STRAIN AGING IN NICKEL 200
WALTER RAYMOND CRIBB
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
UNIVERSITY OF FLORIDA
S1 ilI II II I II III i lH 1 I8 11I
3 1262 08552 4618
To Mom and Dad
Sincere appreciation is due many people in this department for
their help during my entire stay at the University of Florida. Most
sincere thanks are due Professor Robert E. Reed-Hill whose continued
guidance and encouragement made this dissertation possible.
Many thanks to Professor F.N. Rhines who first encouraged me and
gave me confidence to strive for a higher degree in metallurgy and
whose continued interest in my program is appreciated.
I would also like to thank the members of my committee,
Drs. Martin A. Eisenberg, Craig S. Hartley and John J. Hren for fruitful
discussions of my work.
Many thanks to my colleagues Messrs. Juan R. Donoso, R.M. Chhatre,
Francisco Boratto and to the laboratory assistants C. Barnes and
M. Brimanson who spent many hours of discussion and who cooperated in
the collection and interpretation of experimental data. The preparation
of the final manuscript by Elizabeth Seville is also greatly appreciated.
The financial support of the Army Research Office (Durham), the
International Nickel Company, and the Energy Research and Development
Administration is greatly appreciated.
Finally, I thank my wife, Kathie, whose patience, encouragement
and understanding during my course of study helped make it all possible.
TABLE OF CONTENTS
ACKNOWLEDGMENTS ................................................... iii
LIST OF TABLES .................................................... vii
LIST OF FIGURES ............... .............................. viii
ABSTRACT .............................................. .......... xi
INTRODUCTION ...................................................... 1
I PREVIOUS INVESTIGATIONS ................................... 4
1.1 Static Strain Aging .................................. 4
1.1.1 Historical Aspects ............................ 4
1.1.2 Mechanisms of Static Strain Aging in Metals
Alloys ........................................ 5
1.1.3 Summary of Important Mechanisms of Dislocation
Locking During Aging .......................... 10
1.1.4 Aspects of the Static Strain Aging Experiment.. 11
1.1.5 Static Strain Aging Stages in BCC Metals ...... 13
1.1.6 Static Strain Aging in Nickel and FCC Alloys... 17
1.2 Dynamic Strain Aging ................................. 19
1.3 Work Hardening in Metals and Alloys .................. 23
1.4 Anelastic Phenomena in Nickel and FCC Ferrous Alloys.. 27
II EXPERIMENTAL PROCEDURES ................................... 35
2.1 Materials ............................................ 35
2.2 Experimental Techniques .............................. 37
2.2.1 Swaging ................... .................... 37
2.2.2 Annealing .................................... 37
2.2.3 Specimen Profile Measurements ................ 37
2.2.4 Tensile Testing .............................. 38
2.2.5 Static Aging Experiments ...................... 38
III EXPERIMENTAL RESULTS .................... .................. 43
3.1 The Behavior of the Lower Yield Stress Increase, Ao... 43
3.2 The LUders Extension, EL ............................. 50
3.3 The Hardening Component, AoH ....................... 50
3.4 Activation Energies .................................. 50
3.5 The Dependence of Ao and EL on Prestrain ............ 53
3.6 Comparison of Nickel 270 and Nickel 200 Static
Strain Aging ....................................... 55
3.7 The Stress-Strain Behaviors .......................... 57
3.8 The Work Hardening Behaviors of Nickel 270 and of
Nickel 200 ........................................... 69
IV DISCUSSION ..................... .......................... 80
4.1 Rationale for Static Strain Aging in Nickel 200 ...... 80
4.2 The Mechanism for Static Strain Aging Exhibited in
Nickel 200 .......................................... 82
4.2.1 The Distribution of Vacancies, Carbon Atoms
and Dislocations After Plastic Deformation .... 82
4.2.2 Vacancy Trapping by Carbon Atoms .............. 82
4.2.3 The Concentration of Carbon-Vacancy Pairs ..... 83
4.2.4 Theory of Initial Schoeck Locking by Carbon-
Vacancy Pairs ..................... ........ 85
4.2.5 The Mechanism Controlling the Increase in Ao
with Time ....................... ............. 96
4.2.6 Regarding the Behavior of Nickel 200 After
the Peak in Ao ...................... ...... 107
4.3 Summary .............................................. 'l
4.4 Comments on the Relationship Between Static Strain
Aging and Dynamic Strain Aging in Nickel 200 ......... 115
CONCLUSIONS AND OBSERVATIONS ...................................... 121
A COMPUTATION OF THE INTERACTION ENERGY BETWEEN A
CARBON-VACANCY PAIR DEFECT AND SCREW DISLOCATIONS IN
FCC METALS ...................................... ... ..... 125
B DETERMINATION OF U(x), THE ENERGY OF A SCREW DISLOCATION
DISPLACED A DISTANCE x FROM THE CENTER OF ITS SNOEK
ATMOSPHERE ............................................... 132
BIBLIOGRAPHY ............................ ......................... 135
BIOGRAPHICAL SKETCH ............................................... 144
LIST OF TABLES
1 Recognized Aspects of Strain Aging ..................... 2
2 The Diffusivity of Carbon in Nickel .................... 21
3 Estimates of the Rate of Vacancy Production During
Plastic Deformation .................................... 32
4 Alloy Compositions ..................................... 36
5 Least Squares Parameters for Static Strain Aging Data
Assuming Ao Is a Function of In t ...................... 45
6 Least Squares Parameters for Static Strain Aging Data
Assuming a Log Ao-Log t Linear Relationship ........... 49
7 The Slopes and Intercepts (at t = Is) of Ao Versus In t
Curves Calculated from Eq. 56 ......................... 108
8 Interaction Energies for Tetragonal Defects in the
FCC Structure ........................................ 128
LIST OF FIGURES
1 General aspects of the classical static strain
aging test .................... ...... ............... 12
2 An example of the stages of the yield return in Nb-O
alloys ; (a) the increase in Ao with time; (b) the
components of AM and their dependence on aging time..... 16
3 Schematic example of stage behavior in polycrystalline
fcc metals ............................................. 25
4 Schematic description of the work hardening behavior in
a metal using a log 9-log a plot ....................... 25
5 Illustrating the method used to determine the aging
parameters EL, Aa= Ly o and AcH = oExt oo. Dashed
loading line indicates the approximate loading line
which would have been observed in the absence of
misalignment of the test specimen .................... 41
6 Selected load-time curves obtained after restraining
a series of specimens 5% at 273"K, aging at 4080K for
the times indicated, and restraining at 2730K ......... 42
7 The time and temperature dependence of the return of
the lower yield stress in Nickel 200. Specimens were
prestrained to a stress level of 265 MPa. The dashed
curves are approximate corrected curves which account
for specimen heat-up in the aging baths ............... 44
8 Normalized aging curves for Nickel 200. The 3730K
curve was normalized to an assumed maximum of 28.5 MPa.
The dashed curves reflect approximate corrections for
the heat-up time of the specimens .................... 47
9 Illustrating the approximate t1/7 power law relation
governing the aging of Nickel 200 at temperatures
below 4480K. Data for the 448K (shown) and 473K
cases do not fit this relation well ................... 48
10 The dependence of the Luders strain on time and
temperature in Nickel 200 ............................ 51
11 The approximate behavior of the secondary hardening
component of the lower yield stress increase
(AcH = "Ext "o) ................. ...................... 52
12 The dependence of Ao and EL on prestrain. Nickel 200
specimens were prestrained at 2730K, aged for
6000 seconds at 4480K, and restrained at 2730K ........... 54
13 (a) The yield return of a Nickel 270 specimen aged for
a time to achieve a maximum in Aofor Nickel 200.
(b) Yield return for a Nickel 200 specimen aged only
one-half as long ......................................... 56
14 True stress-true plastic strain curves for Nickel 270
(- = 4.2 x 10-4 s-l) .................................... 58
15 Variation of the 0.2% yield stress and the ultimate
tensile strength with temperature of Nickel 270
(6 = 4.2 x 10-4 s-1) ............... ..................... 59
16 Variation of the uniform and total elongation with
temperature in Nickel 270 (- = 4.2 x 10-4 s-1) .......... 60
17 True stress-true plastic strain curves for Nickel 200
( = 4.2 x 10-4 s-1) ................. ... ............ 62
18 The temperature dependence of the 0.2% yield stress and
ultimate tensile strength of Nickel 200 ................. 63
19 The temperature and strain rate dependence of the 0.2%
yield stress in Nickel 200 on an expanded stress axis .... 64
20 Variation of the stresses at 5, 11, 19 and 30% plastic
strain with temperature in Nickel 200 .................. 66
21 Variation of the uniform and total elongations with
temperature in Nickel 200. Also shown are the
approximate temperature ranges over which serrations
were observed at the respective strain rates.............. 67
22 Variation of reduction in area with temperature for
Nickel 200 and Nickel 270 ................... ............. 68
23 The log O-log o curves of Nickel 270 (f = 4.2 x 10-4 s ). 70
24 The log e-log a curves of Nickel 200 (C = 4.2 x 10-4 s-1) 71
25 The variation of mil and mIII with temperature in
Nickel 270 (e = 4.2 x 10-4 -1) ....................... 73
26 The variation of mil and mIII with temperature in
Nickel 200 (E = 4.2 x 10-4 s-1) ......................... 74
27 The variation of the work hardening parameter (05%-c0.5%)
with temperature (C = 4.2 x 104 s )................. 76
28 The variation of e2 and e3 (the approximate strains at
which Stages II and III, respectively, begin) with
temperature for Nickel 270 and Nickel 200 deformed at
a strain rate of 4.2 x 10- s ......................... 78
29 The dependence of E3 on temperature and strain rate in
Nickel 200 .............................................. 79
30 A schematic illustration of the assumed configuration
of the carbon-vacancy pair and the three possible
independent orientations that it may assume ............. 87
31 The concentrations of dipoles in each of the three
possible orientations (B' = 0.3 eV (6900 kcal/mole),
A = 0.2 eV (4600 kcal/mole)) ............................ 91
32 Schematic illustration of the growth of a saturated
carbon-vacancy atmosphere. Rs is time dependent and the
concentration within R is assumed to be a fraction, f,
of the carbon concentration ............. ............ 99
33 The aging curves obtained from the model for strain
aging in Nickel 200 (Eq. 56); the dashed lines are the
experimental data (Figure 7) ..... ..................... 109
34 This diagram illustrates the aging stages of Nickel 200.
The solid line represents the experimental scope of
the present investigation .............................. 116
35 The interaction potential u. of a carbon-vacancy dipole
with a screw dislocation for r = b and A/b = 0.2 eV ..... 131
Abstract of Dissertation Presented to the
Graduate Council of the University of Florida in
Partial Fulfillment of the Requirements for
the Degree of Doctor of Philosophy
STRAIN AGING IN NICKEL 200
Walter Raymond Cribb
Chairman: Robert E. Reed-Hill
Major Department: Materials Science and Engineering
Dynamic and static strain aging were observed in commercially
available Nickel 200 which contains principally 1000 ppm carbon as an
alloying impurity. Static strain aging tests were conducted on
annealed tensile specimens which were prestrained at 2730K to a stress
level of 265 MPa (approximately 0.05 strain) at a nominal strain rate
of 4.2 x 103 s-1. Under these conditions, homogeneous plastic flow
was guaranteed to occur. Specimens were aged immediately after pre-
straining for different times at 373, 408, 428, 448 or 4730K and the
time dependence of the return of the lower yield stress was observed.
The return of the yield experiments indicated that AB increased as
In t or approximately as t/7 kinetically and behaved in accordance with
an activation energy of 25 kcal/mole before the observed peak in Ao.
It is demonstrated that the defect responsible for this anomalous increase
in Ac may be the rotation of carbon-vacancy pairs in the strain fields
of dislocations. A quantitative model is derived for the increase in
Ao before the aging peak and it is concluded that several important
stages in the aging of Nickel 200 may occur: (a) the formation of
carbon-vacancy pairs and their initial ordering, (b) the migration
of vacancies in the strain energy gradients of dislocations and the
consequent formation of more carbon-vacancy pairs near dislocations,
(c) the growth of an ordered carbon-vacancy dipole atmosphere,
(d) depletion of free vacancies in the remainder of the lattice
which decreases the flux to the ordered atmosphere and results in a
Ac maximum, (e) the migration of bound vacancies to dislocation sinks
and the resulting decrease in Ac, (f) the migration of carbon atoms in
the strain fields of dislocations and the growth of a Cottrell atmosphere,
and (g) precipitation of graphite during averaging. Items (f) and (g)
are only speculated to occur. This model is different from the Cottrell-
Bilby model and can account for the kinetics and activation energy for
strain aging observed in Nickel 200.
Tensile tests were conducted between 77 and 800oK at nominal strain
rates of 4.2 x 10-5, 10-4, 10-3, and 10-2 s-1. The results of these
experiments confirm that dynamic strain aging (DSA) in Nickel 200 is
exhibited over a temperature interval between 273 and 5750K at
4.2 x 10- s Over the DSA interval, the following phenomena were
exhibited and depended upon the strain rate: the Portevin-Le Chatelier
Effect, yield stress plateaus, ultimate stress peaks, reduction in area
minima and mild ductility minima. An analysis of work hardening indicates
that anomalous work hardening over the DSA interval is very weakly
exhibited. The mechanism for discontinuous yielding is rationalized
to be dynamic Snoek ordering of carbon-vacancy pairs during plastic
deformation and can account for the anomalously low temperature interval
(with respect to the expected mobility of carbon) over which DSA is
observed to occur.
Currently, eight aspects of strain aging are recognized  as
playing a major role in the deformation of polycrystalline metals
(Table 1). The first two are static strain aging phenomena which
are obtained by restraining a set of prestrained specimens that have
been aged at an elevated temperature. The last six aspects listed in
Table 1 are characteristic of dynamic strain aging, i.e., aging which
occurs during plastic deformation. Dynamic strain aging can occur in
both substitutional and interstitial alloys. The most interesting
cases of dynamic strain aging have normally involved interstitial
solutes in transition metals.
Most research on the role of interstitial impurities in the
mechanical behavior of transition metals has been conducted using the
body-centered cubic class of metals such as Fe, Nb, Mo, Ta, 14 and V .
The principal interstitial impurities in these metals which are responsible
for strain aging are N, 0, C and H.
Nickel is the only metal of the commercially important Period IV
transition series of the Periodic Table that is face-centered cubic. It
is also the only fcc transition metal widely used for constructional
purposes. The other fcc transition metals Rh, Pd, Ir, and Pt are less
abundant and have not been used as major construction materials. As such,
in-depth investigations of their mechanical properties have not been
Recognized Aspects of Strain Aging
1. Yield Points
3. Discontinuous Yielding
4. Strain Rate Sensitivity Minimum
5. Ductility Minimum
6. Abnormal and Rate Dependent Work Hardening
7. Yield Stress Plateaus
8. Flow Stress Transients on Changes in Strain Rate
The principal purpose of the present investigation was to
characterize the strain aging phenomena of commercially available
Nickel 200. This alloy contains as its principal strengthening agent
solid solution interstitial carbon (0.15 w/o maximum). To the best
knowledge of the author, a complete classical static strain aging
investigation has never been conducted using an interstitial solid
solution fcc alloy.
A prime goal in the present investigation was to develop a quanti-
tative model that could explain the kinetics and energetic of the return
of the lower yield stress. Furthermore, the tensile behavior of Nickel 200
during constant strain rate tests conducted over a wide range of
temperatures and strain rates was investigated in order to better define
the dynamic strain aging phenomena in Nickel 200.
1.1 Static Strain Aging
1.1.1 Historical Aspects
It has been recognized for a long time that the yield phenomenon
in iron and other bcc metals is closely related to the presence of
interstitial impurity atoms such as carbon or nitrogen. Most strain
aging investigations have centered about the iron and steel industry
since the 1930s when the phenomenon in low carbon steel first became
a major commercial nuisance.
The first metallurgical investigation of aging in mild steel was
conducted by Davenport and Bain  in 1935, who noted that heterogeneous
flow occurred in both annealed and deformed materials after having been
"aged" by storing before working. Subsequent work by Gensamer and
Low  in 1944 related the strain aging and yield point to the presence
of trace amounts of nitrogen and carbon. Since the time of these early
investigations, much interest has continued to center on iron and
other commercially significant body-centered cubic metals such as
vanadium , niobium , tantalum , and molybdenum . At the
present time, very little research effort has been directed to the study
of static strain aging phenomena in face-centered cubic and hexagonal
metals containing interstitial impurities.
1.1.2 Mechanisms of Static Strain Aging in Metals and Alloys
Three main dislocation pinning mechanisms have been postulated
on the basis of experimental evidence in metals and alloys. These are
Cottrell pinning, Suzuki locking and Schoeck locking.
In.all of the previously mentioned investigations of bcc metals,
the most plausible explanation for static strain aging is due to Cottrell
and Bilby  who attributed the effect to the diffusion of interstitial
atoms in solution (e.g., carbon, nitrogen, oxygen or hydrogen) to
dislocations. Their concept relates the increase in flow stress and yield
point return after aging to the migration of solute atoms to the
tensile region about an edge dislocation. The effect of this segregation
is to locally lower the strain energy of the system and to consequently
stabilize the dislocation to the point where an increased flow stress
is required to remobilize the dislocation or to generate mobile dislocations.
The Cottrell mechanism is of major importance in causing the return
of the sharp yield point in steel while an increase in the steel's
ability to work harden and a reduction in ductility (in the later stages
of aging) are probably associated with precipitation of carbides and
nitrides . The major contribution of the Cottrell-Bilby work was
to solve the problem related to the diffusion of an interstitial atom
in the stress field of a dislocation. The solution predicts the time-
temperature dependence of the rate of impurity migration as inferred
from internal friction measurements . Cottrell and Bilby derived
the following relationship for n(t), the number of atoms arriving at the
dislocation in the time t per unit length,
n(t) = 3 ()l1/3 no(Tt)2/3 (1)
where no is the average number of solute atoms per unit volume and
the parameter A is the interaction constant which describes the
tendency for a solute atom or center of dilatation to be attracted
by an edge dislocation's hydrostatic stress field, D is the diffusivity
of the solute and k and T have their usual meanings. The principal
characteristics of Cottrell pinning as manifested in the static strain
aging experiment are (a) a t2/3 time dependence of the lower yield
stress return, and (b) an activation energy for the yield return
approximately equal to that for the migration of interstitial solute
atoms. The model assumes long range migration of solute and probably
involves about 103 atoms jumps  (or a net rms displacement of 30 to
50b). An empirical result is that the increase in stress necessary
to free a dislocation from its atmosphere as measured by Ao is directly
proportional to the number of atoms, n(t), which have arrived at the
dislocation. Thus, the strain energy decrease associated with long
range impurity migration is directly proportional to n(t). This model
with modifications [13,14] has survived for twenty-five years without
its concepts being significantly altered. Excellent reviews 'of the
Cottrell-Bilby theory are available in many places [15-19].
Suzuki  has pointed out that in face-centered cubic metals
containing extended dislocations, a completely different form of
interaction between dislocations and impurity atoms can exist. Since
the stacking fault has a locally different crystal structure from the
matrix, the solid solubility of impurities contained in the matrix can
differ appreciably within the stacking fault and outside. Consequently
a chemical potential exists across the fault, resulting in the
binding of impurity atoms to the stacking fault. Pinning is a result
of the accumulation of solute at the fault. Thus, this type of inter-
action should be characterized by an activation energy due to solute
migration. Unfortunately, while the magnitude of the locking stresses
has been calculated and applied with some success to solid solution
alloys, the kinetics of migration to the faults have not been studied .
Nickel has a stacking fault energy [22,23] of approximately 400 dynes/cm.
The equilibrium separation  between two partial dislocations is
estimated to be only 3b. The magnitude of the yield point produced by
segregation to stacking faults is related to the fault area. Hence, in
other metals such as Ag-6 w/o Al  where faults are estimated to
be 30b wide the effect is more important. Thus, one would not expect
Suzuki locking to be a very important pinning mechanism in nickel .
The third type of pinning is sometimes called short range order
locking and was proposed by Schoeck  and later expanded upon by
Schoeck and Seeger . Schoeck and Seeger considered a bcc lattice
in which the concentration of interstitials is low enough to keep the
interaction between interstitials small. Snoek originally proposed  that
small atom impurities in solid solution occupy the octahedral interstices
at the center of an edge or the center of a face of the unit cell in a
bcc metal. Such sites have tetragonal symmetry since two of the six
solvent atoms surrounding the interstitial site are closer than the other
four. As a result, the octahedral sites may be classified into three
groups depending upon which one of three mutually perpendicular <100>
directions the two nearest neighbor solvent atoms are aligned along.
Thus, the three types of interstitial sites correspond to the three
directions of tetragonality and if no applied stress is acting, the
three kinds of interstitial sites will be occupied by the same fraction
of interstitials; namely, one-third will be in each of the three types
of sites. One may visualize each type of site occupied by an inter-
stitial as a dipole. The principal axis of the tetragonal distortion
gives the orientation of the dipole. If an applied (non-hydrostatic)
stress is acting, the energy of interaction between the stress and the
dipoles will in general depend on the orientation of the dipoles
(i.e., the types of sites occupied by an interstitial atom). As a
consequence, an applied stress will cause a redistribution of dipole
orientations and the population of the sites with lower energy will
increase, whereas the population of the sites with higher energy will
decrease. This process is known as the Snoek effect  and it gives
rise to a well established internal friction peak [30,31,32]. The
activation energy associated with stress induced ordering of interstitial
solute in bcc metals is normally that associated with diffusion of the
impurity . Schoeck  in 1956 pointed out that a similar redis-
tribution of dipole orientations could be effected by the strain field
of a dislocation. By such a process, the energy of the system is lowered
in a period of time approximately that required for one interstitial
atom jump and, therefore, the dislocation becomes locked. Whereas the
locking due to atmosphere formation (Cottrell) requires diffusion of
interstitials over long distances, the locking due to stress induced
ordering of interstitial dipoles is accomplished merely by atomic
rearrangement between neighboring lattice sites and, therefore, takes
place in times which are orders of magnitude faster.
Schoeck and Seeger  examined the process in considerable detail
in 1959. Starting with the interaction energy between the interstitial
solute atoms and the dislocation and assuming the concentration of solute
was small, they showed that the line energy of a dislocation surrounded
by a Snoek ordered atmosphere is decreased by an amount U0 given by
o = 3LkT
U= In (2)
c = total concentration of interstitials
A = an interaction constant
L = cut-off radius
kT = thermal energy
They next derived that the extra applied stress, AT, necessary to
pull the dislocation from the ordered atmosphere is given by
AT 2bA (3)
A more complete derivation of these results is carried out in the
discussion relative to the carbon-vacancy pair (Section 4.2.4) and is
related directly to pinning in Nickel 200.
The possible contribution to the rise in yield stress made by
ordering of solute atoms in the stress fields of dislocations has
generally been ignored probably because it occurs very quickly at the
temperatures that have usually been investigated. Snoek ordering,
however, can explain the rapid static strain aging phenomena observed
by Wilson and Russell  in tensile tests on a low carbon steel and
similar observations on a range of materials (for example, Carpenter
on tantalum-oxygen  and niobium-oxygen ; Owen and Roberts 
on martensite; Rose and Glover  in stainless steel). Support for
this view comes from an investigation by Nakada and Keh  of rapid
strain aging in iron-nitrogen alloy single crystals.
Wilson and Russell  verified that the rise in yield stress at
261K in iron specimens (containing 0.039 w/o carbon) prestrained 4%
was 63% complete in 100 seconds and noted that this time is in reasonable
agreement with relaxation times observed in the case of the elastic
after-effect due to the ordering of carbon in iron. Thus, the process
is complete in roughly the jump time of a carbon atom. It must be
noted that parts of their data were taken with a reduced applied load
which was generally between 80 and 90% of the load at the end of
prestrain. Aging while applying a load has been shown to influence the
size of the yield point and depends strongly upon the fraction of the
prestrain load that is used in aging [39,40,41,42,43]. A similar case
occurs in the data or Nakada and Keh  who used single crystal
Fe-0.l a/o C and N in their investigation.
Although Quist and Carpenter  did not conduct the usual
static strain aging experiments, their investigation of dislocation
pinning in Nb-0 alloys during internal friction measurements is note-
worthy. They conducted their experiments between 273 and 3130K and
attributed damping phenomena to the pinning of dislocations by Snoek
ordering of oxygen interstitial atoms in the strain fields of dislocation
line segments. They observed that pinning was effectively completed
in a period of one oxygen atom jump time.
1.1.3 Sumnaryof Important Mechanisms of Dislocation Locking During Aging
The two most important mechanisms of dislocation locking that may
occur in metals containing dissolved interstitial impurities are related
to (a) the Cottrell-Bilby model and, (b) the Schoeck-Seeger model.
The principal features of the Cottrell-Bilby model are
(1) Solute atoms migrate toward the dislocation over long distances
under the influence of the gradient in elastic interaction energy
between the dislocation and the solute.
(2) t2/3 aging kinetics are predicted by the model and observed
(3) The activation energy for the yield return predicted by the model
and observed experimentally is that for the diffusion of
The principal features of the Schoeck-Seeger model are
(1) Interstitial atoms with tetragonal strain fields reorient in
the strain field of a dislocation.
(2) The aging process by Snoek ordering is completed in approximately
the time required for one atom jump.
(3) The activation energy predicted by this model is that for
diffusion of the interstitial solute.
1.1.4 Aspects of the Static Strain Aging Experiment
Figure 1 illustrates the mechanics of the classical static strain
aging test for a specimen deformed in tension (or compression) at a
constant strain rate. The initial prestrain and unloading cycle gives
the specimen a known deformation history and internal state, i.e.,
a higher "fresh" dislocation density than that in the annealed specimen.
If the material is immediately restrained after unloading, the stress-
strain curve returns to the curve which would have been attained had
the specimen not been unloaded. However, by aging under the proper
conditions (e.g., higher temperature and/or longer times) a yield point
occurs and is followed by a period of Luders flow at constant load
UnSoad, age, retest
Figure 1. General aspects of the classical static strain
before work hardening resumes. In fact, the process of aging results
in a gradual transition from a smooth reloading curve for very short
aging times to a curve similar to that shown in Figure 1.
The important parameters of the reloading curve are oU, oL and
OExt' the upper yield stress, the lower yield stress and the stress
increment obtained by extrapolating the post-yielding curve, respectively.
For short aging times, OExt is equal to o the value of the stress
before unloading. The extrapolated stress, Ext, is determined by
the intercept of the flow curve, i.e., that portion of the stress-strain
curve where uniform strain hardening is present, with the pre-yield
or "elastic" portion of the reloading curve. The experimental parameter,
Ao = L 'o, is the parameter that is normally associated with strain
aging as it is experimentally the easiest to determine.
Accompanying the return of the yield point is the reappearance of
heterogeneous deformation, i.e., the passage of a LUders band down the
specimen gage length, at the lower yield stress, which is also charac-
teristic of annealed metal. During the initial stages of aging, the
lower yield stress increases with aging time as does the size of the
Liders strain. The rate of change of these properties generally increases
with aging time and temperature. After aging for somewhat longer times,
depending on the metal and its history, the variation of Ao and the
LUders strain with time in bcc metals becomes much slower, in many cases
exhibiting a slight decrease with aging time.
1.1.5 Static Strain Aging Stages in BCC Metals
Five stages of aging during static strain aging have been identified
for bcc metals containing interstitials. The first stage has been
explained on the basis of observations of very rapid returns of yield
points in interstitial iron alloys [34,38,44] and internal friction
experiments in other bcc metals [12,35]. The explanation is that very
rapid pinning may be attributed to stress induced ordering of inter-
stitials in the strain fields of dislocations as previously modeled
by Schoeck and Seeger  (Section 1.1.2).
The last four stages have been explained [10,45,46] on the basis
of a Petch equatior of the form
o = o. + 2k d-1/2 (4)
where a is the lower yield stress, a. the lattice friction stress,
k a dislocation locking parameter and 2d is the grain size. This
equation was developed originally by Petch [47,48,49] in order to
provide a method of separating the factors contributing to the lower
yield strength of polycrystalline iron. During the LUders band pro-
pagation, it was believed that unpinned sources release many dislocations
which pile up at the grain boundaries. Thus, a feature of the model
is the grain size and the boundaries are pile-up sites which act as stress
concentrations. The pile-ups are controlled by the grain size and act
in conjunction with the applied stress to unpin nearby dislocations in
a neighboring grain. The friction stress is represented by oi and is
the stress to move an unbound or free dislocation through the lattice.
Rosenfield and Owen  formulated the aging phenomena in terms
of an equation of the form
Ao = AoH + 2k d-1/2
where Ao is the gain in the lower yield stress after aging, AoH the
gain in the hardening component of the lower yield stress increase,
as determined by extrapolating the load-time curve after the Luders
strain back to the reloading curve,and k and d have the usual meanings.
Szkopiak  performed static strain aging experiments on niobium-
oxygen alloys and separated the two components of the yield stress increase of
Eq. 5 as shown in Figure 2. In Figure 2a, the typical return of the
yield stress experiment on a bcc metal shows that at small aging times
the increase in lower yield stress is very rapid (depending upon
temperature of aging) and approaches a maximum. At longer aging times,
the lower yield stress increment shows a slight decrease. In Figure 2b,
the two components of A in Eq. 5 are shown separately.
The five stages of aging that have been observed in alloy systems
such as Nb-0 [6,35], Fe-C [34,45,46], and Fe-N [38,51,52] alloys and
probably occur in Ta [12,18], V , and Mo  as well are:
Stage I: This stage is observed clearly only at low temperatures since
locking occurs by stress induced ordering of interstitials in the strain
fields of dislocations and occurs within the time span of approximately
one solute atom jump. The strength of pinning agrees reasonably well
with the Schoeck-Seeger model.
Stage II: In this stage, k reaches a maximum and remains constant. The
lower yield stress reaches a maximum and the LUders strain increases very
rapidly. The rationale for this stage is that the formation of Cottrell
atmospheres takes place during aging and upon reloading dislocations become
unpinned from their atmospheres.
Stage III: Further increases in the lower yield stress are due to an
increase of the AoH parameter. In this stage, the Luders strain remains
S 10 100 '1000 10000
^ / p9-0-0---0-----.0---0--c
C 2 Oxyoen, ppm
o iN *0600
Fr 10 100 1000 10000
Aging Time, Minutes
Figure 2. An example of the stages of the yield return in
Hb-O alloys ; (a) the increase in Ac with time,
(b) the components of 0A and their dependence on time.
nearly constant as the yield stress increases and enhanced strengthening
occurs. The principal rationale for this hardening is that dislocations
have been aged to the extent that they tend to remain immobile or pinned
upon subsequent reloading. Thus, new or additional dislocations
are created and the yield stress continues to increase.
Stage IV: During this stage, solute continues to be accomodated in the
strain field of dislocations but no longer effects an increase in Ao.
Hence, Ac remains approximately constant.
Stage V: As more and more interstitial solute segragates to dislocations,
a condition of averagingg" is satisfied and precipitates may form;
hence, the loss of a coherent strain field or the robbing of solute near
dislocations and a mild decrease in the hardening component.
The above stages of static strain aging appear to hold true for
most of the body-centered cubic metals containing interstitial oxygen,
carbon or nitrogen. However, in the case of face-centered cubic metals
containing interstitial impurities no complete investigations of the
behavior of the return of the lower yield stress have been carried out.
1.1.6 Static Strain Aging in Nickel and FCC Alloys
Among the fcc commercial alloys, nickel containing carbon is
probably the most significant where an interstitial (carbon) is
deliberately added to improve mechanical properties. Other than pure
nickel, only fcc multicomponent alloys such as the austenitic stainless
steels [37,53,54] contain carbon for similar reasons and exhibit
mechanical properties similar to nickel-carbon alloys.
There exists some experimental evidence related to the static strain
aging of nickel-carbon alloys. In particular, two short notes were
published by Macherauch et al.  and by Macherauch and V6hringer 
regarding static strain aging in Ni-0.05 w/o C after restraining
slightly beyond the initial yield plateau. Their data were plotted
by this author and an approximate t/3 or t1/4 time dependence of the
lower yield stress return was exhibited. They did not speculate on
the kinetics; however, they determined an activation energy of
10.22 kcal/mole in agreement with the activation energy for diffusion
of hydrogen in nickel (see, for example, Boniszewski and Smith ).
The only other investigation relating to nickel-carbon alloy is
due to Sukhovarov  and Sukhovarov et al. . Using compression
specimens deformed at room temperature and aged between 433 and 493K
for various times, they deduced with apparent difficulty (because
serrated flow occurred) that the average activation energy was
30.7 kcal/mole, somewhat lower than the carbon migration energy in
nickel. This author plotted their lower yield stress data and noted
that 6o/AOmax varied approximately as t0.3. They conclude (incorrectly,
it is believed) that the Cottrell-Bilby model explains the rise in
Ao and that probably the formation of precipitates eventually occurs;
they never observed this aspect.
In addition, since serrated flow occurred in the investigation of
Sukhovarov , it is probable that the data were scattered because
the lower yield stress was not as clearly defined as in the present
investigation where yield point measurements were made under conditions
precluding serrated flow. On this basis, their data should be used
Hydrogenated nickel exhibits strain aging behavior [57,60-65] when
deformed below room temperature. Much effort has been directed toward
understanding fracture, ductility, and other embrittlement related
phenomena attributable to hydrogen. Also, serrated flow [57, 60-65] is
exhibited in hydrogenated nickel between approximately 130 and 2250K
 at a nominal strain rate of 10- s The kinetics of static
strain aging in hydrogenated nickel were very briefly investigated by
Boniszewski and Smith  and they concluded that the Cottrell-Bilby
model can account for static strain aging of charged specimens. However,
they did not speculate on the exact kinetics that the experimental
data may have followed.
Marek and Hochman  have demonstrated the existence of static
strain aging effects in AISI 316 alloy and related it to the approximate
activation energy for diffusion of interstitial carbon in austenite.
However, the effect was most marked in the micro-yield region (0.01% proof
stress) with no effect on flow stress after yielding, UTS, or elongation,
which is indicative of a low interstitial/dislocation interaction energy.
1.2 Dynamic Strain Aging
Dynamic strain aging (DSA) is a feature exhibited in most commercial
metals and alloys . In general, aspects of DSA have created very
little interest in the past, probably since in steel it exhibits its
most significant effects over a temperature range around 4500K where
steel is not normally worked. Other bcc metals such as titanium,
tantalum, niobium and vanadium exhibit DSA over a temperature range
where these metals are most needed .
As with steel, nickel containing carbon exhibits its effects at
relatively low temperatures (300 to 5000K, roughly). Early investigations
by Sukhovarov and Kharlova  confirmed that dynamic strain aging
occurs in nickel when alloyed with small amounts of carbon. In a
subsequent investigation Popov and Sukhovarov  indicated that the
apparent activation energies associated with the appearance and
disappearance of serrated flow are 20 and 33 kcal/mole, respectively.
No conclusion regarding the very low activation energy for the onset of
serrated flow was ventured. On the other hand, Nakada and Key 
have indicated that the onset activation energy in Ni-C alloys is
152 kcal/mole and that for the disappearance of serrations is 264
kcal/mole. It is a well established experimental fact that the acti-
vation energy associated with the diffusion of carbon in nickel is
approximately 35 kcal/mole (see Table 2). Generally, in interstitial
alloys the activation energy for the onset of serrated flow is
associated with the diffusion of impurity atoms and is made on the
basis that when the velocity of dislocations is approximately equal to
that of the velocity of the diffusing impurity atoms, a drag or pinning
of dislocations occurs. Thus, the pinning as observed through the
serrated flow phenomenon is assumed to be controlled by the diffusion
of impurity atoms just as in the static strain aging experiment. By
plotting log E versus 1/T, where c is the strain rate at temperature T
where serrated flow is first observed, an activation energy may be
deduced. The values of 152 and 20 kcal/mole for the onset of serrated
flow determined by the preceding authors are much too small to be related
to the diffusion of carbon in nickel. Popov and Sukhovarov  made
no conclusions regarding this apparent anomaly. Nakada and Keh,
however, ventured that pipe diffusion of carbon along dislocation cores
controls serrated flow in nickel.
The Diffusivity of Carbon in Nickel
Do Q Technique
0.048 34.8 Elastic and magnetic aftereffect 
0.13 34.5 Radioactive tracer 
0.1 33.0 Radioactive tracer 
-- 38.5 Thermogravimetric 
-- 39.7 Thenogravimetric 
-- 32.3 Magnetic aftereffect 
Regarding the activation energy associated with the disappearance
of serrations, Kinoshita et al.  proposed that this value may
represent the sum of the activation energies for the diffusion of solute
plus the binding energy of solute atoms to dislocations. On this basis,
Nakada and Keh  have deduced a binding energy of 11.0 kcal/mole
(0.5 eV) for a carbon atom to a dislocation in nickel assuming that
serrated flow in Ni-C alloys is caused by carbon directly. Popov and
Sukhovarov  attributed their value of 333 kcal/mole (1.4 eV) for
the disappearance of serrations to a combination of creep processes
coupled with Cottrell atmosphere formation.
Other than the above nickel-carbon studies and the experimental
work on hydrogenated nickel [57,60-65] which shows strain aging, no other
investigations of the effect of interstitials on the stress-strain and
work hardening behaviors in pure face-centered cubic metals have been
conducted. However, some face-centered cubic ferrous alloys appear to
possess mechanical properties similar to those of nickel-carbon alloys.
In an investigation by Jenkins and Smith  complications due to
substitutional alloying elements such as Cr occurred. Nevertheless,
AISI 330 stainless steel (Fe-15Cr-33Ni-0.4C), exhibits similar dynamic
strain aging trends. A calculation of the energies for the onset and
disappearance of serrations revealed that 26.6 and 62.0 kcal/mole are the
onset and termination activation energies. They indicated that the
onset activation energy is very close to that for vacancy migration in
Fe-30 Ni. As the Portevin-Le Chatelier effect is absent for low carbon
content, they conclude that vacancies alone are not responsible and that
carbon-vacancy pairs account for the observed activation energy. Mention
was not made of the exact mechanism for the pinning during serrated flow.
A similar argument appears to apply in the case of Nickel 200.
Other strain aging effects occur in face-centered cubic alloys
but these arise mainly from the diffusion of substitutional solutes
and are outside the scope of this dissertation.
1.3 Work Hardening in Metals and Alloys
In studying the work hardening of metals and alloys it is desirable
to determine the mechanisms that control the rise in flow stress.
In general, this involves relating the macroscopic behavior to changes
in the microscopic structural features of the metal. For example,
observations of slip line lengths or dislocation structures can
supplement an explanation of work hardening.
From the macroscopic point of view, polycrystalline stress-strain
curves have been shown to be generally piece-wise continuous [75-81].
For example, Figure 3 shows schematically that a polycrystalline face-
centered cubic metal may deform so as to show discontinuities in its
stress-strain behavior. Zankl  and others [76-81] have shown that
these stages can be correlated very well with deformation processes.
According to his experimental work  the identifiable stages are
related to the following processes:
1. The Transition Stage. This extends from zero plastic strain
to approximately 0.1%. In this stage, multiple slip starts first
in the largest grains and then spreads into neighboring grains.
2. Stage I. This begins when all grains have begun to deform
with slip still involving multiple slip systems. Stage I in
polycrystals is thus basically different from the easy glide
Stage I of face-centered cubic crystals. It ends at approximately
E = 1.0%.
3. Stage II. Here slip tends to occur predominantly on a single
(primary)system but with interaction from secondary systems. The
deformation is accordingly analogous to that in Stage II of a fcc
single crystal. Large grains may break down into several regions 
with different primary systems. This stage extends to about
e p5.0% in pure fcc metals such as copper and nickel.
4. Stage III. As in fcc single crystal deformation, this stage
is controlled largely by dynamic recovery and has been associated
with cross slip .
In general, polycrystalline stress-strain curves appear to be
continuous in shape and the stages difficult to identify on such curves.
This is in marked contrast to single crystal stress-strain curves which
often exhibit well-defined stages. A sensitive empirical method 
for detecting polycrystalline stage behavior has been developed as a
logical projection of previous empirical analyses [84-92]. This is
based upon the assumption that each stage of stress-strain behavior can
be reasonably described by a modified Swift  equation:
e = Eo+com (6)
where a is the true stress, E the true plastic strain, m the work
hardening exponent and o. and c are constants.
One may solve very simply for the parameters in Eq. 6 by plotting
log 0 versus log o where 0 = a A schematic example of such a plot
is shown in Figure 4 for a typical face-centered cubic metal such as
copper or nickel. Any straight line on this type of plot has an
equation of the type:
log 0 = (1-m) log o log cm (7)
Figure 3. Schematic example of stage
behavior in polycrystalline
Figure 4. Schematic description of the work hardening behavior
in a metal using a log C-log a plot.
Thus, the value of m typically characterizes the power law
relationship of Eq. 6. An m equal to one is a linear stress-strain
curve and a log 0 versus log o plot would show a line with a zero
slope; a parabolic stress-strain curve would show a (l-m)-value of
-1.0 (i.e., m=2) and so on. High m values correspond to curves with a
great deal of curvature, i.e., very rapidly decreasing work hardening
rate with increasing stress as in Stage III when dynamic recovery processes
reduce the work hardening rate very rapidly with continued deformation.
All other parameters held constant, a high value of m for a single
stress-strain curve would, in general, imply that the material has low
ductility, even though the material might possess a reasonably high
ultimate strength. However, it should be noted that a three or four
stage stress-strain behavior could well lead to a combination of both high
strength and high ductility depending upon the m values of the various
stages and the extent of a particular stage during deformation.
It should be noted that the stage behavior observed by using Eqs. 6
or 7 is within limits independent of the empirical power law equation
used. For example, an analysis based upon the Crussard and Jaoul
method [87-89] using a log a log E diagram shows that discontinuities
occur at the same places on the stress-strain curve as determined by
using a log 0 log a diagram.
In the current investigation, interstitial solute concentration
was the principal alloy variable known to affect stress-strain behavior.
Interstitial elements tend to significantly increase the strength of a
metal while generally decreasing its ductility. This in turn affects
the stage behavior of the parent metal.
Another factor influencing the stage behavior of metals and
alloys is the stacking fault energy. This intrinsic property of a
metal or alloy determines the separation distance of the two partial
dislocations of an extended dislocation .
For high SFE metals like nickel [22,23,94] or aluminum  the
separation distance is small and mobile dislocations may be assumed
to approach total dislocations. In low SFE metals and alloys such as
Ni-40Co and Ni-60Co  this distance becomes appreciable and the
partial may be separated by a wide band of stacking fault. By
effectively varying the geometry of the dislocation by lowering its
stacking fault energy, the deformation behavior might be expected to
change as well. Thus, it would appear that in a low stacking fault
energy metal a dislocation effectively loses a degree of freedom of
movement by virtue of its assuming a planar character. This should
reduce the ability of the material to undergo dynamic recovery involving
either cross-slip or climb.
One may also view a stacking fault as a building block for a
deformation twin. In general, twin boundary energies are lower in lower
stacking fault energy metals. This observation is in agreement with the
fact that twinning plays a greater role in the deformation behavior of
metals and alloys [95,96] with low stacking fault energies. Twinning
was not observed in the present investigation.
1.4 Anelastic Phenomena in Nickel and FCC Ferrous Alloys
Considerable research has been performed for many years on the
effects of interstitial solutes on the strain aging of body-centered
cubic metals and alloys . In addition, much emphasis has shifted
toward examining a variety of internal friction effects (such as the'
Snoek effect, the cold-work peak and dislocation damping behavior)
that can be correlated closely to strain aging phenomena .
In contrast, however, there exists but a dearth of strain aging
and internal friction studies of interstitial solid solutions of face-
centered cubic metals. The reason for this lack of interest probably
stems from the fact that in terms of the mechanical behavior of these
alloys, the interstitials apparently cause a less dramatic effect on
the mechanical properties. In addition, fcc metals are not expected to
exhibit a Snoek peak because of site symmetry [30,32,98,99].
Very different specific mechanisms for the observed relaxation
peaks in fcc metals and alloys have been suggested by various authors.
Adler and Radeloff  reviewed the types of defects which could
account for internal friction in fcc metals and alloys:
(1) interstitial-solute clusters which have noncubic strain
(2) interstitial-substitutional solute clusters in which the
interstitial reorients preferentially under stress if it is a
near neighbor to an immobile substitutional solute [98,99];
(3) interstitial-vacancy complexes of different types, i.e., Wu
and Wang  suggested a defect consisting of one interstitial
occupying a vacancy with a nearest neighbor interstitial in its
Within each category listed above are many possible specific
combinations which could in principle cause a relaxation effect.
There is evidence for relaxation due to carbon pairs in both Ni
and the fcc allotrope of Co, and for oxygen pairs in Ag . The
existence of an internal friction peak associated with dissolved
C in Ni was first reported by KB and Tsien  and further inves-
tigated by KQ, Tsien and Misek . The peak is quite small and
occurs at 5230K for a frequency of 1 Hz. By application of a saturating
magnetic field, the existence of the peak was shown to be unrelated to
the ferromagnetic nature of the sample. Further, the peak was found to
decline in strength as the carbon precipitated from solution. KB and
Tsien pointed out that unassociated C atoms, located at the body-centered
position of the fcc structure and in the equivalent positions midway
along the cube edges, could not be responsible for the relaxation, since
the symmetry of such defects is cubic. After Tsien  found in later
work that the relaxation strength varied essentially as the square of
the carbon content in solution, it became evident from mass-action
considerations that carbon pairs were the responsible defect.
Diamond and Uert  also investigated the diffusion of carbon
in nickel utilizing elastic aftereffect measurements above and below
the Curie temperature and noted no discontinuity in carbon diffusivity.
Hence, magnetic transformation effects do not affect carbon diffusivity.
In addition, they concluded that the elastic aftereffect is due
principally to interstitial diffusion of C-C pairs in agreement with
the results of the previously mentioned group of Chinese investigators
[102-105]. The simplest interstitial pair configuration in their view
consists of two atoms occupying nearest neighbor octahedral sites which
are the largest for fcc metals, e.g., the two sites 00 and 00. The
stress induced reorientation of such pairs (designated 110 pairs) which
gives rise to anelastic effects, is the result of one of the atoms
jumping into an unoccupied nearest neighbor interstitial site. A summary
of Ni-C diffusion data is presented in Table 2. It should be noted
that all methods agree reasonably well with an activation energy of
35 kcal/mole for the migration energy of carbon in nickel. No
distinction is made in the last four references cited in the table
concerning the nature of the mobile species, e.g., dicarbon complexes.
C.T. Tsien  considered the effect of impurities on an internal
friction peak in a carburized 18.5 w/o manganese steel. The principal
experimental observation was that the internal friction peak height
varies linearly with carbon content. It was proposed that the addition
of Mn to Fe-C alloys may reduce the opportunity of forming carbon-
carbon atom pairs and there may be greater probability of forming
Mn-C pairs instead. Thus, in high manganese steels the internal
friction peak is not attributed to rotation of the carbon atom pairs but
due to that of carbon-manganese pairs. As a result, the height of the
internal friction peak was observed to be directly proportional to the
This brings us to the point of the possible mechanism involved in
Nickel 200 which has 0.18 w/o Mn and smaller amounts of iron and copper.
Presuming a pair mechanism (in order to obtain a tetragonal defect which
would account for an internal friction peak) one might presume a possi-
bility of C-C atom pairs or C-Mn atom pairs causing the static strain
aging effects. However, in the investigations previously sited, not one
was conducted using a deformed metal and this factor may be an important
consideration. Hence, a third and possibly fourth speciesmay be involved,
namely, the vacancy and the self-interstitial. It has been demonstrated
by Seitz  that in fcc metals the predominant defect produced
during plastic deformation is the vacancy. Table 3 shows the data of
a number of authors  who have described the vacancy concentration
during plastic deformation for a variety of fcc metals and alloys as
Cy = Ken (8)
where cv = vacancy concentration (atom fraction)
e = true strain
K = proportionality constant
The principal experimental technique used to determine c involves
monitoring resistivity changes during deformation and subsequent
annealing of the specimens [106,108]. The identification of the
defects annealing out during each recovery stage has been the subject
of extensive previous work in nickel. Studies have been made of the
resistivity recovery spectrum following neutron irradiation, electron
irradiation and quenching from high temperatures [109,110]. In addition,
changes in magnetic properties have also been studied in conjunction
with the resistivity recovery process [73,111,112].
On this basis  cold rolled nickel behaves as
c = 2.1 x 10-'4 (9)
In addition, it has been estimated that approximately eight times as
many vacancies as self-interstitials are generated.
Point defects are generally believed to be generated during plastic
deformation by two basic mechanisms [31,113]: (a) nonconservative
motion of jogs on screw (or mixed character) dislocations and
(b) recombination of dislocations containing edge type components.
The second mechanism is due to annihilation of edge dislocations and may
Estimates of the Rate of Vacancy Production
During Plastic Deformation
Material K Type of Deformation
Cu 1.9 x 10-4 tensile elongation
Ni 2.1 x 10-4 cold rolling
Ni 12 x 10- shock forming
NaC1 1 x 10- compression
70-30 Brass 5.9 x 10-4 tensile elongation
Au 2.9 x 10-4 tensile elongation
Al 0.2 x 10-4 tensile elongation
* From Ulitchny and Gibala 
not be important relative to the first mechanism in the production
of vacancies until Stage III deformation occurs. The relation between
vacancy concentration and strain is also probably only valid to strains
of the order of 10%. It has been noted that the vacancy concentration
tends to approach a saturation value at large strains . Thus,
vacancies may play an important role in deformed and aged nickel.
As concerns the manganese impurity in Nickel 200, a qualitative
argument may be made against the existence of Mn-C complexes as opposed
to C-V complexes. The gram atomic volume of Mn  is 7.39 cm while
that for Ni  is 6.59 cm3. Thus, a Mn atom is only approximately
4% oversize on a nickel lattice site. In an interstitial octahedral
lattice site, a carbon atom is about 14% oversize. Relative to binding
to a vacancy, the carbon atom should provide a stronger compressional
center of dilatation than the manganese atom even though in the former
case an octahedral interstitial site is occupied and in the latter a
normal lattice site is occupied. Hence, the binding energy of a vacancy
to a carbon atom should be higher than that of a manganese atom to a
carbon atom or a vacancy. In addition, Nickel 200 contains approximately
three times less manganese than carbon on an atom fraction basis.
The value for the diffusion energy of a vacancy through a lattice
is very sensitive to the presence of impurities which tend to slow down
a freely migrating vacancy because of binding to impurity atoms [116,117].
In pure nickel, the vacancy migration energy is between 0.8 and 0.9 eV
and for impure nickel [117,118] (99.9% pure plus an unspecified amount of
carbon) is approximately 1.1 eV. Thus, one may deduce that the approximate
binding energy of carbon to vacancies is between 0.2 and 0.3 eV. In
short, the carbon-vacancy interaction could cause the formation of a
defect complex which might cause strain aging in Nickel 200. It is
not clear whether or not dicarbon-vacancy defects may be completely
ruled out as a possible complex causing strain aging.
An excellent discussion concerning internal friction and strain
aging to carburized ferrous austenite by Ulitchny and Gibala 
suggests that the relaxation phenomena in these alloys are attributable
to the rotation of carbon-vacancy pairs. Their conclusion is based
upon experiments in which vacancies were produced in stainless steels
by (1) quenching, (2) deformation and (3) irradiation. These processes
have in common that they (a) increase the vacancy concentration in
the metals, (b) increase the observed peak heights of the bound pair
peak and (c) increase the peak heights in proportion to the relative
numbers of vacancies they are anticipated to produce. These alloys
possess mechanical properties quite similar to nickel-carbon alloys.
In addition, the diffusivities of both carbon atoms and vacancies in
the austenitic stainless steels are similar to those in nickel-carbon
alloys  suggesting that a similar mechanism in the present investi-
gation of Nickel 200 should not be ruled out.
Nickel 200 bars of 0.75 inch diameter were obtained through a
local supplier and from the International Nickel Company. These two
heats had slightly different compositions (Table 4); the mechanical
properties as a result were somewhat altered, albeit small. All static
strain aging experiments were conducted utilizing Nickel 200b. The
standard tensile tests were conducted using Nickel 200a. This procedure
was followed in order to minimize possible scatter of the data,
particularly in the static strain aging experiments. In addition,
Nickel 270 was also purchased; its composition also appears in Table 4.
Nickel 200 contains approximately 0.18 w/o Mn and 0.10 w/o C.
The highest equilibrium solubility limit for the nickel-carbon
system is 0.27 w/o carbon. The room temperature solubility limit of
carbon in nickel is only 0.02 w/o . Also, nickel carbides are
unstable in Ni-C alloys [119,121]. The development of visible graphite
in nickel during cooling is generally agreed to occur very slowly.
The present specimens, which were furnace cooled from the annealing
temperature (10730K) at a rate of approximately 2.0/s, are believed
to have retained all of the carbon in excess of the equilibrium solubility
in solution since graphite was not observed either by optical or
transmission electron microscopy of the annealed specimens.
All other impurities less than 100 ppm each.
2.2 Experimental Techniques
The 0.75 inch (19.1mm) bar stock of all the materials were cold
swaged in a Model 3F Fenn rotary swaging machine to a diameter of
0.25 inch (6.4mm). Intermittent annealing was not necessary. The
resulting swaged bars were machined into threaded-end specimens with a
nominal reduced section of 0.8 inch (20mm) and a gage diameter of
0.15 inch (3.8mn).
Annealing was accomplished in a Vacuum Industries Minivac furnace
assembly. This unit utilizes a resistance heated tantalum element.
Pressures as low as 10 millitorr can be maintained. No cold trap
was used. All Nickel 200 specimens were annealed for 30 minutes at
800C (10730K); Nickel 270 specimens were annealed for 32 minutes at
5950C (868K). These treatments resulted in specimens with a mean grain
intercept of approximately 22pM. Annealing twin boundary intercepts
were not counted in obtaining this result.
2.2.3 Specimen Profile Measurements
A Jones and Lamson Optical Comparator capable of measuring to
0.0001 inch (2.5pM) in the vertical and 0.001 inch (25pM) in the
horizontal directions was used to measure the profile of as-annealed
specimens. For all tests a specimen gage length was assumed to be
identical to its reduced section and was determined to within 0.005 inch
(0.13mm) with experience.
2.2.4 Tensile Testing
All tensile testing was performed on two Instron machines (Model TT-C
and Model FDL of 10,000 and 20,000 pound capacities, respectively). The
standard crosshead speed was 0.02 inch/minute resulting in a nominal
specimen strain rate of 4.2 x 10-4 s Three additional strain rates
were also employed with the Nickel 200 specimens. All tests were conducted
between 77 and 9000K. Above 2970K tests were carried out in a capsule
using commercial purity argon gas. At no time was oxidation visible on the
specimen surfaces. Below ambient temperature, liquid nitrogen (770K),
dry ice-acetone (1960K), or ice-water baths were employed.
Load-time curves were processed to yield true stress versus true
plastic strain curves as well as the slope of these curves as a function
of stress or strain. The stage behavior of the specimens was analyzed .
In brief, the procedure involves the plotting of log E versus log o
and identifying portions of the curves through which straight lines may
be passed. Each linear interval is assumed to represent a stage.
This assumption was tested against results of Zankl , Schwink and
Vorbrugg  and others [76,78-81] and a good correlation was obtained
between stages determined in this manner and the method of Zankl and
others using different plotting and metallographic procedures. To each
linear region a different set of parameters (m,c, o) may be deduced
corresponding to the Swift  equation
2.2.5 Static Aging Experiments
Annealed tensile specimens were prestrained approximately 5% to
a stress level of 38.5 ksi (265 MPa) at 2730K and immediately unloaded,
removed from the testing jig and immersed in a silicon oil bath at
473, 448, 428 and 4080K or in a boiling water (distilled) bath for
times as long as 2 x 106 seconds (approximately two weeks). Control
of the constant temperature baths was held to within approximately
one-half degree. Upon completion of the aging treatment, the specimen
was removed and quickly quenched into cold water and tested immediately.
The reloading temperature for the static strain aging tests was 273K
as in the prestrain. It was recognized early in the investigation that
at room temperature and a strain rate of 4.2 x 104 s- (the rate
corresponding to a crosshead speed of 0.02 inch/minute, standard at
this laboratory), discontinuous flow occurred in Nickel 200. To
alleviate this feature it was decided to conduct the prestrains in
ice-water baths at a rate of 4.2 x 10-3 s This had the additional
benefit of producing a stable and reproducible lower yield stress
plateau and, in addition, the ice-water bath assured that specimens
were at the test temperature after removal from the high temperature
Quite apparent from the start was the fact that specimen alignment
offered a problem. Upon removal and replacement of a specimen in the
tensile jig, it was evident that exact repositioning was difficult and
uncertain. Therefore, on restraining a specimen after aging it, a
small bending moment normally develops which may cause yielding to
occur nonunifonnly across the gage section of the specimen. The result
is that the upper yield point as observed on the machine chart was
usually absent. As a consequence all data reported are lower yield
stresses. Compilation of the data included interpreting the Luders
extension as the chart displacement which occurred at constant load
(Figure 5). This method proved to provide the most consistent set of
data and tended to alleviate apparent alignment or reloading displacements.
Occasionally (perhaps 10% of the time), a yield point was observed and
the data fell consistently in line with other LUders extension data
recorded by the former method.
The latent hardening achieved during long term and high temperature
aging treatments was computed by linearly extrapolating the post-
yielding curve back to the reloading line as demonstrated in Figure 5.
This method also proved consistent. However, in most cases of short
aging times or low temperature aging, the extrapolated stress fell
below the prestrain value. This is physically unreasonable and is
attributed to alignment effects which generally eliminate the yield
point as mentioned previously and may cause the extrapolations to come
back to the reloading curve somewhat low. However, the resulting data,
again, proved to be consistent.
As an example of typical experimental results, Figure 6 shows a
series of load-time curves which were obtained after restraining a
series of specimens at 2730K to 5%, aging at various times at 408K,
and restraining at 2730K. Figures 6b and 6d show examples of partial
yield points that were obtained in a few cases during the present inves-
Aged 2.92 x 104s/4480
Ext.- -157 N
Figure 5. Illustrating the method used to determine the aging
parameters EL, AC= oLY o and AOH = OExt o .
The dashed loading line indicates the approximate
loading line which would have been observed in the
absence of misalignment of the test specimen.
^ --157 N
/ s/ 960 s
1.54 x 104s 1.74 x I's
5.78 x 10 s
Figure 6. Selected load-time curves obtained after restraining
a series of specimens 5% at 2730K, aging at 4080K
for the times indicated, and restraining at 2730K.
3.1 The Behavior of the Lower Yield Stress Increase, At
Figure 7 illustrates the dependence of the lower yield stress
increment, Ao, on time and temperature over five decades of time and
at five temperatures. The principal features of Figure 7 are
(1) The curves appear to approach a common value at small times.
It would seem that the data obtained at the higher aging temperatures
and for very short aging times are influenced by the time required to
heat the specimen to temperature. This was confirmed by assuming a
fixed heat-up time and displacing the curve (at each temperature) to
shorter aging times. Thus, a heating time of approximately 40 to 60
seconds straightens out the start of the higher temperature curves to
approximately the same linear dependence as exhibited by the 3730K curve.
In addition, a simple heat transfer calculation indicated that a time
constant of approximately 40 to 60 seconds should describe the specimen
heat-up time. The dashed lines in Figure 7 show the approximate
corrections necessary to account for heating the specimens in the baths.
(2) Each Ao curve shows a roughly linear increase with log t for
times before reaching the maximum in Ac.
(3) All curves show a well-defined peak whose height increases
slightly, the lower the aging temperature.
I 2 3 4 5 6
10 10 10 10 10 10
Figure 7. The time and temperature dependence of the return of
the lower yield stress in Nickel 200. Specimens were
prestrained to a stress level of 265 MPa. The dashed
curves are approximate corrected curves which account
for specimen heat-up in the aging baths.
Least Squares Parameters for Static Strain Aging Data
Assuming Ao Is a Function of In t
480 t 1.43 x 106
240 t 6.62 x 104
60 t 2.16 x 104
30 t 3.4 x 103
Slope Intercept r
2.088 -4.922 0.996
2.647 -3.356 0.998
2.602 1.618 0.995
2.318 6.689 0.998
(4) Ao decreases significantly after max is passed. Just
after the peak, the decrease in Ao is almost linear with log t.
However, at 473"K, the highest temperature investigated, the data at
very long aging times show that the lower yield stress decreases to
a constant value of approximately 17 MPa.
Table 5 lists values obtained by the method of least squares for
the slopes and intercepts (at t=1s) of the aging curves in Figure 7.
A Ao versus In t relationship is assumed to hold for times before
Ac reaches a maximum.
In addition, Figure 8 shows a set of Am curves which were normalized
to their respective maximum peak heights, Ammax. An approximate value
of 28.5 MPa for Aomax was assumed for the 3730K curve since, for the
aging times investigated, a peak was not attained. This diagram has
the effect of making the aging curves more nearly parallel.
Figure 9 is a plot of the increase in lower yield stress versus
t /7 using data from the 373, 408, 428 and 4480K aging curves of
Figure 7. Least squares analysis of log Ao versus log t curves indicated
that Ao varies approximately as the 0.14 and 0.15 power of time. See
Table 6 for the complete results. This represents an approximate time
dependence of t/7
It is important to note that this author prepared a specimen which
had been aged for approximately 6 hours at 5250K (specimen taken from
the undeformed threaded end of a deformed tensile specimen) and observed
it carefully in a transmission electron microscope. No evidence of
precipitates or free graphite in the grains, at dislocations or at grain
boundaries was observed. Thus, it is highly unlikely that precipitation
of carbon occurs during aging between 373 and 4730K in Nickel 200.
Figure 8. Normalized aging curves for Nickel 200. The 3730K
curve was normalized to an assumed maximum of
28.5 MPa. The dashed curves reflect approximate
corrections for the heat-up time of the specimens.
o I 2 3 4 5 6
o I 2 3
Figure 9. Illustrating the approximate t1/7 power law relation
governing the aging of Nickel 200 at temperatures below
4480K. Data for the 4480K (shown) and 473K cases
do not fit this relation well.
Least Squares Parameters for Static Strain Aging Data
Assuming a Log Ao-Log t Linear Relationship
Temperature t (min Slope Intercept r
373 1.0 < 23,752 0.145 0.804 0.993
428 2 t 710 0.137 1.109 0.997
448a 2t 100 0.099 1.232 0.998
473b 10< t 5 30 0.055 1.307 1.000
a Three points
3.2 The Liders Extension, EL
Figure 10 illustrates the dependence of the LUders extension on
log t. The behavior is similar to that exhibited in Figure 7 for
curves of Ao versus log t. However, note that the peak in the Luders
extension occurs (at a given temperature) at an earlier time than the
corresponding peak in Ao. This may be indicative of the onset of
hardening and is consistent with results obtained in bcc metals. Note
also that at long times the extensions tend to return to their short
time values; that is, they do not remain constant after reaching their
maximum values. An interesting point is that the highest temperature
curve (4730K) reaches an apparent minimum at approximately 1500 minutes.
3.3 The Hardening Component, AoH
Figure 11 is a plot of AoH, the hardening component of the increase
in lower yield stress. This parameter was deduced as noted in Figure 5
by using the equation AoH = OExt oo. Figure 11 shows that this
hardening component appears only at discrete times. Note also that
AOH peaks at approximately the same time as Ao and decreases to a value
higher than that observed at very short aging times. It should be noted
that the values of AoH cannot be taken as exact due to alignment problems
which affected the choice of OExt (see Figure 5).
3.4 Activation Energies
In order to establish a mechanism for static strain aging, the
apparent activation energies associated with particular time dependent
aging events were deduced. The activation energy for the return of the
lower yield stress where in the interval an approximate logarithm of
I- 1Iq -I I I I I ,lll -- I I ;11H I I I 1111 I i I 1 111 I] -
448 .' --4 3730
0.0 I I
10 102 103 104 10 106
Figure 10. The dependence of the LUders strain on time and temperature in Nickel 200.
I I I11 1 1 1 M4 I III1 I I IllIr I'll I I I-
. . ..... I ,
. . .. I
101 102 103 104
Figure 11. The approximate behavior of the secondary hardening component of the
lower yield stress increase (AoH= OExt ao).
I I I i 1 M I1 I I I'll I IiP r I . .
time behavior is exhibited was calculated on the basis of the respective
times to achieve a stress increase of 15.0 and 20.0 MPa. On this basis
the activation energy for the return of the lower yield stress in Nickel
200 is 25.2 3.2 and 26.4 2.7 kcal/mole.
The activation energy for the development of a 0.6% LUders
extension is similar, 24.3 kcal/mole. In addition, the shift of the
peaks of Ao versus log t is consistent with an activation energy of
approximately 22 kcal/mole. The downward trend of the aging curves behaves
in a manner corresponding to an activation energy of 29.0 kcal/mole on
the basis of the method of cuts at Ao= 23 MPa.
3.5 The Dependence of Ao and EL on Prestrain
To more fully characterize static strain aging, a series of
specimens were prestrained various amounts and then aged at 4480K for
a fixed time of 6000 seconds, the approximate time required to achieve
the maximum Ao at this temperature when the prestrain was 5% (see
Figure 12 illustrates the dependence of Ao and EL on the amount
of deformation at a constant aging time and temperature. The Ac curve
shows that this parameter increases with prestrain, exhibits a broad
maximum and then decreases slowly. It is interesting that Stage III
of the work hardening behavior (see Section 3.8), as determined from
log O versus log o plots, begins at approximately 18% true strain at
2730K. Stage III is normally associated with dynamic recovery and in
view of the broad peak and subsequent decrease in Ao, it is possible
that Ao is reflecting the dynamic recovery.
1 30- 6
0 5 10 15 20 25 30
Engr. Strain (%)
Figure 12. The dependence of Ao and EL on prestrain. Nickel 200 specimens were
prestrained at 2730K, aged for 6000 seconds at 4480K, and restrained
The Liders extension increases continuously with prestrain as
indicated in Figure 12. The LUders strain is determined not only
by the size of the lower yield stress but also by the magnitude of
the work hardening rate. The latter decreases continuously with strain
and tends to make EL increase with strain. The fact that EL continues
to increase with E in Figure 12 is probably due to this cause. This
is similar to the case of Type A Luders bands which exhibit an increase
in LUders strain during plastic deformation .
3.6 Comparison of Nickel 270 and Nickel 200 Static Strain Aging
Several experimental observations indicate that the higher purity
Nickel 270 does not contain sufficient carbon to give rise to measurable
dynamic strain aging phenomena. Specifically, the Portevin-Le Chatelier
effect was not observed in this metal. Also, even at the highest
temperatures investigated, yield points or yield plateaus were not
observed in annealed material. Thus, Nickel 270 may be nearly repre-
sentative of pure nickel in terms of its mechanical properties.
To test if static strain aging is weakly exhibited in Nickel 270
a specimen was prestrained 5% at 273K and aged for 1200 seconds at
4730K. The resulting curve shown in Figure 13a appears to indicate some
aging since a short yield plateau is exhibited. However, the lower
yield stress increase for this specimen was only 4.76 MPa which is small
compared to the 23.00 MPa value for the commercial purity Nickel 200
specimen (Figure 13b) which was achieved in only one-half this aging time.
It is also possible that a significant portion of the 4.76 MPa yield
effect that has been observed in face-centered cubic metals [17,123].
Thus, one may be reasonably assured that strain aging phenomena in
Nickel 270 are generally weak.
-127 N 600s/473.
Figure 13. (a) The yield return of a Nickel 270 specimen aged for a time to achieve a
maximum in Ao for Nickel 200. (b) Yield return for a Nickel 200 specimen
aged only one-half as long.
3.7 The Stress-Strain Behaviors
The details of the basic mechanical behavior of the high purity
nickel, Nickel 270, are shown in Figures 14-16. Those for commercial
purity Nickel 200 are shown in Figures 17-22. Nickel 200 unlike
Nickel 270 exhibits serrations and yield points.
As indicated in Figure 21, the Portevin-Le Chatelier effect was
observed over four orders of magnitude of strain rate in Nickel 200.
The figure also shows the approximate temperature intervals over which
Types A, B and C serrated flow were observed. Type C serrations were
sudden load drops appearing at regular intervals on the load-time
curve. The serrated flow intervals correspond closely to those observed
by Nakada and Keh  in nickel-carbon alloys indicating that the
presence of the manganese in Nickel 200 does not appreciably affect the
dynamic aging effects. The data of the present investigation are not
extensive enough to calculate the apparent activation energy for the
onset of serrations in Nickel 200 with accuracy. However, the data
appear to be consistent with the apparent activation energy 152 kcal/mole
calculated by Nakada and Keh for the somewhat purer alloys . In
addition, the apparent activation energy for the disappearance of
serrations calculated by Nakada and Keh , 264 kcal/mole, also
appears to be reasonable for Nickel 200.
Figure 14 shows representative stress-strain curves for Nickel 270
obtained at several temperatures. The 0.2% offset flow stress and the
ultimate tensile strengths of Nickel 270 are plotted in Figure 15 as
functions of the temperature. Note that the ultimate stress decreases
monotonically with temperature without any undue irregularity. This
type of stress-temperature variation is characteristic of a metal which
0 0.1 0.2 0.3 0.4 0.5
Figure 14. True stress-true plastic strain curves for Nickel 270 4.2 x
Figure 14. True stress-true plastic strain curves for Nickel 270 (e = 4.2 x I0-4 s1).
0 100 200 300 400 500 600 700 800 900
Figure 15. Variation of the 0.2% yield stress and the ultimate
tensile strength with temperature in Nickel 270
(E = 4.2 x 10-4 s-l.
0 100 200 300 400 500 600
700 800 900
Figure 16. Variation of the uniform and total elongation with
temperature in Nickel 270 (E = 4.2 x 10-4 s1).
does not exhibit pronounced dynamic strain aging. The total and
uniform elongations are illustrated in Figure 16 and show no anomalies.
A minimum in ductility was observed at 8350K and surface cracking was
noted on the specimens. Cracking also appeared on the specimen tested
at 8500K. The Nickel 270 specimens were annealed at 8680K and this
temperature was the upper testing limit. The elongations are reasonably
constant over a wide range of temperature (approximately 200 to 6500K).
A representative sample of Nickel 200 stress-strain curves are
shown in Figure 17. It should be noted that the curves at 300 and 5250K
were serrated. Only average stress-strain behavior can be shown in
these cases. Note that at 525K the curve shows an anomalously high
ultimate strength. The enhanced strengthening during work hardening
is best illustrated in Figure 18 which shows dependence of the 0.2% flow
stress and the ultimate stress on the temperature.
Because of the scale of the drawing in Figure 18 the 0.2% offset
stress appears to decrease monotonically with temperature. However,
a plot of the 0.2% offset stress for Nickel 200 at two strain rates with
the stress axis expanded as in Figure 19 shows that there is a small
yield stress plateau between approximately 300 and 4750K. This is
generally characteristic of dynamic strain aging in bcc and hcp metals.
The stresses were not normalized with respect to the elastic modulus, as
is customary, because nickel exhibits a large magnetostriction [124,125] and the
choice of modulus is uncertain below 626K, the Curie point .
This plateau is weakly exhibited compared to that of titanium [127-129],
for example. In comparison to the 0.2% stresses observed in Nickel 270,
Nickel 200 exhibits a larger temperature dependence (compare Figures 15
S 10- 77. K
S 8 2K 192"K
0 0.1 0.2 0.3 0.4
Figure 17. True stress-true plastic strain curves for Nickel 200 (c = 4.2 x 10-4 s-1).
* 4.2 x 10-5 sec-1
* 4.2 x 104 sec1
0 4.2 x 10-3 sec-
S4.2 x 10-2 sec-
es \ \
0 0.2 I
* I I I I. -
Figure 18. The temperature dependence of the 0.2% yield stress
and ultimate tensile strength of Nickel 200.
_ I I 1 I I 1
I I *
4.2 x 10-4 s"
o 4.2 x 10'3 s"
S 1 I I
Figure 19. The temperature and strain rate dependence of the
0.2% yield stress in Nickel 200 on an expanded
An important feature to note in Figure 18 is that anomalous
strengthening is exhibited between 300 and 6000K. In Figure 20 the
strain dependence of the flow stress is shown for 5, 11, 19, and 31%
plastic strain. This figure demonstrates that only above approximately
11 to 19% plastic strain does the anomalous strengthening become
significant. That is, the strengthening effect is not due to anomalous
work hardening as Sukhovarov and Kharlova  previously suggested.
Note that unlike the behavior of the ultimate tensile strengths plotted
in Figure 18, the stress levels attained at 31% strain exhibit a rate
dependent shift in the peaks. These peaks have a rate dependence
corresponding to an activation energy of approximately 38 kcal/mole.
Figure 21 illustrates the temperature dependence of the uniform
and total elongations in Nickel 200 at several strain rates. The total
elongation at a strain rate of 4.2 x 10- s-l shows a mild ductility
minimum (blue-brittle effect) between approximately 300 and 450K. This
minimum is not well-defined. However, a well-defined but small reduction
in area minimum does occur in Nickel 200 that is strain rate dependent
as shown in Figure 22. This minimum was noted to have shifted in
accordance with an apparent activation energy of approximately 25 kcal/mole.
A reduction in area minimum is not always manifested in dynamic strain
aging . It is interesting to note, however, that 25 kcal/mole is
approximately the activation energy for vacancy migration in nickel [109,118].
Not only is the loss in reduction in area not marked, but the lowest
value recorded is still above 75%. Adjunct observations of the fracture
surfaces under a low-power microscope did not reveal any striking
difference in fracture mode at the reduction in area minimum.
600- N.-- .
300 5 %
4.2 x o10 s'
10 o 4. x 103 s-
4.2 x 10 s
0 100 200 300 400 500 600 700 800 900
Figure 20. Variation of the stresses at 5, 11, 19, and 30% plastic strain with
temperature in Nickel 200.
4.2 x 10 sec'
4.2 x I0 sec' -
o 4.2 x 10-3 sec'-
s80 4.2 x 10-2 sec-
: ./ ,V/ Total
G e- '- o
\Q N. A'--- ,
G '. "
B .C. \" Uniform -
20 L A iABC
1 --- -------1 --- --I---'-
0 200 400 600 800
Figure 21. Variation of the uniform and total elongations with
temperature in Nickel 200. Also shown are the
approximate temperature ranges over which serrations
were observed at the respective strain rates.
96- Ni 270
94 ^ 4.2 x 1064s-
s88 Ni 200
8s .. ..... .. 0. / 42 x 1O- .s-
\. *\ 4.2 x lO s-1
78 \ -
740 20 40 -O
0 200 400 500 SOO !000
Figure 22. Variation of the reduction in area
for Nickel 200 and Nickel 270.
Note that the higher purity Nickel 270 shows more ductility at
all temperatures than does Nickel 200. Although a mild reduction in
area minimum does occur in Nickel 270, it is spread over a wide
interval between approximately 425 and 750K and is not as pronounced
as that in Nickel 200. Even the lowest reduction in area observed in
this investigation is considerably higher than that in most commercially
available bcc metals and alloys.
The strain rate sensitivity in Nickel 200 and Nickel 270 was not
investigated because the temperature interval of serrated flow in
Nickel 200 was some 3000K wide and it was believed that strain rate
changes conducted during discontinuous plastic flow would prove in-
conclusive. It was noted, however, that at room temperature during
moderately heterogeneous plastic flow, changes in rate resulted in the
appearance of flow stress transients in Nickel 200 and a steady state
strain rate sensitivity very close to zero was observed.
In summary, whereas the higher purity Nickel 270 shows no anomalies
in ultimate strength and elongation with increasing temperature, Nickel 200
between 300 and 6000K shows anomalous strengthening, serrated flow, a
small yield stress plateau and a mild elongation minimum.
3.8 The Work Hardening Behavior of Nickel 270 and of Nickel 200
Figures 23 and 24 show a cross-section of the log 0 versus log o
curves for Nickel 270 and Nickel 200, respectively, deformed at a
nominal strain rate of 4.2 x 10-4 s.1 These curves satisfactorily
represent the general trend of work hardening at all strain rates
investigated. No attempt has been made to draw in the straight lines
representing the stage behavior in order to reduce the complexity of
S (Stress in N/n)
7.6 7-8 8 0 8.2
8.4 8.6 8.8
8.4 8.6 8.8
Figure 23. The log 0-log a curves of Nickel 270 (e = 4.2 x 10-4 s- ).
= 4.2x i04 s"7
\ee sooo" t **. e o
(Stress in MPa)
0o 0 0 o
7.8 8.0 82 8-4 8-6
Figure 24. The log 0-log a curves of Nickel 200 (- = 4.2 x 10-4 s ).
The work hardening behavior of Nickel 270 and of Nickel 200 are
similar to those found earlier in pure face-centered cubic metals. The
stages appear in the same manner as Zankl , Schwink and Vorbrugg ,
and others [76,78-81] have shown to be the case for pure face-centered
cubic metals. It should be noted that hexagonal close packed metals
such as zirconium and titanium  as well as body-centered cubic
metals such as iron and niobium  show much higher m values (order
of 7 to 40) than the fcc alloys presently being investigated. That is,
all log o versus log a plots for these metals show much steeper slopes.
Also, these metals tend to show only one or two stages of deformation
behavior indicating that the deformation in these metals is possibly
controlled by a different set of deformation phenomena.
Figures 25 and 26 show the m values obtained for Nickel 270 and
Nickel 200 by measuring the slopes of log 0 versus log a plots at
different temperatures. The error of each particular mil value is
approximately 0.1 as measured by the plausible maximum and minimum
slopes that might conceivably characterize a particular work hardening
stage. It should also be noted that Stages I and III are difficult
to characterize in many cases. The parameter minI is plotted in the
figures only to show trends in the third stage as a function of temperature.
They are not accurately defined since in Stage III log O-log o plots
are not linear but curved. However, Stage II is generally uniquely
defined by a straight line on log O-log a curves.
Nickel 270 and Nickel 200 possess mil values which are close to 1.5
as shown in Figures 25 and 26. Note that in Nickel 200 mlI remains
constant over a wide range of temperatures and is strain rate independent.
E 4 m
0 100 200 300 400 500 600 700 800 90S
Figure 25. The variation of mi[ and milj with temperature in Nickel 270 (E = 4.2 x 10-4 s-1.
7- "' 4.2 x 10-5-'1
7 4.2 X 10-48-1
Nickel 200 o 4.2 x Io-33
0 0 -- o
4o _- o-- o m0
---" ^- ^
0 200 400 600 800 1000
Figure 26. The variation of m11 and mlII with temperature in Nickel 200
(E = 4.2 x 10-4 s-1).
It is important to emphasize that the apparent work hardening peak
observed in Nickel 200 (Figures18 and 20) is not a true work hardening
peak in the sense that Nickel 200 stress-strain curves show anomalous
increases in work hardening over a uniquely defined temperature interval.
The peak is associated with an increase in the uniform elongation
around the temperature of the ultimate stress peak. Figure 27, a plot
of (o5%-0.5%) versus temperature, readily shows this behavior. This
parameter (where o5% and o0.5% are the true stresses at 5 and 0.5%
true plastic strain, respectively) confirms that there is little
temperature dependence of the work hardening. The constancy of mil in
Figure 26 also substantiates this observation. Figures 28 and 29
show very clearly that the onset of Stage III is delayed over exactly
the same temperature interval as develops the peak in ultimate stress.
These facts imply that there is no prominent work hardening peak in
nickel as earlier authors have indicated . There is, however, a
significant delay in the onset of Stage III or of dynamic recovery.
In Stage III deformation in both a polycrystalline or single
crystal fcc metal or alloy, the stress-strain curve shows a high
curvature, i.e., work hardening decreases very rapidly with continued
deformation. Thus, Stage III m values tend to be high. Figures 25 and
26 show that mIII increases with increasing temperature. This is
consistent with the concept that dynamic recovery becomes more important
with increasing temperature.
Now consider the extent or length of Stage II which is not illus-
trated well in the log 0-log o diagrams. In purer metals such as
Nickel 270 it is observed that Stage II, which is governed primarily by
slip on single slip systems within each grain , is lengthened by
0 100 200 300 400 500 600 700 800 900
Figure 27. The variation of the work hardening parameter (5%-' 0.5%) with temperature
(E = 4.2 x 10-4 s-).
the presence of interstitial carbon as in Nickel 200. Figure 28
compares the approximate strain at which Stage II deformation begins,
E2, and that at which Stage III begins (and Stage II ends), E3, for
Nickel 200 and Nickel 270. The principal effect of interstitial
carbon in the DSA interval in this respect is to postpone Stage III
dynamic recovery processes to a later time in the deformation history.
Also the general level of the Nickel 200 curve is higher than that
for Nickel 270. It is not clear at this time how the carbon accounts
for the general delay in Stage III.
Nickel 200 exhibits an e3 maximum over the dynamic strain aging
interval. This maximum is closely related to the maximum exhibited
in the uniform elongation (Figure 21) and accounts for the strengthening
observed over this temperature interval. This maximum in e3 is strain
rate dependent as shown in Figure 29. Not only do the peaks shift to
higher temperatures with increasing strain rate but the peak heights
decrease as well. This is similar to the behavior of the flow stresses
described in Figures 19 and 21. The shift in peaks follows an approximate
activation energy of 37 kcal/mole, similar to that obtained for the
flow stress peaks.
50- 3 NICKEL 270
1 3 NICKEL 200
(All strains ore true plastic strains)
I s? ,. .= Z z--= ..... __ _o" o ....
0 100 200 300 400 500 600 700 800 900
Figure 28. The variation of E2 and E3 (the approximate strains
at which Stages II and III, respectively, begin) with
temperature for Nickel 270 and Nickel 200 deformed at
a strain rate of 4.2 x 10-4 s-1.
I I i I I- I I I I
* 42 x
* 4.2 x
o 4.2 x
> 4.2 x
F F I I F
0 200 400
Figure 29. The dependence of e3 on temperature and strain rate
in Nickel 200.
4.1 Rationale for Static Strain Aging in Nickel 200
The static strain aging data for Nickel 200 aged between 373 and
4730K after a 5% prestrain indicate:
1. The activation energy for the return of the lower yield stress
for times before the maximum in Ao is approximately 253 kcal/mole.
2. The kinetics of the rise in the lower yield stress can be
described by a In t time law.
According to the previous discussion three principal causes for
strain aging in other metals have been identified: (a) Cottrell pinning,
(b) Suzuki locking and (c) Snoek pinning.
It would appear on the outset that aging in Nickel 200 is such that
Cottrell pinning must be ruled out as a candidate mechanism. First,
the kinetics for aging as described by Cottrell and Bilby  are t2/3
In Nickel 200 the rise in Ao with time is much slower, approximately t /7
this is very different from the Cottrell-Bilby time law. Secondly, the
activation energy deduced to govern the early stages of pinning in
Nickel 200 is not consistent with the migration energy of carbon, the
principal impurity in Nickel 200, as the Cottrell-Bilby model would
suggest. The migration energy of carbon in nickel is approximately
35 kcal/mole (see Table 2) and thus significantly different from the
observed activation energy. Accordingly, the random migration distance
for carbon at all temperatures investigated during the time required to
cause maximum strengthening is only about 8b which is a very short
diffusion distance compared to distances involved in the formation of
a Cottrell atmosphere.
Suzuki pinning is not believed to be responsible for the observed
strain aging behavior in Nickel 200 primarily because the stacking fault
energy of pure nickel is very high. Hence, the probability of forming
stable faults in nickel is very low. It is believed that carbon
impurities do not lower the stacking fault energy enough to have a
significant effect with regard to this mechanism.
Snoek pinning by itself cannot account for the rise in Ao unless
anisotropic defects exist in the material in sufficient numbers and
have a sufficiently high interaction energy with dislocations. As will
be demonstrated the carbon-vacancy pair can satisfy these requirements.
However, Snoek pinning should occur in times, very short at the temperatures
investigated, compared to the times observed for the rise in Ao.
The formation of ordered carbon-vacancy pair atmospheres near
dislocations can account for the observed static strain aging behavior.
The very long times required to reach the maximum in Ao can be rationalized
in terms of a stress assisted migration of vacancies toward dislocations
where enhanced trapping by carbon occurs. The result is an accumulation
of ordered carbon-vacancy pairs near the dislocation and the concommitant
growth of an ordered carbon-vacancy pair atmosphere. In short, the
proposed model utilizes aspects of both the Cottrell-Bilby and the
Schoeck-Seeger theories of static strain aging.
In summary the following stages are envisioned: (a) At the end of
deformation vacancies diffuse to and become trapped in large measure
by adjacent carbon atoms. (b) The carbon-vacancy pairs thus formed
undergo Snoek ordering within the stress fields of the dislocations.
(c) Then a slow migration of vacancies toward the dislocation develops
an atmosphere of carbon-vacancy pairs near the dislocation.
(d) Eventually the vacancy concentration decreases because of losses
to sinks. This reduces the pair concentration and causes an eventual
loss of strengthening. These stages will now be considered in detail.
4.2 The Mechanism of Static Strain Aging Exhibited in Nickel 200
4.2.1 The Distribution of Vacancies, Carbon Atoms and Dislocations
After Plastic Deformation
After the prestrain of 5%, the vacancy concentration in nickel
is approximately 10-5 atomic fraction as given by Eq. 9. The
particular heat of Nickel 200 used in this investigation contains
approximately 0.1 w/o or 0.5 a/o carbon. Thus, at 5% strain the carbon
to vacancy ratio is approximately 500 to 1. If the carbon and the
vacancies are distributed at random throughout the nickel lattice, then
the mean carbon atom spacing will be approximately 6b; the mean vacancy
spacing will be approximately 50b.
After plastic deformation to 5% strain, the dislocation density [133,134]
is estimated to be between 3 and 8 x 109 cm-2. Assuming an equidistant
array of straight dislocation lines as a first approximation to the
dislocation configuration, then their mean spacing is approximately
450 to 730b.
4.2.2 Vacancy Trapping by Carbon Atoms
In the absence of other defects such as grain boundaries or
dislocations, vacancies in a metal are attracted to oversized impurity
atoms by a hydrostatic pressure gradient. The strain energy released
when a vacancy is moved from an infinite distance away from an impurity
to the impurity is known as the binding energy of the vacancy-impurity
pair. This phenomenon is commonly called trapping and it is generally
accepted that impurity atoms can trap vacancies in metals. For example,
it has been shown that the presence of carbon in austenitic stainless
steel forestalls radiation induced swelling in certain critical nuclear
reactor parts. This indicates that void formation is hindered by the
presence of carbon due to trapping of vacancies . Trapping of
carbon by vacancies in irradiated mild steel has been demonstrated as
4.2.3 The Concentration of Carbon-Vacancy Pairs
After deformation in Nickel 200 and before aging of a specimen,
it is reasonable to assume that vacancies become trapped by carbon
atoms initially. This probably occurs very rapidly even at 3730K, the
lowest aging temperature used, since the vacancies do not have to travel
far to become trapped by carbon atoms. Vacancies in nickel are very
mobile as evidenced by their approximate 0.8 to 0.9 eV migration energy
and assuming that an equilibrium is established between the carbon-vacancy
pairs and free vacancies, their concentrations may be calculated on
the basis that the binding energy of the carbon-vacancy pair can be
estimated to be 0.2 to 0.3 eV per pair from diffusion data (Section 1.4).
For the moment, it is assumed that the dislocations in the metal do not
affect the concentrations. The concentrations of single (free) vacancies
(c ) and bound vacancies in carbon-vacancy pairs (c ) vary with carbon
concentration (Cc), temperature T, and carbon-vacancy binding energy (B)
according to the equations 
ccv = Z cf eB/kT (11)
cv cf + (12)
v= CC V
where cv is the vacancy concentration generated during plastic defor-
mation, cc is the free carbon concentration and Z is 6, the nearest
neighbor coordination number for a carbon atom in an octahedral site
of the fcc lattice.
Substituting Eq. 12 into Eq. 11 gives
cc = Z(cc-Ccv)(cvcv )eB/kT (13)
For c = 5 x 103 and c = 105 one may write on the basis that
Ccv = Zcc(c -ccv)eB/kT (14)
Substituting a value for B equal to 0.3 eV and a temperature of
408K into Eq. 14 gives the carbon-vacancy pair concentration of
9.93 x 10-6, very close to the total vacancy concentration of 10-5.
The free vacancy concentration from Eq. 12 is then 6.92 x 108 atom
fraction. Thus, almost all (99.3%) vacancies are bound to carbon atoms
based upon the choice of B.
In the absence of carbon atoms the concentration of vacancies at
thermal equilibrium is given by
cv e (15)
where Qf is the vacancy formation energy. At 4080K and a Qf of
approximately 39 kcal/mole (1.7 eV)  the vacancy concentration
is approximately 1.8 x 1021 atom fraction. This is many orders of
magnitude smaller than the free vacancy concentration calculated above
and suggests that the deformed metal is not in its lowest energy state
with regard to numbers of vacancies. Thus, there exists a distinct
tendency for vacancies to migrate to sinks. Because of the high binding
to carbon atoms, vacancies spend a large portion of their migration time
bound to carbon atoms and, hence, the process of annealing to dislocations
and grain boundaries is sluggish and takes a considerable time.
Consider next the influence of a dislocation on the carbon-vacancy
pair concentration. It has been demonstrated that the carbon-vacancy
pair may be visualized as an elastic dipole which can reorient in the
strain field of a dislocation. In Eqs. 11-14, the binding energy, B,
is completely general. That is, in the specific case which includes
Snoek ordering, B becomes position dependent. Specifically,
B = B' + u(r) (16)
where B' is the binding energy of a carbon-vacancy pair and u(r) is
the position dependent interaction energy of a carbon-vacancy pair with
a dislocation. Thus, the effect of u(r), which varies as r- is to
enhance the binding of vacancies to carbon atoms near the dislocation.
This will be explained in detail presently.
4.2.4 Theory of Schoeck Locking by Carbon-Vacancy Pairs
In the case of nickel-carbon alloy, the carbon-vacancy pair acts
as a dipole (Section 1.4). Appendix A presents a calculation of the
approximate interaction energy between an assumed carbon-vacancy
dipole and a screw dislocation in a fcc lattice. The interaction
calculation related to an edge dislocation is more complicated .
However, as indicated first by Nabarro  and later expanded upon
by Cochardt et al. , the strength of interaction between a dis-
location and impurity atoms may be assumed to be very similar whether
the dislocation is in the screw or edge orientation.
Let us consider the case of locking of a screw dislocation by an
ordered atmosphere of dipoles in the fcc lattice. The reasoning is
analogous to that for the calculation made by Schoeck and Seeger 
for carbon (or nitrogen) in alpha iron. However, the interaction
energy for a dipole in a fcc lattice as shown in Figure 35 in Appendix A
is somewhat different. The carbon atoms in nickel are assumed to occupy
octahedral interstitial sites, e.g., the body-centered position of the
fcc unit cell. The six nearest neighbors are face-centered atoms. A
dipole is formed when a vacancy is situated on a face-centered position
as schematically shown in Figure 30. Thus, the carbon-vacancy dipole
may be oriented in one of three possible 100 type directions. These
positions are denoted by an orientation number 1, 2 or 3. The dislocation
line is assumed to lie along one of four 101 type directions.
It is shown in Appendix A that for the specific case of a screw
dislocation, each of the three possible orientations of the carbon-
vacancy dipole interacts differently with the dislocation. This gives
rise to three possible interaction energies and one of the three
orientations is most stable. That is, a carbon-vacancy dipole in,
say, the 1-orientation can flip to another orientation (say, 2) and
the result is that the interaction energy between that particular dipole
Figure 30. A schematic illustration of the assumed configuration
of the carbon-vacancy pair and the three possible
independent orientations that it may assume.