• TABLE OF CONTENTS
HIDE
 Title Page
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Abstract
 Introduction
 Material specifications
 Experimental results
 Discussion of results
 Conclusions
 Bibliography
 Biographical sketch














Title: High temperature compressive creep of sintered nickel
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Permanent Link: http://ufdc.ufl.edu/UF00098682/00001
 Material Information
Title: High temperature compressive creep of sintered nickel
Alternate Title: Compressive creep of sintered nickel
Physical Description: xi, 129 leaves. : illus. ; 28 cm.
Language: English
Creator: Tarr, Walter Ralph, 1945-
Publication Date: 1973
Copyright Date: 1973
 Subjects
Subject: Sintering   ( lcsh )
Metals -- Creep   ( lcsh )
Nickel   ( lcsh )
Materials Science and Engineering thesis Ph. D
Dissertations, Academic -- Materials Science and Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis -- University of Florida.
Bibliography: Bibliography: leaves 122-128.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00098682
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000580516
oclc - 14039012
notis - ADA8621

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Table of Contents
    Title Page
        Page i
        Page ii
    Acknowledgement
        Page iii
    Table of Contents
        Page iv
        Page v
    List of Tables
        Page vi
    List of Figures
        Page vii
        Page viii
        Page ix
        Page x
    Abstract
        Page xi
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
    Material specifications
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
    Experimental results
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
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        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
    Discussion of results
        Page 88
        Page 89
        Page 90
        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
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        Page 113
        Page 114
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
    Conclusions
        Page 120
        Page 121
    Bibliography
        Page 122
        Page 123
        Page 124
        Page 125
        Page 126
        Page 127
        Page 128
    Biographical sketch
        Page 129
        Page 130
        Page 131
        Page 132
Full Text
















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




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