. Thompson. "The Creep/Time Relationship under Constant Tensile Stress," J. Inst . Metals, Vol. 81, 1952-53, p. 83.

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126 59. J. B. Conway and M. J. Mullikin. "Tecimiques for Analyzing Combined First and Second Stage Creep Data," T. A. I. M. E . , Vol. 236, 1966, p. 1629. 60. H. Conrad and W. D. Robertson. "Creep Characteristics of Magnesium Single Crystals from 78° to 36-l°K," T. A. I.M. E . , 1958, p. 536. 61. E. N. da C. Andrade. "The Viscous Flow of Metals, and Allied Phenomena," Proc. Roy Soc . , Vol. 84A, 1910, p. 1. 62. E. N. da C. Andrade. "The Flow in Metals under Large Constant Stresses," Proc. Roy. Soc . , Vol. 90, 1914, p. 329. 63. E. N. da C. Andrade and D. A. Aboav. "The Flow of Polycrystalline Cadmium under Simple Shear," Proc. Roy Soc, 1964, p. 353. 1/3 64. E. N. da C. Andrade. The Validity of the t Law of Flow of Metals," Phil. Mag . , Vol. 7, 1962, p. 2003, 65. T. H. Hazlett and Rosa D. Hansen. "influence of Substructure on the Shape of the Creep Curve," Trans. A. S.M . , Vol. 47, 1955, p. 508. 66. A. H, Cottrell and V. Aytekin. "The Flow of Zinc under Constant Stress," J, Inst. Metals, Vol. 77, 1950, p. 3S9. 67. Vi'. J. Evans and B. Wilshir. "Transient and Steady State Creep Behavior of Nickel, Zinc, and Iron," T.A. I.M. E . , Vol. 242, 1968, p. 1303. 68. T. H. Hazlett and E. R. Parker. "Nature of the Creep Curve," J. of Metals , 1953, p. 318. 69. P. Haasen. "Plastic Deformation of Nickel Single Crystals at Low Temperatures," Phil. Mag . , Vol. 3, 1958, p. 384. 70. H. J. McQueen and J. E. Hockett. "Microstructures of Aluminum Compressed at Various Rates," Met. Trans., Vol. 1, 1970, p. 2997. 71. J. C. Fisher and J. H. Hollomon. "Wanted, Experimental Support for Theories of Plastic Flow. A Symposium on the Plastic Deformation of Crystalline Solids," Mellon Institute, Pittsburg, May, 1950. 72. D. Hardwick, C. M. Sellars, and W. J. McG. Tegart. "The Occurrence of Recrystallization during High Temperature Creep," J. Inst. Metals , Vol. 90; 1961-62, p. 21. 73. C. S. Barrett and L. H. Levenson. "The Structure of Aluminum after Compression," T.A.I.M.E. , 1939-40, p. 112,

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127 74. C. R. Barrett, A. J. Ardoll , and 0. D. Sherby. "influence of Modulus on the Tcmijerature Dependence of the Activation Energy for Creep at High Temperatures," T.A. I.M.E . , Vol. 230, 1964, p. 200. 75. C. R. Barrett and O, D. Sherby. "influence of Stacking Fault Energy on High-Temperature Creep of Pure Metals," T.A. I.M. E . , Vol. 233, 1965, p. 1116. 76. J, Weertman. "Theory of the Influence of Stacking-Fault Width of Split Dislocations on High Temperature Creep Rate," T.A. I.M. E . , Vol. 233, 1965, p. 2069. 77. C. K. L. Davies, P. W. Davies , and B. Wilshire. "The Effect of Variations in Stacking Fault Energy on the Creep of NickelCobalt Alloys," Phil. Mag . , Vol. 12, 1965, p. 827. 78. C, R. Barrett, J. L. Lytton, and 0. D. Sherby. "Effect of Grain Size and Annealing Treatment on Steady-State Creep of Copper," T.A. I.M.E . , Vol, 239, 1967, p, 170, 79. W. A. Wood, G. R. Wilms, and W. A. Rachinger, "Three Basic Stages in the Mechanism of Deformation of Metals at Different Temperatures and Strain Rates," J, Inst. Metals , Vol. 79, 1951, p. 159. 80. J. P. Bennir^on. "The Effect of Heat-Trcr.tirent on the Creep and Creep-Rupture Behavior of a High-Purity Alpha Copper-Aluminum Alloy at 300° and 500°C," J. Inst. Metals , Vol. 91, 1962-63, p. 293. 81. F. N. Rhines, W. E. Bond, and M. A. Kissel. "Grain Boundary Creep in Aluminum Bicrystals," Trans. A. S.M . , Vol. 48, 1956, p. 918. 82. R. G. Connell, Jr., The Microstructural Evolution of Aluminum During the Cou rse of High Temperature Creep , Ph.D. Dissertation, University of Florida, 1973, 83. R. D. Gifkins. "A Mechanism for the Formation of Intergranular Cracks when Boundary Sliding Occurs," Acta Met . , Vol. 4, 1956, p. 98. 84. D. Kramer and E. S. Machlin. "High Temperature Intercrystalline Cracking," Acta Met . , Vol. 6, 1958, p. 454, 85. R, C, Gifkins, Mechanisms of Intergranular Fracture at Elevated Temperatures Fracture, J, Wiley and Sons, New York, 1959, Chap. 27, p. 579. 86. N. J. Grant. "intercrystalline Failure at High Temperatures," Ibid., 1959, Chap. 26, p. 562.

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128 87. S, Gehl. Private Communication, 1973. 88. A. Seeger. "Defects in Crystalline Solids," London: Pliysical Society , Vol. 49, 1955, p. 337. 89. C. R. Smeal. Structural Evolution in Nickel during Annealing Subsequent to Hot Deloriiiation, Ph.D. Dissertation, University of Florida, 1965. 90. J. P. Gillard. Particle Size Dependence of tlie Mechanical Properties of Sintered Copper, Master's Thesis, University of Florida, 1964. 91. R. T. DeHofl and J. P. Gillard. "Relationship Between Microstructure and Mechanical Properties in Sintered Copper," Modern Developments in Powder Metallurgy, Vol. 4, Processes, Plenum Press, New York-London, 1971. 92. G. D. McAdam. "Some Relations of Powder Characteristics to the Elastic Modulus and Shrinkage of Sintered Ferrous Compacts," J. Iron-Steel Inst., Vol. 168, 1951, p. 346.

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BIOGR>\PHICAL SKETCH Walter Ralph Tarr was boi-n September 17, 1945, in Philadelphia, Pennsylvania. He moved to Orange Park, Florida, in 1946, and received primary schooling in the Jacksonville, Florida, school system. He attended high school at Darlington preparatory school in Rome, Georgia, from which he graduated in June, 1963. He entered the University of Florida in June, 1966, and received the Bachelor of Science in Metallurgical Engineering in April, 1967. In September, 1967, he entered the University of Florida Graduate Scliool and received the Master of Metallurgical Engineering in August, 1969, Tlie time from August, 1969, to the present has been spent in doctoral research at the University of Florida. 129

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I ceiHifj' that I have read l;i-iis study and that in iny opinion it conforms to accepLabie standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Frederick N. Rhines , Chairman Professor of Materials Science and Engineering I certify that I have read this study and that in iny opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. ^ e.irM Robert T. DeHoJ Professor of M^erials Science and Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Ellis D. Verink, Jr. Chairman of Department of :,Iaterials Science and Engineering 1 certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. 'H' ( f V<,t^t-vi/ i-'i^u A Edwin II. Hadiock Professor of Mathematics

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I certify tluit I hiwe read this study and that in jny opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for tlie degree of Doctor of Philosophy. JsMes F. Burns A!j;iiociate Director of Planning Analysis This dissertation was submitted to the Dean of the College of Engineering and to the Graduate Council, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. August, 197 3 ^'^^^g^ College of Ehgineerint Dean, Graduate Scliool

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UNIVERSITY OF FLORIDA 3 1262 08553 0185